From a0cfa4f118023d35b767a999d5a2ac4b082857b4 Mon Sep 17 00:00:00 2001 From: Samuel Mimram Date: Fri, 25 Jul 2008 15:12:53 +0200 Subject: Imported Upstream version 8.2~beta3+dfsg --- test-suite/bugs/closed/1519.v | 23 + test-suite/bugs/closed/1780.v | 12 + test-suite/bugs/closed/1787.v | 11 + test-suite/bugs/closed/shouldfail/1703.v | 7 + test-suite/bugs/closed/shouldsucceed/1041.v | 13 + test-suite/bugs/closed/shouldsucceed/1100.v | 12 + test-suite/bugs/closed/shouldsucceed/121.v | 17 + test-suite/bugs/closed/shouldsucceed/1243.v | 12 + test-suite/bugs/closed/shouldsucceed/1302.v | 22 + test-suite/bugs/closed/shouldsucceed/1322.v | 24 + test-suite/bugs/closed/shouldsucceed/1411.v | 35 + test-suite/bugs/closed/shouldsucceed/1414.v | 41 + test-suite/bugs/closed/shouldsucceed/1419.v | 8 + test-suite/bugs/closed/shouldsucceed/1425.v | 19 + test-suite/bugs/closed/shouldsucceed/1446.v | 20 + test-suite/bugs/closed/shouldsucceed/1448.v | 28 + test-suite/bugs/closed/shouldsucceed/1477.v | 18 + test-suite/bugs/closed/shouldsucceed/1483.v | 10 + test-suite/bugs/closed/shouldsucceed/1507.v | 121 + test-suite/bugs/closed/shouldsucceed/1519.v | 14 + test-suite/bugs/closed/shouldsucceed/1568.v | 13 + test-suite/bugs/closed/shouldsucceed/1576.v | 38 + test-suite/bugs/closed/shouldsucceed/1582.v | 15 + test-suite/bugs/closed/shouldsucceed/1604.v | 7 + test-suite/bugs/closed/shouldsucceed/1614.v | 21 + test-suite/bugs/closed/shouldsucceed/1618.v | 23 + test-suite/bugs/closed/shouldsucceed/1634.v | 24 + test-suite/bugs/closed/shouldsucceed/1643.v | 21 + test-suite/bugs/closed/shouldsucceed/1680.v | 9 + test-suite/bugs/closed/shouldsucceed/1683.v | 42 + test-suite/bugs/closed/shouldsucceed/1696.v | 16 + test-suite/bugs/closed/shouldsucceed/1704.v | 17 + test-suite/bugs/closed/shouldsucceed/1718.v | 9 + test-suite/bugs/closed/shouldsucceed/1738.v | 30 + test-suite/bugs/closed/shouldsucceed/1740.v | 23 + test-suite/bugs/closed/shouldsucceed/1754.v | 24 + test-suite/bugs/closed/shouldsucceed/1773.v | 9 + test-suite/bugs/closed/shouldsucceed/1774.v | 18 + test-suite/bugs/closed/shouldsucceed/1775.v | 39 + test-suite/bugs/closed/shouldsucceed/1776.v | 22 + test-suite/bugs/closed/shouldsucceed/1779.v | 25 + test-suite/bugs/closed/shouldsucceed/1784.v | 101 + test-suite/bugs/closed/shouldsucceed/1844.v | 217 + test-suite/bugs/closed/shouldsucceed/1865.v | 18 + test-suite/bugs/closed/shouldsucceed/348.v | 13 + test-suite/bugs/closed/shouldsucceed/38.v | 22 + test-suite/bugs/closed/shouldsucceed/545.v | 5 + test-suite/bugs/closed/shouldsucceed/846.v | 213 + test-suite/bugs/closed/shouldsucceed/931.v | 7 + test-suite/bugs/opened/1773.v | 10 + .../bugs/opened/shouldnotfail/1338.v-disabled | 12 + test-suite/bugs/opened/shouldnotfail/1416.v | 27 + test-suite/bugs/opened/shouldnotfail/1501.v | 93 + test-suite/bugs/opened/shouldnotfail/1596.v | 242 + test-suite/bugs/opened/shouldnotfail/1811.v | 9 + test-suite/bugs/opened/shouldnotfail/743.v | 12 + test-suite/check | 98 +- test-suite/complexity/injection.v | 113 + test-suite/complexity/ring.v | 7 + test-suite/complexity/ring2.v | 51 + test-suite/csdp.cache | 106548 ++++++++++++++++++ test-suite/failure/circular_subtyping1.v | 7 + test-suite/failure/circular_subtyping2.v | 8 + test-suite/failure/fixpoint2.v | 6 + test-suite/failure/guard.v | 10 + test-suite/failure/rewrite_in_hyp2.v | 8 + test-suite/failure/subtyping.v | 21 + test-suite/failure/subtyping2.v | 245 + test-suite/failure/univ_include.v | 30 + test-suite/ide/undo.v | 79 + test-suite/ideal-features/Case9.v | 12 + test-suite/ideal-features/complexity/evars_subst.v | 53 + test-suite/ideal-features/evars_subst.v | 53 + test-suite/ideal-features/universes.v | 43 + test-suite/micromega/bertot.v | 22 + test-suite/micromega/example.v | 347 + test-suite/micromega/heap3_vcgen_25.v | 38 + test-suite/micromega/qexample.v | 62 + test-suite/micromega/rexample.v | 62 + test-suite/micromega/square.v | 61 + test-suite/micromega/zomicron.v | 27 + test-suite/modules/pseudo_circular_with.v | 6 + test-suite/modules/resolver.v | 37 + test-suite/modules/subtyping.v | 46 + test-suite/output/Cases.out | 21 + test-suite/output/Cases.v | 29 + test-suite/output/Fixpoint.out | 14 + test-suite/output/Fixpoint.v | 23 + test-suite/output/Implicit.out | 5 +- test-suite/output/Implicit.v | 19 + test-suite/output/InitSyntax.out | 3 +- test-suite/output/Nametab.out | 36 +- test-suite/output/Nametab.v | 22 +- test-suite/output/Notations.out | 4 + test-suite/output/Notations.v | 10 + test-suite/output/Tactics.out | 2 + test-suite/output/TranspModtype.out | 3 - test-suite/output/ZSyntax.out | 10 +- test-suite/output/reduction.out | 4 + test-suite/output/reduction.v | 13 + test-suite/success/AdvancedCanonicalStructure.v | 144 + test-suite/success/Case18.v | 12 + test-suite/success/Cases-bug1834.v | 13 + test-suite/success/Cases.v | 5 +- test-suite/success/CasesDep.v | 58 +- test-suite/success/Discriminate.v | 23 + test-suite/success/Fixpoint.v | 19 + test-suite/success/ImplicitArguments.v | 17 + test-suite/success/Injection.v | 27 +- test-suite/success/LetPat.v | 55 + test-suite/success/Notations.v | 16 +- test-suite/success/Omega.v | 14 +- test-suite/success/OmegaPre.v | 127 + test-suite/success/ROmega.v | 20 +- test-suite/success/ROmegaPre.v | 127 + test-suite/success/apply.v | 193 +- test-suite/success/cc.v | 9 + test-suite/success/change.v | 6 + test-suite/success/clear.v | 13 +- test-suite/success/conv_pbs.v | 223 + test-suite/success/decl_mode.v | 182 + test-suite/success/dependentind.v | 100 + test-suite/success/destruct.v | 32 + test-suite/success/evars.v | 136 + test-suite/success/extraction.v | 2 +- test-suite/success/fix.v | 59 +- test-suite/success/hyps_inclusion.v | 32 + test-suite/success/implicit.v | 10 + test-suite/success/ltac.v | 47 +- test-suite/success/options.v | 2 +- test-suite/success/parsing.v | 8 + test-suite/success/pattern.v | 7 + test-suite/success/refine.v | 30 + test-suite/success/rewrite.v | 21 + test-suite/success/setoid_test.v | 14 +- test-suite/success/setoid_test2.v | 4 + test-suite/success/setoid_test_function_space.v | 12 +- test-suite/success/specialize.v | 48 + test-suite/success/unification.v | 65 +- test-suite/success/univers.v | 4 + test-suite/typeclasses/NewSetoid.v | 74 + test-suite/typeclasses/clrewrite.v | 111 + test-suite/typeclasses/unification_delta.v | 46 + 143 files changed, 112307 insertions(+), 91 deletions(-) create mode 100644 test-suite/bugs/closed/1519.v create mode 100644 test-suite/bugs/closed/1780.v create mode 100644 test-suite/bugs/closed/1787.v create mode 100644 test-suite/bugs/closed/shouldfail/1703.v create mode 100644 test-suite/bugs/closed/shouldsucceed/1041.v create mode 100644 test-suite/bugs/closed/shouldsucceed/1100.v create mode 100644 test-suite/bugs/closed/shouldsucceed/121.v create mode 100644 test-suite/bugs/closed/shouldsucceed/1243.v create mode 100644 test-suite/bugs/closed/shouldsucceed/1302.v create mode 100644 test-suite/bugs/closed/shouldsucceed/1322.v create mode 100644 test-suite/bugs/closed/shouldsucceed/1411.v create mode 100644 test-suite/bugs/closed/shouldsucceed/1414.v create mode 100644 test-suite/bugs/closed/shouldsucceed/1419.v create mode 100644 test-suite/bugs/closed/shouldsucceed/1425.v create mode 100644 test-suite/bugs/closed/shouldsucceed/1446.v create mode 100644 test-suite/bugs/closed/shouldsucceed/1448.v create mode 100644 test-suite/bugs/closed/shouldsucceed/1477.v create mode 100644 test-suite/bugs/closed/shouldsucceed/1483.v create mode 100644 test-suite/bugs/closed/shouldsucceed/1507.v create mode 100644 test-suite/bugs/closed/shouldsucceed/1519.v create mode 100644 test-suite/bugs/closed/shouldsucceed/1568.v create mode 100644 test-suite/bugs/closed/shouldsucceed/1576.v create mode 100644 test-suite/bugs/closed/shouldsucceed/1582.v create mode 100644 test-suite/bugs/closed/shouldsucceed/1604.v create mode 100644 test-suite/bugs/closed/shouldsucceed/1614.v create mode 100644 test-suite/bugs/closed/shouldsucceed/1618.v create mode 100644 test-suite/bugs/closed/shouldsucceed/1634.v create mode 100644 test-suite/bugs/closed/shouldsucceed/1643.v create mode 100644 test-suite/bugs/closed/shouldsucceed/1680.v create mode 100644 test-suite/bugs/closed/shouldsucceed/1683.v create mode 100644 test-suite/bugs/closed/shouldsucceed/1696.v create mode 100644 test-suite/bugs/closed/shouldsucceed/1704.v create mode 100644 test-suite/bugs/closed/shouldsucceed/1718.v create mode 100644 test-suite/bugs/closed/shouldsucceed/1738.v create mode 100644 test-suite/bugs/closed/shouldsucceed/1740.v create mode 100644 test-suite/bugs/closed/shouldsucceed/1754.v create mode 100644 test-suite/bugs/closed/shouldsucceed/1773.v create mode 100644 test-suite/bugs/closed/shouldsucceed/1774.v create mode 100644 test-suite/bugs/closed/shouldsucceed/1775.v create mode 100644 test-suite/bugs/closed/shouldsucceed/1776.v create mode 100644 test-suite/bugs/closed/shouldsucceed/1779.v create mode 100644 test-suite/bugs/closed/shouldsucceed/1784.v create mode 100644 test-suite/bugs/closed/shouldsucceed/1844.v create mode 100644 test-suite/bugs/closed/shouldsucceed/1865.v create mode 100644 test-suite/bugs/closed/shouldsucceed/348.v create mode 100644 test-suite/bugs/closed/shouldsucceed/38.v create mode 100644 test-suite/bugs/closed/shouldsucceed/545.v create mode 100644 test-suite/bugs/closed/shouldsucceed/846.v create mode 100644 test-suite/bugs/closed/shouldsucceed/931.v create mode 100644 test-suite/bugs/opened/1773.v create mode 100644 test-suite/bugs/opened/shouldnotfail/1338.v-disabled create mode 100644 test-suite/bugs/opened/shouldnotfail/1416.v create mode 100644 test-suite/bugs/opened/shouldnotfail/1501.v create mode 100644 test-suite/bugs/opened/shouldnotfail/1596.v create mode 100644 test-suite/bugs/opened/shouldnotfail/1811.v create mode 100644 test-suite/bugs/opened/shouldnotfail/743.v create mode 100644 test-suite/complexity/injection.v create mode 100644 test-suite/complexity/ring.v create mode 100644 test-suite/complexity/ring2.v create mode 100644 test-suite/csdp.cache create mode 100644 test-suite/failure/circular_subtyping1.v create mode 100644 test-suite/failure/circular_subtyping2.v create mode 100644 test-suite/failure/fixpoint2.v create mode 100644 test-suite/failure/guard.v create mode 100644 test-suite/failure/rewrite_in_hyp2.v create mode 100644 test-suite/failure/subtyping.v create mode 100644 test-suite/failure/subtyping2.v create mode 100644 test-suite/failure/univ_include.v create mode 100644 test-suite/ide/undo.v create mode 100644 test-suite/ideal-features/Case9.v create mode 100644 test-suite/ideal-features/complexity/evars_subst.v create mode 100644 test-suite/ideal-features/evars_subst.v create mode 100644 test-suite/ideal-features/universes.v create mode 100644 test-suite/micromega/bertot.v create mode 100644 test-suite/micromega/example.v create mode 100644 test-suite/micromega/heap3_vcgen_25.v create mode 100644 test-suite/micromega/qexample.v create mode 100644 test-suite/micromega/rexample.v create mode 100644 test-suite/micromega/square.v create mode 100644 test-suite/micromega/zomicron.v create mode 100644 test-suite/modules/pseudo_circular_with.v create mode 100644 test-suite/modules/resolver.v create mode 100644 test-suite/modules/subtyping.v create mode 100644 test-suite/output/reduction.out create mode 100644 test-suite/output/reduction.v create mode 100644 test-suite/success/AdvancedCanonicalStructure.v create mode 100644 test-suite/success/Cases-bug1834.v create mode 100644 test-suite/success/ImplicitArguments.v create mode 100644 test-suite/success/LetPat.v create mode 100644 test-suite/success/OmegaPre.v create mode 100644 test-suite/success/ROmegaPre.v create mode 100644 test-suite/success/change.v create mode 100644 test-suite/success/conv_pbs.v create mode 100644 test-suite/success/decl_mode.v create mode 100644 test-suite/success/dependentind.v create mode 100644 test-suite/success/hyps_inclusion.v create mode 100644 test-suite/success/parsing.v create mode 100644 test-suite/success/pattern.v create mode 100644 test-suite/success/specialize.v create mode 100644 test-suite/typeclasses/NewSetoid.v create mode 100644 test-suite/typeclasses/clrewrite.v create mode 100644 test-suite/typeclasses/unification_delta.v (limited to 'test-suite') diff --git a/test-suite/bugs/closed/1519.v b/test-suite/bugs/closed/1519.v new file mode 100644 index 00000000..98e3e214 --- /dev/null +++ b/test-suite/bugs/closed/1519.v @@ -0,0 +1,23 @@ +Section S. + + Variable A:Prop. + Variable W:A. + + Remark T: A -> A. + intro Z. + rename W into Z_. + rename Z into W. + rename Z_ into Z. + exact Z. + Qed. + + (* bug : + Error: + Unbound reference: In environment + A : Prop + W : A + Z : A + The reference 2 is free + *) + +End S. diff --git a/test-suite/bugs/closed/1780.v b/test-suite/bugs/closed/1780.v new file mode 100644 index 00000000..3929fbae --- /dev/null +++ b/test-suite/bugs/closed/1780.v @@ -0,0 +1,12 @@ + +Definition bug := Eval vm_compute in eq_rect. +(* bug: +Error: Illegal application (Type Error): +The term "eq" of type "forall A : Type, A -> A -> Prop" +cannot be applied to the terms + "x" : "A" + "P" : "A -> Type" + "x0" : "A" +The 1st term has type "A" which should be coercible to +"Type". +*) diff --git a/test-suite/bugs/closed/1787.v b/test-suite/bugs/closed/1787.v new file mode 100644 index 00000000..8e1024e6 --- /dev/null +++ b/test-suite/bugs/closed/1787.v @@ -0,0 +1,11 @@ +Parameter P : nat -> nat -> Prop. +Parameter Q : nat -> nat -> Prop. +Axiom A : forall x x' x'', P x x' -> Q x'' x' -> P x x''. + +Goal (P 1 3) -> (Q 1 3) -> (P 1 1). +intros H H'. +refine ((fun H1 : P 1 _ => let H2 := (_:Q 1 _) in A _ _ _ H1 H2) _). +clear. +Admitted. + + diff --git a/test-suite/bugs/closed/shouldfail/1703.v b/test-suite/bugs/closed/shouldfail/1703.v new file mode 100644 index 00000000..6b5198cc --- /dev/null +++ b/test-suite/bugs/closed/shouldfail/1703.v @@ -0,0 +1,7 @@ +(* Check correct binding of intros until used in Ltac *) + +Ltac intros_until n := intros until n. + +Goal forall i j m n : nat, i = 0 /\ j = 0 /\ m = 0 /\ n = 0. +intro i. +intros until i. diff --git a/test-suite/bugs/closed/shouldsucceed/1041.v b/test-suite/bugs/closed/shouldsucceed/1041.v new file mode 100644 index 00000000..a5de82e0 --- /dev/null +++ b/test-suite/bugs/closed/shouldsucceed/1041.v @@ -0,0 +1,13 @@ +Goal Prop. + +pose (P:=(fun x y :Prop => y)). +evar (Q: (forall X Y,P X Y -> Prop)) . + +instantiate (1:= fun _ => _ ) in (Value of Q). +instantiate (1:= fun _ => _ ) in (Value of Q). +instantiate (1:= fun _ => _ ) in (Value of Q). + +instantiate (1:=H) in (Value of Q). + +Admitted. + diff --git a/test-suite/bugs/closed/shouldsucceed/1100.v b/test-suite/bugs/closed/shouldsucceed/1100.v new file mode 100644 index 00000000..6d619c74 --- /dev/null +++ b/test-suite/bugs/closed/shouldsucceed/1100.v @@ -0,0 +1,12 @@ +Require Import Setoid. + +Parameter P : nat -> Prop. +Parameter Q : nat -> Prop. +Parameter PQ : forall n, P n <-> Q n. + +Lemma PQ2 : forall n, P n -> Q n. + intros. + rewrite PQ in H. + trivial. +Qed. + diff --git a/test-suite/bugs/closed/shouldsucceed/121.v b/test-suite/bugs/closed/shouldsucceed/121.v new file mode 100644 index 00000000..d193aa73 --- /dev/null +++ b/test-suite/bugs/closed/shouldsucceed/121.v @@ -0,0 +1,17 @@ +Require Import Setoid. + +Section Setoid_Bug. + +Variable X:Type -> Type. +Variable Xeq : forall A, (X A) -> (X A) -> Prop. +Hypothesis Xst : forall A, Equivalence (X A) (Xeq A). + +Variable map : forall A B, (A -> B) -> X A -> X B. + +Implicit Arguments map [A B]. + +Goal forall A B (a b:X (B -> A)) (c:X A) (f:A -> B -> A), Xeq _ a b -> Xeq _ b (map f c) -> Xeq _ a (map f c). +intros A B a b c f Hab Hbc. +rewrite Hab. +assumption. +Qed. diff --git a/test-suite/bugs/closed/shouldsucceed/1243.v b/test-suite/bugs/closed/shouldsucceed/1243.v new file mode 100644 index 00000000..7d6781db --- /dev/null +++ b/test-suite/bugs/closed/shouldsucceed/1243.v @@ -0,0 +1,12 @@ +Require Import ZArith. +Require Import Arith. +Open Scope Z_scope. + +Theorem r_ex : (forall x y:nat, x + y = x + y)%nat. +Admitted. + +Theorem r_ex' : forall x y:nat, (x + y = x + y)%nat. +Admitted. + + + diff --git a/test-suite/bugs/closed/shouldsucceed/1302.v b/test-suite/bugs/closed/shouldsucceed/1302.v new file mode 100644 index 00000000..e94dfcfb --- /dev/null +++ b/test-suite/bugs/closed/shouldsucceed/1302.v @@ -0,0 +1,22 @@ +Module Type T. + +Parameter A : Type. + +Inductive L : Type := +| L0 : L (* without this constructor, it works right *) +| L1 : A -> L. + +End T. + +Axiom Tp : Type. + +Module TT : T. + +Definition A : Type := Tp. + +Inductive L : Type := +| L0 : L +| L1 : A -> L. + +End TT. + diff --git a/test-suite/bugs/closed/shouldsucceed/1322.v b/test-suite/bugs/closed/shouldsucceed/1322.v new file mode 100644 index 00000000..7e21aa7c --- /dev/null +++ b/test-suite/bugs/closed/shouldsucceed/1322.v @@ -0,0 +1,24 @@ +Require Import Setoid. + +Section transition_gen. + +Variable I : Type. +Variable I_eq :I -> I -> Prop. +Variable I_eq_equiv : Setoid_Theory I I_eq. + +(* Add Relation I I_eq + reflexivity proved by I_eq_equiv.(Seq_refl I I_eq) + symmetry proved by I_eq_equiv.(Seq_sym I I_eq) + transitivity proved by I_eq_equiv.(Seq_trans I I_eq) +as I_eq_relation. *) + +Add Setoid I I_eq I_eq_equiv as I_with_eq. + +Variable F : I -> Type. +Variable F_morphism : forall i j, I_eq i j -> F i = F j. + + +Add Morphism F with signature I_eq ==> (@eq _) as F_morphism2. +Admitted. + +End transition_gen. diff --git a/test-suite/bugs/closed/shouldsucceed/1411.v b/test-suite/bugs/closed/shouldsucceed/1411.v new file mode 100644 index 00000000..e330d46f --- /dev/null +++ b/test-suite/bugs/closed/shouldsucceed/1411.v @@ -0,0 +1,35 @@ +Require Import List. +Require Import Program. + +Inductive Tree : Set := +| Br : Tree -> Tree -> Tree +| No : nat -> Tree +. + +(* given a tree, we want to know which lists can + be used to navigate exactly to a node *) +Inductive Exact : Tree -> list bool -> Prop := +| exDone n : Exact (No n) nil +| exLeft l r p: Exact l p -> Exact (Br l r) (true::p) +| exRight l r p: Exact r p -> Exact (Br l r) (false::p) +. + +Definition unreachable A : False -> A. +intros. +destruct H. +Defined. + +Program Fixpoint fetch t p (x:Exact t p) {struct t} := + match t, p with + | No p' , nil => p' + | No p' , _::_ => unreachable nat _ + | Br l r, nil => unreachable nat _ + | Br l r, true::t => fetch l t _ + | Br l r, false::t => fetch r t _ + end. + +Next Obligation. inversion x. Qed. +Next Obligation. inversion x. Qed. +Next Obligation. inversion x; trivial. Qed. +Next Obligation. inversion x; trivial. Qed. + diff --git a/test-suite/bugs/closed/shouldsucceed/1414.v b/test-suite/bugs/closed/shouldsucceed/1414.v new file mode 100644 index 00000000..d3c00808 --- /dev/null +++ b/test-suite/bugs/closed/shouldsucceed/1414.v @@ -0,0 +1,41 @@ +Require Import ZArith Coq.Program.Wf Coq.Program.Utils. + +Parameter data:Set. + +Inductive t : Set := + | Leaf : t + | Node : t -> data -> t -> Z -> t. + +Parameter avl : t -> Prop. +Parameter bst : t -> Prop. +Parameter In : data -> t -> Prop. +Parameter cardinal : t -> nat. +Definition card2 (s:t*t) := let (s1,s2) := s in cardinal s1 + cardinal s2. + +Parameter split : data -> t -> t*(bool*t). +Parameter join : t -> data -> t -> t. +Parameter add : data -> t -> t. + +Program Fixpoint union + (s:t*t) + (hb1: bst (fst s))(ha1: avl (fst s))(hb2: bst (snd s))(hb2: avl (snd s)) + { measure card2 s } : + {s' : t | bst s' /\ avl s' /\ forall x, In x s' <-> In x (fst s) \/ In x (snd +s)} := + match s with + | (Leaf,t2) => t2 + | (t1,Leaf) => t1 + | (Node l1 v1 r1 h1, Node l2 v2 r2 h2) => + if (Z_ge_lt_dec h1 h2) then + if (Z_eq_dec h2 1) + then add v2 (fst s) + else + let (l2', r2') := split v1 (snd s) in + join (union (l1,l2') _ _ _ _) v1 (union (r1,snd r2') _ _ _ _) + else + if (Z_eq_dec h1 1) + then add v1 (snd s) + else + let (l1', r1') := split v2 (fst s) in + join (union (l1',l2) _ _ _ _) v2 (union (snd r1',r2) _ _ _ _) + end. diff --git a/test-suite/bugs/closed/shouldsucceed/1419.v b/test-suite/bugs/closed/shouldsucceed/1419.v new file mode 100644 index 00000000..d021107d --- /dev/null +++ b/test-suite/bugs/closed/shouldsucceed/1419.v @@ -0,0 +1,8 @@ +Goal True. + set(a := 0). + set(b := a). + unfold a in b. + clear a. + Eval vm_compute in b. + trivial. +Qed. diff --git a/test-suite/bugs/closed/shouldsucceed/1425.v b/test-suite/bugs/closed/shouldsucceed/1425.v new file mode 100644 index 00000000..8e26209a --- /dev/null +++ b/test-suite/bugs/closed/shouldsucceed/1425.v @@ -0,0 +1,19 @@ +Require Import Setoid. + +Parameter recursion : forall A : Set, A -> (nat -> A -> A) -> nat -> A. + +Axiom recursion_S : + forall (A : Set) (EA : relation A) (a : A) (f : nat -> A -> A) (n : nat), + EA (recursion A a f (S n)) (f n (recursion A a f n)). + +Goal forall n : nat, recursion nat 0 (fun _ _ => 1) (S n) = 1. +intro n. +rewrite recursion_S. +reflexivity. +Qed. + +Goal forall n : nat, recursion nat 0 (fun _ _ => 1) (S n) = 1. +intro n. +setoid_rewrite recursion_S. +reflexivity. +Qed. \ No newline at end of file diff --git a/test-suite/bugs/closed/shouldsucceed/1446.v b/test-suite/bugs/closed/shouldsucceed/1446.v new file mode 100644 index 00000000..d4e7cea8 --- /dev/null +++ b/test-suite/bugs/closed/shouldsucceed/1446.v @@ -0,0 +1,20 @@ +Lemma not_true_eq_false : forall (b:bool), b <> true -> b = false. +Proof. + destruct b;intros;trivial. + elim H. + exact (refl_equal true). +Qed. + +Section BUG. + + Variable b : bool. + Hypothesis H : b <> true. + Hypothesis H0 : b = true. + Hypothesis H1 : b <> true. + + Goal False. + rewrite (not_true_eq_false _ H) in * |-. + contradiction. + Qed. + +End BUG. diff --git a/test-suite/bugs/closed/shouldsucceed/1448.v b/test-suite/bugs/closed/shouldsucceed/1448.v new file mode 100644 index 00000000..fe3b4c8b --- /dev/null +++ b/test-suite/bugs/closed/shouldsucceed/1448.v @@ -0,0 +1,28 @@ +Require Import Relations. +Require Import Setoid. +Require Import Ring_theory. +Require Import Ring_base. + + +Variable R : Type. +Variable Rone Rzero : R. +Variable Rplus Rmult Rminus : R -> R -> R. +Variable Rneg : R -> R. + +Lemma my_ring_theory : @ring_theory R Rzero Rone Rplus Rmult Rminus Rneg (@eq +R). +Admitted. + +Variable Req : R -> R -> Prop. + +Hypothesis Req_refl : reflexive _ Req. +Hypothesis Req_sym : symmetric _ Req. +Hypothesis Req_trans : transitive _ Req. + +Add Relation R Req + reflexivity proved by Req_refl + symmetry proved by Req_sym + transitivity proved by Req_trans + as Req_rel. + +Add Ring my_ring : my_ring_theory (abstract). diff --git a/test-suite/bugs/closed/shouldsucceed/1477.v b/test-suite/bugs/closed/shouldsucceed/1477.v new file mode 100644 index 00000000..dfc8c328 --- /dev/null +++ b/test-suite/bugs/closed/shouldsucceed/1477.v @@ -0,0 +1,18 @@ +Inductive I : Set := + | A : nat -> nat -> I + | B : nat -> nat -> I. + +Definition foo1 (x:I) : nat := + match x with + | A a b | B a b => S b + end. + +Definition foo2 (x:I) : nat := + match x with + | A _ b | B b _ => S b + end. + +Definition foo (x:I) : nat := + match x with + | A a b | B b a => S b + end. diff --git a/test-suite/bugs/closed/shouldsucceed/1483.v b/test-suite/bugs/closed/shouldsucceed/1483.v new file mode 100644 index 00000000..a3d7f168 --- /dev/null +++ b/test-suite/bugs/closed/shouldsucceed/1483.v @@ -0,0 +1,10 @@ +Require Import BinPos. + +Definition P := (fun x : positive => x = xH). + +Goal forall (p q : positive), P q -> q = p -> P p. +intros; congruence. +Qed. + + + diff --git a/test-suite/bugs/closed/shouldsucceed/1507.v b/test-suite/bugs/closed/shouldsucceed/1507.v new file mode 100644 index 00000000..b484c7dc --- /dev/null +++ b/test-suite/bugs/closed/shouldsucceed/1507.v @@ -0,0 +1,121 @@ +(* + Implementing reals a la Stolzenberg + + Danko Ilik, March 2007 + svn revision: $Id: 1507.v 10068 2007-08-10 12:06:59Z notin $ + + XField.v -- (unfinished) axiomatisation of the theories of real and + rational intervals. +*) + +Definition associative (A:Type)(op:A->A->A) := + forall x y z:A, op (op x y) z = op x (op y z). + +Definition commutative (A:Type)(op:A->A->A) := + forall x y:A, op x y = op y x. + +Definition trichotomous (A:Type)(R:A->A->Prop) := + forall x y:A, R x y \/ x=y \/ R y x. + +Definition relation (A:Type) := A -> A -> Prop. +Definition reflexive (A:Type)(R:relation A) := forall x:A, R x x. +Definition transitive (A:Type)(R:relation A) := + forall x y z:A, R x y -> R y z -> R x z. +Definition symmetric (A:Type)(R:relation A) := forall x y:A, R x y -> R y x. + +Record interval (X:Set)(le:X->X->Prop) : Set := + interval_make { + interval_left : X; + interval_right : X; + interval_nonempty : le interval_left interval_right + }. + +Record I (grnd:Set)(le:grnd->grnd->Prop) : Type := Imake { + Icar := interval grnd le; + Iplus : Icar -> Icar -> Icar; + Imult : Icar -> Icar -> Icar; + Izero : Icar; + Ione : Icar; + Iopp : Icar -> Icar; + Iinv : Icar -> Icar; + Ic : Icar -> Icar -> Prop; (* consistency *) + (* monoids *) + Iplus_assoc : associative Icar Iplus; + Imult_assoc : associative Icar Imult; + (* abelian groups *) + Iplus_comm : commutative Icar Iplus; + Imult_comm : commutative Icar Imult; + Iplus_0_l : forall x:Icar, Ic (Iplus Izero x) x; + Iplus_0_r : forall x:Icar, Ic (Iplus x Izero) x; + Imult_0_l : forall x:Icar, Ic (Imult Ione x) x; + Imult_0_r : forall x:Icar, Ic (Imult x Ione) x; + Iplus_opp_r : forall x:Icar, Ic (Iplus x (Iopp x)) (Izero); + Imult_inv_r : forall x:Icar, ~(Ic x Izero) -> Ic (Imult x (Iinv x)) Ione; + (* distributive laws *) + Imult_plus_distr_l : forall x x' y y' z z' z'', + Ic x x' -> Ic y y' -> Ic z z' -> Ic z z'' -> + Ic (Imult (Iplus x y) z) (Iplus (Imult x' z') (Imult y' z'')); + (* order and lattice structure *) + Ilt : Icar -> Icar -> Prop; + Ilc := fun (x y:Icar) => Ilt x y \/ Ic x y; + Isup : Icar -> Icar -> Icar; + Iinf : Icar -> Icar -> Icar; + Ilt_trans : transitive _ lt; + Ilt_trich : forall x y:Icar, Ilt x y \/ Ic x y \/ Ilt y x; + Isup_lub : forall x y z:Icar, Ilc x z -> Ilc y z -> Ilc (Isup x y) z; + Iinf_glb : forall x y z:Icar, Ilc x y -> Ilc x z -> Ilc x (Iinf y z); + (* order preserves operations? *) + (* properties of Ic *) + Ic_refl : reflexive _ Ic; + Ic_sym : symmetric _ Ic +}. + +Definition interval_set (X:Set)(le:X->X->Prop) := + (interval X le) -> Prop. (* can be Set as well *) +Check interval_set. +Check Ic. +Definition consistent (X:Set)(le:X->X->Prop)(TI:I X le)(p:interval_set X le) := + forall I J:interval X le, p I -> p J -> (Ic X le TI) I J. +Check consistent. +(* define 'fine' *) + +Record N (grnd:Set)(le:grnd->grnd->Prop)(grndI:I grnd le) : Type := Nmake { + Ncar := interval_set grnd le; + Nplus : Ncar -> Ncar -> Ncar; + Nmult : Ncar -> Ncar -> Ncar; + Nzero : Ncar; + None : Ncar; + Nopp : Ncar -> Ncar; + Ninv : Ncar -> Ncar; + Nc : Ncar -> Ncar -> Prop; (* Ncistency *) + (* monoids *) + Nplus_assoc : associative Ncar Nplus; + Nmult_assoc : associative Ncar Nmult; + (* abelian groups *) + Nplus_comm : commutative Ncar Nplus; + Nmult_comm : commutative Ncar Nmult; + Nplus_0_l : forall x:Ncar, Nc (Nplus Nzero x) x; + Nplus_0_r : forall x:Ncar, Nc (Nplus x Nzero) x; + Nmult_0_l : forall x:Ncar, Nc (Nmult None x) x; + Nmult_0_r : forall x:Ncar, Nc (Nmult x None) x; + Nplus_opp_r : forall x:Ncar, Nc (Nplus x (Nopp x)) (Nzero); + Nmult_inv_r : forall x:Ncar, ~(Nc x Nzero) -> Nc (Nmult x (Ninv x)) None; + (* distributive laws *) + Nmult_plus_distr_l : forall x x' y y' z z' z'', + Nc x x' -> Nc y y' -> Nc z z' -> Nc z z'' -> + Nc (Nmult (Nplus x y) z) (Nplus (Nmult x' z') (Nmult y' z'')); + (* order and lattice structure *) + Nlt : Ncar -> Ncar -> Prop; + Nlc := fun (x y:Ncar) => Nlt x y \/ Nc x y; + Nsup : Ncar -> Ncar -> Ncar; + Ninf : Ncar -> Ncar -> Ncar; + Nlt_trans : transitive _ lt; + Nlt_trich : forall x y:Ncar, Nlt x y \/ Nc x y \/ Nlt y x; + Nsup_lub : forall x y z:Ncar, Nlc x z -> Nlc y z -> Nlc (Nsup x y) z; + Ninf_glb : forall x y z:Ncar, Nlc x y -> Nlc x z -> Nlc x (Ninf y z); + (* order preserves operations? *) + (* properties of Nc *) + Nc_refl : reflexive _ Nc; + Nc_sym : symmetric _ Nc +}. + diff --git a/test-suite/bugs/closed/shouldsucceed/1519.v b/test-suite/bugs/closed/shouldsucceed/1519.v new file mode 100644 index 00000000..66bab241 --- /dev/null +++ b/test-suite/bugs/closed/shouldsucceed/1519.v @@ -0,0 +1,14 @@ +Section S. + + Variable A:Prop. + Variable W:A. + + Remark T: A -> A. + intro Z. + rename W into Z_. + rename Z into W. + rename Z_ into Z. + exact Z. + Qed. + +End S. diff --git a/test-suite/bugs/closed/shouldsucceed/1568.v b/test-suite/bugs/closed/shouldsucceed/1568.v new file mode 100644 index 00000000..9f10f749 --- /dev/null +++ b/test-suite/bugs/closed/shouldsucceed/1568.v @@ -0,0 +1,13 @@ +CoInductive A: Set := + mk_A: B -> A +with B: Set := + mk_B: A -> B. + +CoFixpoint a:A := mk_A b +with b:B := mk_B a. + +Goal b = match a with mk_A a1 => a1 end. + simpl. reflexivity. +Qed. + + diff --git a/test-suite/bugs/closed/shouldsucceed/1576.v b/test-suite/bugs/closed/shouldsucceed/1576.v new file mode 100644 index 00000000..c9ebbd14 --- /dev/null +++ b/test-suite/bugs/closed/shouldsucceed/1576.v @@ -0,0 +1,38 @@ +Module Type TA. +Parameter t : Set. +End TA. + +Module Type TB. +Declare Module A: TA. +End TB. + +Module Type TC. +Declare Module B : TB. +End TC. + +Module Type TD. + +Declare Module B: TB . +Declare Module C: TC + with Module B := B . +End TD. + +Module Type TE. +Declare Module D : TD. +End TE. + +Module Type TF. +Declare Module E: TE. +End TF. + +Module G (D: TD). +Module B' := D.C.B. +End G. + +Module H (F: TF). +Module I := G(F.E.D). +End H. + +Declare Module F: TF. +Module K := H(F). + diff --git a/test-suite/bugs/closed/shouldsucceed/1582.v b/test-suite/bugs/closed/shouldsucceed/1582.v new file mode 100644 index 00000000..47953a66 --- /dev/null +++ b/test-suite/bugs/closed/shouldsucceed/1582.v @@ -0,0 +1,15 @@ +Require Import Peano_dec. + +Definition fact_F : + forall (n:nat), + (forall m, m nat) -> + nat. +refine + (fun n fact_rec => + if eq_nat_dec n 0 then + 1 + else + let fn := fact_rec (n-1) _ in + n * fn). +Admitted. + diff --git a/test-suite/bugs/closed/shouldsucceed/1604.v b/test-suite/bugs/closed/shouldsucceed/1604.v new file mode 100644 index 00000000..22c3df82 --- /dev/null +++ b/test-suite/bugs/closed/shouldsucceed/1604.v @@ -0,0 +1,7 @@ +Require Import Setoid. + +Parameter F : nat -> nat. +Axiom F_id : forall n : nat, n = F n. +Goal forall n : nat, F n = n. +intro n. setoid_rewrite F_id at 3. reflexivity. +Qed. diff --git a/test-suite/bugs/closed/shouldsucceed/1614.v b/test-suite/bugs/closed/shouldsucceed/1614.v new file mode 100644 index 00000000..6bc165d4 --- /dev/null +++ b/test-suite/bugs/closed/shouldsucceed/1614.v @@ -0,0 +1,21 @@ +Require Import Ring. +Require Import ArithRing. + +Fixpoint eq_nat_bool (x y : nat) {struct x} : bool := +match x, y with +| 0, 0 => true +| S x', S y' => eq_nat_bool x' y' +| _, _ => false +end. + +Theorem eq_nat_bool_implies_eq : forall x y, eq_nat_bool x y = true -> x = y. +Proof. +induction x; destruct y; simpl; intro H; try (reflexivity || inversion H). +apply IHx in H; rewrite H; reflexivity. +Qed. + +Add Ring MyNatSRing : natSRth (decidable eq_nat_bool_implies_eq). + +Goal 0 = 0. + ring. +Qed. diff --git a/test-suite/bugs/closed/shouldsucceed/1618.v b/test-suite/bugs/closed/shouldsucceed/1618.v new file mode 100644 index 00000000..a90290bf --- /dev/null +++ b/test-suite/bugs/closed/shouldsucceed/1618.v @@ -0,0 +1,23 @@ +Inductive A: Set := +| A1: nat -> A. + +Definition A_size (a: A) : nat := + match a with + | A1 n => 0 + end. + +Require Import Recdef. + +Function n3 (P: A -> Prop) (f: forall n, P (A1 n)) (a: A) {struct a} : P a := + match a return (P a) with + | A1 n => f n + end. + + +Function n1 (P: A -> Prop) (f: forall n, P (A1 n)) (a: A) {measure A_size a} : +P +a := + match a return (P a) with + | A1 n => f n + end. + diff --git a/test-suite/bugs/closed/shouldsucceed/1634.v b/test-suite/bugs/closed/shouldsucceed/1634.v new file mode 100644 index 00000000..e0c540f3 --- /dev/null +++ b/test-suite/bugs/closed/shouldsucceed/1634.v @@ -0,0 +1,24 @@ +Require Export Relation_Definitions. +Require Export Setoid. + +Variable A : Type. +Variable S : A -> Type. +Variable Seq : forall {a:A}, relation (S a). + +Hypothesis Seq_refl : forall {a:A} (x : S a), Seq x x. +Hypothesis Seq_sym : forall {a:A} (x y : S a), Seq x y -> Seq y x. +Hypothesis Seq_trans : forall {a:A} (x y z : S a), Seq x y -> Seq y z -> +Seq x z. + +Add Parametric Relation a : (S a) Seq + reflexivity proved by Seq_refl + symmetry proved by Seq_sym + transitivity proved by Seq_trans + as S_Setoid. + +Goal forall (a : A) (x y : S a), Seq x y -> Seq x y. + intros a x y H. + setoid_replace x with y. + reflexivity. + trivial. +Qed. diff --git a/test-suite/bugs/closed/shouldsucceed/1643.v b/test-suite/bugs/closed/shouldsucceed/1643.v new file mode 100644 index 00000000..4114987d --- /dev/null +++ b/test-suite/bugs/closed/shouldsucceed/1643.v @@ -0,0 +1,21 @@ +(* Check some aspects of that the algorithm used to possibly reuse a + global name in the recursive calls (coinductive case) *) + +CoInductive Str : Set := Cons (h:nat) (t:Str). + +Definition decomp_func (s:Str) := + match s with + | Cons h t => Cons h t + end. + +Theorem decomp s: s = decomp_func s. +Proof. + intros s. + case s; simpl; reflexivity. +Qed. + +Definition zeros := (cofix z : Str := Cons 0 z). +Lemma zeros_rw : zeros = Cons 0 zeros. + rewrite (decomp zeros). + simpl. +Admitted. diff --git a/test-suite/bugs/closed/shouldsucceed/1680.v b/test-suite/bugs/closed/shouldsucceed/1680.v new file mode 100644 index 00000000..524c7bab --- /dev/null +++ b/test-suite/bugs/closed/shouldsucceed/1680.v @@ -0,0 +1,9 @@ +Ltac int1 := let h := fresh in intro h. + +Goal nat -> nat -> True. + let h' := fresh in (let h := fresh in intro h); intro h'. + Restart. let h' := fresh in int1; intro h'. + trivial. +Qed. + + diff --git a/test-suite/bugs/closed/shouldsucceed/1683.v b/test-suite/bugs/closed/shouldsucceed/1683.v new file mode 100644 index 00000000..1571ee20 --- /dev/null +++ b/test-suite/bugs/closed/shouldsucceed/1683.v @@ -0,0 +1,42 @@ +Require Import Setoid. + +Section SetoidBug. + +Variable ms : Type. +Variable ms_type : ms -> Type. +Variable ms_eq : forall (A:ms), relation (ms_type A). + +Variable CR : ms. + +Record Ring : Type := +{Ring_type : Type}. + +Variable foo : forall (A:Ring), nat -> Ring_type A. +Variable IR : Ring. +Variable IRasCR : Ring_type IR -> ms_type CR. + +Definition CRasCRing : Ring := Build_Ring (ms_type CR). + +Hypothesis ms_refl : forall A x, ms_eq A x x. +Hypothesis ms_sym : forall A x y, ms_eq A x y -> ms_eq A y x. +Hypothesis ms_trans : forall A x y z, ms_eq A x y -> ms_eq A y z -> ms_eq A x z. + +Add Parametric Relation A : (ms_type A) (ms_eq A) + reflexivity proved by (ms_refl A) + symmetry proved by (ms_sym A) + transitivity proved by (ms_trans A) + as ms_Setoid. + +Hypothesis foobar : forall n, ms_eq CR (IRasCR (foo IR n)) (foo CRasCRing n). + +Goal forall (b:ms_type CR), + ms_eq CR (IRasCR (foo IR O)) b -> + ms_eq CR (IRasCR (foo IR O)) b. +intros b H. +rewrite foobar. +rewrite foobar in H. +assumption. +Qed. + + + diff --git a/test-suite/bugs/closed/shouldsucceed/1696.v b/test-suite/bugs/closed/shouldsucceed/1696.v new file mode 100644 index 00000000..0826428a --- /dev/null +++ b/test-suite/bugs/closed/shouldsucceed/1696.v @@ -0,0 +1,16 @@ +Require Import Setoid. + +Inductive mynat := z : mynat | s : mynat -> mynat. + +Parameter E : mynat -> mynat -> Prop. +Axiom E_equiv : equiv mynat E. + +Add Relation mynat E + reflexivity proved by (proj1 E_equiv) + symmetry proved by (proj2 (proj2 E_equiv)) + transitivity proved by (proj1 (proj2 E_equiv)) +as E_rel. + +Notation "x == y" := (E x y) (at level 70). + +Goal z == s z -> s z == z. intros H. setoid_rewrite H at 2. reflexivity. Qed. diff --git a/test-suite/bugs/closed/shouldsucceed/1704.v b/test-suite/bugs/closed/shouldsucceed/1704.v new file mode 100644 index 00000000..4b02d5f9 --- /dev/null +++ b/test-suite/bugs/closed/shouldsucceed/1704.v @@ -0,0 +1,17 @@ + +Require Import Setoid. +Parameter E : nat -> nat -> Prop. +Axiom E_equiv : equiv nat E. +Add Relation nat E +reflexivity proved by (proj1 E_equiv) +symmetry proved by (proj2 (proj2 E_equiv)) +transitivity proved by (proj1 (proj2 E_equiv)) +as E_rel. +Notation "x == y" := (E x y) (at level 70, no associativity). +Axiom r : False -> 0 == 1. +Goal 0 == 0. +Proof. +rewrite r. +reflexivity. +admit. +Qed. diff --git a/test-suite/bugs/closed/shouldsucceed/1718.v b/test-suite/bugs/closed/shouldsucceed/1718.v new file mode 100644 index 00000000..715fa941 --- /dev/null +++ b/test-suite/bugs/closed/shouldsucceed/1718.v @@ -0,0 +1,9 @@ +(* lazy delta unfolding used to miss delta on rels and vars (fixed in 10172) *) + +Check + let g := fun _ => 0 in + fix f (n : nat) := + match n with + | 0 => g f + | S n' => 0 + end. diff --git a/test-suite/bugs/closed/shouldsucceed/1738.v b/test-suite/bugs/closed/shouldsucceed/1738.v new file mode 100644 index 00000000..0deed366 --- /dev/null +++ b/test-suite/bugs/closed/shouldsucceed/1738.v @@ -0,0 +1,30 @@ +Require Import FSets. + +Module SomeSetoids (Import M:FSetInterface.S). + +Lemma Equal_refl : forall s, s[=]s. +Proof. red; split; auto. Qed. + +Add Relation t Equal + reflexivity proved by Equal_refl + symmetry proved by eq_sym + transitivity proved by eq_trans + as EqualSetoid. + +Add Morphism Empty with signature Equal ==> iff as Empty_m. +Proof. +unfold Equal, Empty; firstorder. +Qed. + +End SomeSetoids. + +Module Test (Import M:FSetInterface.S). + Module A:=SomeSetoids M. + Module B:=SomeSetoids M. (* lots of warning *) + + Lemma Test : forall s s', s[=]s' -> Empty s -> Empty s'. + intros. + rewrite H in H0. + assumption. +Qed. +End Test. \ No newline at end of file diff --git a/test-suite/bugs/closed/shouldsucceed/1740.v b/test-suite/bugs/closed/shouldsucceed/1740.v new file mode 100644 index 00000000..d9ce546a --- /dev/null +++ b/test-suite/bugs/closed/shouldsucceed/1740.v @@ -0,0 +1,23 @@ +(* Check that expansion of alias in pattern-matching compilation is no + longer dependent of whether the pattern-matching problem occurs in a + typed context or at toplevel (solved from revision 10883) *) + +Definition f := + fun n m : nat => + match n, m with + | O, _ => O + | n, O => n + | _, _ => O + end. + +Goal f = + fun n m : nat => + match n, m with + | O, _ => O + | n, O => n + | _, _ => O + end. + unfold f. + reflexivity. +Qed. + diff --git a/test-suite/bugs/closed/shouldsucceed/1754.v b/test-suite/bugs/closed/shouldsucceed/1754.v new file mode 100644 index 00000000..06b8dce8 --- /dev/null +++ b/test-suite/bugs/closed/shouldsucceed/1754.v @@ -0,0 +1,24 @@ +Axiom hp : Set. +Axiom cont : nat -> hp -> Prop. +Axiom sconj : (hp -> Prop) -> (hp -> Prop) -> hp -> Prop. +Axiom sconjImpl : forall h A B, + (sconj A B) h -> forall (A' B': hp -> Prop), + (forall h', A h' -> A' h') -> + (forall h', B h' -> B' h') -> + (sconj A' B') h. + +Definition cont' (h:hp) := exists y, cont y h. + +Lemma foo : forall h x y A, + (sconj (cont x) (sconj (cont y) A)) h -> + (sconj cont' (sconj cont' A)) h. +Proof. + intros h x y A H. + eapply sconjImpl. + 2:intros h' Hp'; econstructor; apply Hp'. + 2:intros h' Hp'; eapply sconjImpl. + 3:intros h'' Hp''; econstructor; apply Hp''. + 3:intros h'' Hp''; apply Hp''. + 2:apply Hp'. + clear H. +Admitted. diff --git a/test-suite/bugs/closed/shouldsucceed/1773.v b/test-suite/bugs/closed/shouldsucceed/1773.v new file mode 100644 index 00000000..211af89b --- /dev/null +++ b/test-suite/bugs/closed/shouldsucceed/1773.v @@ -0,0 +1,9 @@ +(* An occur-check test was done too early *) + +Goal forall B C : nat -> nat -> Prop, forall k, + (exists A, (forall k', C A k' -> B A k') -> B A k). +Proof. + intros B C k. + econstructor. + intros X. + apply X. (* used to fail here *) diff --git a/test-suite/bugs/closed/shouldsucceed/1774.v b/test-suite/bugs/closed/shouldsucceed/1774.v new file mode 100644 index 00000000..4c24b481 --- /dev/null +++ b/test-suite/bugs/closed/shouldsucceed/1774.v @@ -0,0 +1,18 @@ +Axiom pl : (nat -> Prop) -> (nat -> Prop) -> (nat -> Prop). +Axiom plImp : forall k P Q, + pl P Q k -> forall (P':nat -> Prop), + (forall k', P k' -> P' k') -> forall (Q':nat -> Prop), + (forall k', Q k' -> Q' k') -> + pl P' Q' k. + +Definition nexists (P:nat -> nat -> Prop) : nat -> Prop := + fun k' => exists k, P k k'. + +Goal forall k (A:nat -> nat -> Prop) (B:nat -> Prop), + pl (nexists A) B k. +intros. +eapply plImp. +2:intros m' M'; econstructor; apply M'. +2:intros m' M'; apply M'. +simpl. +Admitted. diff --git a/test-suite/bugs/closed/shouldsucceed/1775.v b/test-suite/bugs/closed/shouldsucceed/1775.v new file mode 100644 index 00000000..dab4120b --- /dev/null +++ b/test-suite/bugs/closed/shouldsucceed/1775.v @@ -0,0 +1,39 @@ +Axiom pair : nat -> nat -> nat -> Prop. +Axiom pl : (nat -> Prop) -> (nat -> Prop) -> (nat -> Prop). +Axiom plImp : forall k P Q, + pl P Q k -> forall (P':nat -> Prop), + (forall k', P k' -> P' k') -> forall (Q':nat -> Prop), + (forall k', Q k' -> Q' k') -> + pl P' Q' k. + +Definition nexists (P:nat -> nat -> Prop) : nat -> Prop := + fun k' => exists k, P k k'. + +Goal forall s k k' m, + (pl k' (nexists (fun w => (nexists (fun b => pl (pair w w) + (pl (pair s b) + (nexists (fun w0 => (nexists (fun a => pl (pair b w0) + (nexists (fun w1 => (nexists (fun c => pl + (pair a w1) (pl (pair a c) k))))))))))))))) m. +intros. +eapply plImp; [ | eauto | intros ]. +2:econstructor. +2:econstructor. +2:eapply plImp; [ | eauto | intros ]. +3:eapply plImp; [ | eauto | intros ]. +4:econstructor. +4:econstructor. +4:eapply plImp; [ | eauto | intros ]. +5:econstructor. +5:econstructor. +5:eauto. +4:eauto. +3:eauto. +2:eauto. + +assert (X := 1). +clear X. (* very slow! *) + +simpl. (* exception Not_found *) + +Admitted. diff --git a/test-suite/bugs/closed/shouldsucceed/1776.v b/test-suite/bugs/closed/shouldsucceed/1776.v new file mode 100644 index 00000000..abf85455 --- /dev/null +++ b/test-suite/bugs/closed/shouldsucceed/1776.v @@ -0,0 +1,22 @@ +Axiom pair : nat -> nat -> nat -> Prop. +Axiom pl : (nat -> Prop) -> (nat -> Prop) -> (nat -> Prop). +Axiom plImpR : forall k P Q, + pl P Q k -> forall (Q':nat -> Prop), + (forall k', Q k' -> Q' k') -> + pl P Q' k. + +Definition nexists (P:nat -> nat -> Prop) : nat -> Prop := + fun k' => exists k, P k k'. + +Goal forall a A m, + True -> + (pl A (nexists (fun x => (nexists + (fun y => pl (pair a (S x)) (pair a (S y))))))) m. +Proof. + intros. + eapply plImpR; [ | intros; econstructor; econstructor; eauto]. + clear H; + match goal with + | |- (pl _ (pl (pair _ ?x) _)) _ => replace x with 0 + end. +Admitted. diff --git a/test-suite/bugs/closed/shouldsucceed/1779.v b/test-suite/bugs/closed/shouldsucceed/1779.v new file mode 100644 index 00000000..95bb66b9 --- /dev/null +++ b/test-suite/bugs/closed/shouldsucceed/1779.v @@ -0,0 +1,25 @@ +Require Import Div2. + +Lemma double_div2: forall n, div2 (double n) = n. +exact (fun n => let _subcase := + let _cofact := fun _ : 0 = 0 => refl_equal 0 in + _cofact (let _fact := refl_equal 0 in _fact) in + let _subcase0 := + fun (m : nat) (Hrec : div2 (double m) = m) => + let _fact := f_equal div2 (double_S m) in + let _eq := trans_eq _fact (refl_equal (S (div2 (double m)))) in + let _eq0 := + trans_eq _eq + (trans_eq + (f_equal (fun f : nat -> nat => f (div2 (double m))) + (refl_equal S)) (f_equal S Hrec)) in + _eq0 in + (fix _fix (__ : nat) : div2 (double __) = __ := + match __ as n return (div2 (double n) = n) with + | 0 => _subcase + | S __0 => + (fun _hrec : div2 (double __0) = __0 => _subcase0 __0 _hrec) + (_fix __0) + end) n). +Guarded. +Defined. diff --git a/test-suite/bugs/closed/shouldsucceed/1784.v b/test-suite/bugs/closed/shouldsucceed/1784.v new file mode 100644 index 00000000..616dd26f --- /dev/null +++ b/test-suite/bugs/closed/shouldsucceed/1784.v @@ -0,0 +1,101 @@ +Require Import List. +Require Import ZArith. +Require String. Open Scope string_scope. +Ltac Case s := let c := fresh "case" in set (c := s). + +Set Implicit Arguments. +Unset Strict Implicit. + +Inductive sv : Set := +| I : Z -> sv +| S : list sv -> sv. + +Section sv_induction. + +Variables + (VP: sv -> Prop) + (LP: list sv -> Prop) + + (VPint: forall n, VP (I n)) + (VPset: forall vs, LP vs -> VP (S vs)) + (lpcons: forall v vs, VP v -> LP vs -> LP (v::vs)) + (lpnil: LP nil). + +Fixpoint setl_value_indp (x:sv) {struct x}: VP x := + match x as x return VP x with + | I n => VPint n + | S vs => + VPset + ((fix values_indp (vs:list sv) {struct vs}: (LP vs) := + match vs as vs return LP vs with + | nil => lpnil + | v::vs => lpcons (setl_value_indp v) (values_indp vs) + end) vs) + end. +End sv_induction. + +Inductive slt : sv -> sv -> Prop := +| IC : forall z, slt (I z) (I z) +| IS : forall vs vs', slist_in vs vs' -> slt (S vs) (S vs') + +with sin : sv -> list sv -> Prop := +| Ihd : forall s s' sv', slt s s' -> sin s (s'::sv') +| Itl : forall s s' sv', sin s sv' -> sin s (s'::sv') + +with slist_in : list sv -> list sv -> Prop := +| Inil : forall sv', + slist_in nil sv' +| Icons : forall s sv sv', + sin s sv' -> + slist_in sv sv' -> + slist_in (s::sv) sv'. + +Hint Constructors sin slt slist_in. + +Require Import Program. + +Program Fixpoint lt_dec (x y:sv) { struct x } : {slt x y}+{~slt x y} := + match x with + | I x => + match y with + | I y => if (Z_eq_dec x y) then in_left else in_right + | S ys => in_right + end + | S xs => + match y with + | I y => in_right + | S ys => + let fix list_in (xs ys:list sv) {struct xs} : + {slist_in xs ys} + {~slist_in xs ys} := + match xs with + | nil => in_left + | x::xs => + let fix elem_in (ys:list sv) : {sin x ys}+{~sin x ys} := + match ys with + | nil => in_right + | y::ys => if lt_dec x y then in_left else if elem_in + ys then in_left else in_right + end + in + if elem_in ys then + if list_in xs ys then in_left else in_right + else in_right + end + in if list_in xs ys then in_left else in_right + end + end. + +Next Obligation. apply H; inversion H0; subst; trivial. Defined. +Next Obligation. inversion H. Defined. +Next Obligation. inversion H. Defined. +Next Obligation. inversion H; subst. Defined. +Next Obligation. + contradict H. inversion H1; subst. assumption. + contradict H0; assumption. Defined. +Next Obligation. + contradict H0. inversion H1; subst. assumption. Defined. +Next Obligation. + contradict H. inversion H0; subst. assumption. Defined. +Next Obligation. + contradict H. inversion H0; subst; auto. Defined. + diff --git a/test-suite/bugs/closed/shouldsucceed/1844.v b/test-suite/bugs/closed/shouldsucceed/1844.v new file mode 100644 index 00000000..545f2615 --- /dev/null +++ b/test-suite/bugs/closed/shouldsucceed/1844.v @@ -0,0 +1,217 @@ +Require Import ZArith. + +Definition zeq := Z_eq_dec. + +Definition update (A: Set) (x: Z) (v: A) (s: Z -> A) : Z -> A := + fun y => if zeq x y then v else s y. + +Implicit Arguments update [A]. + +Definition ident := Z. +Parameter operator: Set. +Parameter value: Set. +Parameter is_true: value -> Prop. +Definition label := Z. + +Inductive expr : Set := + | Evar: ident -> expr + | Econst: value -> expr + | Eop: operator -> expr -> expr -> expr. + +Inductive stmt : Set := + | Sskip: stmt + | Sassign: ident -> expr -> stmt + | Scall: ident -> ident -> expr -> stmt (* x := f(e) *) + | Sreturn: expr -> stmt + | Sseq: stmt -> stmt -> stmt + | Sifthenelse: expr -> stmt -> stmt -> stmt + | Sloop: stmt -> stmt + | Sblock: stmt -> stmt + | Sexit: nat -> stmt + | Slabel: label -> stmt -> stmt + | Sgoto: label -> stmt. + +Record function : Set := mkfunction { + fn_param: ident; + fn_body: stmt +}. + +Parameter program: ident -> option function. + +Parameter main_function: ident. + +Definition store := ident -> value. + +Parameter empty_store : store. + +Parameter eval_op: operator -> value -> value -> option value. + +Fixpoint eval_expr (st: store) (e: expr) {struct e} : option value := + match e with + | Evar v => Some (st v) + | Econst v => Some v + | Eop op e1 e2 => + match eval_expr st e1, eval_expr st e2 with + | Some v1, Some v2 => eval_op op v1 v2 + | _, _ => None + end + end. + +Inductive outcome: Set := + | Onormal: outcome + | Oexit: nat -> outcome + | Ogoto: label -> outcome + | Oreturn: value -> outcome. + +Definition outcome_block (out: outcome) : outcome := + match out with + | Onormal => Onormal + | Oexit O => Onormal + | Oexit (S m) => Oexit m + | Ogoto lbl => Ogoto lbl + | Oreturn v => Oreturn v + end. + +Fixpoint label_defined (lbl: label) (s: stmt) {struct s}: Prop := + match s with + | Sskip => False + | Sassign id e => False + | Scall id fn e => False + | Sreturn e => False + | Sseq s1 s2 => label_defined lbl s1 \/ label_defined lbl s2 + | Sifthenelse e s1 s2 => label_defined lbl s1 \/ label_defined lbl s2 + | Sloop s1 => label_defined lbl s1 + | Sblock s1 => label_defined lbl s1 + | Sexit n => False + | Slabel lbl1 s1 => lbl1 = lbl \/ label_defined lbl s1 + | Sgoto lbl => False + end. + +Inductive exec : stmt -> store -> outcome -> store -> Prop := + | exec_skip: forall st, + exec Sskip st Onormal st + | exec_assign: forall id e st v, + eval_expr st e = Some v -> + exec (Sassign id e) st Onormal (update id v st) + | exec_call: forall id fn e st v1 f v2 st', + eval_expr st e = Some v1 -> + program fn = Some f -> + exec_function f (update f.(fn_param) v1 empty_store) v2 st' -> + exec (Scall id fn e) st Onormal (update id v2 st) + | exec_return: forall e st v, + eval_expr st e = Some v -> + exec (Sreturn e) st (Oreturn v) st + | exec_seq_2: forall s1 s2 st st1 out' st', + exec s1 st Onormal st1 -> exec s2 st1 out' st' -> + exec (Sseq s1 s2) st out' st' + | exec_seq_1: forall s1 s2 st out st', + exec s1 st out st' -> out <> Onormal -> + exec (Sseq s1 s2) st out st' + | exec_ifthenelse_true: forall e s1 s2 st out st' v, + eval_expr st e = Some v -> is_true v -> exec s1 st out st' -> + exec (Sifthenelse e s1 s2) st out st' + | exec_ifthenelse_false: forall e s1 s2 st out st' v, + eval_expr st e = Some v -> ~is_true v -> exec s2 st out st' -> + exec (Sifthenelse e s1 s2) st out st' + | exec_loop_loop: forall s st st1 out' st', + exec s st Onormal st1 -> + exec (Sloop s) st1 out' st' -> + exec (Sloop s) st out' st' + | exec_loop_stop: forall s st st' out, + exec s st out st' -> out <> Onormal -> + exec (Sloop s) st out st' + | exec_block: forall s st out st', + exec s st out st' -> + exec (Sblock s) st (outcome_block out) st' + | exec_exit: forall n st, + exec (Sexit n) st (Oexit n) st + | exec_label: forall s lbl st st' out, + exec s st out st' -> + exec (Slabel lbl s) st out st' + | exec_goto: forall st lbl, + exec (Sgoto lbl) st (Ogoto lbl) st + +(** [execg lbl stmt st out st'] starts executing at label [lbl] within [s], + in initial store [st]. The result of the execution is the outcome + [out] with final store [st']. *) + +with execg: label -> stmt -> store -> outcome -> store -> Prop := + | execg_left_seq_2: forall lbl s1 s2 st st1 out' st', + execg lbl s1 st Onormal st1 -> exec s2 st1 out' st' -> + execg lbl (Sseq s1 s2) st out' st' + | execg_left_seq_1: forall lbl s1 s2 st out st', + execg lbl s1 st out st' -> out <> Onormal -> + execg lbl (Sseq s1 s2) st out st' + | execg_right_seq: forall lbl s1 s2 st out st', + ~(label_defined lbl s1) -> + execg lbl s2 st out st' -> + execg lbl (Sseq s1 s2) st out st' + | execg_ifthenelse_left: forall lbl e s1 s2 st out st', + execg lbl s1 st out st' -> + execg lbl (Sifthenelse e s1 s2) st out st' + | execg_ifthenelse_right: forall lbl e s1 s2 st out st', + ~(label_defined lbl s1) -> + execg lbl s2 st out st' -> + execg lbl (Sifthenelse e s1 s2) st out st' + | execg_loop_loop: forall lbl s st st1 out' st', + execg lbl s st Onormal st1 -> + exec (Sloop s) st1 out' st' -> + execg lbl (Sloop s) st out' st' + | execg_loop_stop: forall lbl s st st' out, + execg lbl s st out st' -> out <> Onormal -> + execg lbl (Sloop s) st out st' + | execg_block: forall lbl s st out st', + execg lbl s st out st' -> + execg lbl (Sblock s) st (outcome_block out) st' + | execg_label_found: forall lbl s st st' out, + exec s st out st' -> + execg lbl (Slabel lbl s) st out st' + | execg_label_notfound: forall lbl s lbl' st st' out, + lbl' <> lbl -> + execg lbl s st out st' -> + execg lbl (Slabel lbl' s) st out st' + +(** [exec_finish out st st'] takes the outcome [out] and the store [st] + at the end of the evaluation of the program. If [out] is a [goto], + execute again the program starting at the corresponding label. + Iterate this way until [out] is [Onormal]. *) + +with exec_finish: function -> outcome -> store -> value -> store -> Prop := + | exec_finish_normal: forall f st v, + exec_finish f (Oreturn v) st v st + | exec_finish_goto: forall f lbl st out v st1 st', + execg lbl f.(fn_body) st out st1 -> + exec_finish f out st1 v st' -> + exec_finish f (Ogoto lbl) st v st' + +(** Execution of a function *) + +with exec_function: function -> store -> value -> store -> Prop := + | exec_function_intro: forall f st out st1 v st', + exec f.(fn_body) st out st1 -> + exec_finish f out st1 v st' -> + exec_function f st v st'. + +Scheme exec_ind4:= Minimality for exec Sort Prop + with execg_ind4:= Minimality for execg Sort Prop + with exec_finish_ind4 := Minimality for exec_finish Sort Prop + with exec_function_ind4 := Minimality for exec_function Sort Prop. + +Scheme exec_dind4:= Induction for exec Sort Prop + with execg_dind4:= Minimality for execg Sort Prop + with exec_finish_dind4 := Induction for exec_finish Sort Prop + with exec_function_dind4 := Induction for exec_function Sort Prop. + +Combined Scheme exec_inductiond from exec_dind4, execg_dind4, exec_finish_dind4, + exec_function_dind4. + +Scheme exec_dind4' := Induction for exec Sort Prop + with execg_dind4' := Induction for execg Sort Prop + with exec_finish_dind4' := Induction for exec_finish Sort Prop + with exec_function_dind4' := Induction for exec_function Sort Prop. + +Combined Scheme exec_induction from exec_ind4, execg_ind4, exec_finish_ind4, + exec_function_ind4. + +Combined Scheme exec_inductiond' from exec_dind4', execg_dind4', exec_finish_dind4', + exec_function_dind4'. diff --git a/test-suite/bugs/closed/shouldsucceed/1865.v b/test-suite/bugs/closed/shouldsucceed/1865.v new file mode 100644 index 00000000..17c19989 --- /dev/null +++ b/test-suite/bugs/closed/shouldsucceed/1865.v @@ -0,0 +1,18 @@ +(* Check that tactics (here dependent inversion) do not generate + conversion problems T <= U with sup's of universes in U *) + +(* Submitted by David Nowak *) + +Inductive list (A:Set) : nat -> Set := +| nil : list A O +| cons : forall n, A -> list A n -> list A (S n). + +Definition f (n:nat) : Type := + match n with + | O => bool + | _ => unit + end. + +Goal forall A n, list A n -> f n. +intros A n. +dependent inversion n. diff --git a/test-suite/bugs/closed/shouldsucceed/348.v b/test-suite/bugs/closed/shouldsucceed/348.v new file mode 100644 index 00000000..28cc5cb1 --- /dev/null +++ b/test-suite/bugs/closed/shouldsucceed/348.v @@ -0,0 +1,13 @@ +Module Type S. + Parameter empty: Set. +End S. + +Module D (M:S). + Import M. + Definition empty:=nat. +End D. + +Module D' (M:S). + Import M. + Definition empty:Set. exact nat. Save. +End D'. diff --git a/test-suite/bugs/closed/shouldsucceed/38.v b/test-suite/bugs/closed/shouldsucceed/38.v new file mode 100644 index 00000000..7bc04b1f --- /dev/null +++ b/test-suite/bugs/closed/shouldsucceed/38.v @@ -0,0 +1,22 @@ +Require Import Setoid. + +Variable A : Set. + +Inductive liste : Set := +| vide : liste +| c : A -> liste -> liste. + +Inductive e : A -> liste -> Prop := +| ec : forall (x : A) (l : liste), e x (c x l) +| ee : forall (x y : A) (l : liste), e x l -> e x (c y l). + +Definition same := fun (l m : liste) => forall (x : A), e x l <-> e x m. + +Definition same_refl (x:liste) : (same x x). + unfold same; split; intros; trivial. +Save. + +Goal forall (x:liste), (same x x). + intro. + apply (same_refl x). +Qed. diff --git a/test-suite/bugs/closed/shouldsucceed/545.v b/test-suite/bugs/closed/shouldsucceed/545.v new file mode 100644 index 00000000..926af7dd --- /dev/null +++ b/test-suite/bugs/closed/shouldsucceed/545.v @@ -0,0 +1,5 @@ +Require Export Reals. + +Parameter toto : nat -> nat -> nat. + +Notation " e # f " := (toto e f) (at level 30, f at level 0). diff --git a/test-suite/bugs/closed/shouldsucceed/846.v b/test-suite/bugs/closed/shouldsucceed/846.v new file mode 100644 index 00000000..a963b225 --- /dev/null +++ b/test-suite/bugs/closed/shouldsucceed/846.v @@ -0,0 +1,213 @@ +Set Implicit Arguments. + +Open Scope type_scope. + +Inductive One : Set := inOne: One. + +Definition maybe: forall A B:Set,(A -> B) -> One + A -> One + B. +Proof. + intros A B f c. + case c. + left; assumption. + right; apply f; assumption. +Defined. + +Definition id (A:Set)(a:A):=a. + +Definition LamF (X: Set -> Set)(A:Set) :Set := + A + (X A)*(X A) + X(One + A). + +Definition LamF' (X: Set -> Set)(A:Set) :Set := + LamF X A. + +Require Import List. +Require Import Bool. + +Definition index := list bool. + +Inductive L (A:Set) : index -> Set := + initL: A -> L A nil + | pluslL: forall l:index, One -> L A (false::l) + | plusrL: forall l:index, L A l -> L A (false::l) + | varL: forall l:index, L A l -> L A (true::l) + | appL: forall l:index, L A (true::l) -> L A (true::l) -> L A (true::l) + | absL: forall l:index, L A (true::false::l) -> L A (true::l). + +Scheme L_rec_simp := Minimality for L Sort Set. + +Definition Lam' (A:Set) := L A (true::nil). + +Definition aczelapp: forall (l1 l2: index)(A:Set), L (L A l2) l1 -> L A + (l1++l2). +Proof. + intros l1 l2 A. + generalize l1. + clear l1. + (* Check (fun i:index => L A (i++l2)). *) + apply (L_rec_simp (A:=L A l2) (fun i:index => L A (i++l2))). + trivial. + intros l o. + simpl app. + apply pluslL; assumption. + intros l _ t. + simpl app. + apply plusrL; assumption. + intros l _ t. + simpl app. + apply varL; assumption. + intros l _ t1 _ t2. + simpl app in *|-*. + Check 0. + apply appL; [exact t1| exact t2]. + intros l _ t. + simpl app in *|-*. + Check 0. + apply absL; assumption. +Defined. + +Definition monL: forall (l:index)(A:Set)(B:Set), (A->B) -> L A l -> L B l. +Proof. + intros l A B f. + intro t. + elim t. + intro a. + exact (initL (f a)). + intros i u. + exact (pluslL _ _ u). + intros i _ r. + exact (plusrL r). + intros i _ r. + exact (varL r). + intros i _ r1 _ r2. + exact (appL r1 r2). + intros i _ r. + exact (absL r). +Defined. + +Definition lam': forall (A B:Set), (A -> B) -> Lam' A -> Lam' B. +Proof. + intros A B f t. + unfold Lam' in *|-*. + Check 0. + exact (monL f t). +Defined. + +Definition inLam': forall A:Set, LamF' Lam' A -> Lam' A. +Proof. + intros A [[a|[t1 t2]]|r]. + unfold Lam'. + exact (varL (initL a)). + exact (appL t1 t2). + unfold Lam' in * |- *. + Check 0. + apply absL. + change (L A ((true::nil) ++ (false::nil))). + apply aczelapp. + (* Check (fun x:One + A => (match (maybe (fun a:A => initL a) x) with + | inl u => pluslL _ _ u + | inr t' => plusrL t' end)). *) + exact (monL (fun x:One + A => + (match (maybe (fun a:A => initL a) x) with + | inl u => pluslL _ _ u + | inr t' => plusrL t' end)) r). +Defined. + +Section minimal. + +Definition sub1 (F G: Set -> Set):= forall A:Set, F A->G A. +Hypothesis G: Set -> Set. +Hypothesis step: sub1 (LamF' G) G. + +Fixpoint L'(A:Set)(i:index){struct i} : Set := + match i with + nil => A + | false::l => One + L' A l + | true::l => G (L' A l) + end. + +Definition LinL': forall (A:Set)(i:index), L A i -> L' A i. +Proof. + intros A i t. + elim t. + intro a. + unfold L'. + assumption. + intros l u. + left; assumption. + intros l _ r. + right; assumption. + intros l _ r. + apply (step (A:=L' A l)). + exact (inl _ (inl _ r)). + intros l _ r1 _ r2. + apply (step (A:=L' A l)). + (* unfold L' in * |- *. + Check 0. *) + exact (inl _ (inr _ (pair r1 r2))). + intros l _ r. + apply (step (A:=L' A l)). + exact (inr _ r). +Defined. + +Definition L'inG: forall A: Set, L' A (true::nil) -> G A. +Proof. + intros A t. + unfold L' in t. + assumption. +Defined. + +Definition Itbasic: sub1 Lam' G. +Proof. + intros A t. + apply L'inG. + unfold Lam' in t. + exact (LinL' t). +Defined. + +End minimal. + +Definition recid := Itbasic inLam'. + +Definition L'Lam'inL: forall (i:index)(A:Set), L' Lam' A i -> L A i. +Proof. + intros i A t. + induction i. + unfold L' in t. + apply initL. + assumption. + induction a. + simpl L' in t. + apply (aczelapp (l1:=true::nil) (l2:=i)). + exact (lam' IHi t). + simpl L' in t. + induction t. + exact (pluslL _ _ a). + exact (plusrL (IHi b)). +Defined. + + +Lemma recidgen: forall(A:Set)(i:index)(t:L A i), L'Lam'inL i A (LinL' inLam' t) + = t. +Proof. + intros A i t. + induction t. + trivial. + trivial. + simpl. + rewrite IHt. + trivial. + simpl L'Lam'inL. + rewrite IHt. + trivial. + simpl L'Lam'inL. + simpl L'Lam'inL in IHt1. + unfold lam' in IHt1. + simpl L'Lam'inL in IHt2. + unfold lam' in IHt2. + + (* going on. This fails for the original solution. *) + rewrite IHt1. + rewrite IHt2. + trivial. +Abort. (* one goal still left *) + diff --git a/test-suite/bugs/closed/shouldsucceed/931.v b/test-suite/bugs/closed/shouldsucceed/931.v new file mode 100644 index 00000000..21f15e72 --- /dev/null +++ b/test-suite/bugs/closed/shouldsucceed/931.v @@ -0,0 +1,7 @@ +Parameter P : forall n : nat, n=n -> Prop. + +Goal Prop. + refine (P _ _). + instantiate (1:=0). + trivial. +Qed. diff --git a/test-suite/bugs/opened/1773.v b/test-suite/bugs/opened/1773.v new file mode 100644 index 00000000..4aabf19c --- /dev/null +++ b/test-suite/bugs/opened/1773.v @@ -0,0 +1,10 @@ +Goal forall B C : nat -> nat -> Prop, forall k, C 0 k -> + (exists A, (forall k', C A k' -> B A k') -> B A k). +Proof. + intros B C k H. + econstructor. + intros X. + apply X. + apply H. +Qed. + diff --git a/test-suite/bugs/opened/shouldnotfail/1338.v-disabled b/test-suite/bugs/opened/shouldnotfail/1338.v-disabled new file mode 100644 index 00000000..f383d534 --- /dev/null +++ b/test-suite/bugs/opened/shouldnotfail/1338.v-disabled @@ -0,0 +1,12 @@ +Require Import Omega. + +Goal forall x, 0 <= x -> x <= 20 -> +x <> 0 + -> x <> 1 -> x <> 2 -> x <> 3 -> x <>4 -> x <> 5 -> x <> 6 -> x <> 7 -> x <> 8 +-> x <> 9 -> x <> 10 + -> x <> 11 -> x <> 12 -> x <> 13 -> x <> 14 -> x <> 15 -> x <> 16 -> x <> 17 +-> x <> 18 -> x <> 19 -> x <> 20 -> False. +Proof. + intros. + omega. +Qed. diff --git a/test-suite/bugs/opened/shouldnotfail/1416.v b/test-suite/bugs/opened/shouldnotfail/1416.v new file mode 100644 index 00000000..c6f4302d --- /dev/null +++ b/test-suite/bugs/opened/shouldnotfail/1416.v @@ -0,0 +1,27 @@ +Set Implicit Arguments. + +Record Place (Env A: Type) : Type := { + read: Env -> A ; + write: Env -> A -> Env ; + write_read: forall (e:Env), (write e (read e))=e +}. + +Hint Rewrite -> write_read: placeeq. + +Record sumPl (Env A B: Type) (vL:(Place Env A)) (vR:(Place Env B)) : Type := + { + mkEnv: A -> B -> Env ; + mkEnv2writeL: forall (e:Env) (x:A), (mkEnv x (read vR e))=(write vL e x) + }. + +(* when the following line is commented, the bug does not appear *) +Hint Rewrite -> mkEnv2writeL: placeeq. + +Lemma autorewrite_raise_anomaly: forall (Env A:Type) (e: Env) (p:Place Env A), + (exists e1:Env, e=(write p e1 (read p e))). +Proof. + intros Env A e p; eapply ex_intro. + autorewrite with placeeq. (* Here is the bug *) + auto. +Qed. + diff --git a/test-suite/bugs/opened/shouldnotfail/1501.v b/test-suite/bugs/opened/shouldnotfail/1501.v new file mode 100644 index 00000000..85c09dbd --- /dev/null +++ b/test-suite/bugs/opened/shouldnotfail/1501.v @@ -0,0 +1,93 @@ +Set Implicit Arguments. + + +Require Export Relation_Definitions. +Require Export Setoid. + + +Section Essais. + +(* Parametrized Setoid *) +Parameter K : Type -> Type. +Parameter equiv : forall A : Type, K A -> K A -> Prop. +Parameter equiv_refl : forall (A : Type) (x : K A), equiv x x. +Parameter equiv_sym : forall (A : Type) (x y : K A), equiv x y -> equiv y x. +Parameter equiv_trans : forall (A : Type) (x y z : K A), equiv x y -> equiv y z +-> equiv x z. + +(* basic operations *) +Parameter val : forall A : Type, A -> K A. +Parameter bind : forall A B : Type, K A -> (A -> K B) -> K B. + +Parameter + bind_compat : + forall (A B : Type) (m1 m2 : K A) (f1 f2 : A -> K B), + equiv m1 m2 -> + (forall x : A, equiv (f1 x) (f2 x)) -> equiv (bind m1 f1) (bind m2 f2). + +(* monad axioms *) +Parameter + bind_val_l : + forall (A B : Type) (a : A) (f : A -> K B), equiv (bind (val a) f) (f a). +Parameter + bind_val_r : + forall (A : Type) (m : K A), equiv (bind m (fun a => val a)) m. +Parameter + bind_assoc : + forall (A B C : Type) (m : K A) (f : A -> K B) (g : B -> K C), + equiv (bind (bind m f) g) (bind m (fun a => bind (f a) g)). + + +Hint Resolve equiv_refl equiv_sym equiv_trans: monad. + +Add Relation K equiv + reflexivity proved by (@equiv_refl) + symmetry proved by (@equiv_sym) + transitivity proved by (@equiv_trans) + as equiv_rel. + +Definition fequiv (A B: Type) (f g: A -> K B) := forall (x:A), (equiv (f x) (g +x)). + +Lemma fequiv_refl : forall (A B: Type) (f : A -> K B), fequiv f f. +Proof. + unfold fequiv; auto with monad. +Qed. + +Lemma fequiv_sym : forall (A B: Type) (x y : A -> K B), fequiv x y -> fequiv y +x. +Proof. + unfold fequiv; auto with monad. +Qed. + +Lemma fequiv_trans : forall (A B: Type) (x y z : A -> K B), fequiv x y -> +fequiv +y z -> fequiv x z. +Proof. + unfold fequiv; intros; eapply equiv_trans; auto with monad. +Qed. + +Add Relation (fun (A B:Type) => A -> K B) fequiv + reflexivity proved by (@fequiv_refl) + symmetry proved by (@fequiv_sym) + transitivity proved by (@fequiv_trans) + as fequiv_rel. + +Add Morphism bind + with signature equiv ==> fequiv ==> equiv + as bind_mor. +Proof. + unfold fequiv; intros; apply bind_compat; auto. +Qed. + +Lemma test: + forall (A B: Type) (m1 m2 m3: K A) (f: A -> A -> K B), + (equiv m1 m2) -> (equiv m2 m3) -> + equiv (bind m1 (fun a => bind m2 (fun a' => f a a'))) + (bind m2 (fun a => bind m3 (fun a' => f a a'))). +Proof. + intros A B m1 m2 m3 f H1 H2. + setoid_rewrite H1. (* this works *) + setoid_rewrite H2. + trivial by equiv_refl. +Qed. diff --git a/test-suite/bugs/opened/shouldnotfail/1596.v b/test-suite/bugs/opened/shouldnotfail/1596.v new file mode 100644 index 00000000..766bf524 --- /dev/null +++ b/test-suite/bugs/opened/shouldnotfail/1596.v @@ -0,0 +1,242 @@ + +Require Import Relations. +Require Import FSets. +Require Import Arith. + +Lemma Bool_elim_bool : forall (b:bool),b=true \/ b=false. + destruct b;try tauto. +Qed. + +Module OrderedPair (X:OrderedType) (Y:OrderedType) <: OrderedType with +Definition t := (X.t * Y.t)%type. + Definition t := (X.t * Y.t)%type. + + Definition eq (xy1:t) (xy2:t) := + let (x1,y1) := xy1 in + let (x2,y2) := xy2 in + (X.eq x1 x2) /\ (Y.eq y1 y2). + + Definition lt (xy1:t) (xy2:t) := + let (x1,y1) := xy1 in + let (x2,y2) := xy2 in + (X.lt x1 x2) \/ ((X.eq x1 x2) /\ (Y.lt y1 y2)). + + Lemma eq_refl : forall (x:t),(eq x x). + destruct x. + unfold eq. + split;[apply X.eq_refl | apply Y.eq_refl]. + Qed. + + Lemma eq_sym : forall (x y:t),(eq x y)->(eq y x). + destruct x;destruct y;unfold eq;intro. + elim H;clear H;intros. + split;[apply X.eq_sym | apply Y.eq_sym];trivial. + Qed. + + Lemma eq_trans : forall (x y z:t),(eq x y)->(eq y z)->(eq x z). + unfold eq;destruct x;destruct y;destruct z;intros. + elim H;clear H;intros. + elim H0;clear H0;intros. + split;[eapply X.eq_trans | eapply Y.eq_trans];eauto. + Qed. + + Lemma lt_trans : forall (x y z:t),(lt x y)->(lt y z)->(lt x z). + unfold lt;destruct x;destruct y;destruct z;intros. + case H;clear H;intro. + case H0;clear H0;intro. + left. + eapply X.lt_trans;eauto. + elim H0;clear H0;intros. + left. + case (X.compare t0 t4);trivial;intros. + generalize (X.eq_sym H0);intro. + generalize (X.eq_trans e H2);intro. + elim (X.lt_not_eq H H3). + generalize (X.lt_trans l H);intro. + generalize (X.eq_sym H0);intro. + elim (X.lt_not_eq H2 H3). + elim H;clear H;intros. + case H0;clear H0;intro. + left. + case (X.compare t0 t4);trivial;intros. + generalize (X.eq_sym H);intro. + generalize (X.eq_trans H2 e);intro. + elim (X.lt_not_eq H0 H3). + generalize (X.lt_trans H0 l);intro. + generalize (X.eq_sym H);intro. + elim (X.lt_not_eq H2 H3). + elim H0;clear H0;intros. + right. + split. + eauto. + eauto. + Qed. + + Lemma lt_not_eq : forall (x y:t),(lt x y)->~(eq x y). + unfold lt, eq;destruct x;destruct y;intro;intro. + elim H0;clear H0;intros. + case H. + intro. + apply (X.lt_not_eq H2 H0). + intro. + elim H2;clear H2;intros. + apply (Y.lt_not_eq H3 H1). + Qed. + + Definition compare : forall (x y:t),(Compare lt eq x y). + destruct x;destruct y. + case (X.compare t0 t2);intro. + apply LT. + left;trivial. + case (Y.compare t1 t3);intro. + apply LT. + right. + tauto. + apply EQ. + split;trivial. + apply GT. + right;auto. + apply GT. + left;trivial. + Defined. + + Hint Immediate eq_sym. + Hint Resolve eq_refl eq_trans lt_not_eq lt_trans. +End OrderedPair. + +Module MessageSpi. + Inductive message : Set := + | MNam : nat -> message. + + Definition t := message. + + Fixpoint message_lt (m n:message) {struct m} : Prop := + match (m,n) with + | (MNam n1,MNam n2) => n1 < n2 + end. + + Module Ord <: OrderedType with Definition t := message with Definition eq := +@eq message. + Definition t := message. + Definition eq := @eq message. + Definition lt := message_lt. + + Lemma eq_refl : forall (x:t),eq x x. + unfold eq;auto. + Qed. + + Lemma eq_sym : forall (x y:t),(eq x y )->(eq y x). + unfold eq;auto. + Qed. + + Lemma eq_trans : forall (x y z:t),(eq x y)->(eq y z)->(eq x z). + unfold eq;auto;intros;congruence. + Qed. + + Lemma lt_trans : forall (x y z:t),(lt x y)->(lt y z)->(lt x z). + unfold lt. + induction x;destruct y;simpl;try tauto;destruct z;try tauto;intros. + omega. + Qed. + + Lemma lt_not_eq : forall (x y:t),(lt x y)->~(eq x y). + unfold eq;unfold lt. + induction x;destruct y;simpl;try tauto;intro;red;intro;try (discriminate +H0);injection H0;intros. + elim (lt_irrefl n);try omega. + Qed. + + Definition compare : forall (x y:t),(Compare lt eq x y). + unfold lt, eq. + induction x;destruct y;intros;try (apply LT;simpl;trivial;fail);try +(apply +GT;simpl;trivial;fail). + case (lt_eq_lt_dec n n0);intros;try (case s;clear s;intros). + apply LT;trivial. + apply EQ;trivial. + rewrite e;trivial. + apply GT;trivial. + Defined. + + Hint Immediate eq_sym. + Hint Resolve eq_refl eq_trans lt_not_eq lt_trans. + End Ord. + + Theorem eq_dec : forall (m n:message),{m=n}+{~(m=n)}. + intros. + case (Ord.compare m n);intro;[right | left | right];try (red;intro). + elim (Ord.lt_not_eq m n);auto. + rewrite e;auto. + elim (Ord.lt_not_eq n m);auto. + Defined. +End MessageSpi. + +Module MessagePair := OrderedPair MessageSpi.Ord MessageSpi.Ord. + +Module Type Hedge := FSetInterface.S with Module E := MessagePair. + +Module A (H:Hedge). + Definition hedge := H.t. + + Definition message_relation := relation MessageSpi.message. + + Definition relation_of_hedge (h:hedge) (m n:MessageSpi.message) := H.In (m,n) +h. + + Inductive hedge_synthesis_relation (h:message_relation) : message_relation := + | SynInc : forall (m n:MessageSpi.message),(h m +n)->(hedge_synthesis_relation h m n). + + Fixpoint hedge_in_synthesis (h:hedge) (m:MessageSpi.message) +(n:MessageSpi.message) {struct m} : bool := + if H.mem (m,n) h + then true + else false. + + Definition hedge_synthesis_spec (h:hedge) := hedge_synthesis_relation +(relation_of_hedge h). + + Lemma hedge_in_synthesis_impl_hedge_synthesis_spec : forall (h:hedge),forall +(m n:MessageSpi.message),(hedge_in_synthesis h m n)=true->(hedge_synthesis_spec +h m n). + unfold hedge_synthesis_spec;unfold relation_of_hedge. + induction m;simpl;intro. + elim (Bool_elim_bool (H.mem (MessageSpi.MNam n,n0) h));intros. + apply SynInc;apply H.mem_2;trivial. + rewrite H in H0. (* !! possible here !! *) + discriminate H0. + Qed. +End A. + +Module B (H:Hedge). + Definition hedge := H.t. + + Definition message_relation := relation MessageSpi.t. + + Definition relation_of_hedge (h:hedge) (m n:MessageSpi.t) := H.In (m,n) h. + + Inductive hedge_synthesis_relation (h:message_relation) : message_relation := + | SynInc : forall (m n:MessageSpi.t),(h m n)->(hedge_synthesis_relation h m +n). + + Fixpoint hedge_in_synthesis (h:hedge) (m:MessageSpi.t) (n:MessageSpi.t) +{struct m} : bool := + if H.mem (m,n) h + then true + else false. + + Definition hedge_synthesis_spec (h:hedge) := hedge_synthesis_relation +(relation_of_hedge h). + + Lemma hedge_in_synthesis_impl_hedge_synthesis_spec : forall (h:hedge),forall +(m n:MessageSpi.t),(hedge_in_synthesis h m n)=true->(hedge_synthesis_spec h m +n). + unfold hedge_synthesis_spec;unfold relation_of_hedge. + induction m;simpl;intro. + elim (Bool_elim_bool (H.mem (MessageSpi.MNam n,n0) h));intros. + apply SynInc;apply H.mem_2;trivial. + + rewrite H in H0. (* !! impossible here !! *) + discriminate H0. + Qed. +End B. \ No newline at end of file diff --git a/test-suite/bugs/opened/shouldnotfail/1811.v b/test-suite/bugs/opened/shouldnotfail/1811.v new file mode 100644 index 00000000..037b7cb2 --- /dev/null +++ b/test-suite/bugs/opened/shouldnotfail/1811.v @@ -0,0 +1,9 @@ +Require Export Bool. + +Lemma neg2xor : forall b, xorb true b = negb b. +Proof. auto. Qed. + +Goal forall b1 b2, (negb b1 = b2) -> xorb true b1 = b2. +Proof. + intros b1 b2. + rewrite neg2xor. \ No newline at end of file diff --git a/test-suite/bugs/opened/shouldnotfail/743.v b/test-suite/bugs/opened/shouldnotfail/743.v new file mode 100644 index 00000000..f1eee6c1 --- /dev/null +++ b/test-suite/bugs/opened/shouldnotfail/743.v @@ -0,0 +1,12 @@ +Require Import Omega. + +Lemma foo : forall n m : Z, (n >= 0)%Z -> (n * m >= 0)%Z -> (n <= n + n * m)%Z. +Proof. + intros. omega. +Qed. + +Lemma foo' : forall n m : nat, n <= n + n * m. +Proof. + intros. omega. +Qed. + diff --git a/test-suite/check b/test-suite/check index 504e96cc..f2307d40 100755 --- a/test-suite/check +++ b/test-suite/check @@ -106,6 +106,7 @@ test_interactive() { # La fonction suivante teste en interactif # It expects a line "(* Expected time < XXX.YYs *)" in the .v file # with exactly two digits after the dot +# The reference for time is a 6120 bogomips cpu test_complexity() { if [ -f /proc/cpuinfo ]; then if grep -q bogomips /proc/cpuinfo; then # i386, ppc @@ -145,28 +146,119 @@ test_complexity() { fi } +test_bugs () { + # Process verifications concerning submitted bugs. A message is + # printed for all opened bugs (still active or seems to be closed). + # For closed bugs that behave as expected, no message is printed + + # All files are assumed to have <# of the bug>.v as a name + + echo "Testing opened bugs..." + # We first test opened bugs that should not succeed + files=`/bin/ls -1 $1/opened/shoulnotsucceed/*.v 2> /dev/null` + for f in $files; do + nbtests=`expr $nbtests + 1` + printf " "$f"..." + $command $f $2 > /dev/null 2>&1 + if [ $? = 0 ]; then + echo "still active" + nbtestsok=`expr $nbtestsok + 1` + else + echo "Error! (bug seems to be closed, please check)" + fi + done + + # And opened bugs that should not fail + files=`/bin/ls -1 $1/opened/shouldnotfail/*.v 2> /dev/null` + for f in $files; do + nbtests=`expr $nbtests + 1` + printf " "$f"..." + $command $f > /dev/null 2>&1 + if [ $? != 0 ]; then + echo "still active" + nbtestsok=`expr $nbtestsok + 1` + else + echo "Error! (bug seems to be closed, please check)" + fi + done + + echo "Testing closed bugs..." + # Then closed bugs that should succeed + files=`/bin/ls -1 $1/closed/shouldsucceed/*.v 2> /dev/null` + for f in $files; do + nbtests=`expr $nbtests + 1` + printf " "$f"..." + $command $f $2 > /dev/null 2>&1 + if [ $? = 0 ]; then + echo "Ok" + nbtestsok=`expr $nbtestsok + 1` + else + echo "Error! (bug seems to be opened, please check)" + fi + done + + + # At last, we test closed bugs that should fail + files=`/bin/ls -1 $1/closed/shouldfail/*.v 2> /dev/null` + for f in $files; do + nbtests=`expr $nbtests + 1` + printf " "$f"..." + $command $f > /dev/null 2>&1 + if [ $? != 0 ]; then + echo "Ok" + nbtestsok=`expr $nbtestsok + 1` + else + echo "Error! (bug seems to be opened, please check)" + fi + done + +} + +test_features () { + # Process verifications concerning submitted bugs. A message is + # printed for all opened bugs (still active or seem to be closed. + # For closed bugs that behave as expected, no message is printed + + echo "Testing wishes..." + files=`/bin/ls -1 $1/*.v 2> /dev/null` + for f in $files; do + nbtests=`expr $nbtests + 1` + printf " "$f"..." + $command $f $2 > /dev/null 2>&1 + if [ $? != 0 ]; then + echo "still wished" + nbtestsok=`expr $nbtestsok + 1` + else + echo "Good news! (wish seems to be granted, please check)" + fi + done +} + # Programme principal echo "Success tests" test_success success echo "Failure tests" test_failure failure +echo "Bugs tests" +test_bugs bugs echo "Output tests" test_output output echo "Parser tests" test_parser parser echo "Interactive tests" test_interactive interactive +echo "Micromega tests" +test_success micromega echo "Complexity tests" test_complexity complexity echo "Module tests" $coqtop -compile modules/Nat $coqtop -compile modules/plik test_success modules "-I modules -impredicative-set" +#echo "Ideal-features tests" +#test_features ideal-features pourcentage=`expr 100 \* $nbtestsok / $nbtests` echo echo "$nbtestsok tests passed over $nbtests, i.e. $pourcentage %" - -#echo "Ideal-features tests" -#test_success ideal-features diff --git a/test-suite/complexity/injection.v b/test-suite/complexity/injection.v new file mode 100644 index 00000000..eb01133e --- /dev/null +++ b/test-suite/complexity/injection.v @@ -0,0 +1,113 @@ +(* This example, submitted by A. Appel, checks the efficiency of + injection (see bug #1173) *) +(* Expected time < 1.50s *) + +Set Implicit Arguments. + +Record joinable (t: Type) : Type := Joinable { + is_empty: t -> Prop; + join: t -> t -> t -> Prop; + join_com: forall a b c, join a b c -> join b a c; + join_empty: forall e a b, is_empty e -> join e a b -> a=b; + exists_empty: forall a, exists e, is_empty e /\ join e a a; + join_empty2: forall a b c, join a b c -> is_empty c -> is_empty a; + join_empty3: forall e a, join e a a -> is_empty e; + join_assoc: forall a b c d e, join a b d -> join d c e -> + exists f, join b c f /\ join a f e; + join_eq: forall x y z z', join x y z -> join x y z' -> z = z'; + cancellation: forall a1 a2 b c, join a1 b c -> join a2 b c -> a1=a2 +}. + +Record joinmap (key: Type) (t: Type) (j : joinable t) : Type + := Joinmap { + jm_t : Type; + jm_j : joinable jm_t; + lookup: jm_t -> key -> t; + prim : forall (f: key -> t) (e: t), + (forall k, j.(join) e (f k) (f k)) -> + jm_t; + join_rule: forall s1 s2 s, + jm_j.(join) s1 s2 s <-> + forall x, j.(join) (lookup s1 x) (lookup s2 x) (lookup s x); + empty_rule: forall e x, jm_j.(is_empty) e -> j.(is_empty) (lookup e x); + prim_rule: forall f e pf k, lookup (prim f e pf) k = f k; + ext: forall s1 s2, + (forall x, lookup s1 x = lookup s2 x) <-> s1 = s2; + can_join: forall s1 s2, + (forall x, exists v, + j.(join) (lookup s1 x) (lookup s2 x) v) -> + exists s3, jm_j.(join) s1 s2 s3; + can_split: forall s1 s3, + (forall x, exists v, + j.(join) (lookup s1 x) v (lookup s3 x)) -> + exists s2, jm_j.(join) s1 s2 s3 +}. + +Parameter mkJoinmap : forall (key: Type) (t: Type) (j: joinable t), +joinmap key j. + +Parameter ADMIT: forall p: Prop, p. +Implicit Arguments ADMIT [p]. + +Module Share. +Parameter jb : joinable bool. +Definition jm: joinmap nat jb := mkJoinmap nat jb. +Definition t := jm.(jm_t). +Definition j := jm.(jm_j). +Parameter nonempty: t -> Prop. +End Share. + +Section Own. + +Variable inv : Type. + +Inductive own : Type := + | NO + | VAL' : forall sh, Share.nonempty sh -> own + | LK : forall sh, Share.nonempty sh -> Share.t -> inv -> own + | CT : forall sh, Share.nonempty sh -> own + | FUN: forall sh, Share.nonempty sh -> inv -> own. + +Definition own_join (a b c: own) : Prop := + match a , b , c with + | NO , _ , _ => b=c + | _ , NO , _ => a=c + | VAL' sa _ , VAL' sb _, VAL' sc _ => Share.j.(join) sa sb sc + | LK sa pa ha fa, LK sb pb hb fb, LK sc pc hc fc => + Share.j.(join) sa sb sc /\ + Share.j.(join) ha hb hc /\ + fa=fc /\ + fb=fc + | CT sa pa , CT sb pb, CT sc pc => Share.j.(join) sa sb sc + | FUN sa pa fa, FUN sb pb fb, FUN sc pc fc => + Share.j.(join) sa sb sc /\ fa=fc /\ fb=fc + | _ , _ , _ => False + end. + +Definition own_is_empty (a: own) := a=NO. + +Definition jown : joinable own := + Joinable own_is_empty own_join + ADMIT ADMIT ADMIT ADMIT ADMIT ADMIT ADMIT ADMIT . +End Own. + +Fixpoint sinv (n: nat) : Type := + match n with + | O => unit + | S n => prodT (sinv n) (own (sinv n) -> unit -> Prop) + end. + +Parameter address: Set. + +Definition jm (n: nat) := mkJoinmap address (jown (sinv n)). + +Definition worldfun (n: nat) := (jm n).(jm_t). + +Inductive world : Type := + mk_world: forall n, worldfun n -> world. + +Lemma test: forall n1 w1 n2 w2, mk_world n1 w1 = mk_world n2 w2 -> + n1 = n2. +Proof. +intros. +Time injection H. diff --git a/test-suite/complexity/ring.v b/test-suite/complexity/ring.v new file mode 100644 index 00000000..5a541bc2 --- /dev/null +++ b/test-suite/complexity/ring.v @@ -0,0 +1,7 @@ +(* This example, checks the efficiency of the abstract machine used by ring *) +(* Expected time < 1.00s *) + +Require Import ZArith. +Open Scope Z_scope. +Goal forall a, a+a+a+a+a+a+a+a+a+a+a+a+a = a*13. +Time intro; ring. diff --git a/test-suite/complexity/ring2.v b/test-suite/complexity/ring2.v new file mode 100644 index 00000000..9f9685dd --- /dev/null +++ b/test-suite/complexity/ring2.v @@ -0,0 +1,51 @@ +(* This example, checks the efficiency of the abstract machine used by ring *) +(* Expected time < 1.00s *) + +Require Import BinInt. + +Definition Zplus x y := +match x with +| 0%Z => y +| Zpos x' => + match y with + | 0%Z => x + | Zpos y' => Zpos (x' + y') + | Zneg y' => + match (x' ?= y')%positive Eq with + | Eq => 0%Z + | Lt => Zneg (y' - x') + | Gt => Zpos (x' - y') + end + end +| Zneg x' => + match y with + | 0%Z => x + | Zpos y' => + match (x' ?= y')%positive Eq with + | Eq => 0%Z + | Lt => Zpos (y' - x') + | Gt => Zneg (x' - y') + end + | Zneg y' => Zneg (x' + y') + end +end. + +Require Import Ring. + +Lemma Zth : ring_theory Z0 (Zpos xH) Zplus Zmult Zminus Zopp (@eq Z). +Admitted. + +Ltac Zcst t := + match isZcst t with + true => t + | _ => constr:NotConstant + end. + +Add Ring Zr : Zth + (decidable Zeqb_ok, constants [Zcst]). + +Open Scope Z_scope. +Infix "+" := Zplus : Z_scope. + +Goal forall a, a+a+a+a+a+a+a+a+a+a+a+a+a = a*13. +Time intro; ring. diff --git a/test-suite/csdp.cache b/test-suite/csdp.cache new file mode 100644 index 00000000..59ff450c --- /dev/null +++ b/test-suite/csdp.cache @@ -0,0 +1,106548 @@ +*** REQUEST *** +"" +3 +3 +4 1 1 +0.10485760000000000000e7 -0.52428800000000000000e6 0.52428800000000000000e6 +0 1 1 2 -0.52428800000000000000e6 +0 1 1 4 0.52428800000000000000e6 +0 1 2 2 -0.10485760000000000000e7 +0 1 4 4 0.10485760000000000000e7 +0 2 1 1 -0.10485760000000000000e7 +1 1 1 1 0.10485760000000000000e7 +1 1 1 2 0.52428800000000000000e6 +1 1 1 4 -0.52428800000000000000e6 +1 1 2 2 0.10485760000000000000e7 +1 1 4 4 -0.10485760000000000000e7 +1 2 1 1 0.10485760000000000000e7 +2 1 1 3 0.10485760000000000000e7 +2 1 1 4 -0.52428800000000000000e6 +2 1 4 4 -0.10485760000000000000e7 +3 1 1 2 -0.52428800000000000000e6 +3 1 1 4 0.52428800000000000000e6 +3 3 1 1 0.10485760000000000000e7 +*** ANSWER *** +Infeasible +*** END *** +*** REQUEST *** +"" +8 +4 +4 1 4 1 +-0.52428800000000000000e6 0.10485760000000000000e7 -0.52428800000000000000e6 0.0 -0.10485760000000000000e7 0.52428800000000000000e6 0.0 0.10485760000000000000e7 +0 1 1 2 -0.26214400000000000000e6 +0 1 1 4 0.26214400000000000000e6 +0 2 1 1 -0.52428800000000000000e6 +0 3 1 2 -0.26214400000000000000e6 +0 3 1 4 -0.26214400000000000000e6 +1 1 2 3 0.52428800000000000000e6 +1 1 3 4 -0.52428800000000000000e6 +1 3 1 4 -0.26214400000000000000e6 +1 3 4 4 -0.52428800000000000000e6 +2 1 1 1 0.52428800000000000000e6 +2 1 1 2 0.26214400000000000000e6 +2 1 1 4 -0.26214400000000000000e6 +2 2 1 1 0.52428800000000000000e6 +2 3 1 2 0.26214400000000000000e6 +2 3 1 4 0.26214400000000000000e6 +3 1 1 3 0.52428800000000000000e6 +3 1 1 4 -0.26214400000000000000e6 +3 1 4 4 -0.52428800000000000000e6 +4 1 2 2 0.52428800000000000000e6 +4 1 4 4 -0.52428800000000000000e6 +4 3 1 2 -0.26214400000000000000e6 +4 3 1 4 -0.26214400000000000000e6 +5 1 2 4 0.52428800000000000000e6 +5 1 4 4 -0.10485760000000000000e7 +5 3 1 4 -0.52428800000000000000e6 +6 1 1 2 -0.26214400000000000000e6 +6 1 1 4 0.26214400000000000000e6 +6 3 1 1 0.52428800000000000000e6 +7 1 2 3 -0.52428800000000000000e6 +7 1 3 4 0.52428800000000000000e6 +7 3 1 3 0.52428800000000000000e6 +8 1 1 2 0.26214400000000000000e6 +8 1 1 4 -0.26214400000000000000e6 +8 1 2 3 -0.52428800000000000000e6 +8 1 3 4 0.52428800000000000000e6 +8 3 1 2 0.26214400000000000000e6 +8 3 2 2 0.52428800000000000000e6 +8 4 1 1 0.52428800000000000000e6 +*** ANSWER *** +Infeasible +*** END *** +*** REQUEST *** +"" +51 +4 +10 4 4 1 +0.52428800000000000000e6 0.0 0.0 -0.52428800000000000000e6 0.0 0.0 0.0 0.0 0.0 0.0 0.10485760000000000000e7 0.0 0.0 -0.10485760000000000000e7 0.0 0.10485760000000000000e7 0.52428800000000000000e6 0.0 0.0 0.0 0.0 0.0 0.10485760000000000000e7 0.0 0.0 0.0 0.0 0.52428800000000000000e6 -0.52428800000000000000e6 0.0 0.0 0.0 0.52428800000000000000e6 0.0 0.0 0.0 -0.10485760000000000000e7 0.10485760000000000000e7 0.0 0.52428800000000000000e6 0.0 0.10485760000000000000e7 0.0 0.10485760000000000000e7 0.0 -0.10485760000000000000e7 0.52428800000000000000e6 0.0 0.0 0.52428800000000000000e6 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3.552627545817120709e-04 +1 3 1 1 3.552627545817120709e-04 +1 4 1 1 2.621440007164657000e+05 +1 5 1 1 2.621440007164657000e+05 +1 6 1 1 3.552627545817120709e-04 +2 1 1 1 9.999999999999990008e-01 +2 2 1 1 4.901085593438081922e+00 +2 3 1 1 4.901085593438081922e+00 +2 4 1 1 1.042302185589578071e-15 +2 5 1 1 1.042302185589578071e-15 +2 6 1 1 4.901085593438081922e+00 +*** END *** +*** REQUEST *** +"" +2 +7 +1 1 1 1 1 1 1 +0.10485760000000000000e7 0.10485760000000000000e7 +0 1 1 1 0.52428800000000000000e6 +1 1 1 1 0.10485760000000000000e7 +1 3 1 1 0.52428800000000000000e6 +1 4 1 1 0.52428800000000000000e6 +2 1 1 1 0.10485760000000000000e7 +2 5 1 1 0.52428800000000000000e6 +2 6 1 1 0.52428800000000000000e6 +*** ANSWER *** +2.499997645979282479e-01 2.500002357495276217e-01 +1 1 1 1 6.745550242878593436e-04 +1 2 1 1 3.102211906109383389e-04 +1 3 1 1 1.310718768917397974e+05 +1 4 1 1 1.310718768917397974e+05 +1 5 1 1 1.310721239108695008e+05 +1 6 1 1 1.310721239108695008e+05 +1 7 1 1 3.102211906109383389e-04 +2 1 1 1 9.999999999999985567e-01 +2 2 1 1 1.664730264895515788e+00 +2 3 1 1 1.437930271481947813e-15 +2 4 1 1 1.437930271481947813e-15 +2 5 1 1 1.410287126255177107e-15 +2 6 1 1 1.410287126255177107e-15 +2 7 1 1 1.664730264895515788e+00 +*** END *** +*** REQUEST *** +"" +4 +5 +3 1 1 1 1 +0.52428800000000000000e6 0.10485760000000000000e7 0.26214400000000000000e6 0.52428800000000000000e6 +0 1 1 2 0.26214400000000000000e6 +0 4 1 1 -0.52428800000000000000e6 +1 1 1 1 0.52428800000000000000e6 +1 1 1 2 -0.26214400000000000000e6 +1 4 1 1 0.52428800000000000000e6 +2 1 1 3 0.52428800000000000000e6 +2 1 2 3 -0.52428800000000000000e6 +2 4 1 1 0.10485760000000000000e7 +2 5 1 1 0.10485760000000000000e7 +3 1 2 3 0.26214400000000000000e6 +3 2 1 1 0.52428800000000000000e6 +4 1 1 2 0.26214400000000000000e6 +4 1 2 3 -0.26214400000000000000e6 +4 3 1 1 0.52428800000000000000e6 +4 5 1 1 0.52428800000000000000e6 +*** ANSWER *** +6.390535959450866983e-11 -7.081165828606712792e-11 9.999999998131693379e-01 9.999999999222820568e-01 +1 1 1 1 8.686329382893162934e-05 +1 1 1 2 -3.712570269949944015e-05 +1 1 1 3 -3.712570269948556236e-05 +1 1 2 2 5.335848065784630154e-05 +1 1 2 3 8.522459157680231092e-06 +1 1 3 3 5.335848065784630154e-05 +1 2 1 1 5.242879999554053647e+05 +1 3 1 1 5.242880000126119703e+05 +1 4 1 1 5.242880000126118539e+05 +1 5 1 1 5.242879999383604736e+05 +2 1 1 1 2.499999999280670515e+00 +2 1 1 2 1.499999999460502220e+00 +2 1 1 3 1.499999999460500666e+00 +2 1 2 2 3.620947120705871214e+00 +2 1 2 3 4.999999998201666296e-01 +2 1 3 3 3.620947120705780176e+00 +2 2 1 1 1.798323704529754762e-10 +2 3 1 1 1.798323696005608919e-10 +2 4 1 1 1.798323696005600647e-10 +2 5 1 1 1.798323677204703494e-10 +*** END *** +*** REQUEST *** +"" +5 +3 +3 1 1 +0.0 -0.52428800000000000000e6 0.0 0.10485760000000000000e7 0.0 +0 1 2 3 0.52428800000000000000e6 +0 2 1 1 -0.10485760000000000000e7 +1 1 2 3 -0.52428800000000000000e6 +2 1 2 2 -0.10485760000000000000e7 +3 1 1 2 -0.52428800000000000000e6 +4 1 1 1 0.10485760000000000000e7 +4 1 2 3 -0.52428800000000000000e6 +4 2 1 1 0.10485760000000000000e7 +5 1 1 3 -0.52428800000000000000e6 +5 1 2 3 0.52428800000000000000e6 +5 2 1 1 -0.10485760000000000000e7 +5 3 1 1 0.10485760000000000000e7 +*** ANSWER *** +-9.999999998715584093e-01 1.284406218496803786e-10 -7.783128073916068263e-31 -1.284409534299150764e-10 6.631567026046208180e-16 +1 1 1 1 3.476886429670015314e-10 +1 1 1 2 4.080600651617307598e-25 +1 1 1 3 -3.476851012951714394e-10 +1 1 2 2 6.953757192769094094e-10 +1 1 2 3 8.665201604627535488e-21 +1 1 3 3 1.346804488723699154e-04 +1 2 1 1 1.048575999999999651e+06 +1 3 1 1 1.346811442425725237e-04 +2 1 1 1 9.999999999960526020e-01 +2 1 1 2 -4.433000231874575034e-17 +2 1 1 3 8.049700100463470729e-07 +2 1 2 2 4.999999999869032541e-01 +2 1 2 3 -2.087243697581483313e-17 +2 1 3 3 8.049886141043881407e-07 +2 2 1 1 3.315809821104277243e-16 +2 3 1 1 8.049700105932944581e-07 +*** END *** +*** REQUEST *** +"" +5 +3 +3 1 1 +0.0 -0.52428800000000000000e6 0.0 0.10485760000000000000e7 0.0 +0 1 2 3 -0.52428800000000000000e6 +0 2 1 1 -0.10485760000000000000e7 +1 1 2 3 -0.52428800000000000000e6 +2 1 2 2 -0.10485760000000000000e7 +3 1 1 2 -0.52428800000000000000e6 +4 1 1 1 0.10485760000000000000e7 +4 1 2 3 0.52428800000000000000e6 +4 2 1 1 0.10485760000000000000e7 +5 1 1 3 -0.52428800000000000000e6 +5 1 2 3 -0.52428800000000000000e6 +5 2 1 1 -0.10485760000000000000e7 +5 3 1 1 0.10485760000000000000e7 +*** ANSWER *** +9.999999998715584093e-01 1.284406218496803786e-10 7.783128073916068263e-31 -1.284409534299150764e-10 6.631567026046208180e-16 +1 1 1 1 3.476886429670015314e-10 +1 1 1 2 -4.080600651617307598e-25 +1 1 1 3 -3.476851012951714394e-10 +1 1 2 2 6.953757192769094094e-10 +1 1 2 3 -8.665201604627535488e-21 +1 1 3 3 1.346804488723699154e-04 +1 2 1 1 1.048575999999999651e+06 +1 3 1 1 1.346811442425725237e-04 +2 1 1 1 9.999999999960526020e-01 +2 1 1 2 4.433000231874575034e-17 +2 1 1 3 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8.686499997310158372e-05 +1 1 1 2 3.712637526269381340e-05 +1 1 1 3 -3.712637526272124372e-05 +1 1 2 2 5.335941618249645350e-05 +1 1 2 3 -8.522644434525800334e-06 +1 1 3 3 5.335941618249645350e-05 +1 2 1 1 5.242879999554048409e+05 +1 3 1 1 5.242880000126123196e+05 +1 4 1 1 5.242880000126122031e+05 +1 5 1 1 5.242879999383596005e+05 +2 1 1 1 2.499999999280643870e+00 +2 1 1 2 -1.499999999460482680e+00 +2 1 1 3 1.499999999460482902e+00 +2 1 2 2 3.621013004357011233e+00 +2 1 2 3 -4.999999998201609674e-01 +2 1 3 3 3.621013004357259035e+00 +2 2 1 1 1.798390204629782096e-10 +2 3 1 1 1.798390196105975397e-10 +2 4 1 1 1.798390196106000213e-10 +2 5 1 1 1.798390177302902759e-10 +*** END *** +*** REQUEST *** +"" +5 +3 +3 1 1 +-0.52428800000000000000e6 0.0 0.10485760000000000000e7 0.0 0.0 +0 1 2 3 0.52428800000000000000e6 +0 2 1 1 -0.10485760000000000000e7 +1 1 3 3 -0.10485760000000000000e7 +2 1 2 3 -0.52428800000000000000e6 +3 1 1 1 0.10485760000000000000e7 +3 1 2 3 -0.52428800000000000000e6 +3 2 1 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+0 1 2 3 -0.52428800000000000000e6 +0 2 1 1 -0.10485760000000000000e7 +1 1 3 3 -0.10485760000000000000e7 +2 1 2 3 -0.52428800000000000000e6 +3 1 1 1 0.10485760000000000000e7 +3 1 2 3 0.52428800000000000000e6 +3 2 1 1 0.10485760000000000000e7 +4 1 1 3 0.10485760000000000000e7 +5 1 1 2 -0.52428800000000000000e6 +5 1 2 3 -0.52428800000000000000e6 +5 2 1 1 -0.10485760000000000000e7 +5 3 1 1 0.10485760000000000000e7 +*** ANSWER *** +2.417243834881730172e-10 9.999999997582740274e-01 -2.417249248510537096e-10 6.516102507854656631e-31 1.082378559825435644e-15 +1 1 1 1 5.676625496526350850e-10 +1 1 1 2 -5.674780903737580028e-10 +1 1 1 3 6.832628703276204432e-25 +1 1 2 2 2.534675224631680567e-04 +1 1 2 3 -1.228971102411588713e-18 +1 1 3 3 1.135322673535390481e-09 +1 2 1 1 1.048575999999999418e+06 +1 3 1 1 2.534686574193489601e-04 +2 1 1 1 9.999999999989667154e-01 +2 1 1 2 1.646717610768319847e-06 +2 1 1 3 -5.112710586318704261e-17 +2 1 2 2 1.646890679667584597e-06 +2 1 2 3 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0.10485760000000000000e7 +*** ANSWER *** +2.417243834881730172e-10 9.999999997582740274e-01 -2.417249248510537096e-10 -6.516102507854656631e-31 1.082378559825435644e-15 +1 1 1 1 5.676625496526350850e-10 +1 1 1 2 5.674780903737580028e-10 +1 1 1 3 -6.832628703276204432e-25 +1 1 2 2 2.534675224631680567e-04 +1 1 2 3 -1.228971102411588713e-18 +1 1 3 3 1.135322673535390481e-09 +1 2 1 1 1.048575999999999418e+06 +1 3 1 1 2.534686574193489601e-04 +2 1 1 1 9.999999999989667154e-01 +2 1 1 2 -1.646717610768319847e-06 +2 1 1 3 5.112710586318704261e-17 +2 1 2 2 1.646890679667584597e-06 +2 1 2 3 -9.378268007442111308e-18 +2 1 3 3 5.000000000000000000e-01 +2 2 1 1 5.413640376397729861e-16 +2 3 1 1 1.646717611279745635e-06 +*** END *** +*** REQUEST *** +"" +4 +5 +3 1 1 1 1 +0.52428800000000000000e6 -0.10485760000000000000e7 0.26214400000000000000e6 0.52428800000000000000e6 +0 1 1 2 0.26214400000000000000e6 +0 4 1 1 -0.52428800000000000000e6 +1 1 1 1 0.52428800000000000000e6 +1 1 1 2 -0.26214400000000000000e6 +1 4 1 1 0.52428800000000000000e6 +2 1 1 3 0.52428800000000000000e6 +2 1 2 3 -0.52428800000000000000e6 +2 4 1 1 -0.10485760000000000000e7 +2 5 1 1 -0.10485760000000000000e7 +3 1 2 3 -0.26214400000000000000e6 +3 2 1 1 0.52428800000000000000e6 +4 1 1 2 0.26214400000000000000e6 +4 1 2 3 0.26214400000000000000e6 +4 3 1 1 0.52428800000000000000e6 +4 5 1 1 0.52428800000000000000e6 +*** ANSWER *** +6.390550264518323903e-11 7.081185573184761103e-11 9.999999998131687828e-01 9.999999999222817237e-01 +1 1 1 1 8.686351428452204412e-05 +1 1 1 2 -3.712580621795203914e-05 +1 1 1 3 3.712580621793892029e-05 +1 1 2 2 5.335862611368378042e-05 +1 1 2 3 -8.522486255170660984e-06 +1 1 3 3 5.335862611368378042e-05 +1 2 1 1 5.242879999554052483e+05 +1 3 1 1 5.242880000126118539e+05 +1 4 1 1 5.242880000126118539e+05 +1 5 1 1 5.242879999383602408e+05 +2 1 1 1 2.499999999280668295e+00 +2 1 1 2 1.499999999460501110e+00 +2 1 1 3 -1.499999999460502442e+00 +2 1 2 2 3.620948442164833914e+00 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+9.999999998715584093e-01 1.284406218496803786e-10 -7.783128073916068263e-31 -1.284409534299150764e-10 6.631567026046208180e-16 +1 1 1 1 3.476886429670015314e-10 +1 1 1 2 4.080600651617307598e-25 +1 1 1 3 3.476851012951714394e-10 +1 1 2 2 6.953757192769094094e-10 +1 1 2 3 -8.665201604627535488e-21 +1 1 3 3 1.346804488723699154e-04 +1 2 1 1 1.048575999999999651e+06 +1 3 1 1 1.346811442425725237e-04 +2 1 1 1 9.999999999960526020e-01 +2 1 1 2 -4.433000231874575034e-17 +2 1 1 3 -8.049700100463470729e-07 +2 1 2 2 4.999999999869032541e-01 +2 1 2 3 2.087243697581483313e-17 +2 1 3 3 8.049886141043881407e-07 +2 2 1 1 3.315809821104277243e-16 +2 3 1 1 8.049700105932944581e-07 +*** END *** +*** REQUEST *** +"" +4 +5 +3 1 1 1 1 +0.52428800000000000000e6 -0.10485760000000000000e7 0.26214400000000000000e6 0.52428800000000000000e6 +0 1 1 2 -0.26214400000000000000e6 +0 4 1 1 -0.52428800000000000000e6 +1 1 1 1 0.52428800000000000000e6 +1 1 1 2 0.26214400000000000000e6 +1 4 1 1 0.52428800000000000000e6 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1 0.10485760000000000000e7 +2 1 1 1 -0.10485760000000000000e7 +2 4 1 1 0.10485760000000000000e7 +2 5 1 1 0.10485760000000000000e7 +*** ANSWER *** +Infeasible +*** END *** +*** REQUEST *** +"" +14 +15 +3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 +0.26214400000000000000e6 -0.52428800000000000000e6 0.52428800000000000000e6 -0.78643200000000000000e6 -0.52428800000000000000e6 -0.52428800000000000000e6 0.26214400000000000000e6 0.26214400000000000000e6 0.52428800000000000000e6 0.52428800000000000000e6 0.26214400000000000000e6 0.0 0.26214400000000000000e6 0.10485760000000000000e7 +0 1 1 2 0.52428800000000000000e6 +0 2 1 1 0.52428800000000000000e6 +0 4 1 1 -0.52428800000000000000e6 +1 1 1 1 0.52428800000000000000e6 +1 1 1 2 -0.52428800000000000000e6 +1 2 1 1 -0.52428800000000000000e6 +1 4 1 1 0.52428800000000000000e6 +2 1 1 3 0.52428800000000000000e6 +2 12 1 1 -0.10485760000000000000e7 +3 1 1 2 -0.26214400000000000000e6 +3 1 2 2 0.52428800000000000000e6 +3 8 1 1 0.52428800000000000000e6 +4 1 1 2 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0.52428800000000000000e6 +1 4 1 1 0.52428800000000000000e6 +1 5 1 1 0.52428800000000000000e6 +*** ANSWER *** +Infeasible +*** END *** +*** REQUEST *** +"" +10 +11 +4 1 1 1 1 1 1 1 1 1 1 +0.65536000000000000000e5 -0.78643200000000000000e6 -0.11796480000000000000e7 0.17694720000000000000e7 -0.11796480000000000000e7 0.58982400000000000000e6 0.19660800000000000000e6 0.58982400000000000000e6 0.0 0.58982400000000000000e6 +0 1 1 2 0.98304000000000000000e5 +0 1 2 3 0.32768000000000000000e5 +0 1 3 3 0.65536000000000000000e5 +0 1 3 4 0.32768000000000000000e5 +0 2 1 1 0.19660800000000000000e6 +0 6 1 1 0.65536000000000000000e5 +0 8 1 1 0.19660800000000000000e6 +1 1 1 1 0.58982400000000000000e6 +1 1 1 2 -0.98304000000000000000e5 +1 1 2 3 -0.32768000000000000000e5 +1 1 3 3 -0.65536000000000000000e5 +1 1 3 4 -0.32768000000000000000e5 +1 2 1 1 -0.19660800000000000000e6 +1 6 1 1 -0.65536000000000000000e5 +1 8 1 1 -0.19660800000000000000e6 +2 1 1 3 0.58982400000000000000e6 +2 1 2 3 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+*** ANSWER *** +Infeasible +*** END *** +*** REQUEST *** +"" +41 +16 +4 1 4 4 1 4 1 1 1 4 1 1 1 1 1 1 +0.26214400000000000000e6 -0.52428800000000000000e6 -0.52428800000000000000e6 0.0 -0.52428800000000000000e6 -0.52428800000000000000e6 0.26214400000000000000e6 0.0 0.52428800000000000000e6 0.78643200000000000000e6 -0.10485760000000000000e7 0.26214400000000000000e6 0.0 0.10485760000000000000e7 0.10485760000000000000e7 -0.52428800000000000000e6 -0.52428800000000000000e6 -0.52428800000000000000e6 -0.52428800000000000000e6 -0.52428800000000000000e6 -0.52428800000000000000e6 0.26214400000000000000e6 -0.52428800000000000000e6 0.0 0.0 -0.52428800000000000000e6 -0.52428800000000000000e6 -0.52428800000000000000e6 0.78643200000000000000e6 -0.26214400000000000000e6 0.26214400000000000000e6 0.26214400000000000000e6 -0.52428800000000000000e6 0.52428800000000000000e6 -0.52428800000000000000e6 -0.52428800000000000000e6 0.10485760000000000000e7 0.26214400000000000000e6 0.26214400000000000000e6 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3 3 0.26214400000000000000e6 +37 10 3 4 0.13107200000000000000e6 +37 16 1 1 0.26214400000000000000e6 +38 3 1 4 -0.65536000000000000000e5 +38 11 1 1 0.13107200000000000000e6 +39 4 4 4 0.13107200000000000000e6 +39 10 2 2 0.13107200000000000000e6 +39 12 1 1 -0.39321600000000000000e6 +39 13 1 1 0.13107200000000000000e6 +39 16 1 1 0.13107200000000000000e6 +40 10 1 3 -0.65536000000000000000e5 +40 14 1 1 0.13107200000000000000e6 +41 3 3 4 -0.65536000000000000000e5 +41 15 1 1 0.13107200000000000000e6 +*** ANSWER *** +-2.796428333061710846e-10 -5.145505709403082136e-12 -5.145505710399421184e-12 -5.065723613441632291e-11 5.112487019279347381e-11 5.112487019517472000e-11 -5.065723614645774618e-11 5.112487019298682728e-11 -5.065723613233761803e-11 -3.227934490141472682e-10 -2.726207292780503898e-11 8.167675251916435826e-11 3.251989134141424605e-10 8.167675250840997632e-11 8.167675251988690053e-11 -1.518635855095441632e-10 1.133140151751466980e-11 1.133166704855965140e-11 1.464637579379667940e-11 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4 1.483236495771939278e+00 +2 6 3 3 9.601334358294710825e-01 +2 6 3 4 -5.167635035298775437e-01 +2 6 4 4 1.483236496470112575e+00 +2 7 1 1 3.142191282587846857e+00 +2 8 1 1 1.483236496702845075e+00 +2 9 1 1 1.396360650674838475e-09 +2 10 1 1 2.074713573300015934e+00 +2 10 1 2 -5.167635032971558129e-01 +2 10 1 3 -5.167635032971482634e-01 +2 10 1 4 1.154764439095756212e-01 +2 10 2 2 1.483236496470117016e+00 +2 10 2 3 1.483236495771938612e+00 +2 10 2 4 -5.167635035298842050e-01 +2 10 3 3 1.483236496470120791e+00 +2 10 3 4 -5.167635035298876467e-01 +2 10 4 4 9.601334358185252826e-01 +2 11 1 1 3.142191282584773759e+00 +2 12 1 1 1.483236496702849072e+00 +2 13 1 1 1.396360650674434811e-09 +2 14 1 1 1.483236496702852181e+00 +2 15 1 1 1.396360650674362019e-09 +2 16 1 1 3.483236495771939722e+00 +*** END *** +*** REQUEST *** +"" +2 +2 +4 1 +-0.26214400000000000000e6 -0.13107200000000000000e7 +0 1 2 2 0.52428800000000000000e6 +0 1 3 3 0.52428800000000000000e6 +0 1 4 4 0.52428800000000000000e6 +1 1 1 1 0.52428800000000000000e6 +1 1 2 2 -0.52428800000000000000e6 +1 1 3 3 -0.52428800000000000000e6 +1 1 4 4 -0.52428800000000000000e6 +2 1 2 2 -0.15728640000000000000e7 +2 1 2 3 0.52428800000000000000e6 +2 1 2 4 0.52428800000000000000e6 +2 1 3 3 -0.15728640000000000000e7 +2 1 3 4 0.52428800000000000000e6 +2 1 4 4 -0.15728640000000000000e7 +2 2 1 1 -0.52428800000000000000e6 +*** ANSWER *** +-1.369805830780025199e-10 -9.999999997258860462e-01 +1 1 1 1 4.004402490975419925e-07 +1 1 2 2 1.048575999712891062e+06 +1 1 2 3 -5.242879998562853434e+05 +1 1 2 4 -5.242879998562853434e+05 +1 1 3 3 1.048575999712891062e+06 +1 1 3 4 -5.242879998562853434e+05 +1 1 4 4 1.048575999712891062e+06 +1 2 1 1 5.242879999285030644e+05 +2 1 1 1 1.999999999995417443e+00 +2 1 2 2 8.333333333287741285e-01 +2 1 2 3 8.333333333282649802e-01 +2 1 2 4 8.333333333328124537e-01 +2 1 3 3 8.333333333287741285e-01 +2 1 3 4 8.333333333328124537e-01 +2 1 4 4 8.333333333378689645e-01 +2 2 1 1 1.527559509425708661e-12 +*** END *** +*** REQUEST *** +"" +2 +2 +5 1 +-0.19660800000000000000e6 -0.11141120000000000000e7 +0 1 2 2 0.26214400000000000000e6 +0 1 3 3 0.26214400000000000000e6 +0 1 4 4 0.26214400000000000000e6 +0 1 5 5 0.26214400000000000000e6 +1 1 1 1 0.26214400000000000000e6 +1 1 2 2 -0.26214400000000000000e6 +1 1 3 3 -0.26214400000000000000e6 +1 1 4 4 -0.26214400000000000000e6 +1 1 5 5 -0.26214400000000000000e6 +2 1 2 2 -0.10485760000000000000e7 +2 1 2 3 0.26214400000000000000e6 +2 1 2 4 0.26214400000000000000e6 +2 1 2 5 0.26214400000000000000e6 +2 1 3 3 -0.10485760000000000000e7 +2 1 3 4 0.26214400000000000000e6 +2 1 3 5 0.26214400000000000000e6 +2 1 4 4 -0.10485760000000000000e7 +2 1 4 5 0.26214400000000000000e6 +2 1 5 5 -0.10485760000000000000e7 +2 2 1 1 -0.26214400000000000000e6 +*** ANSWER *** +-2.348240940930787258e-09 -9.999999946942671469e-01 +1 1 1 1 9.050318275803589940e-04 +1 1 2 2 7.864319965727222152e+05 +1 1 2 3 -2.621439986091339670e+05 +1 1 2 4 -2.621439986091339670e+05 +1 1 2 5 -2.621439986091339670e+05 +1 1 3 3 7.864319965727222152e+05 +1 1 3 4 -2.621439986091339670e+05 +1 1 3 5 -2.621439986091339670e+05 +1 1 4 4 7.864319965727222152e+05 +1 1 4 5 -2.621439986091339670e+05 +1 1 5 5 7.864319965727222152e+05 +1 2 1 1 2.621440001297430717e+05 +2 1 1 1 3.499999985499439692e+00 +2 1 2 2 1.062499996374859812e+00 +2 1 2 3 1.062499995468575209e+00 +2 1 2 4 1.062499995468575209e+00 +2 1 2 5 1.062499995468574987e+00 +2 1 3 3 1.062499996374860034e+00 +2 1 3 4 1.062499995468575431e+00 +2 1 3 5 1.062499995468574987e+00 +2 1 4 4 1.062499996374860034e+00 +2 1 4 5 1.062499995468574987e+00 +2 1 5 5 1.062499996374859368e+00 +2 2 1 1 3.625141883504653676e-09 +*** END *** +*** REQUEST *** +"" +4 +5 +3 1 1 1 1 +0.52428800000000000000e6 -0.10485760000000000000e7 0.52428800000000000000e6 0.10485760000000000000e7 +0 1 1 2 0.13107200000000000000e6 +0 1 2 3 -0.13107200000000000000e6 +0 2 1 1 -0.26214400000000000000e6 +0 4 1 1 0.26214400000000000000e6 +1 1 1 1 0.26214400000000000000e6 +1 1 1 2 -0.13107200000000000000e6 +1 1 2 3 0.13107200000000000000e6 +1 2 1 1 0.26214400000000000000e6 +1 4 1 1 -0.26214400000000000000e6 +2 1 1 2 -0.26214400000000000000e6 +2 1 1 3 0.26214400000000000000e6 +2 1 2 3 0.26214400000000000000e6 +2 2 1 1 0.52428800000000000000e6 +2 4 1 1 -0.10485760000000000000e7 +3 1 2 3 -0.13107200000000000000e6 +3 2 1 1 -0.26214400000000000000e6 +3 3 1 1 0.26214400000000000000e6 +3 4 1 1 0.26214400000000000000e6 +4 1 1 2 0.13107200000000000000e6 +4 1 2 3 -0.13107200000000000000e6 +4 4 1 1 0.26214400000000000000e6 +4 5 1 1 0.26214400000000000000e6 +*** ANSWER *** +4.548904692939137619e-10 -1.674174344389079182e-09 9.029409809493680191e-10 9.999999937581930398e-01 +1 1 1 1 6.148414788495325939e-04 +1 1 1 2 -4.388747580510582447e-04 +1 1 1 3 -4.388747593355307730e-04 +1 1 2 2 4.955946716669514668e-04 +1 1 2 3 3.205244787119754246e-04 +1 1 3 3 4.955946716669514668e-04 +1 2 1 1 2.621439995003913937e+05 +1 3 1 1 7.322952321769417294e-04 +1 4 1 1 7.322952176238087252e-04 +1 5 1 1 2.621439988593424496e+05 +2 1 1 1 5.999999993617382010e+00 +2 1 1 2 3.534311092067301097e+00 +2 1 1 3 3.534311093010847671e+00 +2 1 2 2 4.314346557842309693e+00 +2 1 2 3 1.068622194652080637e+00 +2 1 3 3 4.314346558915080898e+00 +2 2 1 1 3.191312840597110303e-09 +2 3 1 1 1.534311098449921529e+00 +2 4 1 1 1.534311099393473210e+00 +2 5 1 1 3.191307237696616244e-09 +*** END *** +*** REQUEST *** +"" +4 +5 +3 1 1 1 1 +0.52428800000000000000e6 -0.10485760000000000000e7 0.52428800000000000000e6 0.15728640000000000000e7 +0 1 1 2 -0.13107200000000000000e6 +0 1 2 3 0.13107200000000000000e6 +0 2 1 1 0.26214400000000000000e6 +0 4 1 1 -0.26214400000000000000e6 +1 1 1 1 0.26214400000000000000e6 +1 1 1 2 0.13107200000000000000e6 +1 1 2 3 -0.13107200000000000000e6 +1 2 1 1 -0.26214400000000000000e6 +1 4 1 1 0.26214400000000000000e6 +2 1 1 2 0.52428800000000000000e6 +2 1 1 3 0.26214400000000000000e6 +2 1 2 3 -0.52428800000000000000e6 +2 2 1 1 -0.10485760000000000000e7 +2 4 1 1 0.52428800000000000000e6 +3 1 1 2 -0.39321600000000000000e6 +3 1 2 3 0.26214400000000000000e6 +3 2 1 1 0.52428800000000000000e6 +3 3 1 1 0.26214400000000000000e6 +3 4 1 1 -0.52428800000000000000e6 +4 1 1 2 0.26214400000000000000e6 +4 1 2 3 -0.13107200000000000000e6 +4 4 1 1 0.52428800000000000000e6 +4 5 1 1 0.26214400000000000000e6 +*** ANSWER *** +9.046097392403201396e-10 -4.087614502059694096e-10 9.999999977383847716e-01 9.999999965640337107e-01 +1 1 1 1 3.604559925710001944e-04 +1 1 1 2 -1.071543616027025719e-04 +1 1 1 3 -1.071543616027936449e-04 +1 1 2 2 1.233179770875857117e-04 +1 1 2 3 -4.677015315264715454e-05 +1 1 3 3 1.233179770875857117e-04 +1 2 1 1 2.621439991290596954e+05 +1 3 1 1 2.621439995304491022e+05 +1 4 1 1 2.621439995304490731e+05 +1 5 1 1 2.621439992226000177e+05 +2 1 1 1 9.999999991249831410e+00 +2 1 1 2 1.399999998468725870e+01 +2 1 1 3 1.399999998468733686e+01 +2 1 2 2 2.719350304632718718e+01 +2 1 2 3 2.199999997593712564e+01 +2 1 3 3 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8 1 1 -0.26214400000000000000e6 +12 10 1 1 0.26214400000000000000e6 +13 8 1 1 0.26214400000000000000e6 +13 11 1 1 0.26214400000000000000e6 +14 1 1 2 0.13107200000000000000e6 +14 1 1 4 -0.13107200000000000000e6 +14 4 1 1 0.26214400000000000000e6 +14 13 1 1 0.26214400000000000000e6 +15 14 1 1 0.26214400000000000000e6 +15 20 1 1 -0.26214400000000000000e6 +16 15 1 1 0.26214400000000000000e6 +16 20 1 1 0.26214400000000000000e6 +17 16 1 1 0.26214400000000000000e6 +17 17 1 1 0.26214400000000000000e6 +18 1 1 2 -0.13107200000000000000e6 +18 1 1 4 0.13107200000000000000e6 +18 4 1 1 -0.26214400000000000000e6 +18 18 1 1 0.26214400000000000000e6 +19 19 1 1 0.26214400000000000000e6 +19 20 1 1 0.26214400000000000000e6 +20 16 1 1 0.26214400000000000000e6 +20 21 1 1 0.26214400000000000000e6 +21 16 1 1 -0.26214400000000000000e6 +21 22 1 1 0.26214400000000000000e6 +22 1 1 4 0.58982400000000000000e6 +22 1 2 3 0.26214400000000000000e6 +22 1 4 4 -0.26214400000000000000e6 +22 2 1 1 0.26214400000000000000e6 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+2 1 2 2 4.769230750932913487e+00 +2 1 2 3 1.769230760081863529e+00 +2 1 2 4 1.769230760081884180e+00 +2 1 3 3 4.769230750933013852e+00 +2 1 3 4 1.769230760081862863e+00 +2 1 4 4 4.769230750932993423e+00 +2 2 1 1 4.574446394022880727e-09 +2 3 1 1 1.999999998856389016e+00 +2 4 1 1 1.143612126719995731e-09 +2 5 1 1 4.574428482139560291e-09 +2 6 1 1 1.999999998856391015e+00 +2 7 1 1 4.574429208583087058e-09 +2 8 1 1 1.999999995425566279e+00 +2 9 1 1 1.143612126720002348e-09 +2 10 1 1 1.999999995425567167e+00 +2 11 1 1 4.574426398049007239e-09 +2 12 1 1 4.574428482139586761e-09 +2 13 1 1 1.999999998856391903e+00 +2 14 1 1 4.574427803316053766e-09 +2 15 1 1 1.999999995425571608e+00 +2 16 1 1 4.574427803316027296e-09 +2 17 1 1 1.999999995425572497e+00 +2 18 1 1 1.143612126720002348e-09 +2 19 1 1 1.999999995425571608e+00 +2 20 1 1 4.574427803316053766e-09 +2 21 1 1 1.999999995425572497e+00 +2 22 1 1 4.574427803316027296e-09 +2 23 1 1 4.574428482139586761e-09 +*** END *** +*** REQUEST *** +"" +3 +7 +1 1 1 1 1 1 1 +0.0 0.0 0.0 +0 1 1 1 0.52428800000000000000e6 +1 1 1 1 -0.10485760000000000000e7 +1 2 1 1 0.52428800000000000000e6 +1 3 1 1 0.52428800000000000000e6 +2 1 1 1 -0.10485760000000000000e7 +2 4 1 1 0.52428800000000000000e6 +2 5 1 1 0.52428800000000000000e6 +3 1 1 1 -0.10485760000000000000e7 +3 6 1 1 0.52428800000000000000e6 +3 7 1 1 0.52428800000000000000e6 +*** ANSWER *** +Infeasible +*** END *** +*** REQUEST *** +"" +22 +23 +4 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 +0.98304000000000000000e5 0.29491200000000000000e6 -0.11796480000000000000e7 -0.39321600000000000000e6 0.75366400000000000000e6 0.19660800000000000000e6 0.19660800000000000000e6 -0.13107200000000000000e6 0.49152000000000000000e5 0.98304000000000000000e5 0.14745600000000000000e6 0.29491200000000000000e6 0.0 0.19660800000000000000e6 0.39321600000000000000e6 0.0 0.39321600000000000000e6 0.0 0.0 0.98304000000000000000e5 -0.98304000000000000000e5 0.10485760000000000000e7 +0 1 1 4 0.16384000000000000000e5 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+17 16 1 1 0.65536000000000000000e5 +17 17 1 1 0.65536000000000000000e5 +18 1 1 2 -0.32768000000000000000e5 +18 1 1 4 0.32768000000000000000e5 +18 4 1 1 -0.65536000000000000000e5 +18 18 1 1 0.65536000000000000000e5 +19 1 1 2 -0.65536000000000000000e5 +19 1 1 4 0.65536000000000000000e5 +19 4 1 1 -0.13107200000000000000e6 +19 19 1 1 0.65536000000000000000e5 +19 20 1 1 0.65536000000000000000e5 +20 1 1 2 -0.65536000000000000000e5 +20 1 2 3 0.16384000000000000000e5 +20 16 1 1 0.32768000000000000000e5 +20 21 1 1 0.65536000000000000000e5 +21 1 1 4 0.65536000000000000000e5 +21 1 2 3 -0.16384000000000000000e5 +21 4 1 1 -0.13107200000000000000e6 +21 16 1 1 -0.32768000000000000000e5 +21 22 1 1 0.65536000000000000000e5 +22 1 1 4 -0.49152000000000000000e5 +22 1 2 3 0.49152000000000000000e5 +22 1 4 4 -0.65536000000000000000e5 +22 2 1 1 0.65536000000000000000e5 +22 4 1 1 0.88473600000000000000e6 +22 8 1 1 -0.13107200000000000000e6 +22 12 1 1 0.65536000000000000000e5 +22 16 1 1 0.32768000000000000000e5 +22 20 1 1 0.13107200000000000000e6 +22 23 1 1 0.65536000000000000000e5 +*** ANSWER *** +4.049512478004994521e-09 -7.853528065000316224e-10 2.098746827559298714e-09 -1.064002179143037410e-09 2.098746826197792513e-09 -1.064002178236080190e-09 -3.533807468735688266e-10 9.999999893727561373e-01 -3.533807468734935532e-10 -4.066578641307421796e-10 6.106671844491684542e-01 3.473323508561638184e-01 2.694664478268185004e+00 -3.533807468737202007e-10 -4.066578641307620320e-10 3.473327911937711954e-01 3.473340419483763042e-01 6.106687190982799107e-01 3.473330062104405536e-01 3.473326192695437298e-01 2.694666638300601047e+00 9.999999893727561373e-01 +1 1 1 1 2.955311598780135246e-04 +1 1 1 2 -5.146888158159813008e-05 +1 1 1 3 -5.146888152678607241e-05 +1 1 1 4 -5.146888156371399840e-05 +1 1 2 2 1.676857822104013684e-04 +1 1 2 3 -6.973044675111467021e-05 +1 1 2 4 -6.973044681231809969e-05 +1 1 3 3 1.676857821211741317e-04 +1 1 3 4 -6.973044675287975135e-05 +1 1 4 4 1.676857822024493960e-04 +1 2 1 1 6.553599919613178645e+04 +1 3 1 1 6.983149492369882839e-06 +1 4 1 1 4.002087485256239597e+04 +1 5 1 1 6.553599933367525227e+04 +1 6 1 1 6.983149492374788854e-06 +1 7 1 1 3.491580335803661558e-06 +1 8 1 1 2.276275983412596543e+04 +1 9 1 1 4.002068463020300987e+04 +1 10 1 1 2.276277297585186170e+04 +1 11 1 1 1.765975312779260857e+05 +1 12 1 1 6.553599933367525227e+04 +1 13 1 1 6.983149492359935285e-06 +1 14 1 1 3.491580335802333410e-06 +1 15 1 1 2.276280183381729876e+04 +1 16 1 1 3.491580335807320740e-06 +1 17 1 1 2.276288380327109917e+04 +1 18 1 1 4.002078520496717829e+04 +1 19 1 1 2.276281592514974545e+04 +1 20 1 1 1.765976162269152992e+05 +1 21 1 1 2.276279056659112757e+04 +1 22 1 1 1.765976728378105036e+05 +1 23 1 1 6.553599933367525227e+04 +2 1 1 1 1.699999994384707236e+01 +2 1 1 2 3.099999989341090512e+01 +2 1 1 3 3.099999989341162276e+01 +2 1 1 4 3.099999989341045747e+01 +2 1 2 2 5.999999980617106132e+01 +2 1 2 3 5.899999979955705243e+01 +2 1 2 4 5.899999979955698848e+01 +2 1 3 3 5.999999980620715689e+01 +2 1 3 4 5.899999979955813956e+01 +2 1 4 4 5.999999980617731410e+01 +2 2 1 1 3.509895568585119103e-09 +2 3 1 1 3.399999988197636469e+01 +2 4 1 1 5.716149613856589889e-09 +2 5 1 1 3.509889572509242164e-09 +2 6 1 1 3.399999988197478018e+01 +2 7 1 1 6.799999975382014838e+01 +2 8 1 1 1.013005840234281783e-08 +2 9 1 1 5.716805148766916003e-09 +2 10 1 1 1.012989429842144469e-08 +2 11 1 1 1.303353071688916570e-09 +2 12 1 1 3.509889572509255399e-09 +2 13 1 1 3.399999988197728129e+01 +2 14 1 1 6.799999975382074524e+01 +2 15 1 1 1.012958682617309905e-08 +2 16 1 1 6.799999975381710726e+01 +2 17 1 1 1.012872991779920873e-08 +2 18 1 1 5.716487784110908985e-09 +2 19 1 1 1.012945825278146321e-08 +2 20 1 1 1.303338019016667580e-09 +2 21 1 1 1.012966020393385883e-08 +2 22 1 1 1.303327157037172274e-09 +2 23 1 1 3.509889572509255399e-09 +*** END *** +*** REQUEST *** +"" +5 +5 +3 1 1 1 1 +0.52428800000000000000e6 -0.10485760000000000000e7 0.10485760000000000000e7 0.52428800000000000000e6 0.52428800000000000000e6 +0 1 2 3 0.26214400000000000000e6 +1 1 1 1 0.52428800000000000000e6 +1 1 2 3 -0.26214400000000000000e6 +2 1 1 3 0.52428800000000000000e6 +2 4 1 1 -0.10485760000000000000e7 +3 1 1 2 -0.26214400000000000000e6 +3 1 2 2 0.52428800000000000000e6 +3 1 2 3 0.26214400000000000000e6 +3 1 3 3 0.52428800000000000000e6 +3 2 1 1 0.52428800000000000000e6 +3 4 1 1 -0.52428800000000000000e6 +4 1 1 2 -0.26214400000000000000e6 +4 3 1 1 0.52428800000000000000e6 +5 1 2 3 -0.26214400000000000000e6 +5 5 1 1 0.52428800000000000000e6 +*** ANSWER *** +9.047144637004025380e-01 -5.064741821662422927e-01 1.012948364956070213e+00 -6.235856335248027958e-10 -5.845221297834649404e-10 +1 1 1 1 4.743309372861008742e+05 +1 1 1 2 -2.655383360195748392e+05 +1 1 1 3 -2.655383360195748392e+05 +1 1 2 2 5.310766729076325428e+05 +1 1 2 3 -2.337711320360052632e+05 +1 1 3 3 5.310766729076325428e+05 +1 2 1 1 5.310766729076325428e+05 +1 3 1 1 2.146057993971965325e-04 +1 4 1 1 2.146057993971661748e-04 +1 5 1 1 2.350863256467333393e-04 +2 1 1 1 4.943559570850903917e+00 +2 1 1 2 4.415339358856920526e+00 +2 1 1 3 4.415339358856921415e+00 +2 1 2 2 3.943559572351147846e+00 +2 1 2 3 3.943559570850906582e+00 +2 1 3 3 3.943559572351153619e+00 +2 2 1 1 2.160644606377368460e-09 +2 3 1 1 5.415339358856919638e+00 +2 4 1 1 5.415339358856934737e+00 +2 5 1 1 4.943559570850906582e+00 +*** END *** +*** REQUEST *** +"" +4 +4 +3 1 1 1 +0.0 -0.10485760000000000000e7 0.52428800000000000000e6 0.52428800000000000000e6 +0 4 1 1 0.52428800000000000000e6 +1 1 1 1 0.52428800000000000000e6 +1 4 1 1 -0.52428800000000000000e6 +2 1 2 3 0.52428800000000000000e6 +2 4 1 1 -0.10485760000000000000e7 +3 1 1 2 -0.26214400000000000000e6 +3 2 1 1 0.52428800000000000000e6 +4 1 1 3 -0.26214400000000000000e6 +4 3 1 1 0.52428800000000000000e6 +*** ANSWER *** +Infeasible +*** END *** +*** REQUEST *** +"" +13 +5 +3 1 3 3 1 +0.0 0.0 0.52428800000000000000e6 -0.10485760000000000000e7 0.52428800000000000000e6 0.52428800000000000000e6 0.52428800000000000000e6 0.0 0.0 0.0 0.52428800000000000000e6 -0.10485760000000000000e7 0.52428800000000000000e6 +0 1 2 3 0.26214400000000000000e6 +1 1 2 3 -0.26214400000000000000e6 +1 2 1 1 -0.52428800000000000000e6 +1 3 1 2 -0.26214400000000000000e6 +1 3 2 3 0.26214400000000000000e6 +1 4 1 1 0.52428800000000000000e6 +1 4 1 3 -0.26214400000000000000e6 +2 1 1 2 0.26214400000000000000e6 +2 3 2 3 -0.26214400000000000000e6 +3 1 1 1 0.52428800000000000000e6 +3 1 2 3 -0.26214400000000000000e6 +4 1 1 3 0.52428800000000000000e6 +4 4 1 1 -0.10485760000000000000e7 +5 1 2 2 0.52428800000000000000e6 +5 3 1 2 -0.26214400000000000000e6 +6 1 3 3 0.52428800000000000000e6 +6 4 1 3 -0.26214400000000000000e6 +7 1 1 2 -0.26214400000000000000e6 +7 3 1 1 0.52428800000000000000e6 +8 1 2 3 -0.52428800000000000000e6 +8 3 1 3 0.52428800000000000000e6 +9 1 2 3 -0.26214400000000000000e6 +9 2 1 1 -0.52428800000000000000e6 +9 3 1 2 -0.26214400000000000000e6 +9 3 2 3 0.26214400000000000000e6 +9 3 3 3 0.52428800000000000000e6 +9 4 1 3 -0.26214400000000000000e6 +10 1 2 3 -0.52428800000000000000e6 +10 4 1 2 0.52428800000000000000e6 +11 3 2 3 -0.26214400000000000000e6 +11 4 2 2 0.52428800000000000000e6 +12 1 2 3 -0.52428800000000000000e6 +12 2 1 1 -0.10485760000000000000e7 +12 3 1 2 -0.52428800000000000000e6 +12 3 2 3 0.52428800000000000000e6 +12 4 1 3 -0.52428800000000000000e6 +12 4 2 3 0.52428800000000000000e6 +13 1 2 3 -0.26214400000000000000e6 +13 5 1 1 0.52428800000000000000e6 +*** ANSWER *** +-1.012948329551812909e+00 -1.012948329551812909e+00 9.047145732130862372e-01 -5.064741647124204604e-01 1.012948329986513407e+00 1.012948329986513407e+00 -1.269719777217911070e-10 -2.267145002100386557e-10 1.807584410822154742e-10 -2.267145002104232947e-10 1.807584410826844857e-10 -3.495881670031764897e-10 -2.576717013002858655e-10 +1 1 1 1 4.743309943659727578e+05 +1 1 1 2 -2.655383268687454984e+05 +1 1 1 3 -2.655383268687454984e+05 +1 1 2 2 5.310766542371993419e+05 +1 1 2 3 -2.337711697371662303e+05 +1 1 3 3 5.310766542371993419e+05 +1 2 1 1 5.310766542810912943e+05 +1 3 1 1 1.386602794478742143e-04 +1 3 1 2 2.194599384597073792e-05 +1 3 1 3 -1.188636918861207467e-04 +1 3 2 2 2.052301637036763049e-04 +1 3 2 3 -1.832848809016356280e-04 +1 3 3 3 2.999996452617888915e-04 +1 4 1 1 1.386602794479904407e-04 +1 4 1 2 -1.188636918863224083e-04 +1 4 1 3 2.194599384612041203e-05 +1 4 2 2 2.999996452620360896e-04 +1 4 2 3 -1.832848809017613954e-04 +1 4 3 3 2.052301637036763049e-04 +1 5 1 1 7.013598277235181221e-05 +2 1 1 1 4.943559575736863998e+00 +2 1 1 2 4.415339364265365774e+00 +2 1 1 3 4.415339364265380873e+00 +2 1 2 2 3.943559576120588606e+00 +2 1 2 3 3.943559575736873768e+00 +2 1 3 3 3.943559576120614807e+00 +2 2 1 1 5.526448483074430500e-10 +2 3 1 1 5.415339364265365774e+00 +2 3 1 2 2.943559576120634347e+00 +2 3 1 3 3.943559575736864442e+00 +2 3 2 2 5.028789771976822642e+00 +2 3 2 3 4.415339364265383537e+00 +2 3 3 3 5.415339364265284949e+00 +2 4 1 1 5.415339364265358668e+00 +2 4 1 2 3.943559575736877765e+00 +2 4 1 3 2.943559576120583277e+00 +2 4 2 2 5.415339364265393307e+00 +2 4 2 3 4.415339364265369326e+00 +2 4 3 3 5.028789771976716061e+00 +2 5 1 1 4.943559575736879985e+00 +*** END *** +*** REQUEST *** +"" +3 +4 +3 1 1 1 +-0.10485760000000000000e7 0.52428800000000000000e6 0.52428800000000000000e6 +0 1 1 1 0.52428800000000000000e6 +1 1 2 3 0.52428800000000000000e6 +1 4 1 1 -0.10485760000000000000e7 +2 1 1 2 -0.26214400000000000000e6 +2 2 1 1 0.52428800000000000000e6 +3 1 1 3 -0.26214400000000000000e6 +3 3 1 1 0.52428800000000000000e6 +*** ANSWER *** +Infeasible +*** END *** +*** REQUEST *** +"" +9 +4 +3 3 3 1 +0.0 0.52428800000000000000e6 -0.10485760000000000000e7 0.0 0.52428800000000000000e6 0.52428800000000000000e6 -0.10485760000000000000e7 0.52428800000000000000e6 0.52428800000000000000e6 +0 1 1 1 0.52428800000000000000e6 +1 1 2 3 0.52428800000000000000e6 +1 3 1 2 -0.52428800000000000000e6 +2 1 1 2 -0.26214400000000000000e6 +2 2 1 1 0.52428800000000000000e6 +3 1 2 2 -0.10485760000000000000e7 +3 2 1 2 0.52428800000000000000e6 +4 2 1 3 0.52428800000000000000e6 +4 3 1 2 -0.52428800000000000000e6 +5 2 3 3 0.52428800000000000000e6 +5 3 2 3 -0.26214400000000000000e6 +6 1 1 3 -0.26214400000000000000e6 +6 3 1 1 0.52428800000000000000e6 +7 1 3 3 -0.10485760000000000000e7 +7 3 1 3 0.52428800000000000000e6 +8 2 2 3 -0.26214400000000000000e6 +8 3 2 2 0.52428800000000000000e6 +9 3 1 2 -0.26214400000000000000e6 +9 4 1 1 0.52428800000000000000e6 +*** ANSWER *** +Infeasible +*** END *** +*** REQUEST *** +"" +25 +5 +6 1 3 3 3 +0.0 0.0 0.13107200000000000000e6 0.0 0.0 0.0 -0.10485760000000000000e7 0.13107200000000000000e6 -0.26214400000000000000e6 0.13107200000000000000e6 0.13107200000000000000e6 0.0 0.13107200000000000000e6 0.0 0.13107200000000000000e6 0.13107200000000000000e6 0.0 0.13107200000000000000e6 0.0 0.13107200000000000000e6 0.0 0.0 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-0.52428800000000000000e6 +24 5 2 3 0.52428800000000000000e6 +25 1 5 6 -0.26214400000000000000e6 +25 5 3 3 0.52428800000000000000e6 +*** ANSWER *** +-4.113697398682738004e-09 8.215094087406949078e-09 1.106563519105026888e-08 -6.332908356568953188e-09 -2.931819407167173368e-05 -2.931818908533051569e-05 -5.000000074902808400e-01 1.106405735886701213e-08 -4.451398475879184303e-09 9.999643968605362865e-01 5.868338520830287551e-09 -1.415827732183235363e-09 8.903640791049248497e-09 -7.865132682789377989e-09 8.902267568543103993e-09 5.889851427419620259e-09 -1.423050516012667677e-09 8.903577047039871176e-09 -7.862722209332731223e-09 1.916770858206847272e-09 -2.334896842407189883e-12 -4.728327014591874540e-13 5.419760765973143563e-09 -5.673174330751571568e-09 5.419709023311579812e-09 +1 1 1 1 5.145820320597975853e-03 +1 1 1 2 -1.538349733204534900e-03 +1 1 1 3 -2.156762181760575343e-03 +1 1 1 4 -1.543989212589488933e-03 +1 1 1 5 4.307075248898414518e-03 +1 1 1 6 -2.154287943343585060e-03 +1 1 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-1.478241289070492609e-11 +1 1 1 1 3.495253334203167469e+05 +1 1 1 2 -6.990506665331815602e+05 +1 1 2 2 1.398101333420316689e+06 +1 2 1 1 1.398101333420316689e+06 +1 3 1 1 3.229526064989188434e-04 +2 1 1 1 1.999999999076024881e+00 +2 1 1 2 9.999999992811959837e-01 +2 1 2 2 4.999999998586800998e-01 +2 2 1 1 3.464905364927463821e-10 +2 3 1 1 1.499999999281195651e+00 +*** END *** +*** REQUEST *** +"" +1 +6 +1 1 1 1 1 1 +-0.10485760000000000000e7 +0 1 1 1 0.10485760000000000000e7 +1 1 1 1 -0.10485760000000000000e7 +1 2 1 1 -0.10485760000000000000e7 +1 3 1 1 0.10485760000000000000e7 +1 4 1 1 -0.10485760000000000000e7 +1 5 1 1 0.10485760000000000000e7 +1 6 1 1 -0.10485760000000000000e7 +*** ANSWER *** +Infeasible +*** END *** +*** REQUEST *** +"" +16 +16 +5 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 +0.11796480000000000000e7 -0.52428800000000000000e6 -0.52428800000000000000e6 0.13107200000000000000e7 -0.52428800000000000000e6 0.10485760000000000000e7 -0.52428800000000000000e6 0.91750400000000000000e6 0.91750400000000000000e6 0.26214400000000000000e6 0.26214400000000000000e6 0.26214400000000000000e6 0.26214400000000000000e6 0.0 0.26214400000000000000e6 0.78643200000000000000e6 +0 1 1 4 -0.39321600000000000000e6 +0 1 2 2 0.26214400000000000000e6 +0 1 2 5 -0.13107200000000000000e6 +0 1 3 3 -0.26214400000000000000e6 +0 1 3 4 0.26214400000000000000e6 +0 1 4 4 -0.26214400000000000000e6 +0 1 4 5 0.13107200000000000000e6 +0 2 1 1 -0.52428800000000000000e6 +0 4 1 1 -0.26214400000000000000e6 +0 6 1 1 -0.52428800000000000000e6 +0 8 1 1 0.52428800000000000000e6 +0 10 1 1 -0.26214400000000000000e6 +0 12 1 1 -0.52428800000000000000e6 +1 1 1 1 0.52428800000000000000e6 +1 1 1 4 0.39321600000000000000e6 +1 1 2 2 -0.26214400000000000000e6 +1 1 2 5 0.13107200000000000000e6 +1 1 3 3 0.26214400000000000000e6 +1 1 3 4 -0.26214400000000000000e6 +1 1 4 4 0.26214400000000000000e6 +1 1 4 5 -0.13107200000000000000e6 +1 2 1 1 0.52428800000000000000e6 +1 4 1 1 0.26214400000000000000e6 +1 6 1 1 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4 0.13107200000000000000e6 +8 1 2 2 -0.26214400000000000000e6 +8 1 2 5 -0.13107200000000000000e6 +8 1 3 3 0.26214400000000000000e6 +8 1 3 4 -0.26214400000000000000e6 +8 1 4 4 0.26214400000000000000e6 +8 1 4 5 -0.39321600000000000000e6 +8 1 5 5 0.52428800000000000000e6 +8 4 1 1 -0.26214400000000000000e6 +8 6 1 1 0.52428800000000000000e6 +8 10 1 1 0.78643200000000000000e6 +9 1 1 4 0.13107200000000000000e6 +9 1 2 2 -0.26214400000000000000e6 +9 1 2 5 0.13107200000000000000e6 +9 1 3 3 0.26214400000000000000e6 +9 1 3 4 -0.26214400000000000000e6 +9 1 4 4 0.26214400000000000000e6 +9 1 4 5 -0.13107200000000000000e6 +9 3 1 1 0.52428800000000000000e6 +9 4 1 1 0.26214400000000000000e6 +9 6 1 1 0.52428800000000000000e6 +9 10 1 1 0.26214400000000000000e6 +10 1 1 4 -0.26214400000000000000e6 +10 5 1 1 0.52428800000000000000e6 +11 1 4 5 -0.26214400000000000000e6 +11 7 1 1 0.52428800000000000000e6 +12 1 3 3 -0.52428800000000000000e6 +12 1 3 4 0.26214400000000000000e6 +12 8 1 1 0.52428800000000000000e6 +12 9 1 1 0.52428800000000000000e6 +12 10 1 1 -0.52428800000000000000e6 +12 16 1 1 0.52428800000000000000e6 +13 1 3 4 -0.26214400000000000000e6 +13 11 1 1 0.52428800000000000000e6 +14 1 1 4 -0.26214400000000000000e6 +14 1 2 2 0.52428800000000000000e6 +14 1 2 5 -0.26214400000000000000e6 +14 1 3 4 0.26214400000000000000e6 +14 1 4 4 -0.52428800000000000000e6 +14 1 4 5 0.26214400000000000000e6 +14 6 1 1 -0.52428800000000000000e6 +14 12 1 1 0.52428800000000000000e6 +14 13 1 1 0.52428800000000000000e6 +14 16 1 1 -0.52428800000000000000e6 +15 1 2 5 -0.26214400000000000000e6 +15 14 1 1 0.52428800000000000000e6 +16 1 1 4 0.26214400000000000000e6 +16 1 3 4 -0.26214400000000000000e6 +16 1 4 4 0.52428800000000000000e6 +16 1 4 5 -0.26214400000000000000e6 +16 6 1 1 0.52428800000000000000e6 +16 15 1 1 0.52428800000000000000e6 +*** ANSWER *** +-2.510945831846816927e-10 7.584564995981076880e-11 -3.980910209918642198e-10 1.344946711011189854e-10 -8.782665206711593718e-11 -5.852309807939336404e-11 -6.669457535662038939e-11 9.130977785251912681e-10 9.999999956372092047e-01 9.999999994808139725e-01 -8.835712425264707961e-11 9.999999984230395489e-01 4.308129358900289983e-10 9.999999981672165195e-01 -8.823106083428535072e-11 -1.165612788739154225e-10 +1 1 1 1 2.212302206669363239e-04 +1 1 1 2 3.976496412612926835e-05 +1 1 1 3 -2.087143452137825081e-04 +1 1 1 4 3.968027478773667252e-05 +1 1 1 5 7.051394212226347064e-05 +1 1 2 2 2.915950003628733217e-04 +1 1 2 3 -4.604645975896408047e-05 +1 1 2 4 -3.068295804584898805e-05 +1 1 2 5 -1.855933114523877075e-04 +1 1 3 3 2.800322674859963973e-04 +1 1 3 4 -4.591486881397235237e-05 +1 1 3 5 -3.496716552457179071e-05 +1 1 4 4 2.916795673287685825e-04 +1 1 4 5 -1.856025585861981186e-04 +1 1 5 5 8.316023056030817651e-04 +1 2 1 1 5.242880002212302061e+05 +1 3 1 1 5.242879980655172840e+05 +1 4 1 1 5.242879989745246130e+05 +1 5 1 1 5.242880000806730241e+05 +1 6 1 1 5.242879993920542765e+05 +1 7 1 1 3.065515175354948871e-04 +1 8 1 1 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1.153361302937487176e+00 +2 8 1 1 3.999999996272334268e+00 +2 9 1 1 5.734957845436244747e-10 +2 10 1 1 4.758726891861830288e-01 +2 11 1 1 7.118080333013501182e-01 +2 12 1 1 2.867478780824246656e-10 +2 13 1 1 5.734957129228942403e-10 +2 14 1 1 1.153489309883686920e+00 +2 15 1 1 1.093937070702268199e+00 +2 16 1 1 7.097821616243046305e-01 +*** END *** +*** REQUEST *** +"" +1 +6 +1 1 1 1 1 1 +0.10485760000000000000e7 +0 1 1 1 0.10485760000000000000e7 +1 1 1 1 0.10485760000000000000e7 +1 2 1 1 0.10485760000000000000e7 +1 3 1 1 0.10485760000000000000e7 +1 4 1 1 -0.10485760000000000000e7 +1 5 1 1 0.10485760000000000000e7 +1 6 1 1 -0.10485760000000000000e7 +*** ANSWER *** +Infeasible +*** END *** +*** REQUEST *** +"" +16 +16 +5 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 +-0.26214400000000000000e6 -0.52428800000000000000e6 -0.52428800000000000000e6 0.15728640000000000000e7 -0.52428800000000000000e6 0.0 -0.26214400000000000000e6 -0.52428800000000000000e6 0.10485760000000000000e7 0.26214400000000000000e6 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4.999999999177147103e-01 +1 1 1 1 7.179446380522872096e-09 +1 1 2 2 4.884728511558652836e-09 +1 1 3 3 4.884728533079615974e-09 +1 1 4 4 1.273445781270666261e-09 +1 1 5 5 3.568164078541628250e-09 +1 1 6 6 3.568164092148815501e-09 +1 1 7 7 1.438016387172196853e-09 +1 1 8 8 5.000000041441609033e-01 +1 1 9 9 5.000000041441609033e-01 +2 1 1 1 1.361603717443017059e-01 +2 1 2 2 2.887940324864630703e-01 +2 1 3 3 2.887940323968900547e-01 +2 1 4 4 5.781475570704999178e-01 +2 1 5 5 3.585456340583702550e-01 +2 1 6 6 3.585456339687972394e-01 +2 1 7 7 5.580128146738018158e-01 +2 1 8 8 2.098544929105395392e-09 +2 1 9 9 2.098544929105395392e-09 +*** END *** +*** REQUEST *** +"" +3 +1 +9 +0.10000000000000000000e1 0.10000000000000000000e1 0.10000000000000000000e1 0.10000000000000000000e1 0.10000000000000000000e1 0.10000000000000000000e1 0.10000000000000000000e1 0.10000000000000000000e1 0.10000000000000000000e1 +0 1 1 1 -0.10000000000000000000e1 +0 1 2 2 -0.40000000000000000000e1 +0 1 3 3 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REQUEST *** +"" +5 +5 +4 1 1 1 1 +0.52428800000000000000e6 -0.10485760000000000000e7 -0.52428800000000000000e6 -0.15728640000000000000e7 0.10485760000000000000e7 +0 1 2 2 0.52428800000000000000e6 +0 1 4 4 -0.52428800000000000000e6 +0 2 1 1 -0.52428800000000000000e6 +0 4 1 1 0.52428800000000000000e6 +1 1 1 1 0.52428800000000000000e6 +1 1 2 2 -0.52428800000000000000e6 +1 1 4 4 0.52428800000000000000e6 +1 2 1 1 0.52428800000000000000e6 +1 4 1 1 -0.52428800000000000000e6 +2 1 1 2 0.52428800000000000000e6 +2 1 1 4 -0.52428800000000000000e6 +2 4 1 1 -0.10485760000000000000e7 +3 1 1 3 0.52428800000000000000e6 +3 1 1 4 -0.26214400000000000000e6 +3 1 4 4 -0.52428800000000000000e6 +4 1 2 2 -0.52428800000000000000e6 +4 1 2 4 0.52428800000000000000e6 +4 1 4 4 -0.52428800000000000000e6 +4 5 1 1 -0.52428800000000000000e6 +5 3 1 1 0.52428800000000000000e6 +5 4 1 1 0.52428800000000000000e6 +*** ANSWER *** +Failure +*** END *** +*** REQUEST *** +"" +20 +7 +4 1 4 1 4 1 1 +-0.52428800000000000000e6 0.10485760000000000000e7 -0.52428800000000000000e6 0.0 -0.10485760000000000000e7 0.52428800000000000000e6 0.0 0.0 0.0 0.10485760000000000000e7 0.10485760000000000000e7 0.52428800000000000000e6 0.0 0.0 0.10485760000000000000e7 0.0 0.0 0.0 0.10485760000000000000e7 0.52428800000000000000e6 +0 1 1 2 0.26214400000000000000e6 +0 1 1 4 -0.26214400000000000000e6 +0 2 1 1 -0.52428800000000000000e6 +0 3 1 2 -0.26214400000000000000e6 +0 5 1 4 0.26214400000000000000e6 +1 1 2 3 0.52428800000000000000e6 +1 1 3 4 -0.52428800000000000000e6 +1 5 1 4 -0.26214400000000000000e6 +1 5 4 4 -0.52428800000000000000e6 +2 1 1 1 0.52428800000000000000e6 +2 1 1 2 -0.26214400000000000000e6 +2 1 1 4 0.26214400000000000000e6 +2 2 1 1 0.52428800000000000000e6 +2 3 1 2 0.26214400000000000000e6 +2 5 1 4 -0.26214400000000000000e6 +3 1 1 3 0.52428800000000000000e6 +3 1 1 4 -0.26214400000000000000e6 +3 1 4 4 -0.52428800000000000000e6 +4 1 2 2 0.52428800000000000000e6 +4 1 4 4 -0.52428800000000000000e6 +4 3 1 2 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-5.878340507562113329e-11 1.443375661877718541e-01 7.735026948774698097e-02 -1.056624327919023082e-01 -1.878285492550673151e-10 1.443375666874154029e-01 2.565781949174762027e-10 1.443375668147542368e-01 2.565786864113415496e-10 2.942145218318752536e-10 -5.878238521589696054e-11 +1 1 1 1 3.819403205883547918e-05 +1 1 1 2 -1.224733049205359824e-05 +1 1 1 3 1.158126407231101153e-05 +1 1 1 4 6.456704127512840957e-06 +1 1 2 2 8.596374633833324744e-05 +1 1 2 3 -3.328802848049413742e-06 +1 1 2 4 -1.645862409268672010e-05 +1 1 3 3 1.663034366678906723e-04 +1 1 3 4 3.328802848049413742e-06 +1 1 4 4 2.679791111105120707e-04 +1 2 1 1 5.242880000381940044e+05 +1 3 1 1 5.648418178682285361e+05 +1 3 1 2 2.067464544649153540e+05 +1 3 1 3 3.675181430842708319e-04 +1 3 1 4 2.067464537865202001e+05 +1 3 2 2 7.567445456437776738e+04 +1 3 2 3 1.345208686568937634e-04 +1 3 2 4 7.567445423017386929e+04 +1 3 3 3 1.354840027876034331e-04 +1 3 3 4 1.345211263412294384e-04 +1 3 4 4 7.567445406775796437e+04 +1 4 1 1 8.589389131903515245e-05 +1 5 1 1 4.055381825549533096e+04 +1 5 1 2 -5.539754556360087736e+04 +1 5 1 3 -9.847625443184073249e-05 +1 5 1 4 -5.539754572539421497e+04 +1 5 2 2 7.567445432971508126e+04 +1 5 2 3 1.345208686568937634e-04 +1 5 2 4 7.567445423017386929e+04 +1 5 3 3 1.354840027876034331e-04 +1 5 3 4 1.345211263412294384e-04 +1 5 4 4 7.567445477174385451e+04 +1 6 1 1 3.205565798900817526e-04 +1 7 1 1 1.354845374878180936e-04 +2 1 1 1 3.732050806982203373e+00 +2 1 1 2 4.978949133196186594e-01 +2 1 1 3 -1.308568436669261814e-01 +2 1 1 4 -7.945535675086745631e-02 +2 1 2 2 1.972442206524292363e+00 +2 1 2 3 6.164317095563820459e-02 +2 1 2 4 3.950919296356215638e-01 +2 1 3 3 1.074614358661167834e+00 +2 1 3 4 6.164314293620330037e-02 +2 1 4 4 8.177416694170173139e-01 +2 2 1 1 1.955575535633660102e-10 +2 3 1 1 4.226497299295132737e-01 +2 3 1 2 -5.773502768886704661e-01 +2 3 1 3 -2.801943794662026982e-08 +2 3 1 4 -5.773502602186049160e-01 +2 3 2 2 1.577350183915906534e+00 +2 3 2 3 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-8.033532523347130644e-10 +1 1 1 1 9.639215222160258208e-10 +1 2 1 1 1.048575999157623970e+06 +1 3 1 1 1.445882272036933453e-09 +1 4 1 1 1.048576000000000931e+06 +2 1 1 1 1.499999999685651009e+00 +2 2 1 1 1.378900983392931975e-15 +2 3 1 1 9.999999999999862332e-01 +2 4 1 1 1.378900796134651217e-15 +*** END *** +*** REQUEST *** +"" +1 +3 +1 1 1 +0.10485760000000000000e7 +0 1 1 1 0.10485760000000000000e7 +1 1 1 1 0.10485760000000000000e7 +1 2 1 1 -0.10485760000000000000e7 +1 3 1 1 0.10485760000000000000e7 +*** ANSWER *** +Infeasible +*** END *** +*** REQUEST *** +"" +5 +5 +4 1 1 1 1 +0.10485760000000000000e7 0.0 0.52428800000000000000e6 0.52428800000000000000e6 0.0 +0 2 1 1 -0.52428800000000000000e6 +1 1 1 1 0.52428800000000000000e6 +1 2 1 1 0.52428800000000000000e6 +2 1 1 3 0.52428800000000000000e6 +2 1 1 4 -0.52428800000000000000e6 +2 2 1 1 -0.10485760000000000000e7 +2 4 1 1 0.10485760000000000000e7 +3 1 1 2 -0.52428800000000000000e6 +3 1 1 4 0.26214400000000000000e6 +3 1 3 3 0.52428800000000000000e6 +3 2 1 1 0.52428800000000000000e6 +3 4 1 1 -0.52428800000000000000e6 +4 2 1 1 0.52428800000000000000e6 +4 3 1 1 0.52428800000000000000e6 +4 4 1 1 -0.52428800000000000000e6 +5 1 1 2 -0.52428800000000000000e6 +5 1 1 4 0.26214400000000000000e6 +5 1 3 4 0.52428800000000000000e6 +5 1 4 4 -0.52428800000000000000e6 +5 5 1 1 0.52428800000000000000e6 +*** ANSWER *** +-1.338594917701584393e-10 -4.876570677399720908e-12 -8.432248596379257249e-11 -1.376003305176662146e-10 6.303077531793304895e-11 +1 1 1 1 1.961387163584582007e-06 +1 1 1 2 1.116298839109634367e-05 +1 1 1 3 -2.556727487312544875e-06 +1 1 1 4 -3.024766708235593078e-06 +1 1 2 2 7.214231238477719979e-05 +1 1 3 3 2.793304486379264481e-05 +1 1 3 4 3.304627912988848237e-05 +1 1 4 4 3.909603325488893426e-05 +1 2 1 1 5.242879998907233821e+05 +1 3 1 1 1.102983309069068926e-10 +1 4 1 1 1.833803270175834998e-04 +1 5 1 1 1.051885915146662243e-04 +2 1 1 1 1.999999999825280872e+00 +2 1 1 2 -3.095056099254819282e-01 +2 1 1 3 8.388821521212311283e-02 +2 1 1 4 8.388917358587567874e-02 +2 1 2 2 4.789927494245199008e-02 +2 1 2 3 -1.307058076260208049e-02 +2 1 2 4 -1.290714134044862460e-02 +2 1 3 3 2.971005649372479018e-01 +2 1 3 4 -2.447309307272341194e-01 +2 1 4 4 2.134402019028047992e-01 +2 2 1 1 2.103712716147778344e-16 +2 3 1 1 1.000000958427416542e+00 +2 4 1 1 9.583793370118670507e-07 +2 5 1 1 1.669900717227676154e-06 +*** END *** +*** REQUEST *** +"" +4 +2 +3 1 +-0.52428800000000000000e6 0.52428800000000000000e6 0.10485760000000000000e7 0.0 +0 1 2 2 0.10485760000000000000e7 +0 1 3 3 -0.10485760000000000000e7 +0 2 1 1 -0.10485760000000000000e7 +1 1 2 3 0.52428800000000000000e6 +1 1 3 3 -0.10485760000000000000e7 +2 1 2 2 0.10485760000000000000e7 +2 1 2 3 -0.52428800000000000000e6 +3 1 1 1 0.10485760000000000000e7 +3 1 2 2 -0.10485760000000000000e7 +3 1 3 3 0.10485760000000000000e7 +3 2 1 1 0.10485760000000000000e7 +4 1 1 2 -0.10485760000000000000e7 +4 1 1 3 0.10485760000000000000e7 +*** ANSWER *** +9.999995669872646653e-01 9.999987009619675238e-01 -8.660253659925441563e-07 0.000000000000000000e+00 +1 1 1 1 3.962767353149487803e-08 +1 1 2 2 4.540467642000610149e-01 +1 1 2 3 4.540466709859902750e-01 +1 1 3 3 4.540468014726645185e-01 +1 2 1 1 1.048576000000039581e+06 +2 1 1 1 9.999999999999281686e-01 +2 1 2 2 2.500000307927105481e-01 +2 1 2 3 -2.499999692072846225e-01 +2 1 3 3 2.500000307927234822e-01 +2 2 1 1 5.333451642288094782e-14 +*** END *** +*** REQUEST *** +"" +4 +2 +3 1 +-0.52428800000000000000e6 0.52428800000000000000e6 0.10485760000000000000e7 0.0 +0 1 2 2 -0.10485760000000000000e7 +0 1 3 3 0.10485760000000000000e7 +0 2 1 1 -0.10485760000000000000e7 +1 1 2 3 0.52428800000000000000e6 +1 1 3 3 -0.10485760000000000000e7 +2 1 2 2 0.10485760000000000000e7 +2 1 2 3 -0.52428800000000000000e6 +3 1 1 1 0.10485760000000000000e7 +3 1 2 2 0.10485760000000000000e7 +3 1 3 3 -0.10485760000000000000e7 +3 2 1 1 0.10485760000000000000e7 +4 1 1 2 -0.10485760000000000000e7 +4 1 1 3 0.10485760000000000000e7 +*** ANSWER *** +-9.999998331245307792e-01 -9.999999443745658523e-01 -1.112500350952176353e-07 0.000000000000000000e+00 +1 1 1 1 1.642036506765975901e-11 +1 1 2 2 5.832749536206643937e-02 +1 1 2 3 5.832705836608864658e-02 +1 1 3 3 5.832662143581340830e-02 +1 2 1 1 1.048576000000000000e+06 +2 1 1 1 9.999999999999996669e-01 +2 1 2 2 2.499998068521827044e-01 +2 1 2 3 -2.500000893194189722e-01 +2 1 3 3 2.500003721368480036e-01 +2 2 1 1 2.465190328815661892e-32 +*** END *** +*** REQUEST *** +"" +4 +2 +3 1 +-0.52428800000000000000e6 -0.52428800000000000000e6 0.10485760000000000000e7 0.0 +0 1 2 2 0.10485760000000000000e7 +0 1 3 3 -0.10485760000000000000e7 +0 2 1 1 -0.10485760000000000000e7 +1 1 2 3 -0.52428800000000000000e6 +1 1 3 3 -0.10485760000000000000e7 +2 1 2 2 -0.10485760000000000000e7 +2 1 2 3 -0.52428800000000000000e6 +3 1 1 1 0.10485760000000000000e7 +3 1 2 2 -0.10485760000000000000e7 +3 1 3 3 0.10485760000000000000e7 +3 2 1 1 0.10485760000000000000e7 +4 1 1 2 0.10485760000000000000e7 +4 1 1 3 0.10485760000000000000e7 +*** ANSWER *** +9.999995669872646653e-01 -9.999987009619675238e-01 -8.660253659925441563e-07 0.000000000000000000e+00 +1 1 1 1 3.962767353149487803e-08 +1 1 2 2 4.540467642000610149e-01 +1 1 2 3 -4.540466709859902750e-01 +1 1 3 3 4.540468014726645185e-01 +1 2 1 1 1.048576000000039581e+06 +2 1 1 1 9.999999999999281686e-01 +2 1 2 2 2.500000307927105481e-01 +2 1 2 3 2.499999692072846225e-01 +2 1 3 3 2.500000307927234822e-01 +2 2 1 1 5.333451642288094782e-14 +*** END *** +*** REQUEST *** +"" +4 +2 +3 1 +-0.52428800000000000000e6 -0.52428800000000000000e6 0.10485760000000000000e7 0.0 +0 1 2 2 -0.10485760000000000000e7 +0 1 3 3 0.10485760000000000000e7 +0 2 1 1 -0.10485760000000000000e7 +1 1 2 3 -0.52428800000000000000e6 +1 1 3 3 -0.10485760000000000000e7 +2 1 2 2 -0.10485760000000000000e7 +2 1 2 3 -0.52428800000000000000e6 +3 1 1 1 0.10485760000000000000e7 +3 1 2 2 0.10485760000000000000e7 +3 1 3 3 -0.10485760000000000000e7 +3 2 1 1 0.10485760000000000000e7 +4 1 1 2 0.10485760000000000000e7 +4 1 1 3 0.10485760000000000000e7 +*** ANSWER *** +-9.999998331245307792e-01 9.999999443745658523e-01 -1.112500350952176353e-07 0.000000000000000000e+00 +1 1 1 1 1.642036506765975901e-11 +1 1 2 2 5.832749536206643937e-02 +1 1 2 3 -5.832705836608864658e-02 +1 1 3 3 5.832662143581340830e-02 +1 2 1 1 1.048576000000000000e+06 +2 1 1 1 9.999999999999996669e-01 +2 1 2 2 2.499998068521827044e-01 +2 1 2 3 2.500000893194189722e-01 +2 1 3 3 2.500003721368480036e-01 +2 2 1 1 2.465190328815661892e-32 +*** END *** +*** REQUEST *** +"" +1 +5 +1 1 1 1 1 +0.10485760000000000000e7 +0 1 1 1 0.10485760000000000000e7 +1 2 1 1 0.10485760000000000000e7 +1 4 1 1 0.10485760000000000000e7 +*** ANSWER *** +Infeasible +*** END *** +*** REQUEST *** +"" +13 +11 +5 1 1 1 1 1 1 1 1 1 1 +0.15728640000000000000e7 -0.10485760000000000000e7 -0.10485760000000000000e7 0.10485760000000000000e7 0.10485760000000000000e7 0.10485760000000000000e7 0.0 0.10485760000000000000e7 0.10485760000000000000e7 0.0 0.10485760000000000000e7 0.10485760000000000000e7 0.10485760000000000000e7 +0 1 1 1 0.52428800000000000000e6 +1 1 4 4 0.10485760000000000000e7 +1 6 1 1 0.52428800000000000000e6 +2 1 1 2 0.52428800000000000000e6 +2 1 2 3 0.52428800000000000000e6 +2 4 1 1 -0.10485760000000000000e7 +3 1 1 4 0.52428800000000000000e6 +3 8 1 1 -0.10485760000000000000e7 +4 1 2 2 0.52428800000000000000e6 +4 6 1 1 0.52428800000000000000e6 +5 1 2 4 0.52428800000000000000e6 +5 9 1 1 0.10485760000000000000e7 +6 1 3 3 0.52428800000000000000e6 +6 6 1 1 0.52428800000000000000e6 +7 1 4 4 -0.52428800000000000000e6 +7 1 5 5 0.52428800000000000000e6 +8 1 2 3 -0.26214400000000000000e6 +8 2 1 1 0.52428800000000000000e6 +8 4 1 1 0.52428800000000000000e6 +9 1 1 1 0.52428800000000000000e6 +9 1 1 3 0.26214400000000000000e6 +9 3 1 1 0.52428800000000000000e6 +10 1 2 3 0.26214400000000000000e6 +10 4 1 1 -0.52428800000000000000e6 +10 5 1 1 0.52428800000000000000e6 +11 4 1 1 0.52428800000000000000e6 +11 7 1 1 0.52428800000000000000e6 +12 1 3 4 0.26214400000000000000e6 +12 8 1 1 0.52428800000000000000e6 +12 10 1 1 0.52428800000000000000e6 +13 9 1 1 0.52428800000000000000e6 +13 11 1 1 0.52428800000000000000e6 +*** ANSWER *** +1.491607500493158475e-10 -2.946260586897868525e-25 1.192686814972796844e-10 1.574303654274453910e-11 2.080232249849451083e-24 1.170819464678145350e+00 1.458414260046146013e-10 4.060381611148327209e-10 1.447214523119946250e+00 4.060381611148343752e-10 4.060381611148294122e-10 4.928738059904181593e-10 4.060381611148277578e-10 +1 1 1 1 2.344692080938835279e+05 +1 1 1 2 -1.544689070583509693e-19 +1 1 1 3 3.793786039487551898e+05 +1 1 1 4 6.253113848484577117e-05 +1 1 2 2 2.046271191861112615e-04 +1 1 2 3 3.810179772744665476e-19 +1 1 2 4 1.090640805809069009e-18 +1 1 3 3 6.138465956935486756e+05 +1 1 3 4 1.292039109975521780e-04 +1 1 4 4 2.763167071297943644e-04 +1 1 5 5 2.728361436002968432e-04 +1 2 1 1 4.092541694577598449e-04 +1 3 1 1 7.587572080938835861e+05 +1 4 1 1 4.092541694577598449e-04 +1 5 1 1 4.092541694577633143e-04 +1 6 1 1 6.138465957800056785e+05 +1 7 1 1 4.092541694577598449e-04 +1 8 1 1 3.297187790686018430e-04 +1 9 1 1 4.092541694577598449e-04 +1 10 1 1 4.547810560382933853e-04 +1 11 1 1 4.092541694577598449e-04 +2 1 1 1 5.236067975094374383e+00 +2 1 1 2 -4.180129510443609950e-16 +2 1 1 3 -3.236067975651311546e+00 +2 1 1 4 5.031018360597926398e-01 +2 1 2 2 1.999999999311909527e+00 +2 1 2 3 2.583501648248632324e-16 +2 1 2 4 5.150626177396930724e-17 +2 1 3 3 1.999999999311873555e+00 +2 1 3 4 -3.109408375486479303e-01 +2 1 4 4 1.499999999655955429e+00 +2 1 5 5 1.499999999655954985e+00 +2 2 1 1 1.000000000000000222e+00 +2 3 1 1 5.567308407420794632e-10 +2 4 1 1 1.000000000000000000e+00 +2 5 1 1 9.999999999999996669e-01 +2 6 1 1 6.880904095754841013e-10 +2 7 1 1 1.000000000000000000e+00 +2 8 1 1 1.503101836059808738e+00 +2 9 1 1 9.999999999999998890e-01 +2 10 1 1 8.078390014888369164e-01 +2 11 1 1 1.000000000000000222e+00 +*** END *** +*** REQUEST *** +"" +1 +5 +1 1 1 1 1 +0.15728640000000000000e7 +0 1 1 1 0.10485760000000000000e7 +1 1 1 1 0.10485760000000000000e7 +1 2 1 1 0.10485760000000000000e7 +1 5 1 1 0.10485760000000000000e7 +*** ANSWER *** +1.000000001957216389e+00 +1 1 1 1 3.452177815527975729e-03 +1 2 1 1 1.048576003452177858e+06 +1 3 1 1 1.399887753448717312e-03 +1 4 1 1 1.399887753448717312e-03 +1 5 1 1 1.048576003452177858e+06 +2 1 1 1 1.499999999999996891e+00 +2 2 1 1 1.625838482485675356e-15 +2 3 1 1 2.922314168167987170e+00 +2 4 1 1 2.922314168167987170e+00 +2 5 1 1 1.625838482485675356e-15 +*** END *** +*** REQUEST *** +"" +10 +8 +5 1 1 1 1 1 1 1 +0.26214400000000000000e6 0.78643200000000000000e6 -0.52428800000000000000e6 -0.52428800000000000000e6 0.0 -0.52428800000000000000e6 0.10485760000000000000e7 0.0 -0.26214400000000000000e6 0.52428800000000000000e6 +0 1 3 3 -0.10485760000000000000e7 +0 1 4 4 0.52428800000000000000e6 +0 2 1 1 -0.52428800000000000000e6 +1 1 3 3 0.10485760000000000000e7 +1 1 4 4 -0.52428800000000000000e6 +2 1 1 1 0.52428800000000000000e6 +2 1 3 3 0.10485760000000000000e7 +2 1 4 4 -0.52428800000000000000e6 +2 2 1 1 0.52428800000000000000e6 +3 1 1 2 0.52428800000000000000e6 +3 4 1 1 -0.10485760000000000000e7 +4 1 1 3 0.52428800000000000000e6 +4 6 1 1 -0.10485760000000000000e7 +5 1 2 2 0.52428800000000000000e6 +5 1 4 4 -0.52428800000000000000e6 +6 1 2 3 0.52428800000000000000e6 +6 8 1 1 -0.10485760000000000000e7 +7 1 2 4 0.52428800000000000000e6 +7 4 1 1 0.10485760000000000000e7 +7 5 1 1 0.10485760000000000000e7 +8 1 3 3 -0.52428800000000000000e6 +8 1 5 5 0.52428800000000000000e6 +9 1 1 4 0.26214400000000000000e6 +9 1 3 3 -0.10485760000000000000e7 +9 1 4 4 0.52428800000000000000e6 +9 2 1 1 -0.52428800000000000000e6 +9 3 1 1 0.52428800000000000000e6 +10 1 3 4 0.26214400000000000000e6 +10 6 1 1 0.52428800000000000000e6 +10 7 1 1 0.52428800000000000000e6 +*** ANSWER *** +-9.999999995891341031e-01 -3.803473486621178888e-10 -6.700393916482747952e-12 -5.428871525357892679e-12 4.357318402697323595e-11 1.224368895784648765e-10 -1.397522156751196915e-10 -1.881197163293053418e-10 1.961501144259765512e-10 -2.678331179220082914e-10 +1 1 1 1 6.945594704874666694e-05 +1 1 1 2 -3.512936125684906958e-06 +1 1 1 3 -2.846292194286838837e-06 +1 1 1 4 5.141957559608319704e-05 +1 1 2 2 2.917123952912454438e-04 +1 1 2 3 6.419219196331419318e-05 +1 1 2 4 -7.327040965187715284e-05 +1 1 3 3 1.938191092966602865e-04 +1 1 3 4 -7.021084486454694153e-05 +1 1 4 4 3.328611961756211546e-04 +1 1 5 5 1.702385879492527253e-04 +1 2 1 1 5.242879999666168005e+05 +1 3 1 1 3.717066489762766573e-04 +1 4 1 1 1.293525507317268286e-04 +1 5 1 1 1.223266784803576923e-04 +1 6 1 1 1.341383924435904373e-04 +1 7 1 1 1.284458080550170307e-04 +1 8 1 1 1.404831138574836116e-04 +2 1 1 1 9.999999999048130306e-01 +2 1 1 2 -9.791805858089613901e-02 +2 1 1 3 -7.495940148985721918e-02 +2 1 1 4 -1.761119473870640384e-01 +2 1 2 2 2.862965238970243131e-01 +2 1 2 3 -6.789572938328512774e-02 +2 1 2 4 1.173483178028186941e-01 +2 1 3 3 3.931482619485121011e-01 +2 1 3 4 1.011591097635078512e-01 +2 1 4 4 2.862965238970242576e-01 +2 1 5 5 3.931482619485121566e-01 +2 2 1 1 9.518727013297796622e-11 +2 3 1 1 1.761119474822513409e-01 +2 4 1 1 4.020819414191039165e-01 +2 5 1 1 4.805697407780772368e-01 +2 6 1 1 4.250405985101427531e-01 +2 7 1 1 4.738002917263492431e-01 +2 8 1 1 4.321042706167148584e-01 +*** END *** +*** REQUEST *** +"" +10 +8 +5 1 1 1 1 1 1 1 +0.26214400000000000000e6 0.26214400000000000000e6 -0.52428800000000000000e6 -0.52428800000000000000e6 0.0 -0.52428800000000000000e6 0.10485760000000000000e7 0.0 0.26214400000000000000e6 0.52428800000000000000e6 +0 1 3 3 0.10485760000000000000e7 +0 1 4 4 -0.52428800000000000000e6 +0 2 1 1 -0.52428800000000000000e6 +1 1 3 3 0.10485760000000000000e7 +1 1 4 4 -0.52428800000000000000e6 +2 1 1 1 0.52428800000000000000e6 +2 1 3 3 -0.10485760000000000000e7 +2 1 4 4 0.52428800000000000000e6 +2 2 1 1 0.52428800000000000000e6 +3 1 1 2 0.52428800000000000000e6 +3 4 1 1 -0.10485760000000000000e7 +4 1 1 3 0.52428800000000000000e6 +4 6 1 1 -0.10485760000000000000e7 +5 1 2 2 0.52428800000000000000e6 +5 1 4 4 -0.52428800000000000000e6 +6 1 2 3 0.52428800000000000000e6 +6 8 1 1 -0.10485760000000000000e7 +7 1 2 4 0.52428800000000000000e6 +7 4 1 1 0.10485760000000000000e7 +7 5 1 1 0.10485760000000000000e7 +8 1 3 3 -0.52428800000000000000e6 +8 1 5 5 0.52428800000000000000e6 +9 1 1 4 0.26214400000000000000e6 +9 1 3 3 0.10485760000000000000e7 +9 1 4 4 -0.52428800000000000000e6 +9 2 1 1 -0.52428800000000000000e6 +9 3 1 1 0.52428800000000000000e6 +10 1 3 4 0.26214400000000000000e6 +10 6 1 1 0.52428800000000000000e6 +10 7 1 1 0.52428800000000000000e6 +*** ANSWER *** +9.999999992578435526e-01 -3.803621179669960753e-10 -6.700611093044749451e-12 -5.429040383980874669e-12 4.357544632633943844e-11 1.224427165113750327e-10 -1.397590492693696129e-10 -1.881286560854844638e-10 1.961553626130812178e-10 -2.678452895980398204e-10 +1 1 1 1 6.945800898995211844e-05 +1 1 1 2 -3.513049988750245600e-06 +1 1 1 3 -2.846380724836564818e-06 +1 1 1 4 5.142095137684356276e-05 +1 1 2 2 2.917233866981758933e-04 +1 1 2 3 6.419524695431579314e-05 +1 1 2 4 -7.327399242333925561e-05 +1 1 3 3 1.938259237923606500e-04 +1 1 3 4 -7.021403559638855069e-05 +1 1 4 4 3.328737160779339510e-04 +1 1 5 5 1.702437062528860783e-04 +1 2 1 1 5.242879999666161020e+05 +1 3 1 1 3.717192058483196823e-04 +1 4 1 1 1.293554182254532357e-04 +1 5 1 1 1.223293182479527445e-04 +1 6 1 1 1.341419933515285851e-04 +1 7 1 1 1.284492319018545881e-04 +1 8 1 1 1.404868091860003200e-04 +2 1 1 1 9.999999999048114763e-01 +2 1 1 2 -9.791875554850019980e-02 +2 1 1 3 -7.495921678613150230e-02 +2 1 1 4 -1.761120526754002824e-01 +2 1 2 2 2.862954232683553313e-01 +2 1 2 3 -6.789625167944521311e-02 +2 1 2 4 1.173501309850062402e-01 +2 1 3 3 3.931477116341772216e-01 +2 1 3 4 1.011600384885519704e-01 +2 1 4 4 2.862954232683553313e-01 +2 1 5 5 3.931477116341773326e-01 +2 2 1 1 9.518835915348206933e-11 +2 3 1 1 1.761120527705894168e-01 +2 4 1 1 4.020812444514997308e-01 +2 5 1 1 4.805686245634940290e-01 +2 6 1 1 4.250407832138684561e-01 +2 7 1 1 4.737991782975795041e-01 +2 8 1 1 4.321037483205548702e-01 +*** END *** +*** REQUEST *** +"" +13 +11 +5 1 1 1 1 1 1 1 1 1 1 +0.15728640000000000000e7 -0.10485760000000000000e7 -0.10485760000000000000e7 0.10485760000000000000e7 0.10485760000000000000e7 0.10485760000000000000e7 0.0 0.10485760000000000000e7 0.10485760000000000000e7 0.0 0.10485760000000000000e7 0.10485760000000000000e7 0.10485760000000000000e7 +0 1 1 1 0.52428800000000000000e6 +1 1 4 4 0.10485760000000000000e7 +1 6 1 1 0.52428800000000000000e6 +2 1 1 2 0.52428800000000000000e6 +2 1 2 3 -0.52428800000000000000e6 +2 4 1 1 -0.10485760000000000000e7 +3 1 1 4 0.52428800000000000000e6 +3 8 1 1 -0.10485760000000000000e7 +4 1 2 2 0.52428800000000000000e6 +4 6 1 1 0.52428800000000000000e6 +5 1 2 4 0.52428800000000000000e6 +5 9 1 1 0.10485760000000000000e7 +6 1 3 3 0.52428800000000000000e6 +6 6 1 1 0.52428800000000000000e6 +7 1 4 4 -0.52428800000000000000e6 +7 1 5 5 0.52428800000000000000e6 +8 1 2 3 0.26214400000000000000e6 +8 2 1 1 0.52428800000000000000e6 +8 4 1 1 0.52428800000000000000e6 +9 1 1 1 0.52428800000000000000e6 +9 1 1 3 -0.26214400000000000000e6 +9 3 1 1 0.52428800000000000000e6 +10 1 2 3 -0.26214400000000000000e6 +10 4 1 1 -0.52428800000000000000e6 +10 5 1 1 0.52428800000000000000e6 +11 4 1 1 0.52428800000000000000e6 +11 7 1 1 0.52428800000000000000e6 +12 1 3 4 -0.26214400000000000000e6 +12 8 1 1 0.52428800000000000000e6 +12 10 1 1 0.52428800000000000000e6 +13 9 1 1 0.52428800000000000000e6 +13 11 1 1 0.52428800000000000000e6 +*** ANSWER *** +1.492389361104177029e-10 -5.414006260063542034e-26 1.193034345414183999e-10 1.580132269315673874e-11 -3.822602920229432166e-25 1.170819464637501417e+00 1.459189285079053882e-10 4.061540963088140009e-10 1.447214523160652133e+00 4.061540963088156553e-10 4.061540963088156553e-10 4.930152203813611015e-10 4.061540963088140009e-10 +1 1 1 1 2.344692081152248720e+05 +1 1 1 2 -2.838498514076194326e-20 +1 1 1 3 -3.793786039594259928e+05 +1 1 1 4 6.254935908885117003e-05 +1 1 2 2 2.046573439116062404e-04 +1 1 2 3 -1.807183432951896983e-19 +1 1 2 4 -2.004144839841248531e-19 +1 1 3 3 6.138465956722392002e+05 +1 1 3 4 -1.292409819316515246e-04 +1 1 4 4 2.763577235208210248e-04 +1 1 5 5 2.728764432290099393e-04 +1 2 1 1 4.093146188850118466e-04 +1 3 1 1 7.587572081152248429e+05 +1 4 1 1 4.093146188850118466e-04 +1 5 1 1 4.093146188850118466e-04 +1 6 1 1 6.138465957587677985e+05 +1 7 1 1 4.093146188850118466e-04 +1 8 1 1 3.297561457250566472e-04 +1 9 1 1 4.093146188850135814e-04 +1 10 1 1 4.548548639027594209e-04 +1 11 1 1 4.093146188850118466e-04 +2 1 1 1 5.236067975094174543e+00 +2 1 1 2 -1.034045711543959444e-15 +2 1 1 3 3.236067975651042428e+00 +2 1 1 4 5.031158753095015257e-01 +2 1 2 2 1.999999999311752097e+00 +2 1 2 3 -6.390572893185565781e-16 +2 1 2 4 -2.752195281539649504e-16 +2 1 3 3 1.999999999311723231e+00 +2 1 3 4 3.109495151127604218e-01 +2 1 4 4 1.499999999655875937e+00 +2 1 5 5 1.499999999655876382e+00 +2 2 1 1 1.000000000000000888e+00 +2 3 1 1 5.568581590258357525e-10 +2 4 1 1 9.999999999999995559e-01 +2 5 1 1 9.999999999999991118e-01 +2 6 1 1 6.882477664469128551e-10 +2 7 1 1 1.000000000000000222e+00 +2 8 1 1 1.503115875309488425e+00 +2 9 1 1 1.000000000000000222e+00 +2 10 1 1 8.078336398032637256e-01 +2 11 1 1 9.999999999999994449e-01 +*** END *** +*** REQUEST *** +"" +10 +8 +5 1 1 1 1 1 1 1 +0.26214400000000000000e6 0.78643200000000000000e6 -0.52428800000000000000e6 -0.52428800000000000000e6 0.0 -0.52428800000000000000e6 -0.10485760000000000000e7 0.0 -0.26214400000000000000e6 0.52428800000000000000e6 +0 1 3 3 -0.10485760000000000000e7 +0 1 4 4 0.52428800000000000000e6 +0 2 1 1 -0.52428800000000000000e6 +1 1 3 3 0.10485760000000000000e7 +1 1 4 4 -0.52428800000000000000e6 +2 1 1 1 0.52428800000000000000e6 +2 1 3 3 0.10485760000000000000e7 +2 1 4 4 -0.52428800000000000000e6 +2 2 1 1 0.52428800000000000000e6 +3 1 1 2 0.52428800000000000000e6 +3 4 1 1 -0.10485760000000000000e7 +4 1 1 3 0.52428800000000000000e6 +4 6 1 1 -0.10485760000000000000e7 +5 1 2 2 0.52428800000000000000e6 +5 1 4 4 -0.52428800000000000000e6 +6 1 2 3 0.52428800000000000000e6 +6 8 1 1 -0.10485760000000000000e7 +7 1 2 4 0.52428800000000000000e6 +7 4 1 1 -0.10485760000000000000e7 +7 5 1 1 -0.10485760000000000000e7 +8 1 3 3 -0.52428800000000000000e6 +8 1 5 5 0.52428800000000000000e6 +9 1 1 4 -0.26214400000000000000e6 +9 1 3 3 -0.10485760000000000000e7 +9 1 4 4 0.52428800000000000000e6 +9 2 1 1 -0.52428800000000000000e6 +9 3 1 1 0.52428800000000000000e6 +10 1 3 4 -0.26214400000000000000e6 +10 6 1 1 0.52428800000000000000e6 +10 7 1 1 0.52428800000000000000e6 +*** ANSWER *** +-9.999999995884889525e-01 -3.810702490824998314e-10 -6.736049984565948920e-12 -5.444970347363611579e-12 4.367510600526014834e-11 1.227416529920419783e-10 1.401233411982328640e-10 -1.886161028276272925e-10 1.964405220582090356e-10 -2.684361283113760051e-10 +1 1 1 1 6.957824710356660253e-05 +1 1 1 2 -3.531630174308112227e-06 +1 1 1 3 -2.854732613478573188e-06 +1 1 1 4 -5.149570421442714943e-05 +1 1 2 2 2.922671398318177002e-04 +1 1 2 3 6.435197576389170473e-05 +1 1 2 4 7.346498631013911179e-05 +1 1 3 3 1.941947017891744801e-04 +1 1 3 4 7.036892042005735148e-05 +1 1 4 4 3.335021955722895434e-04 +1 1 5 5 1.704796465352414331e-04 +1 2 1 1 5.242879999665868236e+05 +1 3 1 1 3.723602142833857057e-04 +1 4 1 1 1.295020935828698413e-04 +1 5 1 1 1.224388332342540506e-04 +1 6 1 1 1.343404302413743652e-04 +1 7 1 1 1.286309650144171375e-04 +1 8 1 1 1.406648543267486479e-04 +2 1 1 1 9.999999999048063692e-01 +2 1 1 2 -9.795776109657357289e-02 +2 1 1 3 -7.486293410754249478e-02 +2 1 1 4 1.760544474048320318e-01 +2 1 2 2 2.860583275573886364e-01 +2 1 2 3 -6.792470349951823527e-02 +2 1 2 4 -1.175072693384005135e-01 +2 1 3 3 3.930291637786945125e-01 +2 1 3 4 -1.012001156063697394e-01 +2 1 4 4 2.860583275573886919e-01 +2 1 5 5 3.930291637786945680e-01 +2 2 1 1 9.519245368151487941e-11 +2 3 1 1 1.760544475000250519e-01 +2 4 1 1 4.020422389034264410e-01 +2 5 1 1 4.804504917581729484e-01 +2 6 1 1 4.251370658924574775e-01 +2 7 1 1 4.736628185011726999e-01 +2 8 1 1 4.320752965004817647e-01 +*** END *** +*** REQUEST *** +"" +10 +8 +5 1 1 1 1 1 1 1 +0.26214400000000000000e6 0.26214400000000000000e6 -0.52428800000000000000e6 -0.52428800000000000000e6 0.0 -0.52428800000000000000e6 -0.10485760000000000000e7 0.0 0.26214400000000000000e6 0.52428800000000000000e6 +0 1 3 3 0.10485760000000000000e7 +0 1 4 4 -0.52428800000000000000e6 +0 2 1 1 -0.52428800000000000000e6 +1 1 3 3 0.10485760000000000000e7 +1 1 4 4 -0.52428800000000000000e6 +2 1 1 1 0.52428800000000000000e6 +2 1 3 3 -0.10485760000000000000e7 +2 1 4 4 0.52428800000000000000e6 +2 2 1 1 0.52428800000000000000e6 +3 1 1 2 0.52428800000000000000e6 +3 4 1 1 -0.10485760000000000000e7 +4 1 1 3 0.52428800000000000000e6 +4 6 1 1 -0.10485760000000000000e7 +5 1 2 2 0.52428800000000000000e6 +5 1 4 4 -0.52428800000000000000e6 +6 1 2 3 0.52428800000000000000e6 +6 8 1 1 -0.10485760000000000000e7 +7 1 2 4 0.52428800000000000000e6 +7 4 1 1 -0.10485760000000000000e7 +7 5 1 1 -0.10485760000000000000e7 +8 1 3 3 -0.52428800000000000000e6 +8 1 5 5 0.52428800000000000000e6 +9 1 1 4 -0.26214400000000000000e6 +9 1 3 3 0.10485760000000000000e7 +9 1 4 4 -0.52428800000000000000e6 +9 2 1 1 -0.52428800000000000000e6 +9 3 1 1 0.52428800000000000000e6 +10 1 3 4 -0.26214400000000000000e6 +10 6 1 1 0.52428800000000000000e6 +10 7 1 1 0.52428800000000000000e6 +*** ANSWER *** +9.999999992564915230e-01 -3.810695576889143537e-10 -6.735625426342454187e-12 -5.444777627013238453e-12 4.367506358700158526e-11 1.227413030293301348e-10 1.401229005084607075e-10 -1.886153909364574320e-10 1.964397041031435087e-10 -2.684354364726813310e-10 +1 1 1 1 6.957817438412523987e-05 +1 1 1 2 -3.531407583526232621e-06 +1 1 1 3 -2.854631572511516762e-06 +1 1 1 4 -5.149548979241445196e-05 +1 1 2 2 2.922666823836324659e-04 +1 1 2 3 6.435179228264143771e-05 +1 1 2 4 7.346475526177984744e-05 +1 1 3 3 1.941943637436432425e-04 +1 1 3 4 7.036873905869457484e-05 +1 1 4 4 3.335015036236895630e-04 +1 1 5 5 1.704795845624373744e-04 +1 2 1 1 5.242879999665871728e+05 +1 3 1 1 3.723593502305598893e-04 +1 4 1 1 1.295016752892227258e-04 +1 5 1 1 1.224388601221695558e-04 +1 6 1 1 1.343401556733645440e-04 +1 7 1 1 1.286308925283409683e-04 +1 8 1 1 1.406647860804472426e-04 +2 1 1 1 9.999999999048075905e-01 +2 1 1 2 -9.795735713603917483e-02 +2 1 1 3 -7.486315305695728783e-02 +2 1 1 4 1.760541517543041112e-01 +2 1 2 2 2.860587828470143590e-01 +2 1 2 3 -6.792434344894913989e-02 +2 1 2 4 -1.175060159893176470e-01 +2 1 3 3 3.930293914235066244e-01 +2 1 3 4 -1.011994963720127400e-01 +2 1 4 4 2.860587828470145255e-01 +2 1 5 5 3.930293914235067909e-01 +2 2 1 1 9.519167358025126290e-11 +2 3 1 1 1.760541518494961044e-01 +2 4 1 1 4.020426428639607419e-01 +2 5 1 1 4.804513411467217221e-01 +2 6 1 1 4.251368469430427677e-01 +2 7 1 1 4.736636566849445895e-01 +2 8 1 1 4.320756565510509017e-01 +*** END *** +*** REQUEST *** +"" +1 +4 +1 1 1 1 +0.10485760000000000000e7 +0 1 1 1 0.52428800000000000000e6 +1 1 1 1 0.10485760000000000000e7 +1 2 1 1 0.52428800000000000000e6 +1 3 1 1 0.52428800000000000000e6 +*** ANSWER *** +5.000000006943153830e-01 +1 1 1 1 1.290417214877562224e-03 +1 2 1 1 2.621440009263960528e+05 +1 3 1 1 2.621440009263960528e+05 +1 4 1 1 5.623748076465434273e-04 +2 1 1 1 9.999999999999984457e-01 +2 2 1 1 1.665972352747017299e-15 +2 3 1 1 1.665972352747017299e-15 +2 4 1 1 1.637537031929143128e+00 +*** END *** +*** REQUEST *** +"" +1 +4 +1 1 1 1 +0.15728640000000000000e7 +0 1 1 1 0.10485760000000000000e7 +1 1 1 1 0.10485760000000000000e7 +1 2 1 1 0.52428800000000000000e6 +1 3 1 1 0.10485760000000000000e7 +1 4 1 1 -0.10485760000000000000e7 +*** ANSWER *** +Infeasible +*** END *** +*** REQUEST *** +"" +7 +7 +3 1 1 1 1 1 1 +0.10485760000000000000e7 0.52428800000000000000e6 0.26214400000000000000e6 0.10485760000000000000e7 0.13107200000000000000e7 0.52428800000000000000e6 0.52428800000000000000e6 +0 1 1 1 0.10485760000000000000e7 +1 1 2 3 0.52428800000000000000e6 +1 2 1 1 0.52428800000000000000e6 +1 4 1 1 0.52428800000000000000e6 +1 6 1 1 0.10485760000000000000e7 +2 1 1 2 -0.10485760000000000000e7 +2 1 1 3 0.10485760000000000000e7 +2 2 1 1 0.10485760000000000000e7 +3 1 2 2 0.10485760000000000000e7 +3 1 2 3 -0.52428800000000000000e6 +3 6 1 1 -0.52428800000000000000e6 +4 1 2 3 -0.52428800000000000000e6 +4 1 3 3 0.10485760000000000000e7 +4 2 1 1 0.52428800000000000000e6 +4 4 1 1 0.52428800000000000000e6 +5 1 1 1 0.10485760000000000000e7 +5 1 1 2 -0.52428800000000000000e6 +5 2 1 1 0.52428800000000000000e6 +5 3 1 1 0.10485760000000000000e7 +6 1 1 2 -0.52428800000000000000e6 +6 5 1 1 0.10485760000000000000e7 +7 1 1 2 0.52428800000000000000e6 +7 1 2 3 -0.52428800000000000000e6 +7 7 1 1 0.10485760000000000000e7 +*** ANSWER *** +9.999999985586283113e-01 -9.282233207833762598e-10 2.416410040619999275e-09 7.287384010613641448e-10 1.000000001150653572e+00 -1.678412777448631064e-10 9.999999957510178339e-01 +1 1 1 1 2.123588660274164375e-03 +1 1 1 2 -1.769654364154091275e-03 +1 1 1 3 -9.733126968137495449e-04 +1 1 2 2 3.450830535535617805e-03 +1 1 2 3 -1.769670706440063662e-04 +1 1 3 3 1.681178558413772006e-03 +1 2 1 1 1.048576000173377106e+06 +1 3 1 1 1.048576002123588696e+06 +1 4 1 1 5.242880005434158957e+05 +1 5 1 1 7.410466251298562790e-04 +1 6 1 1 1.048575998138758354e+06 +1 7 1 1 1.048575996461660252e+06 +2 1 1 1 2.749999992995243225e+00 +2 1 1 2 1.499999995096669370e+00 +2 1 1 3 1.749999994396194358e+00 +2 1 2 2 1.249999997198100399e+00 +2 1 2 3 9.999999964976236111e-01 +2 1 3 3 1.999999994396199687e+00 +2 2 1 1 1.400950902881645464e-09 +2 3 1 1 1.400951113825400542e-09 +2 4 1 1 2.801898309253689249e-09 +2 5 1 1 1.999999995096668037e+00 +2 6 1 1 1.400952195814864889e-09 +2 7 1 1 1.400955085529339772e-09 +*** END *** +*** REQUEST *** +"" +1 +4 +1 1 1 1 +-0.10485760000000000000e7 +0 1 1 1 0.52428800000000000000e6 +1 1 1 1 0.52428800000000000000e6 +1 2 1 1 -0.52428800000000000000e6 +1 3 1 1 0.52428800000000000000e6 +1 4 1 1 -0.10485760000000000000e7 +*** ANSWER *** +Infeasible +*** END *** +*** REQUEST *** +"" +7 +7 +3 1 1 1 1 1 1 +-0.15728640000000000000e7 0.52428800000000000000e6 -0.52428800000000000000e6 0.78643200000000000000e6 0.10485760000000000000e7 0.78643200000000000000e6 0.26214400000000000000e6 +0 1 1 1 0.10485760000000000000e7 +1 1 2 3 -0.52428800000000000000e6 +1 2 1 1 -0.10485760000000000000e7 +1 4 1 1 -0.10485760000000000000e7 +1 6 1 1 -0.10485760000000000000e7 +2 1 1 2 -0.52428800000000000000e6 +2 1 1 3 0.10485760000000000000e7 +2 2 1 1 0.10485760000000000000e7 +3 1 2 2 0.10485760000000000000e7 +3 1 2 3 -0.10485760000000000000e7 +3 2 1 1 -0.10485760000000000000e7 +3 4 1 1 -0.10485760000000000000e7 +4 1 2 3 -0.26214400000000000000e6 +4 1 3 3 0.10485760000000000000e7 +4 6 1 1 0.52428800000000000000e6 +5 1 1 1 0.10485760000000000000e7 +5 1 1 2 -0.52428800000000000000e6 +5 3 1 1 0.10485760000000000000e7 +6 1 1 2 -0.26214400000000000000e6 +6 2 1 1 0.52428800000000000000e6 +6 5 1 1 0.10485760000000000000e7 +7 1 1 2 0.26214400000000000000e6 +7 1 2 3 -0.52428800000000000000e6 +7 2 1 1 -0.52428800000000000000e6 +7 7 1 1 0.10485760000000000000e7 +*** ANSWER *** +-2.122682326267485209e+00 7.752558743508156103e-02 1.165856920741376257e+00 9.814639206878961880e-03 1.612372975707343281e+00 -5.204790215550311268e-10 3.519523024615122119e-08 +1 1 1 1 6.421196079141121591e+05 +1 1 1 2 -8.859935285101566697e+05 +1 1 1 3 8.129147037032808294e+04 +1 1 2 2 1.222489589062118437e+06 +1 1 2 3 -1.121655822818670131e+05 +1 1 3 3 1.029139765980135235e+04 +1 2 1 1 1.084595610608764226e+06 +1 3 1 1 1.690695607914112275e+06 +1 4 1 1 1.003304158963754307e+06 +1 5 1 1 1.993047227803988741e-03 +1 6 1 1 2.230939443047560286e+06 +1 7 1 1 3.944368278889842649e-02 +2 1 1 1 4.259591772956758504e+00 +2 1 1 2 3.259591775595432228e+00 +2 1 1 3 1.879795885741197825e+00 +2 1 2 2 2.499999987441589688e+00 +2 1 2 3 1.499999989441199277e+00 +2 1 3 3 1.499999993720805946e+00 +2 2 1 1 4.113025632613441975e-09 +2 3 1 1 2.638667510379978050e-09 +2 4 1 1 4.446179952225849587e-09 +2 5 1 1 2.379795885741203598e+00 +2 6 1 1 1.999588384178727381e-09 +2 7 1 1 1.202041036999986628e-01 +*** END *** +*** REQUEST *** +"" +1 +4 +1 1 1 1 +0.15728640000000000000e7 +0 1 1 1 0.52428800000000000000e6 +1 1 1 1 0.10485760000000000000e7 +1 2 1 1 0.52428800000000000000e6 +1 3 1 1 0.52428800000000000000e6 +1 4 1 1 -0.52428800000000000000e6 +*** ANSWER *** +Infeasible +*** END *** +*** REQUEST *** +"" +7 +7 +3 1 1 1 1 1 1 +0.10485760000000000000e7 0.10485760000000000000e7 0.78643200000000000000e6 0.52428800000000000000e6 -0.52428800000000000000e6 0.78643200000000000000e6 -0.26214400000000000000e6 +0 1 1 2 -0.39321600000000000000e6 +0 1 2 3 -0.13107200000000000000e6 +0 2 1 1 -0.78643200000000000000e6 +0 4 1 1 -0.26214400000000000000e6 +0 6 1 1 -0.52428800000000000000e6 +1 1 1 1 0.52428800000000000000e6 +1 1 1 2 0.39321600000000000000e6 +1 1 2 3 0.13107200000000000000e6 +1 2 1 1 0.78643200000000000000e6 +1 4 1 1 0.26214400000000000000e6 +1 6 1 1 0.52428800000000000000e6 +2 1 1 2 0.26214400000000000000e6 +2 1 1 3 0.52428800000000000000e6 +2 1 2 3 0.26214400000000000000e6 +2 2 1 1 0.52428800000000000000e6 +2 4 1 1 0.52428800000000000000e6 +2 6 1 1 0.10485760000000000000e7 +3 1 1 2 0.26214400000000000000e6 +3 1 2 2 0.52428800000000000000e6 +3 1 2 3 -0.26214400000000000000e6 +3 2 1 1 0.52428800000000000000e6 +3 4 1 1 0.52428800000000000000e6 +4 1 1 2 0.13107200000000000000e6 +4 1 2 3 -0.13107200000000000000e6 +4 1 3 3 0.52428800000000000000e6 +4 2 1 1 0.26214400000000000000e6 +4 4 1 1 0.26214400000000000000e6 +5 1 1 2 -0.65536000000000000000e6 +5 1 2 3 -0.13107200000000000000e6 +5 2 1 1 -0.78643200000000000000e6 +5 3 1 1 0.52428800000000000000e6 +5 4 1 1 -0.26214400000000000000e6 +5 6 1 1 -0.52428800000000000000e6 +6 1 1 2 0.13107200000000000000e6 +6 1 2 3 0.13107200000000000000e6 +6 2 1 1 0.26214400000000000000e6 +6 4 1 1 0.26214400000000000000e6 +6 5 1 1 0.52428800000000000000e6 +6 6 1 1 0.52428800000000000000e6 +7 1 1 2 -0.13107200000000000000e6 +7 1 2 3 -0.39321600000000000000e6 +7 2 1 1 -0.26214400000000000000e6 +7 4 1 1 -0.26214400000000000000e6 +7 6 1 1 -0.52428800000000000000e6 +7 7 1 1 0.52428800000000000000e6 +*** ANSWER *** +-7.608360275419644920e-10 -7.798072457369716546e-11 -8.013859884436968844e-10 -7.171668043536295414e-10 5.714285702070482920e-01 -7.988172012271727674e-10 1.428571434699175968e-01 +1 1 1 1 5.560274682077934530e-05 +1 1 1 2 -8.176870375087877353e-06 +1 1 1 3 -4.088435812529453948e-05 +1 1 2 2 3.434288891953024645e-05 +1 1 2 3 -1.635386148034894142e-06 +1 1 3 3 7.849799650774358199e-05 +1 2 1 1 2.995931426548591116e+05 +1 3 1 1 2.995931426712128450e+05 +1 4 1 1 7.489828527046926320e+04 +1 5 1 1 3.568967323170778479e-05 +1 6 1 1 1.497965713027546590e+05 +1 7 1 1 7.489828649005611078e+04 +2 1 1 1 1.357142856728937641e+00 +2 1 1 2 3.571428568738232445e-01 +2 1 1 3 7.142857137476383844e-01 +2 1 2 2 1.357142856728940306e+00 +2 1 2 3 2.142857143271021947e-01 +2 1 3 3 9.285714283644747047e-01 +2 2 1 1 1.448673344637826035e-10 +2 3 1 1 1.448673288269433621e-10 +2 4 1 1 5.794697349261452038e-10 +2 5 1 1 1.214285713747635498e+00 +2 6 1 1 2.897347029504898006e-10 +2 7 1 1 5.794683254243045175e-10 +*** END *** +*** REQUEST *** +"" +5 +5 +3 1 1 1 1 +0.10485760000000000000e7 -0.10485760000000000000e7 -0.52428800000000000000e6 0.0 0.10485760000000000000e7 +0 2 1 1 -0.52428800000000000000e6 +1 1 1 1 0.52428800000000000000e6 +1 2 1 1 0.52428800000000000000e6 +2 1 1 2 0.52428800000000000000e6 +2 4 1 1 -0.10485760000000000000e7 +3 1 2 2 -0.10485760000000000000e7 +3 1 3 3 0.52428800000000000000e6 +4 1 1 3 -0.26214400000000000000e6 +4 2 1 1 -0.52428800000000000000e6 +4 3 1 1 0.52428800000000000000e6 +5 1 2 3 -0.26214400000000000000e6 +5 4 1 1 0.52428800000000000000e6 +5 5 1 1 0.52428800000000000000e6 +*** ANSWER *** +-4.457229613295930973e-10 6.115897346811394566e-17 1.833869924093994424e-10 -3.451031505601001684e-16 -4.457225765264029824e-10 +1 1 1 1 1.376100633449915924e-10 +1 1 1 2 3.206491588165052434e-11 +1 1 1 3 9.046672030042689854e-11 +1 1 2 2 4.139213860695481126e-05 +1 1 2 3 1.168434991009373834e-04 +1 1 3 3 3.298349370359715885e-04 +1 2 1 1 5.242880000000003492e+05 +1 3 1 1 2.336871566261909672e-04 +1 4 1 1 2.752279266958520360e-10 +1 5 1 1 3.393577580175436896e-10 +2 1 1 1 2.000000000038513637e+00 +2 1 1 2 1.679352122297247312e-04 +2 1 1 3 2.183096486070790850e-06 +2 1 2 2 5.333764953618103100e-01 +2 1 2 3 -1.886894755874139185e-01 +2 1 3 3 6.675299065681922217e-02 +2 2 1 1 5.248430535658322443e-16 +2 3 1 1 2.183106356807534618e-06 +2 4 1 1 1.000167935332526570e+00 +2 5 1 1 8.111425888609598012e-01 +*** END *** diff --git a/test-suite/failure/circular_subtyping1.v b/test-suite/failure/circular_subtyping1.v new file mode 100644 index 00000000..0b3a8688 --- /dev/null +++ b/test-suite/failure/circular_subtyping1.v @@ -0,0 +1,7 @@ +(* subtyping verification in presence of pseudo-circularity*) +Module Type S. End S. +Module Type T. Declare Module M:S. End T. + +Module N:S. End N. +Module NN <: T. Module M:=N. End NN. +Module P <: T with Module M:=NN := NN. diff --git a/test-suite/failure/circular_subtyping2.v b/test-suite/failure/circular_subtyping2.v new file mode 100644 index 00000000..3bacdc65 --- /dev/null +++ b/test-suite/failure/circular_subtyping2.v @@ -0,0 +1,8 @@ +(*subtyping verification in presence of pseudo-circularity at functor application *) +Module Type S. End S. +Module Type T. Declare Module M:S. End T. +Module N:S. End N. + +Module F (X:S) (Y:T with Module M:=X). End F. + +Module G := F N N. \ No newline at end of file diff --git a/test-suite/failure/fixpoint2.v b/test-suite/failure/fixpoint2.v new file mode 100644 index 00000000..d2f02ea1 --- /dev/null +++ b/test-suite/failure/fixpoint2.v @@ -0,0 +1,6 @@ +(* Check Guard in proofs *) + +Goal nat->nat. +fix f 1. +intro n; apply f; assumption. +Guarded. diff --git a/test-suite/failure/guard.v b/test-suite/failure/guard.v new file mode 100644 index 00000000..46208c29 --- /dev/null +++ b/test-suite/failure/guard.v @@ -0,0 +1,10 @@ +(************************************************************************) +(* v * The Coq Proof Assistant / The Coq Development Team *) +(* phi(x)) t" with "t" not rewritable used to behave as a + beta-normalization tactic instead of raising the expected message + "nothing to rewrite" *) + +Goal forall b, S b = O -> (fun a => 0 = (S a)) b -> True. + intros b H H0. + rewrite H in H0. diff --git a/test-suite/failure/subtyping.v b/test-suite/failure/subtyping.v new file mode 100644 index 00000000..35fd2036 --- /dev/null +++ b/test-suite/failure/subtyping.v @@ -0,0 +1,21 @@ +(* A variant of bug #1302 that must fail *) + +Module Type T. + + Parameter A : Type. + + Inductive L : Prop := + | L0 + | L1 : (A -> Prop) -> L. + +End T. + +Module TT : T. + + Parameter A : Type. + + Inductive L : Type := + | L0 + | L1 : (A -> Prop) -> L. + +End TT. diff --git a/test-suite/failure/subtyping2.v b/test-suite/failure/subtyping2.v new file mode 100644 index 00000000..0a75ae45 --- /dev/null +++ b/test-suite/failure/subtyping2.v @@ -0,0 +1,245 @@ +(* Check that no constraints on inductive types disappear at subtyping *) + +Module Type S. + +Record A0 : Type := (* Type_i' *) + i0 {X0 : Type; R0 : X0 -> X0 -> Prop}. (* X0: Type_j' *) + +Variable i0' : forall X0 : Type, (X0 -> X0 -> Prop) -> A0. + +End S. + +Module M. + +Record A0 : Type := (* Type_i' *) + i0 {X0 : Type; R0 : X0 -> X0 -> Prop}. (* X0: Type_j' *) + +Definition i0' := i0 : forall X0 : Type, (X0 -> X0 -> Prop) -> A0. + +End M. + +(* The rest of this file formalizes Burali-Forti paradox *) +(* (if the constraint between i0' and A0 is lost, the proof goes through) *) + + Inductive ACC (A : Type) (R : A -> A -> Prop) : A -> Prop := + ACC_intro : + forall x : A, (forall y : A, R y x -> ACC A R y) -> ACC A R x. + + Lemma ACC_nonreflexive : + forall (A : Type) (R : A -> A -> Prop) (x : A), + ACC A R x -> R x x -> False. +simple induction 1; intros. +exact (H1 x0 H2 H2). +Qed. + + Definition WF (A : Type) (R : A -> A -> Prop) := forall x : A, ACC A R x. + + +Section Inverse_Image. + + Variables (A B : Type) (R : B -> B -> Prop) (f : A -> B). + + Definition Rof (x y : A) : Prop := R (f x) (f y). + + Remark ACC_lemma : + forall y : B, ACC B R y -> forall x : A, y = f x -> ACC A Rof x. + simple induction 1; intros. + constructor; intros. + apply (H1 (f y0)); trivial. + elim H2 using eq_ind_r; trivial. + Qed. + + Lemma ACC_inverse_image : forall x : A, ACC B R (f x) -> ACC A Rof x. + intros; apply (ACC_lemma (f x)); trivial. + Qed. + + Lemma WF_inverse_image : WF B R -> WF A Rof. + red in |- *; intros; apply ACC_inverse_image; auto. + Qed. + +End Inverse_Image. + +Section Burali_Forti_Paradox. + + Definition morphism (A : Type) (R : A -> A -> Prop) + (B : Type) (S : B -> B -> Prop) (f : A -> B) := + forall x y : A, R x y -> S (f x) (f y). + + (* The hypothesis of the paradox: + assumes there exists an universal system of notations, i.e: + - A type A0 + - An injection i0 from relations on any type into A0 + - The proof that i0 is injective modulo morphism + *) + Variable A0 : Type. (* Type_i *) + Variable i0 : forall X : Type, (X -> X -> Prop) -> A0. (* X: Type_j *) + Hypothesis + inj : + forall (X1 : Type) (R1 : X1 -> X1 -> Prop) (X2 : Type) + (R2 : X2 -> X2 -> Prop), + i0 X1 R1 = i0 X2 R2 -> exists f : X1 -> X2, morphism X1 R1 X2 R2 f. + + (* Embedding of x in y: x and y are images of 2 well founded relations + R1 and R2, the ordinal of R2 being strictly greater than that of R1. + *) + Record emb (x y : A0) : Prop := + {X1 : Type; + R1 : X1 -> X1 -> Prop; + eqx : x = i0 X1 R1; + X2 : Type; + R2 : X2 -> X2 -> Prop; + eqy : y = i0 X2 R2; + W2 : WF X2 R2; + f : X1 -> X2; + fmorph : morphism X1 R1 X2 R2 f; + maj : X2; + majf : forall z : X1, R2 (f z) maj}. + + + Lemma emb_trans : forall x y z : A0, emb x y -> emb y z -> emb x z. +intros. +case H; intros. +case H0; intros. +generalize eqx0; clear eqx0. +elim eqy using eq_ind_r; intro. +case (inj _ _ _ _ eqx0); intros. +exists X1 R1 X3 R3 (fun x : X1 => f0 (x0 (f x))) maj0; trivial. +red in |- *; auto. +Defined. + + + Lemma ACC_emb : + forall (X : Type) (R : X -> X -> Prop) (x : X), + ACC X R x -> + forall (Y : Type) (S : Y -> Y -> Prop) (f : Y -> X), + morphism Y S X R f -> (forall y : Y, R (f y) x) -> ACC A0 emb (i0 Y S). +simple induction 1; intros. +constructor; intros. +case H4; intros. +elim eqx using eq_ind_r. +case (inj X2 R2 Y S). +apply sym_eq; assumption. + +intros. +apply H1 with (y := f (x1 maj)) (f := fun x : X1 => f (x1 (f0 x))); + try red in |- *; auto. +Defined. + + (* The embedding relation is well founded *) + Lemma WF_emb : WF A0 emb. +constructor; intros. +case H; intros. +elim eqx using eq_ind_r. +apply ACC_emb with (X := X2) (R := R2) (x := maj) (f := f); trivial. +Defined. + + + (* The following definition enforces Type_j >= Type_i *) + Definition Omega : A0 := i0 A0 emb. + + +Section Subsets. + + Variable a : A0. + + (* We define the type of elements of A0 smaller than a w.r.t embedding. + The Record is in Type, but it is possible to avoid such structure. *) + Record sub : Type := {witness : A0; emb_wit : emb witness a}. + + (* F is its image through i0 *) + Definition F : A0 := i0 sub (Rof _ _ emb witness). + + (* F is embedded in Omega: + - the witness projection is a morphism + - a is an upper bound because emb_wit proves that witness is + smaller than a. + *) + Lemma F_emb_Omega : emb F Omega. +exists sub (Rof _ _ emb witness) A0 emb witness a; trivial. +exact WF_emb. + +red in |- *; trivial. + +exact emb_wit. +Defined. + +End Subsets. + + + Definition fsub (a b : A0) (H : emb a b) (x : sub a) : + sub b := Build_sub _ (witness _ x) (emb_trans _ _ _ (emb_wit _ x) H). + + (* F is a morphism: a < b => F(a) < F(b) + - the morphism from F(a) to F(b) is fsub above + - the upper bound is a, which is in F(b) since a < b + *) + Lemma F_morphism : morphism A0 emb A0 emb F. +red in |- *; intros. +exists + (sub x) + (Rof _ _ emb (witness x)) + (sub y) + (Rof _ _ emb (witness y)) + (fsub x y H) + (Build_sub _ x H); trivial. +apply WF_inverse_image. +exact WF_emb. + +unfold morphism, Rof, fsub in |- *; simpl in |- *; intros. +trivial. + +unfold Rof, fsub in |- *; simpl in |- *; intros. +apply emb_wit. +Defined. + + + (* Omega is embedded in itself: + - F is a morphism + - Omega is an upper bound of the image of F + *) + Lemma Omega_refl : emb Omega Omega. +exists A0 emb A0 emb F Omega; trivial. +exact WF_emb. + +exact F_morphism. + +exact F_emb_Omega. +Defined. + + (* The paradox is that Omega cannot be embedded in itself, since + the embedding relation is well founded. + *) + Theorem Burali_Forti : False. +apply ACC_nonreflexive with A0 emb Omega. +apply WF_emb. + +exact Omega_refl. + +Defined. + +End Burali_Forti_Paradox. + +Import M. + + (* Note: this proof uses a large elimination of A0. *) + Lemma inj : + forall (X1 : Type) (R1 : X1 -> X1 -> Prop) (X2 : Type) + (R2 : X2 -> X2 -> Prop), + i0' X1 R1 = i0' X2 R2 -> exists f : X1 -> X2, morphism X1 R1 X2 R2 f. +intros. +change + match i0' X1 R1, i0' X2 R2 with + | i0 x1 r1, i0 x2 r2 => exists f : _, morphism x1 r1 x2 r2 f + end in |- *. +case H; simpl in |- *. +exists (fun x : X1 => x). +red in |- *; trivial. +Defined. + +(* The following command raises 'Error: Universe Inconsistency'. + To allow large elimination of A0, i0 must not be a large constructor. + Hence, the constraint Type_j' < Type_i' is added, which is incompatible + with the constraint j >= i in the paradox. +*) + + Definition Paradox : False := Burali_Forti A0 i0' inj. diff --git a/test-suite/failure/univ_include.v b/test-suite/failure/univ_include.v new file mode 100644 index 00000000..4be70d88 --- /dev/null +++ b/test-suite/failure/univ_include.v @@ -0,0 +1,30 @@ +Definition T := Type. +Definition U := Type. + +Module Type MT. + Parameter t : T. +End MT. + +Module Type MU. + Parameter t : U. +End MU. + +Module F (E : MT). + Definition elt :T := E.t. +End F. + +Module G (E : MU). + Include F E. +Print Universes. (* U <= T *) +End G. +Print Universes. (* Check if constraint is lost *) + +Module Mt. + Definition t := T. +End Mt. + +Module P := G Mt. (* should yield Universe inconsistency *) +(* ... otherwise the following command will show that T has type T! *) +Eval cbv delta [P.elt Mt.t] in P.elt. + + diff --git a/test-suite/ide/undo.v b/test-suite/ide/undo.v new file mode 100644 index 00000000..60c2e657 --- /dev/null +++ b/test-suite/ide/undo.v @@ -0,0 +1,79 @@ +(* Here are a sequences of scripts to test interactively with undo and + replay in coqide proof sessions *) + +(* Undoing arbitrary commands, as first step *) + +Theorem a : O=O. +Ltac f x := x. +assert True by trivial. +trivial. +Qed. + +(* Undoing arbitrary commands, as non-first step *) + +Theorem b : O=O. +assert True by trivial. +Ltac g x := x. +assert True by trivial. +trivial. +Qed. + +(* Undoing declarations, as first step *) +(* was bugged in 8.1 *) + +Theorem c : O=O. +Inductive T : Type := I. +trivial. +Qed. + +(* Undoing declarations, as first step *) +(* new in 8.2 *) + +Theorem d : O=O. +Definition e := O. +Definition f := O. +assert True by trivial. +trivial. +Qed. + +(* Undoing declarations, as non-first step *) +(* new in 8.2 *) + +Theorem h : O=O. +assert True by trivial. +Definition i := O. +Definition j := O. +assert True by trivial. +trivial. +Qed. + +(* Undoing declarations, interleaved with proof steps *) +(* new in 8.2 *) + +Theorem k : O=O. +assert True by trivial. +Definition l := O. +assert True by trivial. +Definition m := O. +assert True by trivial. +trivial. +Qed. + +(* Undoing declarations, interleaved with proof steps and commands *) +(* new in 8.2 *) + +Theorem n : O=O. +assert True by trivial. +Definition o := O. +Ltac h x := x. +assert True by trivial. +Focus. +Definition p := O. +assert True by trivial. +trivial. +Qed. + +(* Undoing declarations, not in proof *) + +Definition q := O. +Definition r := O. diff --git a/test-suite/ideal-features/Case9.v b/test-suite/ideal-features/Case9.v new file mode 100644 index 00000000..800c431e --- /dev/null +++ b/test-suite/ideal-features/Case9.v @@ -0,0 +1,12 @@ +(* Exemple soumis par Pierre Corbineau (bug #1671) *) + +CoInductive hdlist : unit -> Type := +| cons : hdlist tt -> hdlist tt. + +Variable P : forall bo, hdlist bo -> Prop. +Variable all : forall bo l, P bo l. + +Definition F (l:hdlist tt) : P tt l := +match l in hdlist u return P u l with +| cons (cons l') => all tt _ +end. diff --git a/test-suite/ideal-features/complexity/evars_subst.v b/test-suite/ideal-features/complexity/evars_subst.v new file mode 100644 index 00000000..6f9f86a9 --- /dev/null +++ b/test-suite/ideal-features/complexity/evars_subst.v @@ -0,0 +1,53 @@ +(* Bug report #932 *) +(* Expected time < 1.00s *) + +(* Let n be the number of let-in. The complexity comes from the fact + that each implicit arguments of f was in a larger and larger + context. To compute the type of "let _ := f ?Tn 0 in f ?T 0", + "f ?Tn 0" is substituted in the type of "f ?T 0" which is ?T. This + type is an evar instantiated on the n variables denoting the "f ?Ti 0". + One obtain "?T[1;...;n-1;f ?Tn[1;...;n-1] 0]". To compute the + type of "let _ := f ?Tn-1 0 in let _ := f ?Tn 0 in f ?T 0", another + substitution is done leading to + "?T[1;...;n-2;f ?Tn[1;...;n-2] 0;f ?Tn[1;...;n-2;f ?Tn[1;...;n-2] 0] 0]" + and so on. At the end, we get a term of exponential size *) + +(* A way to cut the complexity could have been to remove the dependency in + anonymous variables in evars but this breaks intuitive behaviour + (see Case15.v); another approach could be to substitute lazily + and/or to simultaneously substitute let binders and evars *) + +Variable P : Set -> Set. +Variable f : forall A : Set, A -> P A. + +Time Check + let _ := f _ 0 in + let _ := f _ 0 in + let _ := f _ 0 in + let _ := f _ 0 in + + let _ := f _ 0 in + let _ := f _ 0 in + let _ := f _ 0 in + let _ := f _ 0 in + + let _ := f _ 0 in + let _ := f _ 0 in + let _ := f _ 0 in + let _ := f _ 0 in + let _ := f _ 0 in + + let _ := f _ 0 in + let _ := f _ 0 in + let _ := f _ 0 in + let _ := f _ 0 in + let _ := f _ 0 in + + let _ := f _ 0 in + let _ := f _ 0 in + let _ := f _ 0 in + let _ := f _ 0 in + let _ := f _ 0 in + + f _ 0. + diff --git a/test-suite/ideal-features/evars_subst.v b/test-suite/ideal-features/evars_subst.v new file mode 100644 index 00000000..6f9f86a9 --- /dev/null +++ b/test-suite/ideal-features/evars_subst.v @@ -0,0 +1,53 @@ +(* Bug report #932 *) +(* Expected time < 1.00s *) + +(* Let n be the number of let-in. The complexity comes from the fact + that each implicit arguments of f was in a larger and larger + context. To compute the type of "let _ := f ?Tn 0 in f ?T 0", + "f ?Tn 0" is substituted in the type of "f ?T 0" which is ?T. This + type is an evar instantiated on the n variables denoting the "f ?Ti 0". + One obtain "?T[1;...;n-1;f ?Tn[1;...;n-1] 0]". To compute the + type of "let _ := f ?Tn-1 0 in let _ := f ?Tn 0 in f ?T 0", another + substitution is done leading to + "?T[1;...;n-2;f ?Tn[1;...;n-2] 0;f ?Tn[1;...;n-2;f ?Tn[1;...;n-2] 0] 0]" + and so on. At the end, we get a term of exponential size *) + +(* A way to cut the complexity could have been to remove the dependency in + anonymous variables in evars but this breaks intuitive behaviour + (see Case15.v); another approach could be to substitute lazily + and/or to simultaneously substitute let binders and evars *) + +Variable P : Set -> Set. +Variable f : forall A : Set, A -> P A. + +Time Check + let _ := f _ 0 in + let _ := f _ 0 in + let _ := f _ 0 in + let _ := f _ 0 in + + let _ := f _ 0 in + let _ := f _ 0 in + let _ := f _ 0 in + let _ := f _ 0 in + + let _ := f _ 0 in + let _ := f _ 0 in + let _ := f _ 0 in + let _ := f _ 0 in + let _ := f _ 0 in + + let _ := f _ 0 in + let _ := f _ 0 in + let _ := f _ 0 in + let _ := f _ 0 in + let _ := f _ 0 in + + let _ := f _ 0 in + let _ := f _ 0 in + let _ := f _ 0 in + let _ := f _ 0 in + let _ := f _ 0 in + + f _ 0. + diff --git a/test-suite/ideal-features/universes.v b/test-suite/ideal-features/universes.v new file mode 100644 index 00000000..6db4cfe1 --- /dev/null +++ b/test-suite/ideal-features/universes.v @@ -0,0 +1,43 @@ +(* Some issues with polymorphic inductive types *) + +(* 1- upper constraints with respect to non polymorphic inductive types *) + +Unset Elimination Schemes. +Definition Ty := Type (* Top.1 *). + +Inductive Q (A:Type (* Top.2 *)) : Prop := q : A -> Q A. +Inductive T (B:Type (* Top.3 *)) := t : B -> Q (T B) -> T B. +(* ajoute Top.4 <= Top.2 inutilement: + 4 est l'univers utilisé dans le calcul du type polymorphe de T *) +Definition C := T Ty. +(* ajoute Top.1 < Top.3 : + Top.3 jour le rôle de pivot pour propager les contraintes supérieures qu'on + a sur l'argument B de T: Top.3 sera réutilisé plus tard comme majorant + des arguments effectifs de T, propageant à cette occasion les contraintes + supérieures sur Top.3 *) + +(* We need either that Q is polymorphic on A (though it is in Type) or + that the constraint Top.1 < Top.2 is set (and it is not set!) *) + +(* 2- upper constraints with respect to unfoldable constants *) + +Definition f (A:Type (* Top.1 *)) := True. +Inductive R := r : f R -> R. +(* ajoute Top.3 <= Top.1 inutilement: + Top.3 est l'univers utilisé dans le calcul du type polymorphe de R *) + +(* mais il manque la contrainte que l'univers de R est plus petit que Top.1 + ce qui l'empêcherait en fait d'être vraiment polymorphe *) + +(* 3- constraints with respect to global constants *) + +Inductive S (A:Ty) := s : A -> S A. + +(* Q est considéré polymorphique vis à vis de A alors que le type de A + n'est pas une variable mais un univers déjà existant *) + +(* Malgré tout la contrainte Ty < Ty est ajoutée (car Ty est vu comme + un pivot pour propager les contraintes sur le type A, comme si Q était + vraiment polymorphique, ce qu'il n'est pas parce que Ty est une + constante). Et heureusement qu'elle est ajouté car elle évite de + pouvoir typer "Q Ty" *) diff --git a/test-suite/micromega/bertot.v b/test-suite/micromega/bertot.v new file mode 100644 index 00000000..6951fcd3 --- /dev/null +++ b/test-suite/micromega/bertot.v @@ -0,0 +1,22 @@ +(************************************************************************) +(* *) +(* Micromega: A reflexive tactic using the Positivstellensatz *) +(* *) +(* Frédéric Besson (Irisa/Inria) 2006-2008 *) +(* *) +(************************************************************************) + +Require Import ZArith. +Require Import Micromegatac. + +Open Scope Z_scope. + +Goal (forall x y n, + ( ~ x < n /\ x <= n /\ 2 * y = x*(x+1) -> 2 * y = n*(n+1)) + /\ + (x < n /\ x <= n /\ 2 * y = x * (x+1) -> x + 1 <= n /\ 2 *(x+1+y) = (x+1)*(x+2))). +Proof. + intros. + micromega Z. +Qed. + diff --git a/test-suite/micromega/example.v b/test-suite/micromega/example.v new file mode 100644 index 00000000..dc78ace5 --- /dev/null +++ b/test-suite/micromega/example.v @@ -0,0 +1,347 @@ +(************************************************************************) +(* *) +(* Micromega: A reflexive tactic using the Positivstellensatz *) +(* *) +(* Frédéric Besson (Irisa/Inria) 2006-2008 *) +(* *) +(************************************************************************) + +Require Import ZArith. +Require Import Micromegatac. +Require Import Ring_normalize. +Open Scope Z_scope. +Require Import ZMicromega. +Require Import VarMap. + +(* false in Q : x=1/2 and n=1 *) + +Lemma not_so_easy : forall x n : Z, + 2*x + 1 <= 2 *n -> x <= n-1. +Proof. + intros. + zfarkas. +Qed. + + +(* From Laurent Théry *) + +Lemma some_pol : forall x, 4 * x ^ 2 + 3 * x + 2 >= 0. +Proof. + intros. + micromega Z. +Qed. + + +Lemma Zdiscr: forall a b c x, + a * x ^ 2 + b * x + c = 0 -> b ^ 2 - 4 * a * c >= 0. +Proof. + intros ; micromega Z. +Qed. + + +Lemma plus_minus : forall x y, + 0 = x + y -> 0 = x -y -> 0 = x /\ 0 = y. +Proof. + intros. + zfarkas. +Qed. + + + +Lemma mplus_minus : forall x y, + x + y >= 0 -> x -y >= 0 -> x^2 - y^2 >= 0. +Proof. + intros; micromega Z. +Qed. + +Lemma pol3: forall x y, 0 <= x + y -> + x^3 + 3*x^2*y + 3*x* y^2 + y^3 >= 0. +Proof. + intros; micromega Z. +Qed. + + +(* Motivating example from: Expressiveness + Automation + Soundness: + Towards COmbining SMT Solvers and Interactive Proof Assistants *) +Parameter rho : Z. +Parameter rho_ge : rho >= 0. +Parameter correct : Z -> Z -> Prop. + + +Definition rbound1 (C:Z -> Z -> Z) : Prop := + forall p s t, correct p t /\ s <= t -> C p t - C p s <= (1-rho)*(t-s). + +Definition rbound2 (C:Z -> Z -> Z) : Prop := + forall p s t, correct p t /\ s <= t -> (1-rho)*(t-s) <= C p t - C p s. + + +Lemma bounded_drift : forall s t p q C D, s <= t /\ correct p t /\ correct q t /\ + rbound1 C /\ rbound2 C /\ rbound1 D /\ rbound2 D -> + Zabs (C p t - D q t) <= Zabs (C p s - D q s) + 2 * rho * (t- s). +Proof. + intros. + generalize (Zabs_eq (C p t - D q t)). + generalize (Zabs_non_eq (C p t - D q t)). + generalize (Zabs_eq (C p s -D q s)). + generalize (Zabs_non_eq (C p s - D q s)). + unfold rbound2 in H. + unfold rbound1 in H. + intuition. + generalize (H6 _ _ _ (conj H H4)). + generalize (H7 _ _ _ (conj H H4)). + generalize (H8 _ _ _ (conj H H4)). + generalize (H10 _ _ _ (conj H H4)). + generalize (H6 _ _ _ (conj H5 H4)). + generalize (H7 _ _ _ (conj H5 H4)). + generalize (H8 _ _ _ (conj H5 H4)). + generalize (H10 _ _ _ (conj H5 H4)). + generalize rho_ge. + micromega Z. +Qed. + +(* Rule of signs *) + +Lemma sign_pos_pos: forall x y, + x > 0 -> y > 0 -> x*y > 0. +Proof. + intros; micromega Z. +Qed. + +Lemma sign_pos_zero: forall x y, + x > 0 -> y = 0 -> x*y = 0. +Proof. + intros; micromega Z. +Qed. + +Lemma sign_pos_neg: forall x y, + x > 0 -> y < 0 -> x*y < 0. +Proof. + intros; micromega Z. +Qed. + +Lemma sign_zer_pos: forall x y, + x = 0 -> y > 0 -> x*y = 0. +Proof. + intros; micromega Z. +Qed. + +Lemma sign_zero_zero: forall x y, + x = 0 -> y = 0 -> x*y = 0. +Proof. + intros; micromega Z. +Qed. + +Lemma sign_zero_neg: forall x y, + x = 0 -> y < 0 -> x*y = 0. +Proof. + intros; micromega Z. +Qed. + +Lemma sign_neg_pos: forall x y, + x < 0 -> y > 0 -> x*y < 0. +Proof. + intros; micromega Z. +Qed. + +Lemma sign_neg_zero: forall x y, + x < 0 -> y = 0 -> x*y = 0. +Proof. + intros; micromega Z. +Qed. + +Lemma sign_neg_neg: forall x y, + x < 0 -> y < 0 -> x*y > 0. +Proof. + intros; micromega Z. +Qed. + + +(* Other (simple) examples *) + +Lemma binomial : forall x y, (x+y)^2 = x^2 + 2*x*y + y^2. +Proof. + intros. + zfarkas. +Qed. + +Lemma product : forall x y, x >= 0 -> y >= 0 -> x * y >= 0. +Proof. + intros. + micromega Z. +Qed. + + +Lemma product_strict : forall x y, x > 0 -> y > 0 -> x * y > 0. +Proof. + intros. + micromega Z. +Qed. + + +Lemma pow_2_pos : forall x, x ^ 2 + 1 = 0 -> False. +Proof. + intros ; micromega Z. +Qed. + +(* Found in Parrilo's talk *) +(* BUG?: certificate with **very** big coefficients *) +Lemma parrilo_ex : forall x y, x - y^2 + 3 >= 0 -> y + x^2 + 2 = 0 -> False. +Proof. + intros. + micromega Z. +Qed. + + +(* from hol_light/Examples/sos.ml *) + +Lemma hol_light1 : forall a1 a2 b1 b2, + a1 >= 0 -> a2 >= 0 -> + (a1 * a1 + a2 * a2 = b1 * b1 + b2 * b2 + 2) -> + (a1 * b1 + a2 * b2 = 0) -> a1 * a2 - b1 * b2 >= 0. +Proof. + intros ; micromega Z. +Qed. + + +Lemma hol_light2 : forall x a, + 3 * x + 7 * a < 4 -> 3 < 2 * x -> a < 0. +Proof. + intros ; micromega Z. +Qed. + +Lemma hol_light3 : forall b a c x, + b ^ 2 < 4 * a * c -> (a * x ^2 + b * x + c = 0) -> False. +Proof. +intros ; micromega Z. +Qed. + +Lemma hol_light4 : forall a c b x, + a * x ^ 2 + b * x + c = 0 -> b ^ 2 >= 4 * a * c. +Proof. +intros ; micromega Z. +Qed. + +Lemma hol_light5 : forall x y, + 0 <= x /\ x <= 1 /\ 0 <= y /\ y <= 1 + -> x ^ 2 + y ^ 2 < 1 \/ + (x - 1) ^ 2 + y ^ 2 < 1 \/ + x ^ 2 + (y - 1) ^ 2 < 1 \/ + (x - 1) ^ 2 + (y - 1) ^ 2 < 1. +Proof. +intros; micromega Z. +Qed. + + + +Lemma hol_light7 : forall x y z, + 0<= x /\ 0 <= y /\ 0 <= z /\ x + y + z <= 3 + -> x * y + x * z + y * z >= 3 * x * y * z. +Proof. +intros ; micromega Z. +Qed. + +Lemma hol_light8 : forall x y z, + x ^ 2 + y ^ 2 + z ^ 2 = 1 -> (x + y + z) ^ 2 <= 3. +Proof. + intros ; micromega Z. +Qed. + +Lemma hol_light9 : forall w x y z, + w ^ 2 + x ^ 2 + y ^ 2 + z ^ 2 = 1 + -> (w + x + y + z) ^ 2 <= 4. +Proof. + intros;micromega Z. +Qed. + +Lemma hol_light10 : forall x y, + x >= 1 /\ y >= 1 -> x * y >= x + y - 1. +Proof. + intros ; micromega Z. +Qed. + +Lemma hol_light11 : forall x y, + x > 1 /\ y > 1 -> x * y > x + y - 1. +Proof. + intros ; micromega Z. +Qed. + + +Lemma hol_light12: forall x y z, + 2 <= x /\ x <= 125841 / 50000 /\ + 2 <= y /\ y <= 125841 / 50000 /\ + 2 <= z /\ z <= 125841 / 50000 + -> 2 * (x * z + x * y + y * z) - (x * x + y * y + z * z) >= 0. +Proof. + intros x y z ; set (e:= (125841 / 50000)). + compute in e. + unfold e ; intros ; micromega Z. +Qed. + +Lemma hol_light14 : forall x y z, + 2 <= x /\ x <= 4 /\ 2 <= y /\ y <= 4 /\ 2 <= z /\ z <= 4 + -> 12 <= 2 * (x * z + x * y + y * z) - (x * x + y * y + z * z). +Proof. + intros ;micromega Z. +Qed. + +(* ------------------------------------------------------------------------- *) +(* Inequality from sci.math (see "Leon-Sotelo, por favor"). *) +(* ------------------------------------------------------------------------- *) + +Lemma hol_light16 : forall x y, + 0 <= x /\ 0 <= y /\ (x * y = 1) + -> x + y <= x ^ 2 + y ^ 2. +Proof. + intros ; micromega Z. +Qed. + +Lemma hol_light17 : forall x y, + 0 <= x /\ 0 <= y /\ (x * y = 1) + -> x * y * (x + y) <= x ^ 2 + y ^ 2. +Proof. + intros ; micromega Z. +Qed. + +Lemma hol_light18 : forall x y, + 0 <= x /\ 0 <= y -> x * y * (x + y) ^ 2 <= (x ^ 2 + y ^ 2) ^ 2. +Proof. + intros ; micromega Z. +Qed. + +(* ------------------------------------------------------------------------- *) +(* Some examples over integers and natural numbers. *) +(* ------------------------------------------------------------------------- *) + +Lemma hol_light19 : forall m n, 2 * m + n = (n + m) + m. +Proof. + intros ; zfarkas. +Qed. + +Lemma hol_light22 : forall n, n >= 0 -> n <= n * n. +Proof. + intros. + micromega Z. +Qed. + + +Lemma hol_light24 : forall x1 y1 x2 y2, x1 >= 0 -> x2 >= 0 -> y1 >= 0 -> y2 >= 0 -> + ((x1 + y1) ^2 + x1 + 1 = (x2 + y2) ^ 2 + x2 + 1) + -> (x1 + y1 = x2 + y2). +Proof. + intros. + micromega Z. +Qed. + +Lemma motzkin' : forall x y, (x^2+y^2+1)*(x^2*y^4 + x^4*y^2 + 1 - 3*x^2*y^2) >= 0. +Proof. + intros ; sos Z. +Qed. + + + +Lemma motzkin : forall x y, (x^2*y^4 + x^4*y^2 + 1 - 3*x^2*y^2) >= 0. +Proof. + intros. + generalize (motzkin' x y). + micromega Z. +Qed. diff --git a/test-suite/micromega/heap3_vcgen_25.v b/test-suite/micromega/heap3_vcgen_25.v new file mode 100644 index 00000000..ec88b68d --- /dev/null +++ b/test-suite/micromega/heap3_vcgen_25.v @@ -0,0 +1,38 @@ +(************************************************************************) +(* *) +(* Micromega: A reflexive tactic using the Positivstellensatz *) +(* *) +(* Frédéric Besson (Irisa/Inria) 2006-2008 *) +(* *) +(************************************************************************) + +Require Import ZArith. +Require Import Micromegatac. + +Open Scope Z_scope. + +Lemma vcgen_25 : forall + (n : Z) + (m : Z) + (jt : Z) + (j : Z) + (it : Z) + (i : Z) + (H0 : 1 * it + -2 * i + -1 = 0) + (H : 1 * jt + -2 * j + -1 = 0) + (H1 : 1 * n + -10 = 0) + (H2 : 0 <= -4028 * i + 6222 * j + 705 * m + -16674) + (H3 : 0 <= -418 * i + 651 * j + 94 * m + -1866) + (H4 : 0 <= -209 * i + 302 * j + 47 * m + -839) + (H5 : 0 <= -1 * i + 1 * j + -1) + (H6 : 0 <= -1 * j + 1 * m + 0) + (H7 : 0 <= 1 * j + 5 * m + -27) + (H8 : 0 <= 2 * j + -1 * m + 2) + (H9 : 0 <= 7 * j + 10 * m + -74) + (H10 : 0 <= 18 * j + -139 * m + 1188) + (H11 : 0 <= 1 * i + 0) + (H13 : 0 <= 121 * i + 810 * j + -7465 * m + 64350), + (1 = -2 * i + it). +Proof. + intros ; zfarkas. +Qed. diff --git a/test-suite/micromega/qexample.v b/test-suite/micromega/qexample.v new file mode 100644 index 00000000..42aff5a4 --- /dev/null +++ b/test-suite/micromega/qexample.v @@ -0,0 +1,62 @@ +(************************************************************************) +(* *) +(* Micromega: A reflexive tactic using the Positivstellensatz *) +(* *) +(* Frédéric Besson (Irisa/Inria) 2006-2008 *) +(* *) +(************************************************************************) + +Require Import Micromegatac. +Require Import QArith. +Require Import Ring_normalize. + +Lemma plus_minus : forall x y, + 0 == x + y -> 0 == x -y -> 0 == x /\ 0 == y. +Proof. + intros. + omicron Q. +Qed. + +(* Other (simple) examples *) +Open Scope Q_scope. + +Lemma binomial : forall x y:Q, ((x+y)^2 == x^2 + (2 # 1) *x*y + y^2). +Proof. + intros. + omicron Q. +Qed. + + +Lemma hol_light19 : forall m n, (2 # 1) * m + n == (n + m) + m. +Proof. + intros ; omicron Q. +Qed. +Open Scope Z_scope. +Open Scope Q_scope. + +Lemma vcgen_25 : forall + (n : Q) + (m : Q) + (jt : Q) + (j : Q) + (it : Q) + (i : Q) + (H0 : 1 * it + (-2 # 1) * i + (-1 # 1) == 0) + (H : 1 * jt + (-2 # 1) * j + (-1 # 1) == 0) + (H1 : 1 * n + (-10 # 1) = 0) + (H2 : 0 <= (-4028 # 1) * i + (6222 # 1) * j + (705 # 1) * m + (-16674 # 1)) + (H3 : 0 <= (-418 # 1) * i + (651 # 1) * j + (94 # 1) * m + (-1866 # 1)) + (H4 : 0 <= (-209 # 1) * i + (302 # 1) * j + (47 # 1) * m + (-839 # 1)) + (H5 : 0 <= (-1 # 1) * i + 1 * j + (-1 # 1)) + (H6 : 0 <= (-1 # 1) * j + 1 * m + (0 # 1)) + (H7 : 0 <= (1 # 1) * j + (5 # 1) * m + (-27 # 1)) + (H8 : 0 <= (2 # 1) * j + (-1 # 1) * m + (2 # 1)) + (H9 : 0 <= (7 # 1) * j + (10 # 1) * m + (-74 # 1)) + (H10 : 0 <= (18 # 1) * j + (-139 # 1) * m + (1188 # 1)) + (H11 : 0 <= 1 * i + (0 # 1)) + (H13 : 0 <= (121 # 1) * i + (810 # 1) * j + (-7465 # 1) * m + (64350 # 1)), + (( 1# 1) == (-2 # 1) * i + it). +Proof. + intros. + omicron Q. +Qed. diff --git a/test-suite/micromega/rexample.v b/test-suite/micromega/rexample.v new file mode 100644 index 00000000..5132dc4e --- /dev/null +++ b/test-suite/micromega/rexample.v @@ -0,0 +1,62 @@ +(************************************************************************) +(* *) +(* Micromega: A reflexive tactic using the Positivstellensatz *) +(* *) +(* Frédéric Besson (Irisa/Inria) 2006-2008 *) +(* *) +(************************************************************************) + +Require Import Micromegatac. +Require Import Reals. +Require Import Ring_normalize. + +Open Scope R_scope. + +Lemma plus_minus : forall x y, + 0 = x + y -> 0 = x -y -> 0 = x /\ 0 = y. +Proof. + intros. + omicron R. +Qed. + +(* Other (simple) examples *) + +Lemma binomial : forall x y, ((x+y)^2 = x^2 + 2 *x*y + y^2). +Proof. + intros. + omicron R. +Qed. + + +Lemma hol_light19 : forall m n, 2 * m + n = (n + m) + m. +Proof. + intros ; omicron R. +Qed. + + +Lemma vcgen_25 : forall + (n : R) + (m : R) + (jt : R) + (j : R) + (it : R) + (i : R) + (H0 : 1 * it + (-2%R ) * i + (-1%R ) = 0) + (H : 1 * jt + (-2 ) * j + (-1 ) = 0) + (H1 : 1 * n + (-10 ) = 0) + (H2 : 0 <= (-4028 ) * i + (6222 ) * j + (705 ) * m + (-16674 )) + (H3 : 0 <= (-418 ) * i + (651 ) * j + (94 ) * m + (-1866 )) + (H4 : 0 <= (-209 ) * i + (302 ) * j + (47 ) * m + (-839 )) + (H5 : 0 <= (-1 ) * i + 1 * j + (-1 )) + (H6 : 0 <= (-1 ) * j + 1 * m + (0 )) + (H7 : 0 <= (1 ) * j + (5 ) * m + (-27 )) + (H8 : 0 <= (2 ) * j + (-1 ) * m + (2 )) + (H9 : 0 <= (7 ) * j + (10 ) * m + (-74 )) + (H10 : 0 <= (18 ) * j + (-139 ) * m + (1188 )) + (H11 : 0 <= 1 * i + (0 )) + (H13 : 0 <= (121 ) * i + (810 ) * j + (-7465 ) * m + (64350 )), + (( 1 ) = (-2 ) * i + it). +Proof. + intros. + omicron R. +Qed. diff --git a/test-suite/micromega/square.v b/test-suite/micromega/square.v new file mode 100644 index 00000000..30c72e8c --- /dev/null +++ b/test-suite/micromega/square.v @@ -0,0 +1,61 @@ +(************************************************************************) +(* *) +(* Micromega: A reflexive tactic using the Positivstellensatz *) +(* *) +(* Frédéric Besson (Irisa/Inria) 2006-2008 *) +(* *) +(************************************************************************) + +Require Import ZArith Zwf Micromegatac QArith. +Open Scope Z_scope. + +Lemma Zabs_square : forall x, (Zabs x)^2 = x^2. +Proof. + intros ; case (Zabs_dec x) ; intros ; micromega Z. +Qed. +Hint Resolve Zabs_pos Zabs_square. + +Lemma integer_statement : ~exists n, exists p, n^2 = 2*p^2 /\ n <> 0. +Proof. +intros [n [p [Heq Hnz]]]; pose (n' := Zabs n); pose (p':=Zabs p). +assert (facts : 0 <= Zabs n /\ 0 <= Zabs p /\ Zabs n^2=n^2 + /\ Zabs p^2 = p^2) by auto. +assert (H : (0 < n' /\ 0 <= p' /\ n' ^2 = 2* p' ^2)) by + (destruct facts as [Hf1 [Hf2 [Hf3 Hf4]]]; unfold n', p' ; micromega Z). +generalize p' H; elim n' using (well_founded_ind (Zwf_well_founded 0)); clear. +intros n IHn p [Hn [Hp Heq]]. +assert (Hzwf : Zwf 0 (2*p-n) n) by (unfold Zwf; micromega Z). +assert (Hdecr : 0 < 2*p-n /\ 0 <= n-p /\ (2*p-n)^2=2*(n-p)^2) by micromega Z. +apply (IHn (2*p-n) Hzwf (n-p) Hdecr). +Qed. + +Open Scope Q_scope. + +Lemma QnumZpower : forall x : Q, Qnum (x ^ 2)%Q = ((Qnum x) ^ 2) %Z. +Proof. + intros. + destruct x. + cbv beta iota zeta delta - [Zmult]. + ring. +Qed. + + +Lemma QdenZpower : forall x : Q, ' Qden (x ^ 2)%Q = ('(Qden x) ^ 2) %Z. +Proof. + intros. + destruct x. + cbv beta iota zeta delta - [Pmult]. + rewrite Pmult_1_r. + reflexivity. +Qed. + +Theorem sqrt2_not_rational : ~exists x:Q, x^2==2#1. +Proof. + unfold Qeq; intros [x]; simpl (Qden (2#1)); rewrite Zmult_1_r. + intros HQeq. + assert (Heq : (Qnum x ^ 2 = 2 * ' Qden x ^ 2%Q)%Z) by + (rewrite QnumZpower in HQeq ; rewrite QdenZpower in HQeq ; auto). + assert (Hnx : (Qnum x <> 0)%Z) + by (intros Hx; simpl in HQeq; rewrite Hx in HQeq; discriminate HQeq). + apply integer_statement; exists (Qnum x); exists (' Qden x); auto. +Qed. diff --git a/test-suite/micromega/zomicron.v b/test-suite/micromega/zomicron.v new file mode 100644 index 00000000..b13654d6 --- /dev/null +++ b/test-suite/micromega/zomicron.v @@ -0,0 +1,27 @@ +Require Import ZArith. +Require Import Micromegatac. +Open Scope Z_scope. + +Lemma two_x_eq_1 : forall x, 2 * x = 1 -> False. +Proof. + intros. + omicron Z. +Qed. + +Lemma two_x_y_eq_1 : forall x y, 2 * x + 2 * y = 1 -> False. +Proof. + intros. + omicron Z. +Qed. + +Lemma two_x_y_z_eq_1 : forall x y z, 2 * x + 2 * y + 2 * z= 1 -> False. +Proof. + intros. + omicron Z. +Qed. + +Lemma omega_nightmare : forall x y, 27 <= 11 * x + 13 * y <= 45 -> 7 * x - 9 * y = 4 -> -10 <= 7 * x - 9 * y <= 4 -> False. +Proof. + intros ; intuition auto. + omicron Z. +Qed. diff --git a/test-suite/modules/pseudo_circular_with.v b/test-suite/modules/pseudo_circular_with.v new file mode 100644 index 00000000..9e46d17e --- /dev/null +++ b/test-suite/modules/pseudo_circular_with.v @@ -0,0 +1,6 @@ +Module Type S. End S. +Module Type T. Declare Module M:S. End T. +Module N:S. End N. + +Module NN:T. Module M:=N. End NN. +Module Type U := T with Module M:=NN. \ No newline at end of file diff --git a/test-suite/modules/resolver.v b/test-suite/modules/resolver.v new file mode 100644 index 00000000..dcfcc98d --- /dev/null +++ b/test-suite/modules/resolver.v @@ -0,0 +1,37 @@ +Module Type TA. +Parameter t : Set. +End TA. + +Module Type TB. +Declare Module A: TA. +End TB. + +Module Type TC. +Declare Module B : TB. +End TC. + +Module Type TD. + +Declare Module B: TB . +Declare Module C: TC + with Module B := B . +End TD. + +Module Type TE. +Declare Module D : TD. +End TE. + +Module Type TF. +Declare Module E: TE. +End TF. + +Module G (D: TD). +Module B' := D.C.B. +End G. + +Module H (F: TF). +Module I := G(F.E.D). +End H. + +Declare Module F: TF. +Module K := H(F). diff --git a/test-suite/modules/subtyping.v b/test-suite/modules/subtyping.v new file mode 100644 index 00000000..2df8e84e --- /dev/null +++ b/test-suite/modules/subtyping.v @@ -0,0 +1,46 @@ +(* Non regression for bug #1302 *) + +(* With universe polymorphism for inductive types, subtyping of + inductive types needs a special treatment: the standard conversion + algorithm does not work as it only knows to deal with constraints of + the form alpha = beta or max(alphas, alphas+1) <= beta, while + subtyping of inductive types in Type generates constraints of the form + max(alphas, alphas+1) <= max(betas, betas+1). + + These constraints are anyway valid by monotonicity of subtyping but we + have to detect it early enough to avoid breaking the standard + algorithm for constraints on algebraic universes. *) + +Module Type T. + + Parameter A : Type (* Top.1 *) . + + Inductive L : Type (* max(Top.1,1) *) := + | L0 + | L1 : (A -> Prop) -> L. + +End T. + +Axiom Tp : Type (* Top.5 *) . + +Module TT : T. + + Definition A : Type (* Top.6 *) := Tp. (* generates Top.5 <= Top.6 *) + + Inductive L : Type (* max(Top.6,1) *) := + | L0 + | L1 : (A -> Prop) -> L. + +End TT. (* Generates Top.6 <= Top.1 (+ auxiliary constraints for L_rect) *) + +(* Note: Top.6 <= Top.1 is generated by subtyping on A; + subtyping of L follows and has not to be checked *) + + + +(* The same bug as #1302 but for Definition *) +(* Check that inferred algebraic universes in interfaces are considered *) + +Module Type U. Definition A := Type -> Type. End U. +Module M:U. Definition A := Type -> Type. End M. + diff --git a/test-suite/output/Cases.out b/test-suite/output/Cases.out index a3033e94..9d0d0658 100644 --- a/test-suite/output/Cases.out +++ b/test-suite/output/Cases.out @@ -6,4 +6,25 @@ fix F (t : t) : P t := end : forall P : t -> Type, (let x := t in forall x0 : x, P x0 -> P (k x0)) -> forall t : t, P t +proj = +fun (x y : nat) (P : nat -> Type) (def : P x) (prf : P y) => +match eq_nat_dec x y with +| left eqprf => + match eqprf in (_ = z) return (P z) with + | refl_equal => def + end +| right _ => prf +end + : forall (x y : nat) (P : nat -> Type), P x -> P y -> P y +Argument scopes are [nat_scope nat_scope _ _ _] +foo = +fix foo (A : Type) (l : list A) {struct l} : option A := + match l with + | nil => None (A:=A) + | x0 :: nil => Some x0 + | x0 :: (_ :: _) as l0 => foo A l0 + end + : forall A : Type, list A -> option A + +Argument scopes are [type_scope list_scope] diff --git a/test-suite/output/Cases.v b/test-suite/output/Cases.v index 452d3603..61f89d40 100644 --- a/test-suite/output/Cases.v +++ b/test-suite/output/Cases.v @@ -4,3 +4,32 @@ Inductive t : Set := k : let x := t in x -> x. Print t_rect. + +(* Do not contract nested patterns with dependent return type *) +(* see bug #1699 *) + +Require Import Arith. + +Definition proj (x y:nat) (P:nat -> Type) (def:P x) (prf:P y) : P y := + match eq_nat_dec x y return P y with + | left eqprf => + match eqprf in (_ = z) return (P z) with + | refl_equal => def + end + | _ => prf + end. + +Print proj. + +(* Use notations even below aliases *) + +Require Import List. + +Fixpoint foo (A:Type) (l:list A) : option A := + match l with + | nil => None + | x0 :: nil => Some x0 + | x0 :: (x1 :: xs) as l0 => foo A l0 + end. + +Print foo. diff --git a/test-suite/output/Fixpoint.out b/test-suite/output/Fixpoint.out index 62c9d395..f4270d3d 100644 --- a/test-suite/output/Fixpoint.out +++ b/test-suite/output/Fixpoint.out @@ -9,3 +9,17 @@ let fix f (m : nat) : nat := match m with | S m' => f m' end in f 0 : nat +fix even_pos_odd_pos 2 + with (odd_pos_even_pos (n:_) (H:odd n) {struct H} : n >= 1). + intros. + destruct H. + omega. + + apply odd_pos_even_pos in H. + omega. + + intros. + destruct H. + apply even_pos_odd_pos in H. + omega. + diff --git a/test-suite/output/Fixpoint.v b/test-suite/output/Fixpoint.v index fc27e8d2..2b13c204 100644 --- a/test-suite/output/Fixpoint.v +++ b/test-suite/output/Fixpoint.v @@ -16,3 +16,26 @@ Check end in f 0. +Require Import ZArith_base Omega. +Open Scope Z_scope. + +Inductive even: Z -> Prop := +| even_base: even 0 +| even_succ: forall n, odd (n - 1) -> even n +with odd: Z -> Prop := +| odd_succ: forall n, even (n - 1) -> odd n. + +Lemma even_pos_odd_pos: forall n, even n -> n >= 0. +Proof. +fix even_pos_odd_pos 2 with (odd_pos_even_pos n (H:odd n) {struct H} : n >= 1). + intros. + destruct H. + omega. + apply odd_pos_even_pos in H. + omega. + intros. + destruct H. + apply even_pos_odd_pos in H. + omega. +Show Script. +Qed. diff --git a/test-suite/output/Implicit.out b/test-suite/output/Implicit.out index 38c5b827..ecfe8505 100644 --- a/test-suite/output/Implicit.out +++ b/test-suite/output/Implicit.out @@ -5,6 +5,9 @@ ex_intro (P:=fun _ : nat => True) (x:=0) I d2 = fun x : nat => d1 (y:=x) : forall x x0 : nat, x0 = x -> x0 = x - Arguments x, x0 are implicit Argument scopes are [nat_scope nat_scope _] +map id (1 :: nil) + : list nat +map id' (1 :: nil) + : list nat diff --git a/test-suite/output/Implicit.v b/test-suite/output/Implicit.v index 0ff7e87f..4c6f2b5d 100644 --- a/test-suite/output/Implicit.v +++ b/test-suite/output/Implicit.v @@ -17,3 +17,22 @@ Definition d1 y x (h : x = y :>nat) := h. Definition d2 x := d1 (y:=x). Print d2. + +(* Check maximal insertion of implicit *) + +Require Import List. + +Open Scope list_scope. + +Set Implicit Arguments. +Set Maximal Implicit Insertion. + +Definition id (A:Type) (x:A) := x. + +Check map id (1::nil). + +Definition id' (A:Type) (x:A) := x. + +Implicit Arguments id' [[A]]. + +Check map id' (1::nil). diff --git a/test-suite/output/InitSyntax.out b/test-suite/output/InitSyntax.out index c7f3ed7d..9299e010 100644 --- a/test-suite/output/InitSyntax.out +++ b/test-suite/output/InitSyntax.out @@ -1,5 +1,6 @@ -Inductive sig2 (A : Type) (P : A -> Prop) (Q : A -> Prop) : Type := +Inductive sig2 (A : Type) (P Q : A -> Prop) : Type := exist2 : forall x : A, P x -> Q x -> sig2 P Q + For sig2: Argument A is implicit For exist2: Argument A is implicit For sig2: Argument scopes are [type_scope type_scope type_scope] diff --git a/test-suite/output/Nametab.out b/test-suite/output/Nametab.out index d0f15f0e..b1883ec0 100644 --- a/test-suite/output/Nametab.out +++ b/test-suite/output/Nametab.out @@ -1,12 +1,12 @@ -Constant Top.Q.N.K.id - (shorter name to refer to it in current context is Q.N.K.id) -Constant Top.Q.N.K.id - (shorter name to refer to it in current context is Q.N.K.id) -Constant Top.Q.N.K.id - (shorter name to refer to it in current context is Q.N.K.id) -Constant Top.Q.N.K.id -Constant Top.Q.N.K.id - (shorter name to refer to it in current context is Q.N.K.id) +Constant Top.Q.N.K.foo + (shorter name to refer to it in current context is Q.N.K.foo) +Constant Top.Q.N.K.foo + (shorter name to refer to it in current context is Q.N.K.foo) +Constant Top.Q.N.K.foo + (shorter name to refer to it in current context is Q.N.K.foo) +Constant Top.Q.N.K.foo +Constant Top.Q.N.K.foo + (shorter name to refer to it in current context is Q.N.K.foo) No module is referred to by basename K No module is referred to by name N.K Module Top.Q.N.K @@ -16,15 +16,15 @@ Module Top.Q.N Module Top.Q.N Module Top.Q Module Top.Q -Constant Top.Q.N.K.id - (shorter name to refer to it in current context is K.id) -Constant Top.Q.N.K.id -Constant Top.Q.N.K.id - (shorter name to refer to it in current context is K.id) -Constant Top.Q.N.K.id - (shorter name to refer to it in current context is K.id) -Constant Top.Q.N.K.id - (shorter name to refer to it in current context is K.id) +Constant Top.Q.N.K.foo + (shorter name to refer to it in current context is K.foo) +Constant Top.Q.N.K.foo +Constant Top.Q.N.K.foo + (shorter name to refer to it in current context is K.foo) +Constant Top.Q.N.K.foo + (shorter name to refer to it in current context is K.foo) +Constant Top.Q.N.K.foo + (shorter name to refer to it in current context is K.foo) Module Top.Q.N.K No module is referred to by name N.K Module Top.Q.N.K diff --git a/test-suite/output/Nametab.v b/test-suite/output/Nametab.v index a1a7579b..357ba982 100644 --- a/test-suite/output/Nametab.v +++ b/test-suite/output/Nametab.v @@ -1,16 +1,16 @@ Module Q. Module N. Module K. - Definition id := Set. + Definition foo := Set. End K. End N. End Q. -(* Bad *) Locate id. -(* Bad *) Locate K.id. -(* Bad *) Locate N.K.id. -(* OK *) Locate Q.N.K.id. -(* OK *) Locate Top.Q.N.K.id. +(* Bad *) Locate foo. +(* Bad *) Locate K.foo. +(* Bad *) Locate N.K.foo. +(* OK *) Locate Q.N.K.foo. +(* OK *) Locate Top.Q.N.K.foo. (* Bad *) Locate Module K. (* Bad *) Locate Module N.K. @@ -28,11 +28,11 @@ End Q. Import Q.N. -(* Bad *) Locate id. -(* OK *) Locate K.id. -(* Bad *) Locate N.K.id. -(* OK *) Locate Q.N.K.id. -(* OK *) Locate Top.Q.N.K.id. +(* Bad *) Locate foo. +(* OK *) Locate K.foo. +(* Bad *) Locate N.K.foo. +(* OK *) Locate Q.N.K.foo. +(* OK *) Locate Top.Q.N.K.foo. (* OK *) Locate Module K. (* Bad *) Locate Module N.K. diff --git a/test-suite/output/Notations.out b/test-suite/output/Notations.out index be4cd4fa..2066a7ef 100644 --- a/test-suite/output/Notations.out +++ b/test-suite/output/Notations.out @@ -46,3 +46,7 @@ fun x : nat => ifn x is succ n then n else 0 : bool -4 : Z +Nil + : forall A : Type, list A +NIL:list nat + : list nat diff --git a/test-suite/output/Notations.v b/test-suite/output/Notations.v index 3cc0a189..6e637aca 100644 --- a/test-suite/output/Notations.v +++ b/test-suite/output/Notations.v @@ -119,3 +119,13 @@ Require Import ZArith. Open Scope Z_scope. Notation "- 4" := (-2 + -2). Check -4. + +(**********************************************************************) +(* Check notations for references with activated or deactivated *) +(* implicit arguments *) + +Notation Nil := @nil. +Check Nil. + +Notation NIL := nil. +Check NIL : list nat. diff --git a/test-suite/output/Tactics.out b/test-suite/output/Tactics.out index 8e8b8059..287e8488 100644 --- a/test-suite/output/Tactics.out +++ b/test-suite/output/Tactics.out @@ -1,4 +1,6 @@ intro H; split; [ a H | e H ]. + intros; match goal with | |- context [if ?X then _ else _] => case X end; trivial. + diff --git a/test-suite/output/TranspModtype.out b/test-suite/output/TranspModtype.out index 41e8648b..f94ed642 100644 --- a/test-suite/output/TranspModtype.out +++ b/test-suite/output/TranspModtype.out @@ -1,10 +1,7 @@ TrM.A = M.A : Set - OpM.A = M.A : Set - TrM.B = M.B : Set - *** [ OpM.B : Set ] diff --git a/test-suite/output/ZSyntax.out b/test-suite/output/ZSyntax.out index cbfb9f20..f23198b0 100644 --- a/test-suite/output/ZSyntax.out +++ b/test-suite/output/ZSyntax.out @@ -2,19 +2,19 @@ : Z fun f : nat -> Z => (f 0%nat + 0)%Z : (nat -> Z) -> Z -fun x : positive => Zpos (xO x) +fun x : positive => Zpos x~0 : positive -> Z fun x : positive => (Zpos x + 1)%Z : positive -> Z fun x : positive => Zpos x : positive -> Z -fun x : positive => Zneg (xO x) +fun x : positive => Zneg x~0 : positive -> Z -fun x : positive => (Zpos (xO x) + 0)%Z +fun x : positive => (Zpos x~0 + 0)%Z : positive -> Z -fun x : positive => (- Zpos (xO x))%Z +fun x : positive => (- Zpos x~0)%Z : positive -> Z -fun x : positive => (- Zpos (xO x) + 0)%Z +fun x : positive => (- Zpos x~0 + 0)%Z : positive -> Z (Z_of_nat 0 + 1)%Z : Z diff --git a/test-suite/output/reduction.out b/test-suite/output/reduction.out new file mode 100644 index 00000000..ff327aa5 --- /dev/null +++ b/test-suite/output/reduction.out @@ -0,0 +1,4 @@ + = a + : nat + = n + 0 + : nat diff --git a/test-suite/output/reduction.v b/test-suite/output/reduction.v new file mode 100644 index 00000000..4a460a83 --- /dev/null +++ b/test-suite/output/reduction.v @@ -0,0 +1,13 @@ +(* Test the behaviour of hnf and simpl introduced in revision *) + +Variable n:nat. +Definition a:=0. + +Eval simpl in (fix plus (n m : nat) {struct n} : nat := + match n with + | 0 => m + | S p => S (p + m) + end) a a. + +Eval hnf in match (plus (S n) O) with S n => n | _ => O end. + diff --git a/test-suite/success/AdvancedCanonicalStructure.v b/test-suite/success/AdvancedCanonicalStructure.v new file mode 100644 index 00000000..8e613dca --- /dev/null +++ b/test-suite/success/AdvancedCanonicalStructure.v @@ -0,0 +1,144 @@ +Section group_morphism. + +(* An example with default canonical structures *) + +Variable A B : Type. +Variable plusA : A -> A -> A. +Variable plusB : B -> B -> B. +Variable zeroA : A. +Variable zeroB : B. +Variable eqA : A -> A -> Prop. +Variable eqB : B -> B -> Prop. +Variable phi : A -> B. + +Record img := { + ia : A; + ib :> B; + prf : phi ia = ib +}. + +Parameter eq_img : forall (i1:img) (i2:img), + eqB (ib i1) (ib i2) -> eqA (ia i1) (ia i2). + +Lemma phi_img (a:A) : img. + intro a. + exists a (phi a). + refine ( refl_equal _). +Defined. +Canonical Structure phi_img. + +Lemma zero_img : img. + exists zeroA zeroB. + admit. +Defined. +Canonical Structure zero_img. + +Lemma plus_img : img -> img -> img. +intros i1 i2. +exists (plusA (ia i1) (ia i2)) (plusB (ib i1) (ib i2)). +admit. +Defined. +Canonical Structure plus_img. + +(* Print Canonical Projections. *) + +Goal forall a1 a2, eqA (plusA a1 zeroA) a2. + intros a1 a2. + refine (eq_img _ _ _). +change (eqB (plusB (phi a1) zeroB) (phi a2)). +Admitted. + +End group_morphism. + +Open Scope type_scope. + +Section type_reification. + +Inductive term :Type := + Fun : term -> term -> term + | Prod : term -> term -> term + | Bool : term + | SET :term + | PROP :term + | TYPE :term + | Var : Type -> term. + +Fixpoint interp (t:term) := + match t with + Bool => bool + | SET => Set + | PROP => Prop + | TYPE => Type + | Fun a b => interp a -> interp b + | Prod a b => interp a * interp b + | Var x => x +end. + +Record interp_pair :Type := + { repr:>term; + abs:>Type; + link: abs = interp repr }. + +Lemma prod_interp :forall (a b:interp_pair),a * b = interp (Prod a b) . +proof. +let a:interp_pair,b:interp_pair. +reconsider thesis as (a * b = interp a * interp b). +thus thesis by (link a),(link b). +end proof. +Qed. + +Lemma fun_interp :forall (a b:interp_pair), (a -> b) = interp (Fun a b). +proof. +let a:interp_pair,b:interp_pair. +reconsider thesis as ((a -> b) = (interp a -> interp b)). +thus thesis using rewrite (link a);rewrite (link b);reflexivity. +end proof. +Qed. + +Canonical Structure ProdCan (a b:interp_pair) := + Build_interp_pair (Prod a b) (a * b) (prod_interp a b). + +Canonical Structure FunCan (a b:interp_pair) := + Build_interp_pair (Fun a b) (a -> b) (fun_interp a b). + +Canonical Structure BoolCan := + Build_interp_pair Bool bool (refl_equal _). + +Canonical Structure VarCan (x:Type) := + Build_interp_pair (Var x) x (refl_equal _). + +Canonical Structure SetCan := + Build_interp_pair SET Set (refl_equal _). + +Canonical Structure PropCan := + Build_interp_pair PROP Prop (refl_equal _). + +Canonical Structure TypeCan := + Build_interp_pair TYPE Type (refl_equal _). + +(* Print Canonical Projections. *) + +Variable A:Type. + +Variable Inhabited: term -> Prop. + +Variable Inhabited_correct: forall p, Inhabited (repr p) -> abs p. + +Lemma L : Prop * A -> bool * (Type -> Set) . +refine (Inhabited_correct _ _). +change (Inhabited (Fun (Prod PROP (Var A)) (Prod Bool (Fun TYPE SET)))). +Admitted. + +Check L : abs _ . + +End type_reification. + + + + + + + + + + diff --git a/test-suite/success/Case18.v b/test-suite/success/Case18.v index 91c80e88..be9ca8d4 100644 --- a/test-suite/success/Case18.v +++ b/test-suite/success/Case18.v @@ -12,3 +12,15 @@ Fixpoint max (n m:nat) {struct m} : nat := | S n', S m' => S (max n' m') | 0, p | p, 0 => p end. + +(* Check bug #1477 *) + +Inductive I : Set := + | A : nat -> nat -> I + | B : nat -> nat -> I. + +Definition foo (x:I) : nat := + match x with + | A a b | B b a => S b + end. + diff --git a/test-suite/success/Cases-bug1834.v b/test-suite/success/Cases-bug1834.v new file mode 100644 index 00000000..543ca0c9 --- /dev/null +++ b/test-suite/success/Cases-bug1834.v @@ -0,0 +1,13 @@ +(* Bug in the computation of generalization *) + +(* The following bug, elaborated by Bruno Barras, is solved from r11083 *) + +Parameter P : unit -> Prop. +Definition T := sig P. +Parameter Q : T -> Prop. +Definition U := sig Q. +Parameter a : U. +Check (match a with exist (exist tt e2) e3 => e3=e3 end). + +(* There is still a form submitted by Pierre Corbineau (#1834) which fails *) + diff --git a/test-suite/success/Cases.v b/test-suite/success/Cases.v index 7c2b7c0b..499c0660 100644 --- a/test-suite/success/Cases.v +++ b/test-suite/success/Cases.v @@ -10,6 +10,10 @@ Type match 0, eq, 0 return nat with | O, x, y => 0 | S x, y, z => x end. +Type match 0, eq, 0 return _ with + | O, x, y => 0 + | S x, y, z => x + end. (* Non dependent form of annotation *) Type match 0, eq return nat with @@ -406,7 +410,6 @@ Type match niln with | x => 0 end. - Type match niln return nat with | niln => 0 | consn n a l => a diff --git a/test-suite/success/CasesDep.v b/test-suite/success/CasesDep.v index 0477377e..49bd77fc 100644 --- a/test-suite/success/CasesDep.v +++ b/test-suite/success/CasesDep.v @@ -71,13 +71,9 @@ Inductive Setoid : Type := Definition elem (A : Setoid) := let (S, R, e) := A in S. -(* : Grammar is replaced by Notation *) - Definition equal (A : Setoid) := let (S, R, e) as s return (Relation (elem s)) := A in R. -(* : Grammar is replaced by Notation *) - Axiom prf_equiv : forall A : Setoid, Equivalence (elem A) (equal A). Axiom prf_refl : forall A : Setoid, Reflexive (elem A) (equal A). @@ -430,3 +426,57 @@ Definition f0 (F : False) (ty : bool) : bProp ty := | _, false => F | _, true => I end. + +(* Simplification of bug/wish #1671 *) + +Inductive I : unit -> Type := +| C : forall a, I a -> I tt. + +(* +Definition F (l:I tt) : l = l := +match l return l = l with +| C tt (C _ l') => refl_equal (C tt (C _ l')) +end. + +one would expect that the compilation of F (this involves +some kind of pattern-unification) would produce: +*) + +Definition F (l:I tt) : l = l := +match l return l = l with +| C tt l' => match l' return C _ l' = C _ l' with C _ l'' => refl_equal (C tt (C _ l'')) end +end. + +Inductive J : nat -> Type := +| D : forall a, J (S a) -> J a. + +(* +Definition G (l:J O) : l = l := +match l return l = l with +| D O (D 1 l') => refl_equal (D O (D 1 l')) +| D _ _ => refl_equal _ +end. + +one would expect that the compilation of G (this involves inversion) +would produce: +*) + +Definition G (l:J O) : l = l := +match l return l = l with +| D 0 l'' => + match l'' as _l'' in J n return + match n return forall l:J n, Prop with + | O => fun _ => l = l + | S p => fun l'' => D p l'' = D p l'' + end _l'' with + | D 1 l' => refl_equal (D O (D 1 l')) + | _ => refl_equal _ + end +| _ => refl_equal _ +end. + +Fixpoint app {A} {n m} (v : listn A n) (w : listn A m) : listn A (n + m) := + match v with + | niln => w + | consn a n' v' => consn _ a _ (app v' w) + end. diff --git a/test-suite/success/Discriminate.v b/test-suite/success/Discriminate.v index f28c83de..b57c5478 100644 --- a/test-suite/success/Discriminate.v +++ b/test-suite/success/Discriminate.v @@ -9,3 +9,26 @@ Qed. Lemma l2 : forall H : 0 = 1, H = H. discriminate H. Qed. + +(* Check the variants of discriminate *) + +Goal O = S O -> True. +discriminate 1. +Undo. +intros. +discriminate H. +Undo. +Ltac g x := discriminate x. +g H. +Abort. + +Goal (forall x y : nat, x = y -> x = S y) -> True. +intros. +try discriminate (H O) || exact I. +Qed. + +Goal (forall x y : nat, x = y -> x = S y) -> True. +intros. +ediscriminate (H O). +instantiate (1:=O). +Abort. diff --git a/test-suite/success/Fixpoint.v b/test-suite/success/Fixpoint.v index 680046da..cf821073 100644 --- a/test-suite/success/Fixpoint.v +++ b/test-suite/success/Fixpoint.v @@ -29,3 +29,22 @@ CoFixpoint g (n:nat) (m:=pred n) (l:Stream m) (p:=S n) : Stream p := Eval compute in (fun l => match g 2 (Consn 0 6 l) with Consn _ a _ => a end). +(* Check inference of simple types in presence of non ambiguous + dependencies (needs revision 10125) *) + +Section folding. + +Inductive vector (A:Type) : nat -> Type := + | Vnil : vector A 0 + | Vcons : forall (a:A) (n:nat), vector A n -> vector A (S n). + +Variables (B C : Set) (g : B -> C -> C) (c : C). + +Fixpoint foldrn n bs := + match bs with + | Vnil => c + | Vcons b _ tl => g b (foldrn _ tl) + end. + +End folding. + diff --git a/test-suite/success/ImplicitArguments.v b/test-suite/success/ImplicitArguments.v new file mode 100644 index 00000000..e7795733 --- /dev/null +++ b/test-suite/success/ImplicitArguments.v @@ -0,0 +1,17 @@ +Inductive vector {A : Type} : nat -> Type := +| vnil : vector 0 +| vcons : A -> forall {n'}, vector n' -> vector (S n'). + +Require Import Coq.Program.Program. + +Program Definition head {A : Type} {n : nat} (v : vector A (S n)) : vector A n := + match v with + | vnil => ! + | vcons a n' v' => v' + end. + +Fixpoint app {A : Type} {n m : nat} (v : vector A n) (w : vector A m) : vector A (n + m) := + match v in vector _ n return vector A (n + m) with + | vnil => w + | vcons a n' v' => vcons a (app v' w) + end. diff --git a/test-suite/success/Injection.v b/test-suite/success/Injection.v index 606e884a..867d7374 100644 --- a/test-suite/success/Injection.v +++ b/test-suite/success/Injection.v @@ -43,6 +43,29 @@ intros; injection H as Hyt Hxz. exact Hxz. Qed. +(* Check the variants of injection *) + +Goal forall x y, S x = S y -> True. +injection 1 as H'. +Undo. +intros. +injection H as H'. +Undo. +Ltac f x := injection x. +f H. +Abort. + +Goal (forall x y : nat, x = y -> S x = S y) -> True. +intros. +try injection (H O) || exact I. +Qed. + +Goal (forall x y : nat, x = y -> S x = S y) -> True. +intros. +einjection (H O). +instantiate (1:=O). +Abort. + (* Injection does not projects at positions in Prop... allow it? Inductive t (A:Prop) : Set := c : A -> t A. @@ -53,7 +76,7 @@ Abort. *) -(* Accept does not project on discriminable positions... allow it? +(* Injection does not project on discriminable positions... allow it? Goal 1=2 -> 1=0. intro H. @@ -61,4 +84,4 @@ injection H. intro; assumption. Qed. - *) +*) diff --git a/test-suite/success/LetPat.v b/test-suite/success/LetPat.v new file mode 100644 index 00000000..545b8aeb --- /dev/null +++ b/test-suite/success/LetPat.v @@ -0,0 +1,55 @@ +(* Simple let-patterns *) +Variable A B : Type. + +Definition l1 (t : A * B * B) : A := let '(x, y, z) := t in x. +Print l1. +Definition l2 (t : (A * B) * B) : A := let '((x, y), z) := t in x. +Definition l3 (t : A * (B * B)) : A := let '(x, (y, z)) := t in x. +Print l3. + +Record someT (A : Type) := mkT { a : nat; b: A }. + +Definition l4 A (t : someT A) : nat := let 'mkT x y := t in x. +Print l4. +Print sigT. + +Definition l5 A (B : A -> Type) (t : sigT B) : B (projT1 t) := + let 'existT x y := t return B (projT1 t) in y. + +Definition l6 A (B : A -> Type) (t : sigT B) : B (projT1 t) := + let 'existT x y as t' := t return B (projT1 t') in y. + +Definition l7 A (B : A -> Type) (t : sigT B) : B (projT1 t) := + let 'existT x y as t' in sigT _ := t return B (projT1 t') in y. + +Definition l8 A (B : A -> Type) (t : sigT B) : B (projT1 t) := + match t with + existT x y => y + end. + +(** An example from algebra, using let' and inference of return clauses + to deconstruct contexts. *) + +Record a_category (A : Type) (hom : A -> A -> Type) := { }. + +Definition category := { A : Type & { hom : A -> A -> Type & a_category A hom } }. + +Record a_functor (A : Type) (hom : A -> A -> Type) (C : a_category A hom) := { }. + +Notation " x :& y " := (@existT _ _ x y) (right associativity, at level 55) : core_scope. + +Definition functor (c d : category) := + let ' A :& homA :& CA := c in + let ' B :& homB :& CB := d in + A -> B. + +Definition identity_functor (c : category) : functor c c := + let 'A :& homA :& CA := c in + fun x => x. + +Definition functor_composition (a b c : category) : functor a b -> functor b c -> functor a c := + let 'A :& homA :& CA := a in + let 'B :& homB :& CB := b in + let 'C :& homB :& CB := c in + fun f g => + fun x => g (f x). diff --git a/test-suite/success/Notations.v b/test-suite/success/Notations.v index a9e2c59a..facd5509 100644 --- a/test-suite/success/Notations.v +++ b/test-suite/success/Notations.v @@ -1,5 +1,5 @@ (* Check that "where" clause behaves as if given independently of the *) -(* definition (variant of bug #113? submitted by Assia Mahboubi) *) +(* definition (variant of bug #1132 submitted by Assia Mahboubi) *) Fixpoint plus1 (n m:nat) {struct n} : nat := match n with @@ -7,3 +7,17 @@ Fixpoint plus1 (n m:nat) {struct n} : nat := | S p => S (p+m) end where "n + m" := (plus1 n m) : nat_scope. + +(* Check behaviour wrt yet empty levels (see Stephane's bug #1850) *) + +Parameter P : Type -> Type -> Type -> Type. +Notation "e |= t --> v" := (P e t v) (at level 100, t at level 54). +Check (nat |= nat --> nat). + +(* Check that first non empty definition at an empty level can be of any + associativity *) + +Definition marker := O. +Notation "x +1" := (S x) (at level 8, left associativity). +Reset marker. +Notation "x +1" := (S x) (at level 8, right associativity). diff --git a/test-suite/success/Omega.v b/test-suite/success/Omega.v index 2d29a835..ecbf04e4 100644 --- a/test-suite/success/Omega.v +++ b/test-suite/success/Omega.v @@ -10,14 +10,14 @@ intros x y. omega. Qed. -(* Proposed by Pierre Crégut *) +(* Proposed by Pierre Crégut *) Lemma lem2 : forall x : Z, (x < 4)%Z -> (x > 2)%Z -> x = 3%Z. intro. omega. Qed. -(* Proposed by Jean-Christophe Filliâtre *) +(* Proposed by Jean-Christophe Filliâtre *) Lemma lem3 : forall x y : Z, x = y -> (x + x)%Z = (y + y)%Z. Proof. @@ -25,7 +25,7 @@ intros. omega. Qed. -(* Proposed by Jean-Christophe Filliâtre: confusion between an Omega *) +(* Proposed by Jean-Christophe Filliâtre: confusion between an Omega *) (* internal variable and a section variable (June 2001) *) Section A. @@ -87,10 +87,8 @@ Qed. (* Check that the interpretation of mult on nat enforces its positivity *) (* Submitted by Hubert Thierry (bug #743) *) -(* Postponed... problem with goals of the form "(n*m=0)%nat -> (n*m=0)%Z" -Require Omega. -Lemma lem10 : (n, m : nat) (le n (plus n (mult n m))). +(* Postponed... problem with goals of the form "(n*m=0)%nat -> (n*m=0)%Z" *) +Lemma lem10 : forall n m:nat, le n (plus n (mult n m)). Proof. -Intros; Omega. +intros; omega with *. Qed. -*) diff --git a/test-suite/success/OmegaPre.v b/test-suite/success/OmegaPre.v new file mode 100644 index 00000000..bb800b7a --- /dev/null +++ b/test-suite/success/OmegaPre.v @@ -0,0 +1,127 @@ +Require Import ZArith Nnat Omega. +Open Scope Z_scope. + +(** Test of the zify preprocessor for (R)Omega *) + +(* More details in file PreOmega.v + + (r)omega with Z : starts with zify_op + (r)omega with nat : starts with zify_nat + (r)omega with positive : starts with zify_positive + (r)omega with N : starts with uses zify_N + (r)omega with * : starts zify (a saturation of the others) +*) + +(* zify_op *) + +Goal forall a:Z, Zmax a a = a. +intros. +omega with *. +Qed. + +Goal forall a b:Z, Zmax a b = Zmax b a. +intros. +omega with *. +Qed. + +Goal forall a b c:Z, Zmax a (Zmax b c) = Zmax (Zmax a b) c. +intros. +omega with *. +Qed. + +Goal forall a b:Z, Zmax a b + Zmin a b = a + b. +intros. +omega with *. +Qed. + +Goal forall a:Z, (Zabs a)*(Zsgn a) = a. +intros. +zify. +intuition; subst; omega. (* pure multiplication: omega alone can't do it *) +Qed. + +Goal forall a:Z, Zabs a = a -> a >= 0. +intros. +omega with *. +Qed. + +Goal forall a:Z, Zsgn a = a -> a = 1 \/ a = 0 \/ a = -1. +intros. +omega with *. +Qed. + +(* zify_nat *) + +Goal forall m: nat, (m<2)%nat -> (0<= m+m <=2)%nat. +intros. +omega with *. +Qed. + +Goal forall m:nat, (m<1)%nat -> (m=0)%nat. +intros. +omega with *. +Qed. + +Goal forall m: nat, (m<=100)%nat -> (0<= m+m <=200)%nat. +intros. +omega with *. +Qed. +(* 2000 instead of 200: works, but quite slow *) + +Goal forall m: nat, (m*m>=0)%nat. +intros. +omega with *. +Qed. + +(* zify_positive *) + +Goal forall m: positive, (m<2)%positive -> (2 <= m+m /\ m+m <= 2)%positive. +intros. +omega with *. +Qed. + +Goal forall m:positive, (m<2)%positive -> (m=1)%positive. +intros. +omega with *. +Qed. + +Goal forall m: positive, (m<=1000)%positive -> (2<=m+m/\m+m <=2000)%positive. +intros. +omega with *. +Qed. + +Goal forall m: positive, (m*m>=1)%positive. +intros. +omega with *. +Qed. + +(* zify_N *) + +Goal forall m:N, (m<2)%N -> (0 <= m+m /\ m+m <= 2)%N. +intros. +omega with *. +Qed. + +Goal forall m:N, (m<1)%N -> (m=0)%N. +intros. +omega with *. +Qed. + +Goal forall m:N, (m<=1000)%N -> (0<=m+m/\m+m <=2000)%N. +intros. +omega with *. +Qed. + +Goal forall m:N, (m*m>=0)%N. +intros. +omega with *. +Qed. + +(* mix of datatypes *) + +Goal forall p, Z_of_N (N_of_nat (nat_of_N (Npos p))) = Zpos p. +intros. +omega with *. +Qed. + + diff --git a/test-suite/success/ROmega.v b/test-suite/success/ROmega.v index ff1f57df..0c37c59a 100644 --- a/test-suite/success/ROmega.v +++ b/test-suite/success/ROmega.v @@ -68,31 +68,29 @@ Variable n : nat. Variable ap_n : n <> 0. Let delta := f n ap_n. Lemma lem7 : n = n. - (*romega. ---> ROMEGA CANT DEAL WITH NAT*) -Admitted. + romega with nat. +Qed. End C. (* Problem of dependencies *) Require Import Omega. Lemma lem8 : forall H : 0 = 0 -> 0 = 0, H = H -> 0 = 0. intros. -(* romega. ---> ROMEGA CANT DEAL WITH NAT*) -Admitted. +romega with nat. +Qed. (* Bug that what caused by the use of intro_using in Omega *) Require Import Omega. Lemma lem9 : forall p q : nat, ~ (p <= q /\ p < q \/ q <= p /\ p < q) -> p < p \/ p <= p. intros. -(* romega. ---> ROMEGA CANT DEAL WITH NAT*) -Admitted. +romega with nat. +Qed. (* Check that the interpretation of mult on nat enforces its positivity *) (* Submitted by Hubert Thierry (bug #743) *) -(* Postponed... problem with goals of the form "(n*m=0)%nat -> (n*m=0)%Z" -Require Omega. -Lemma lem10 : (n, m : nat) (le n (plus n (mult n m))). +(* Postponed... problem with goals of the form "(n*m=0)%nat -> (n*m=0)%Z" *) +Lemma lem10 : forall n m : nat, le n (plus n (mult n m)). Proof. -Intros; Omega. +intros; romega with nat. Qed. -*) diff --git a/test-suite/success/ROmegaPre.v b/test-suite/success/ROmegaPre.v new file mode 100644 index 00000000..550edca5 --- /dev/null +++ b/test-suite/success/ROmegaPre.v @@ -0,0 +1,127 @@ +Require Import ZArith Nnat ROmega. +Open Scope Z_scope. + +(** Test of the zify preprocessor for (R)Omega *) + +(* More details in file PreOmega.v + + (r)omega with Z : starts with zify_op + (r)omega with nat : starts with zify_nat + (r)omega with positive : starts with zify_positive + (r)omega with N : starts with uses zify_N + (r)omega with * : starts zify (a saturation of the others) +*) + +(* zify_op *) + +Goal forall a:Z, Zmax a a = a. +intros. +romega with *. +Qed. + +Goal forall a b:Z, Zmax a b = Zmax b a. +intros. +romega with *. +Qed. + +Goal forall a b c:Z, Zmax a (Zmax b c) = Zmax (Zmax a b) c. +intros. +romega with *. +Qed. + +Goal forall a b:Z, Zmax a b + Zmin a b = a + b. +intros. +romega with *. +Qed. + +Goal forall a:Z, (Zabs a)*(Zsgn a) = a. +intros. +zify. +intuition; subst; romega. (* pure multiplication: omega alone can't do it *) +Qed. + +Goal forall a:Z, Zabs a = a -> a >= 0. +intros. +romega with *. +Qed. + +Goal forall a:Z, Zsgn a = a -> a = 1 \/ a = 0 \/ a = -1. +intros. +romega with *. +Qed. + +(* zify_nat *) + +Goal forall m: nat, (m<2)%nat -> (0<= m+m <=2)%nat. +intros. +romega with *. +Qed. + +Goal forall m:nat, (m<1)%nat -> (m=0)%nat. +intros. +romega with *. +Qed. + +Goal forall m: nat, (m<=100)%nat -> (0<= m+m <=200)%nat. +intros. +romega with *. +Qed. +(* 2000 instead of 200: works, but quite slow *) + +Goal forall m: nat, (m*m>=0)%nat. +intros. +romega with *. +Qed. + +(* zify_positive *) + +Goal forall m: positive, (m<2)%positive -> (2 <= m+m /\ m+m <= 2)%positive. +intros. +romega with *. +Qed. + +Goal forall m:positive, (m<2)%positive -> (m=1)%positive. +intros. +romega with *. +Qed. + +Goal forall m: positive, (m<=1000)%positive -> (2<=m+m/\m+m <=2000)%positive. +intros. +romega with *. +Qed. + +Goal forall m: positive, (m*m>=1)%positive. +intros. +romega with *. +Qed. + +(* zify_N *) + +Goal forall m:N, (m<2)%N -> (0 <= m+m /\ m+m <= 2)%N. +intros. +romega with *. +Qed. + +Goal forall m:N, (m<1)%N -> (m=0)%N. +intros. +romega with *. +Qed. + +Goal forall m:N, (m<=1000)%N -> (0<=m+m/\m+m <=2000)%N. +intros. +romega with *. +Qed. + +Goal forall m:N, (m*m>=0)%N. +intros. +romega with *. +Qed. + +(* mix of datatypes *) + +Goal forall p, Z_of_N (N_of_nat (nat_of_N (Npos p))) = Zpos p. +intros. +romega with *. +Qed. + + diff --git a/test-suite/success/apply.v b/test-suite/success/apply.v index 4f260696..fcce68b9 100644 --- a/test-suite/success/apply.v +++ b/test-suite/success/apply.v @@ -7,8 +7,197 @@ assumption. Qed. Require Import ZArith. -Open Scope Z_scope. -Goal forall x y z, ~ z <= 0 -> x * z < y * z -> x <= y. +Goal (forall x y z, ~ z <= 0 -> x * z < y * z -> x <= y)%Z. intros; apply Znot_le_gt, Zgt_lt in H. apply Zmult_lt_reg_r, Zlt_le_weak in H0; auto. Qed. + +(* Check if it unfolds when there are not enough premises *) + +Goal forall n, n = S n -> False. +intros. +apply n_Sn in H. +assumption. +Qed. + +(* Check naming in with bindings; printing used to be inconsistent before *) +(* revision 9450 *) + +Notation S':=S (only parsing). +Goal (forall S, S = S' S) -> (forall S, S = S' S). +intros. +apply H with (S0 := S). +Qed. + +(* Check inference of implicit arguments in bindings *) + +Goal exists y : nat -> Type, y 0 = y 0. +exists (fun x => True). +trivial. +Qed. + +(* Check universe handling in typed unificationn *) + +Definition E := Type. +Goal exists y : E, y = y. +exists Prop. +trivial. +Qed. + +Variable Eq : Prop = (Prop -> Prop) :> E. +Goal Prop. +rewrite Eq. +Abort. + +(* Check insertion of coercions in bindings *) + +Coercion eq_true : bool >-> Sortclass. +Goal exists A:Prop, A = A. +exists true. +trivial. +Qed. + +(* Check use of unification of bindings types in specialize *) + +Variable P : nat -> Prop. +Variable L : forall (l : nat), P l -> P l. +Goal P 0 -> True. +intros. +specialize L with (1:=H). +Abort. +Reset P. + +(* Two examples that show that hnf_constr is used when unifying types + of bindings (a simplification of a script from Field_Theory) *) + +Require Import List. +Open Scope list_scope. +Fixpoint P (l : list nat) : Prop := + match l with + | nil => True + | e1 :: nil => e1 = e1 + | e1 :: l1 => e1 = e1 /\ P l1 + end. +Variable L : forall n l, P (n::l) -> P l. + +Goal forall (x:nat) l, P (x::l) -> P l. +intros. +apply L with (1:=H). +Qed. + +Goal forall (x:nat) l, match l with nil => x=x | _::_ => x=x /\ P l end -> P l. +intros. +apply L with (1:=H). +Qed. + +(* The following call to auto fails if the type of the clause + associated to the H is not beta-reduced [but apply H works] + (a simplification of a script from FSetAVL) *) + +Definition apply (f:nat->Prop) := forall x, f x. +Goal apply (fun n => n=0) -> 1=0. +intro H. +auto. +Qed. + +(* The following fails if the coercion Zpos is not introduced around p + before trying a subterm that matches the left-hand-side of the equality + (a simplication of an example taken from Nijmegen/QArith) *) + +Require Import ZArith. +Coercion Zpos : positive >-> Z. +Variable f : Z -> Z -> Z. +Variable g : forall q1 q2 p : Z, f (f q1 p) (f q2 p) = Z0. +Goal forall p q1 q2, f (f q1 (Zpos p)) (f q2 (Zpos p)) = Z0. +intros; rewrite g with (p:=p). +reflexivity. +Qed. + +(* A funny example where the behavior differs depending on which of a + multiple solution to a unification problem is chosen (an instance + of this case can be found in the proof of Buchberger.BuchRed.nf_divp) *) + +Definition succ x := S x. +Goal forall (I : nat -> Set) (P : nat -> Prop) (Q : forall n:nat, I n -> Prop), + (forall x y, P x -> Q x y) -> + (forall x, P (S x)) -> forall y: I (S 0), Q (succ 0) y. +intros. +apply H with (y:=y). +(* [x] had two possible instances: [S 0], coming from unifying the + type of [y] with [I ?n] and [succ 0] coming from the unification with + the goal; only the first one allows to make the next apply (which + does not work modulo delta) working *) +apply H0. +Qed. + +(* A similar example with a arbitrary long conversion between the two + possible instances *) + +Fixpoint compute_succ x := + match x with O => S 0 | S n => S (compute_succ n) end. + +Goal forall (I : nat -> Set) (P : nat -> Prop) (Q : forall n:nat, I n -> Prop), + (forall x y, P x -> Q x y) -> + (forall x, P (S x)) -> forall y: I (S 100), Q (compute_succ 100) y. +intros. +apply H with (y:=y). +apply H0. +Qed. + +(* Another example with multiple convertible solutions to the same + metavariable (extracted from Algebra.Hom_module.Hom_module, 10th + subgoal which precisely fails) *) + +Definition ID (A:Type) := A. +Goal forall f:Type -> Type, + forall (P : forall A:Type, A -> Prop), + (forall (B:Type) x, P (f B) x -> P (f B) x) -> + (forall (A:Type) x, P (f (f A)) x) -> + forall (A:Type) (x:f (f A)), P (f (ID (f A))) x. +intros. +apply H. +(* The parameter [B] had two possible instances: [ID (f A)] by direct + unification and [f A] by unification of the type of [x]; only the + first choice makes the next command fail, as it was + (unfortunately?) in Hom_module *) +try apply H. +unfold ID; apply H0. +Qed. + +(* Test coercion below product and on non meta-free terms in with bindings *) +(* Cf wishes #1408 from E. Makarov *) + +Parameter bool_Prop :> bool -> Prop. +Parameter r : bool -> bool -> bool. +Axiom ax : forall (A : Set) (R : A -> A -> Prop) (x y : A), R x y. + +Theorem t : r true false. +apply ax with (R := r). +Qed. + +(* Check verification of type at unification (submitted by Stéphane Lengrand): + without verification, the first "apply" works what leads to the incorrect + instantiation of x by Prop *) + +Theorem u : ~(forall x:Prop, ~x). +unfold not. +intro. +eapply H. +apply (forall B:Prop,B->B) || (instantiate (1:=True); exact I). +Defined. + +(* Fine-tuning coercion insertion in presence of unfolding (bug #1883) *) + +Parameter name : Set. +Definition atom := name. + +Inductive exp : Set := + | var : atom -> exp. + +Coercion var : atom >-> exp. + +Axiom silly_axiom : forall v : exp, v = v -> False. + +Lemma silly_lemma : forall x : atom, False. +intros x. +apply silly_axiom with (v := x). (* fails *) diff --git a/test-suite/success/cc.v b/test-suite/success/cc.v index fecc8977..94d827fd 100644 --- a/test-suite/success/cc.v +++ b/test-suite/success/cc.v @@ -78,6 +78,14 @@ intros. congruence. Qed. +(* example with implications *) + +Theorem arrow : forall (A B: Prop) (C D:Set) , A=B -> C=D -> +(A -> C) = (B -> D). +congruence. +Qed. + + Set Implicit Arguments. Parameter elt: Set. @@ -94,5 +102,6 @@ Proof. auto. Qed. + \ No newline at end of file diff --git a/test-suite/success/change.v b/test-suite/success/change.v new file mode 100644 index 00000000..cea01712 --- /dev/null +++ b/test-suite/success/change.v @@ -0,0 +1,6 @@ +(* A few tests of the syntax of clauses and of the interpretation of change *) + +Goal let a := 0+0 in a=a. +intro. +change 0 in (value of a). +change ((fun A:Type => A) nat) in (type of a). diff --git a/test-suite/success/clear.v b/test-suite/success/clear.v index 444146f7..8169361c 100644 --- a/test-suite/success/clear.v +++ b/test-suite/success/clear.v @@ -1,6 +1,15 @@ Goal forall x:nat, (forall x, x=0 -> True)->True. intros; eapply H. instantiate (1:=(fun y => _) (S x)). - simpl. - clear x || trivial. + simpl. + clear x. trivial. Qed. + +Goal forall y z, (forall x:nat, x=y -> True) -> y=z -> True. + intros; eapply H. + rename z into z'. + clear H0. + clear z'. + reflexivity. +Qed. + diff --git a/test-suite/success/conv_pbs.v b/test-suite/success/conv_pbs.v new file mode 100644 index 00000000..062c3ee5 --- /dev/null +++ b/test-suite/success/conv_pbs.v @@ -0,0 +1,223 @@ +(* A bit complex but realistic example whose last fixpoint definition + used to fail in 8.1 because of wrong environment in conversion + problems (see revision 9664) *) + +Require Import List. +Require Import Arith. + +Parameter predicate : Set. +Parameter function : Set. +Definition variable := nat. +Definition x0 := 0. +Definition var_eq_dec := eq_nat_dec. + +Inductive term : Set := + | App : function -> term -> term + | Var : variable -> term. + +Definition atom := (predicate * term)%type. + +Inductive formula : Set := + | Atom : atom -> formula + | Imply : formula -> formula -> formula + | Forall : variable -> formula -> formula. + +Notation "A --> B" := (Imply A B) (at level 40). + +Definition substitution range := list (variable * range). + +Fixpoint remove_assoc (A:Set)(x:variable)(rho: substitution A){struct rho} + : substitution A := + match rho with + | nil => rho + | (y,t) :: rho => if var_eq_dec x y then remove_assoc A x rho + else (y,t) :: remove_assoc A x rho + end. + +Fixpoint assoc (A:Set)(x:variable)(rho:substitution A){struct rho} + : option A := + match rho with + | nil => None + | (y,t) :: rho => if var_eq_dec x y then Some t + else assoc A x rho + end. + +Fixpoint subst_term (rho:substitution term)(t:term){struct t} : term := + match t with + | Var x => match assoc _ x rho with + | Some a => a + | None => Var x + end + | App f t' => App f (subst_term rho t') + end. + +Fixpoint subst_formula (rho:substitution term)(A:formula){struct A}:formula := + match A with + | Atom (p,t) => Atom (p, subst_term rho t) + | A --> B => subst_formula rho A --> subst_formula rho B + | Forall y A => Forall y (subst_formula (remove_assoc _ y rho) A) + (* assume t closed *) + end. + +Definition subst A x t := subst_formula ((x,t):: nil) A. + +Record Kripke : Type := { + worlds: Set; + wle : worlds -> worlds -> Type; + wle_refl : forall w, wle w w ; + wle_trans : forall w w' w'', wle w w' -> wle w' w'' -> wle w w''; + domain : Set; + vars : variable -> domain; + funs : function -> domain -> domain; + atoms : worlds -> predicate * domain -> Type; + atoms_mon : forall w w', wle w w' -> forall P, atoms w P -> atoms w' P +}. + +Section Sem. + +Variable K : Kripke. + +Fixpoint sem (rho: substitution (domain K))(t:term){struct t} : domain K := + match t with + | Var x => match assoc _ x rho with + | Some a => a + | None => vars K x + end + | App f t' => funs K f (sem rho t') + end. + +End Sem. + +Notation "w <= w'" := (wle _ w w'). + +Set Implicit Arguments. + +Reserved Notation "w ||- A" (at level 70). + +Definition context := list formula. + +Variable fresh : variable -> context -> Prop. + +Variable fresh_out : context -> variable. + +Axiom fresh_out_spec : forall Gamma, fresh (fresh_out Gamma) Gamma. + +Axiom fresh_peel : forall x A Gamma, fresh x (A::Gamma) -> fresh x Gamma. + +Fixpoint force (K:Kripke)(rho: substitution (domain K))(w:worlds K)(A:formula) + {struct A} : Type := + match A with + | Atom (p,t) => atoms K w (p, sem K rho t) + | A --> B => forall w', w <= w' -> force K rho w' A -> force K rho w' B + | Forall x A => forall w', w <= w' -> forall t, force K ((x,t)::remove_assoc _ x rho) w' A + end. + +Notation "w ||- A" := (force _ nil w A). + +Reserved Notation "Gamma |- A" (at level 70). +Reserved Notation "Gamma ; A |- C" (at level 70, A at next level). + +Inductive context_prefix (Gamma:context) : context -> Type := + | CtxPrefixRefl : context_prefix Gamma Gamma + | CtxPrefixTrans : forall A Gamma', context_prefix Gamma Gamma' -> context_prefix Gamma (cons A Gamma'). + +Inductive in_context (A:formula) : list formula -> Prop := + | InAxiom : forall Gamma, in_context A (cons A Gamma) + | OmWeak : forall Gamma B, in_context A Gamma -> in_context A (cons B Gamma). + +Inductive prove : list formula -> formula -> Type := + | ProofImplyR : forall A B Gamma, prove (cons A Gamma) B + -> prove Gamma (A --> B) + | ProofForallR : forall x A Gamma, (forall y, fresh y (A::Gamma) + -> prove Gamma (subst A x (Var y))) -> prove Gamma (Forall x A) + | ProofCont : forall A Gamma Gamma' C, context_prefix (A::Gamma) Gamma' + -> (prove_stoup Gamma' A C) -> (Gamma' |- C) + +where "Gamma |- A" := (prove Gamma A) + + with prove_stoup : list formula -> formula -> formula -> Type := + | ProofAxiom Gamma C: Gamma ; C |- C + | ProofImplyL Gamma C : forall A B, (Gamma |- A) + -> (prove_stoup Gamma B C) -> (prove_stoup Gamma (A --> B) C) + | ProofForallL Gamma C : forall x t A, (prove_stoup Gamma (subst A x t) C) + -> (prove_stoup Gamma (Forall x A) C) + +where " Gamma ; B |- A " := (prove_stoup Gamma B A). + +Axiom context_prefix_trans : + forall Gamma Gamma' Gamma'', + context_prefix Gamma Gamma' + -> context_prefix Gamma' Gamma'' + -> context_prefix Gamma Gamma''. + +Axiom Weakening : + forall Gamma Gamma' A, + context_prefix Gamma Gamma' -> Gamma |- A -> Gamma' |- A. + +Axiom universal_weakening : + forall Gamma Gamma', context_prefix Gamma Gamma' + -> forall P, Gamma |- Atom P -> Gamma' |- Atom P. + +Canonical Structure Universal := Build_Kripke + context + context_prefix + CtxPrefixRefl + context_prefix_trans + term + Var + App + (fun Gamma P => Gamma |- Atom P) + universal_weakening. + +Axiom subst_commute : + forall A rho x t, + subst_formula ((x,t)::rho) A = subst (subst_formula rho A) x t. + +Axiom subst_formula_atom : + forall rho p t, + Atom (p, sem _ rho t) = subst_formula rho (Atom (p,t)). + +Fixpoint universal_completeness (Gamma:context)(A:formula){struct A} + : forall rho:substitution term, + force _ rho Gamma A -> Gamma |- subst_formula rho A + := + match A + return forall rho, force _ rho Gamma A + -> Gamma |- subst_formula rho A + with + | Atom (p,t) => fun rho H => eq_rect _ (fun A => Gamma |- A) H _ (subst_formula_atom rho p t) + | A --> B => fun rho HImplyAB => + let A' := subst_formula rho A in + ProofImplyR (universal_completeness (A'::Gamma) B rho + (HImplyAB (A'::Gamma)(CtxPrefixTrans A' (CtxPrefixRefl Gamma)) + (universal_completeness_stoup A rho (fun C Gamma' Hle p + => ProofCont Hle p)))) + | Forall x A => fun rho HForallA + => ProofForallR x (fun y Hfresh + => eq_rect _ _ (universal_completeness Gamma A _ + (HForallA Gamma (CtxPrefixRefl Gamma)(Var y))) _ (subst_commute _ _ _ _ )) + end +with universal_completeness_stoup (Gamma:context)(A:formula){struct A} + : forall rho, (forall C Gamma', context_prefix Gamma Gamma' + -> Gamma' ; subst_formula rho A |- C -> Gamma' |- C) + -> force _ rho Gamma A + := + match A return forall rho, + (forall C Gamma', context_prefix Gamma Gamma' + -> Gamma' ; subst_formula rho A |- C + -> Gamma' |- C) + -> force _ rho Gamma A + with + | Atom (p,t) as C => fun rho H + => H _ Gamma (CtxPrefixRefl Gamma)(ProofAxiom _ _) + | A --> B => fun rho H => fun Gamma' Hle HA + => universal_completeness_stoup B rho (fun C Gamma'' Hle' p + => H C Gamma'' (context_prefix_trans Hle Hle') + (ProofImplyL (Weakening Hle' (universal_completeness Gamma' A rho HA)) p)) + | Forall x A => fun rho H => fun Gamma' Hle t + => (universal_completeness_stoup A ((x,t)::remove_assoc _ x rho) + (fun C Gamma'' Hle' p => + H C Gamma'' (context_prefix_trans Hle Hle') + (ProofForallL x t (subst_formula (remove_assoc _ x rho) A) + (eq_rect _ (fun D => Gamma'' ; D |- C) p _ (subst_commute _ _ _ _))))) + end. diff --git a/test-suite/success/decl_mode.v b/test-suite/success/decl_mode.v new file mode 100644 index 00000000..fede31a8 --- /dev/null +++ b/test-suite/success/decl_mode.v @@ -0,0 +1,182 @@ +(* \sqrt 2 is irrationnal, (c) 2006 Pierre Corbineau *) + +Set Firstorder Depth 1. +Require Import ArithRing Wf_nat Peano_dec Div2 Even Lt. + +Lemma double_div2: forall n, div2 (double n) = n. +proof. + assume n:nat. + per induction on n. + suppose it is 0. + suffices (0=0) to show thesis. + thus thesis. + suppose it is (S m) and Hrec:thesis for m. + have (div2 (double (S m))= div2 (S (S (double m)))). + ~= (S (div2 (double m))). + thus ~= (S m) by Hrec. + end induction. +end proof. +Show Script. +Qed. + +Lemma double_inv : forall n m, double n = double m -> n = m . +proof. + let n, m be such that H:(double n = double m). +have (n = div2 (double n)) by double_div2,H. + ~= (div2 (double m)) by H. + thus ~= m by double_div2. +end proof. +Qed. + +Lemma double_mult_l : forall n m, (double (n * m)=n * double m). +proof. + assume n:nat and m:nat. + have (double (n * m) = n*m + n * m). + ~= (n * (m+m)) by * using ring. + thus ~= (n * double m). +end proof. +Qed. + +Lemma double_mult_r : forall n m, (double (n * m)=double n * m). +proof. + assume n:nat and m:nat. + have (double (n * m) = n*m + n * m). + ~= ((n + n) * m) by * using ring. + thus ~= (double n * m). +end proof. +Qed. + +Lemma even_is_even_times_even: forall n, even (n*n) -> even n. +proof. + let n be such that H:(even (n*n)). + per cases of (even n \/ odd n) by even_or_odd. + suppose (odd n). + hence thesis by H,even_mult_inv_r. + end cases. +end proof. +Qed. + +Lemma main_thm_aux: forall n,even n -> +double (double (div2 n *div2 n))=n*n. +proof. + given n such that H:(even n). + *** have (double (double (div2 n * div2 n)) + = double (div2 n) * double (div2 n)) + by double_mult_l,double_mult_r. + thus ~= (n*n) by H,even_double. +end proof. +Qed. + +Require Omega. + +Lemma even_double_n: (forall m, even (double m)). +proof. + assume m:nat. + per induction on m. + suppose it is 0. + thus thesis. + suppose it is (S mm) and thesis for mm. + then H:(even (S (S (mm+mm)))). + have (S (S (mm + mm)) = S mm + S mm) using omega. + hence (even (S mm +S mm)) by H. + end induction. +end proof. +Qed. + +Theorem main_theorem: forall n p, n*n=double (p*p) -> p=0. +proof. + assume n0:nat. + define P n as (forall p, n*n=double (p*p) -> p=0). + claim rec_step: (forall n, (forall m,m P m) -> P n). + let n be such that H:(forall m : nat, m < n -> P m) and p:nat . + per cases of ({n=0}+{n<>0}) by eq_nat_dec. + suppose H1:(n=0). + per cases on p. + suppose it is (S p'). + assume (n * n = double (S p' * S p')). + =~ 0 by H1,mult_n_O. + ~= (S ( p' + p' * S p' + S p'* S p')) + by plus_n_Sm. + hence thesis . + suppose it is 0. + thus thesis. + end cases. + suppose H1:(n<>0). + assume H0:(n*n=double (p*p)). + have (even (double (p*p))) by even_double_n . + then (even (n*n)) by H0. + then H2:(even n) by even_is_even_times_even. + then (double (double (div2 n *div2 n))=n*n) + by main_thm_aux. + ~= (double (p*p)) by H0. + then H':(double (div2 n *div2 n)= p*p) by double_inv. + have (even (double (div2 n *div2 n))) by even_double_n. + then (even (p*p)) by even_double_n,H'. + then H3:(even p) by even_is_even_times_even. + have (double(double (div2 n * div2 n)) = n*n) + by H2,main_thm_aux. + ~= (double (p*p)) by H0. + ~= (double(double (double (div2 p * div2 p)))) + by H3,main_thm_aux. + then H'':(div2 n * div2 n = double (div2 p * div2 p)) + by double_inv. + then (div2 n < n) by lt_div2,neq_O_lt,H1. + then H4:(div2 p=0) by (H (div2 n)),H''. + then (double (div2 p) = double 0). + =~ p by even_double,H3. + thus ~= 0. + end cases. + end claim. + hence thesis by (lt_wf_ind n0 P). +end proof. +Qed. + +Require Import Reals Field. +(*Coercion INR: nat >->R. +Coercion IZR: Z >->R.*) + +Open Scope R_scope. + +Lemma square_abs_square: + forall p,(INR (Zabs_nat p) * INR (Zabs_nat p)) = (IZR p * IZR p). +proof. + assume p:Z. + per cases on p. + suppose it is (0%Z). + thus thesis. + suppose it is (Zpos z). + thus thesis. + suppose it is (Zneg z). + have ((INR (Zabs_nat (Zneg z)) * INR (Zabs_nat (Zneg z))) = + (IZR (Zpos z) * IZR (Zpos z))). + ~= ((- IZR (Zpos z)) * (- IZR (Zpos z))). + thus ~= (IZR (Zneg z) * IZR (Zneg z)). + end cases. +end proof. +Qed. + +Definition irrational (x:R):Prop := + forall (p:Z) (q:nat),q<>0%nat -> x<> (IZR p/INR q). + +Theorem irrationnal_sqrt_2: irrational (sqrt (INR 2%nat)). +proof. + let p:Z,q:nat be such that H:(q<>0%nat) + and H0:(sqrt (INR 2%nat)=(IZR p/INR q)). + have H_in_R:(INR q<>0:>R) by H. + have triv:((IZR p/INR q* INR q) =IZR p :>R) by * using field. + have sqrt2:((sqrt (INR 2%nat) * sqrt (INR 2%nat))= INR 2%nat:>R) by sqrt_def. + have (INR (Zabs_nat p * Zabs_nat p) + = (INR (Zabs_nat p) * INR (Zabs_nat p))) + by mult_INR. + ~= (IZR p* IZR p) by square_abs_square. + ~= ((IZR p/INR q*INR q)*(IZR p/INR q*INR q)) by triv. (* we have to factor because field is too weak *) + ~= ((IZR p/INR q)*(IZR p/INR q)*(INR q*INR q)) using ring. + ~= (sqrt (INR 2%nat) * sqrt (INR 2%nat)*(INR q*INR q)) by H0. + ~= (INR (2%nat * (q*q))) by sqrt2,mult_INR. + then (Zabs_nat p * Zabs_nat p = 2* (q * q))%nat. + ~= ((q*q)+(q*q))%nat. + ~= (Div2.double (q*q)). + then (q=0%nat) by main_theorem. + hence thesis by H. +end proof. +Qed. diff --git a/test-suite/success/dependentind.v b/test-suite/success/dependentind.v new file mode 100644 index 00000000..48255386 --- /dev/null +++ b/test-suite/success/dependentind.v @@ -0,0 +1,100 @@ +Require Import Coq.Program.Program. +Set Implicit Arguments. +Unset Strict Implicit. + +Variable A : Set. + +Inductive vector : nat -> Type := vnil : vector 0 | vcons : A -> forall n, vector n -> vector (S n). + +Goal forall n, forall v : vector (S n), vector n. +Proof. + intros n H. + dependent destruction H. + assumption. +Save. + +Require Import ProofIrrelevance. + +Goal forall n, forall v : vector (S n), exists v' : vector n, exists a : A, v = vcons a v'. +Proof. + intros n v. + dependent destruction v. + exists v ; exists a. + reflexivity. +Save. + +(* Extraction Unnamed_thm. *) + +Inductive type : Type := +| base : type +| arrow : type -> type -> type. + +Notation " t --> t' " := (arrow t t') (at level 20, t' at next level). + +Inductive ctx : Type := +| empty : ctx +| snoc : ctx -> type -> ctx. + +Notation " Γ , Ï„ " := (snoc Γ Ï„) (at level 25, t at next level, left associativity). + +Fixpoint conc (Γ Δ : ctx) : ctx := + match Δ with + | empty => Γ + | snoc Δ' x => snoc (conc Γ Δ') x + end. + +Notation " Γ ; Δ " := (conc Γ Δ) (at level 25, left associativity). + +Inductive term : ctx -> type -> Type := +| ax : forall Γ Ï„, term (Γ, Ï„) Ï„ +| weak : forall Γ Ï„, term Γ Ï„ -> forall Ï„', term (Γ, Ï„') Ï„ +| abs : forall Γ Ï„ Ï„', term (Γ , Ï„) Ï„' -> term Γ (Ï„ --> Ï„') +| app : forall Γ Ï„ Ï„', term Γ (Ï„ --> Ï„') -> term Γ Ï„ -> term Γ Ï„'. + +Lemma weakening : forall Γ Δ Ï„, term (Γ ; Δ) Ï„ -> + forall Ï„', term (Γ , Ï„' ; Δ) Ï„. +Proof with simpl in * ; auto ; simpl_depind. + intros Γ Δ Ï„ H. + + dependent induction H. + + destruct Δ... + apply weak ; apply ax. + + apply ax. + + destruct Δ... + specialize (IHterm Γ empty)... + apply weak... + + apply weak... + + destruct Δ... + apply weak ; apply abs ; apply H. + + apply abs... + specialize (IHterm Γ0 (Δ, t, Ï„))... + + apply app with Ï„... +Qed. + +Lemma exchange : forall Γ Δ α β Ï„, term (Γ, α, β ; Δ) Ï„ -> term (Γ, β, α ; Δ) Ï„. +Proof with simpl in * ; simpl_depind ; auto. + intros until 1. + dependent induction H. + + destruct Δ... + apply weak ; apply ax. + + apply ax. + + destruct Δ... + pose (weakening (Γ:=Γ0) (Δ:=(empty, α)))... + + apply weak... + + apply abs... + specialize (IHterm Γ0 α β (Δ, Ï„))... + + eapply app with Ï„... +Save. diff --git a/test-suite/success/destruct.v b/test-suite/success/destruct.v index 9f938e10..5aa78816 100644 --- a/test-suite/success/destruct.v +++ b/test-suite/success/destruct.v @@ -23,3 +23,35 @@ set (b := true) in *. try destruct b. Abort. +(* Used to fail with error "n is used in conclusion" before revision 9447 *) + +Goal forall n, n = S n. +induction S. +Abort. + +(* Check that elimination with remaining evars do not raise an bad + error message *) + +Theorem Refl : forall P, P <-> P. tauto. Qed. +Goal True. +case Refl || ecase Refl. +Abort. + + +(* Submitted by B. Baydemir (bug #1882) *) + +Require Import List. + +Definition alist R := list (nat * R)%type. + +Section Properties. + Variables A : Type. + Variables a : A. + Variables E : alist A. + + Lemma silly : E = E. + Proof. + clear. induction E. (* this fails. *) + Abort. + +End Properties. diff --git a/test-suite/success/evars.v b/test-suite/success/evars.v index ad69ced1..082cbfbe 100644 --- a/test-suite/success/evars.v +++ b/test-suite/success/evars.v @@ -68,9 +68,145 @@ Proof. trivial. Qed. Hint Resolve contradiction. Goal False. eauto. +Abort. (* This used to fail in V8.1beta because first-order unification was used before using type information *) Check (exist _ O (refl_equal 0) : {n:nat|n=0}). Check (exist _ O I : {n:nat|True}). + +(* An example (initially from Marseille/Fairisle) that involves an evar with + different solutions (Input, Output or bool) that may or may not be + considered distinct depending on which kind of conversion is used *) + +Section A. +Definition STATE := (nat * bool)%type. +Let Input := bool. +Let Output := bool. +Parameter Out : STATE -> Output. +Check fun (s : STATE) (reg : Input) => reg = Out s. +End A. + +(* The return predicate found should be: "in _=U return U" *) +(* (feature already available in V8.0) *) + +Definition g (T1 T2:Type) (x:T1) (e:T1=T2) : T2 := + match e with + | refl_equal => x + end. + +(* An example extracted from FMapAVL which (may) test restriction on + evars problems of the form ?n[args1]=?n[args2] with distinct args1 + and args2 *) + +Set Implicit Arguments. +Parameter t:Set->Set. +Parameter map:forall elt elt' : Set, (elt -> elt') -> t elt -> t elt'. +Parameter avl: forall elt : Set, t elt -> Prop. +Parameter bst: forall elt : Set, t elt -> Prop. +Parameter map_avl: forall (elt elt' : Set) (f : elt -> elt') (m : t elt), + avl m -> avl (map f m). +Parameter map_bst: forall (elt elt' : Set) (f : elt -> elt') (m : t elt), + bst m -> bst (map f m). +Record bbst (elt:Set) : Set := + Bbst {this :> t elt; is_bst : bst this; is_avl: avl this}. +Definition t' := bbst. +Section B. +Variables elt elt': Set. +Definition map' f (m:t' elt) : t' elt' := + Bbst (map_bst f m.(is_bst)) (map_avl f m.(is_avl)). +End B. +Unset Implicit Arguments. + +(* An example from Lexicographic_Exponentiation that tests the + contraction of reducible fixpoints in type inference *) + +Require Import List. +Check (fun (A:Set) (a b x:A) (l:list A) + (H : l ++ cons x nil = cons b (cons a nil)) => + app_inj_tail l (cons b nil) _ _ H). + +(* An example from NMake (simplified), that uses restriction in solve_refl *) + +Parameter h:(nat->nat)->(nat->nat). +Fixpoint G p cont {struct p} := + h (fun n => match p with O => cont | S p => G p cont end n). + +(* An example from Bordeaux/Cantor that applies evar restriction + below a binder *) + +Require Import Relations. +Parameter lex : forall (A B : Set), (forall (a1 a2:A), {a1=a2}+{a1<>a2}) +-> relation A -> relation B -> A * B -> A * B -> Prop. +Check + forall (A B : Set) eq_A_dec o1 o2, + antisymmetric A o1 -> transitive A o1 -> transitive B o2 -> + transitive _ (lex _ _ eq_A_dec o1 o2). + +(* Another example from Julien Forest that tests unification below binders *) + +Require Import List. +Set Implicit Arguments. +Parameter + merge : forall (A B : Set) (eqA : forall (a1 a2 : A), {a1=a2}+{a1<>a2}) + (eqB : forall (b1 b2 : B), {b1=b2}+{b1<>b2}) + (partial_res l : list (A*B)), option (list (A*B)). +Axiom merge_correct : + forall (A B : Set) eqA eqB (l1 l2 : list (A*B)), + (forall a2 b2 c2, In (a2,b2) l2 -> In (a2,c2) l2 -> b2 = c2) -> + match merge eqA eqB l1 l2 with _ => True end. +Unset Implicit Arguments. + +(* An example from Bordeaux/Additions that tests restriction below binders *) + +Section Additions_while. + +Variable A : Set. +Variables P Q : A -> Prop. +Variable le : A -> A -> Prop. +Hypothesis Q_dec : forall s : A, P s -> {Q s} + {~ Q s}. +Hypothesis le_step : forall s : A, ~ Q s -> P s -> {s' | P s' /\ le s' s}. +Hypothesis le_wf : well_founded le. + +Lemma loopexec : forall s : A, P s -> {s' : A | P s' /\ Q s'}. +refine + (well_founded_induction_type le_wf (fun s => _ -> {s' : A | _ /\ _}) + (fun s hr i => + match Q_dec s i with + | left _ => _ + | right _ => + match le_step s _ _ with + | exist s' h' => + match hr s' _ _ with + | exist s'' _ => exist _ s'' _ + end + end + end)). +Abort. + +End Additions_while. + +(* Two examples from G. Melquiond (bugs #1878 and #1884) *) + +Parameter F1 G1 : nat -> Prop. +Goal forall x : nat, F1 x -> G1 x. +refine (fun x H => proj2 (_ x H)). +Abort. + +Goal forall x : nat, F1 x -> G1 x. +refine (fun x H => proj2 (_ x H) _). +Abort. + +(* Remark: the following example does not succeed any longer in 8.2 because, + the algorithm is more general and does exclude a solution that it should + exclude for typing reason. Handling of types and backtracking is still to + be done + +Section S. +Variables A B : nat -> Prop. +Goal forall x : nat, A x -> B x. +refine (fun x H => proj2 (_ x H) _). +Abort. +End S. +*) diff --git a/test-suite/success/extraction.v b/test-suite/success/extraction.v index 0b3060d5..74d87ffa 100644 --- a/test-suite/success/extraction.v +++ b/test-suite/success/extraction.v @@ -84,7 +84,7 @@ Extraction test12. (* type test12 = (__ -> __ -> __) -> __ *) -Definition test13 := match left True I with +Definition test13 := match @left True True I with | left x => 1 | right x => 0 end. diff --git a/test-suite/success/fix.v b/test-suite/success/fix.v index f4a4d36d..78b01f3e 100644 --- a/test-suite/success/fix.v +++ b/test-suite/success/fix.v @@ -1,10 +1,3 @@ -(************************************************************************) -(* v * The Coq Proof Assistant / The Coq Development Team *) -(* rmax (maxVar p) (maxVar q) end. +(* Check bug #1491 *) + +Require Import Streams. + +Definition decomp (s:Stream nat) : Stream nat := + match s with Cons _ s => s end. + +CoFixpoint bx0 : Stream nat := Cons 0 bx1 +with bx1 : Stream nat := Cons 1 bx0. + +Lemma bx0bx : decomp bx0 = bx1. +simpl. (* used to return bx0 in V8.1 and before instead of bx1 *) +reflexivity. +Qed. + +(* Check mutually inductive statements *) + +Require Import ZArith_base Omega. +Open Scope Z_scope. + +Inductive even: Z -> Prop := +| even_base: even 0 +| even_succ: forall n, odd (n - 1) -> even n +with odd: Z -> Prop := +| odd_succ: forall n, even (n - 1) -> odd n. + +Lemma even_pos_odd_pos: forall n, even n -> n >= 0 +with odd_pos_even_pos : forall n, odd n -> n >= 1. +Proof. + intros. + destruct H. + omega. + apply odd_pos_even_pos in H. + omega. + intros. + destruct H. + apply even_pos_odd_pos in H. + omega. +Qed. + +CoInductive a : Prop := acons : b -> a +with b : Prop := bcons : a -> b. + +Lemma a1 : a +with b1 : b. +Proof. +apply acons. +assumption. + +apply bcons. +assumption. +Qed. diff --git a/test-suite/success/hyps_inclusion.v b/test-suite/success/hyps_inclusion.v new file mode 100644 index 00000000..21bfc075 --- /dev/null +++ b/test-suite/success/hyps_inclusion.v @@ -0,0 +1,32 @@ +(* Simplified example for bug #1325 *) + +(* Explanation: the proof engine see section variables as goal + variables; especially, it can change their types so that, at + type-checking, the section variables are not recognized + (Typeops.check_hyps_inclusion raises "types do no match"). It + worked before the introduction of polymorphic inductive types because + tactics were using Typing.type_of and not Typeops.typing; the former + was not checking hyps inclusion so that the discrepancy in the types + of section variables seen as goal variables was not a problem (at the + end, when the proof is completed, the section variable recovers its + original type and all is correct for Typeops) *) + +Section A. +Variable H:not True. +Lemma f:nat->nat. destruct H. exact I. Defined. +Goal f 0=f 1. +red in H. +(* next tactic was failing wrt bug #1325 because type-checking the goal + detected a syntactically different type for the section variable H *) +case 0. +Reset A. + +(* Variant with polymorphic inductive types for bug #1325 *) + +Section A. +Variable H:not True. +Inductive I (n:nat) : Type := C : H=H -> I n. +Goal I 0. +red in H. +case 0. +Reset A. diff --git a/test-suite/success/implicit.v b/test-suite/success/implicit.v index 47c58f04..9034d6a6 100644 --- a/test-suite/success/implicit.v +++ b/test-suite/success/implicit.v @@ -36,3 +36,13 @@ Check (fun x => @ rhs _ _ (f x)). Fixpoint g n := match n with O => true | S n => g n end. Inductive P n : nat -> Prop := c : P n n. + +(* Avoid evars in the computation of implicit arguments (cf r9827) *) + +Require Import List. + +Fixpoint plus n m {struct n} := + match n with + | 0 => m + | S p => S (plus p m) + end. diff --git a/test-suite/success/ltac.v b/test-suite/success/ltac.v index 3f25f703..757cf6a4 100644 --- a/test-suite/success/ltac.v +++ b/test-suite/success/ltac.v @@ -173,5 +173,50 @@ Abort. empty args *) Goal True. -match None with @None => exact I end. +match constr:@None with @None => exact I end. Abort. + +(* Check second-order pattern unification *) + +Ltac to_exist := + match goal with + |- forall x y, @?P x y => + let Q := eval lazy beta in (exists x, forall y, P x y) in + assert (Q->Q) + end. + +Goal forall x y : nat, x = y. +to_exist. exact (fun H => H). +Abort. + +(* Used to fail in V8.1 *) + +Tactic Notation "test" constr(t) integer(n) := + set (k := t) in |- * at n. + +Goal forall x : nat, x = 1 -> x + x + x = 3. +intros x H. +test x 2. +Abort. + +(* Utilisation de let rec sans arguments *) + +Ltac is := + let rec i := match goal with |- ?A -> ?B => intro; i | _ => idtac end in + i. + +Goal True -> True -> True. +is. +exact I. +Abort. + +(* Interférence entre espaces des noms *) + +Ltac O := intro. +Ltac Z1 t := set (x:=t). +Ltac Z2 t := t. +Goal True -> True. +Z1 O. +Z2 ltac:O. +exact I. +Qed. diff --git a/test-suite/success/options.v b/test-suite/success/options.v index bb678150..f43a4694 100644 --- a/test-suite/success/options.v +++ b/test-suite/success/options.v @@ -20,7 +20,7 @@ Parameter i : bool -> nat. Coercion i : bool >-> nat. Add Printing Coercion i. Remove Printing Coercion i. -Test Printing Coercion i. +Test Printing Coercion for i. Test Printing Let. Test Printing If. diff --git a/test-suite/success/parsing.v b/test-suite/success/parsing.v new file mode 100644 index 00000000..d1b679d5 --- /dev/null +++ b/test-suite/success/parsing.v @@ -0,0 +1,8 @@ +Section A. +Notation "*" := O (at level 8). +Notation "**" := O (at level 99). +Notation "***" := O (at level 9). +End A. +Notation "*" := O (at level 8). +Notation "**" := O (at level 99). +Notation "***" := O (at level 9). diff --git a/test-suite/success/pattern.v b/test-suite/success/pattern.v new file mode 100644 index 00000000..28d0bd55 --- /dev/null +++ b/test-suite/success/pattern.v @@ -0,0 +1,7 @@ +(* Test pattern with dependent occurrences; Note that it does not + behave as the succession of three generalize because each + quantification introduces new occurrences that are automatically + abstracted with the numbering still based on the original statement *) + +Goal (id true,id false)=(id true,id true). +generalize bool at 2 4 6 8 10 as B, true at 3 as tt, false as ff. diff --git a/test-suite/success/refine.v b/test-suite/success/refine.v index 4346ce9a..4b636618 100644 --- a/test-suite/success/refine.v +++ b/test-suite/success/refine.v @@ -87,3 +87,33 @@ refine | exist _ _ => _ end). Abort. + + +(* Use to fail because sigma was not propagated to get_type_of *) +(* Revealed by r9310, fixed in r9359 *) + +Goal + forall f : forall a (H:a=a), Prop, + (forall a (H:a = a :> nat), f a H -> True /\ True) -> + True. +intros. +refine (@proj1 _ _ (H 0 _ _)). +Abort. + +(* Use to fail because let-in with metas in the body where rejected + because a priori considered as dependent *) + +Require Import Peano_dec. + +Definition fact_F : + forall (n:nat), + (forall m, m nat) -> + nat. +refine + (fun n fact_rec => + if eq_nat_dec n 0 then + 1 + else + let fn := fact_rec (n-1) _ in + n * fn). +Abort. diff --git a/test-suite/success/rewrite.v b/test-suite/success/rewrite.v index 9629b213..86e55922 100644 --- a/test-suite/success/rewrite.v +++ b/test-suite/success/rewrite.v @@ -17,3 +17,24 @@ intros n n' l l'. dependent rewrite (ax n n' l l'). split; reflexivity. Qed. + +(* Used to raise an anomaly instead of an error in 8.1 *) +(* Submitted by Y. Makarov *) + +Parameter N : Set. +Parameter E : N -> N -> Prop. + +Axiom e : forall (A : Set) (EA : A -> A -> Prop) (a : A), EA a a. + +Theorem th : forall x : N, E x x. +intro x. try rewrite e. +Abort. + +(* Behavior of rewrite wrt conversion *) + +Require Import Arith. + +Goal forall n, 0 + n = n -> True. +intros n H. +rewrite plus_0_l in H. +Abort. diff --git a/test-suite/success/setoid_test.v b/test-suite/success/setoid_test.v index dd1022f0..f49f58e5 100644 --- a/test-suite/success/setoid_test.v +++ b/test-suite/success/setoid_test.v @@ -18,7 +18,7 @@ Definition same (s t : set) : Prop := forall a : A, In a s <-> In a t. Lemma setoid_set : Setoid_Theory set same. -unfold same in |- *; split. +unfold same in |- *; split ; red. red in |- *; auto. red in |- *. @@ -104,3 +104,15 @@ setoid_rewrite <- H. trivial. Qed. +(* Unifying the domain up to delta-conversion (example from emakarov) *) + +Definition id: Set -> Set := fun A => A. +Definition rel : forall A : Set, relation (id A) := @eq. +Definition f: forall A : Set, A -> A := fun A x => x. + +Add Relation (id A) (rel A) as eq_rel. + +Add Morphism (@f A) : f_morph. +Proof. +unfold rel, f. trivial. +Qed. diff --git a/test-suite/success/setoid_test2.v b/test-suite/success/setoid_test2.v index bac1cf14..34fff9d1 100644 --- a/test-suite/success/setoid_test2.v +++ b/test-suite/success/setoid_test2.v @@ -120,6 +120,8 @@ Axiom eqS1: S1 -> S1 -> Prop. Axiom SetoidS1 : Setoid_Theory S1 eqS1. Add Setoid S1 eqS1 SetoidS1 as S1setoid. +Instance eqS1_default : DefaultRelation S1 eqS1. + Axiom eqS1': S1 -> S1 -> Prop. Axiom SetoidS1' : Setoid_Theory S1 eqS1'. Axiom SetoidS1'_bis : Setoid_Theory S1 eqS1'. @@ -218,6 +220,8 @@ Axiom eqS1_test8: S1_test8 -> S1_test8 -> Prop. Axiom SetoidS1_test8 : Setoid_Theory S1_test8 eqS1_test8. Add Setoid S1_test8 eqS1_test8 SetoidS1_test8 as S1_test8setoid. +Instance eqS1_test8_default : DefaultRelation S1_test8 eqS1_test8. + Axiom f_test8 : S2 -> S1_test8. Add Morphism f_test8 : f_compat_test8. Admitted. diff --git a/test-suite/success/setoid_test_function_space.v b/test-suite/success/setoid_test_function_space.v index 1602991d..ead93d91 100644 --- a/test-suite/success/setoid_test_function_space.v +++ b/test-suite/success/setoid_test_function_space.v @@ -26,14 +26,14 @@ Hint Unfold feq. Hint Resolve feq_refl feq_sym feq_trans. Variable K:(nat -> nat)->Prop. Variable K_ext:forall a b, (K a)->(a =f b)->(K b). -Add Relation (fun A B:Type => A -> B) feq - reflexivity proved by feq_refl - symmetry proved by feq_sym - transitivity proved by feq_trans as funsetoid. +Add Parametric Relation (A B : Type) : (A -> B) (@feq A B) + reflexivity proved by (@feq_refl A B) + symmetry proved by (@feq_sym A B) + transitivity proved by (@feq_trans A B) as funsetoid. -Add Morphism K with signature feq ==> iff as K_ext1. +Add Morphism K with signature (@feq nat nat) ==> iff as K_ext1. intuition. apply (K_ext H0 H). -intuition. assert (x2 =f x1);auto. apply (K_ext H0 H1). +intuition. assert (y =f x);auto. apply (K_ext H0 H1). Qed. Lemma three:forall n, forall a, (K a)->(a =f (fun m => (a (n+m))))-> (K (fun m diff --git a/test-suite/success/specialize.v b/test-suite/success/specialize.v new file mode 100644 index 00000000..4929ae4c --- /dev/null +++ b/test-suite/success/specialize.v @@ -0,0 +1,48 @@ + +Goal forall a b c : nat, a = b -> b = c -> forall d, a+d=c+d. +intros. + +(* "compatibility" mode: specializing a global name + means a kind of generalize *) + +specialize trans_equal. intros _. +specialize trans_equal with (1:=H)(2:=H0). intros _. +specialize trans_equal with (x:=a)(y:=b)(z:=c). intros _. +specialize trans_equal with (1:=H)(z:=c). intros _. +specialize trans_equal with nat a b c. intros _. +specialize (@trans_equal nat). intros _. +specialize (@trans_equal _ a b c). intros _. +specialize (trans_equal (x:=a)). intros _. +specialize (trans_equal (x:=a)(y:=b)). intros _. +specialize (trans_equal H H0). intros _. +specialize (trans_equal H0 (z:=b)). intros _. + +(* local "in place" specialization *) +assert (Eq:=trans_equal). + +specialize Eq. +specialize Eq with (1:=H)(2:=H0). Undo. +specialize Eq with (x:=a)(y:=b)(z:=c). Undo. +specialize Eq with (1:=H)(z:=c). Undo. +specialize Eq with nat a b c. Undo. +specialize (Eq nat). Undo. +specialize (Eq _ a b c). Undo. +(* no implicit argument for Eq, hence no (Eq (x:=a)) *) +specialize (Eq _ _ _ _ H H0). Undo. +specialize (Eq _ _ _ b H0). Undo. + +(* +(** strange behavior to inspect more precisely *) + +(* 1) proof aspect : let H:= ... in (fun H => ..) H + presque ok... *) + +(* 2) echoue moins lorsque zero premise de mangé *) +specialize trans_equal with (1:=Eq). (* mal typé !! *) + +(* 3) *) +specialize trans_equal with _ a b c. intros _. +(* Anomaly: Evar ?88 was not declared. Please report. *) +*) + +Abort. \ No newline at end of file diff --git a/test-suite/success/unification.v b/test-suite/success/unification.v index 68869621..91ee18ea 100644 --- a/test-suite/success/unification.v +++ b/test-suite/success/unification.v @@ -15,6 +15,12 @@ Proof. intros; apply (H _ H0). Qed. +Lemma l3 : (forall P, ~(exists x:nat, P x)) + -> forall P:nat->Prop, ~(exists x:nat, P x -> P x). +Proof. +intros; apply H. +Qed. + (* Example submitted for Zenon *) @@ -56,10 +62,67 @@ Require Import Arith. Parameter x y : nat. Parameter G:x=y->x=y->Prop. Parameter K:x<>y->x<>y->Prop. -Lemma l3 : (forall f:x=y->Prop, forall g:x<>y->Prop, +Lemma l4 : (forall f:x=y->Prop, forall g:x<>y->Prop, match eq_nat_dec x y with left a => f a | right a => g a end) -> match eq_nat_dec x y with left a => G a a | right a => K a a end. Proof. intros. apply H. Qed. + + +(* Test unification modulo eta-expansion (if possible) *) + +(* In this example, two instances for ?P (argument of hypothesis H) can be + inferred (one is by unifying the type [Q true] and [?P true] of the + goal and type of [H]; the other is by unifying the argument of [f]); + we need to unify both instances up to allowed eta-expansions of the + instances (eta is allowed if the meta was applied to arguments) + + This used to fail before revision 9389 in trunk +*) + +Lemma l5 : + forall f : (forall P, P true), (forall P, f P = f P) -> + forall Q, f (fun x => Q x) = f (fun x => Q x). +Proof. +intros. +apply H. +Qed. + +(* Test instanciation of evars by unification *) + +Goal (forall x, 0 * x = 0 -> True) -> True. +intros; eapply H. +rewrite <- plus_n_Sm. (* should refine ?x with S ?x' *) +Abort. + +(* Check handling of identity equation between evars *) +(* The example failed to pass until revision 10623 *) + +Lemma l6 : + (forall y, (forall x, (forall z, y = 0 -> y + z = 0) -> y + x = 0) -> True) + -> True. +intros. +eapply H. +intros. +apply H0. (* Check that equation ?n[H] = ?n[H] is correctly considered true *) +reflexivity. +Qed. + +(* Check treatment of metas erased by K-redexes at the time of turning + them to evas *) + +Inductive nonemptyT (t : Type) : Prop := nonemptyT_intro : t -> nonemptyT t. +Goal True. +try case nonemptyT_intro. (* check that it fails w/o anomaly *) +Abort. + +(* Test handling of return type and when it is decided to make the + predicate dependent or not - see "bug" #1851 *) + +Goal forall X (a:X) (f':nat -> X), (exists f : nat -> X, True). +intros. +exists (fun n => match n with O => a | S n' => f' n' end). +constructor. +Qed. diff --git a/test-suite/success/univers.v b/test-suite/success/univers.v index 87edc4de..3c2c0883 100644 --- a/test-suite/success/univers.v +++ b/test-suite/success/univers.v @@ -56,3 +56,7 @@ intro. set (C := forall m, Q m -> Q m). exact I. Qed. + +(* Submitted by Danko Ilik (bug report #1507); related to LetIn *) + +Record U : Type := { A:=Type; a:A }. diff --git a/test-suite/typeclasses/NewSetoid.v b/test-suite/typeclasses/NewSetoid.v new file mode 100644 index 00000000..8ad03880 --- /dev/null +++ b/test-suite/typeclasses/NewSetoid.v @@ -0,0 +1,74 @@ +(************************************************************************) +(* v * The Coq Proof Assistant / The Coq Development Team *) +(* ((not True -> True)) \/ True. + intros. + clrewrite H. + clrewrite <- H. + right ; auto. +Defined. + +Definition reduced_thm := Eval compute in Unnamed_thm. + +(* Print reduced_thm. *) + +Lemma foo [ Setoid a R ] : True. (* forall x y, R x y -> x -> y. *) +Proof. + intros. + Print respect2. + pose setoid_morphism. + pose (respect2 (b0:=b)). + simpl in b0. + unfold binary_respectful in b0. + pose (arrow_morphism R). + pose (respect2 (b0:=b1)). + unfold binary_respectful in b2. + + pose (eq_morphism (A:=a)). + pose (respect2 (b0:=b3)). + unfold binary_respectful in b4. + exact I. +Qed. + +Goal forall A B C (H : A <-> B) (H' : B <-> C), A /\ B <-> B /\ C. + intros. + Set Printing All. + Print iff_morphism. + clrewrite H. + clrewrite H'. + reflexivity. +Defined. + +Goal forall A B C (H : A <-> B) (H' : B <-> C), A /\ B <-> B /\ C. + intros. + rewrite H. + rewrite H'. + reflexivity. +Defined. + +Require Import Setoid_tac. +Require Import Setoid_Prop. + +(* Print Unnamed_thm0. *) +(* Print Unnamed_thm1. *) + + diff --git a/test-suite/typeclasses/clrewrite.v b/test-suite/typeclasses/clrewrite.v new file mode 100644 index 00000000..2978fda2 --- /dev/null +++ b/test-suite/typeclasses/clrewrite.v @@ -0,0 +1,111 @@ + +Set Implicit Arguments. +Unset Strict Implicit. + +Require Import Coq.Classes.Equivalence. + +Section Equiv. + Context [ Equivalence A eqA ]. + + Variables x y z w : A. + + Goal eqA x y -> eqA y x. + intros H ; clrewrite H. + refl. + Qed. + + Tactic Notation "simpl" "*" := auto || relation_tac. + + Goal eqA x y -> eqA y x /\ True. + intros H ; clrewrite H. + split ; simpl*. + Qed. + + Goal eqA x y -> eqA y x /\ eqA x x. + intros H ; clrewrite H. + split ; simpl*. + Qed. + + Goal eqA x y -> eqA y z -> eqA x y. + intros H. + clrewrite H. + intro. refl. + Qed. + + Goal eqA x y -> eqA z y -> eqA x y. + intros H. + clrewrite <- H at 2. + clrewrite <- H at 1. + intro. refl. + Qed. + + Opaque complement. + + Print iff_inverse_impl_binary_morphism. + + Goal eqA x y -> eqA x y -> eqA x y. + intros H. + clrewrite H. + intro. refl. + Qed. + + Goal eqA x y -> eqA x y -> eqA x y. + intros H. + clrewrite <- H. + refl. + Qed. + + Goal eqA x y -> True /\ True /\ False /\ eqA x x -> True /\ True /\ False /\ eqA x y. + Proof. + intros. + clrewrite <- H. + apply H0. + Qed. + +End Equiv. + +Section Trans. + Context [ Transitive A R ]. + + Variables x y z w : A. + + Tactic Notation "simpl" "*" := auto || relation_tac. + +(* Typeclasses eauto := debug. *) + + Goal R x y -> R y x -> R y y -> R x x. + Proof with auto. + intros H H' H''. + + clrewrite <- H' at 2. + clrewrite H at 1... + Qed. + + Goal R x y -> R y z -> R x z. + intros H. + clrewrite H. + refl. + Qed. + + Goal R x y -> R z y -> R x y. + intros H. + clrewrite <- H at 2. + intro. + clrewrite H at 1. + Abort. + + Goal R x y -> True /\ R y z -> True /\ R x z. + Proof. + intros. + clrewrite H. + apply H0. + Qed. + + Goal R x y -> True /\ True /\ False /\ R y z -> True /\ True /\ False /\ R x z. + Proof. + intros. + clrewrite H. + apply H0. + Qed. + +End Trans. diff --git a/test-suite/typeclasses/unification_delta.v b/test-suite/typeclasses/unification_delta.v new file mode 100644 index 00000000..663a837f --- /dev/null +++ b/test-suite/typeclasses/unification_delta.v @@ -0,0 +1,46 @@ +Require Import Coq.Classes.Equivalence. +Require Import Coq.Program.Program. + +Ltac obligations_tactic ::= program_simpl ; simpl_relation. + +Lemma bla : forall [ ! Equivalence A (eqA : relation A) ] x y, eqA x y -> eqA y x. +Proof. + intros. + rewrite H0. + reflexivity. +Defined. + +Lemma bla' : forall [ ! Equivalence A (eqA : relation A) ] x y, eqA x y -> eqA y x. +Proof. + intros. + (* Need delta on [relation] to unify with the right lemmas. *) + rewrite <- H0. + reflexivity. +Qed. + +Axiom euclid : nat -> { x : nat | x > 0 } -> nat. + +Definition eq_proj {A} {s : A -> Prop} : relation (sig s) := + fun x y => `x = `y. + +Program Instance {A : Type} {s : A -> Prop} => Equivalence (sig s) eq_proj. + + Next Obligation. + Proof. + constructor ; red ; intros. + reflexivity. + Qed. + + Admit Obligations. + +Instance Morphism (eq ==> eq_proj ==> eq) euclid. +Proof. +Admitted. + +Goal forall (x : nat) (y : nat | y > 0) (z : nat | z > 0), eq_proj y z -> euclid x y = euclid x z. +Proof. + intros. + (* Breaks if too much delta in unification *) + rewrite H. + reflexivity. +Qed. \ No newline at end of file -- cgit v1.2.3