From 61dc740ed1c3780cccaec00d059a28f0d31d0052 Mon Sep 17 00:00:00 2001 From: Stephane Glondu Date: Mon, 4 Jun 2012 12:07:52 +0200 Subject: Imported Upstream version 8.4~gamma0+really8.4beta2 --- plugins/dp/tests.v | 300 ----------------------------------------------------- 1 file changed, 300 deletions(-) delete mode 100644 plugins/dp/tests.v (limited to 'plugins/dp/tests.v') diff --git a/plugins/dp/tests.v b/plugins/dp/tests.v deleted file mode 100644 index dc85d2ee..00000000 --- a/plugins/dp/tests.v +++ /dev/null @@ -1,300 +0,0 @@ - -Require Import ZArith. -Require Import Classical. -Require Export Reals. - - -(* real numbers *) - -Lemma real_expr: (0 <= 9 * 4)%R. -ergo. -Qed. - -Lemma powerRZ_translation: (powerRZ 2 15 < powerRZ 2 17)%R. -ergo. -Qed. - -Dp_debug. -Dp_timeout 3. - -(* module renamings *) - -Module M. - Parameter t : Set. -End M. - -Lemma test_module_0 : forall x:M.t, x=x. -ergo. -Qed. - -Module N := M. - -Lemma test_module_renaming_0 : forall x:N.t, x=x. -ergo. -Qed. - -Dp_predefined M.t => "int". - -Lemma test_module_renaming_1 : forall x:N.t, x=x. -ergo. -Qed. - -(* Coq lists *) - -Require Export List. - -Lemma test_pol_0 : forall l:list nat, l=l. -ergo. -Qed. - -Parameter nlist: list nat -> Prop. - -Lemma poly_1 : forall l, nlist l -> True. -intros. -simplify. -Qed. - -(* user lists *) - -Inductive list (A:Set) : Set := -| nil : list A -| cons: forall a:A, list A -> list A. - -Fixpoint app (A:Set) (l m:list A) {struct l} : list A := -match l with -| nil => m -| cons a l1 => cons A a (app A l1 m) -end. - -Lemma entail: (nil Z) = app Z (nil Z) (nil Z) -> True. -intros; ergo. -Qed. - -(* polymorphism *) -Require Import List. - -Inductive mylist (A:Set) : Set := - mynil : mylist A -| mycons : forall a:A, mylist A -> mylist A. - -Parameter my_nlist: mylist nat -> Prop. - - Goal forall l, my_nlist l -> True. - intros. - simplify. -Qed. - -(* First example with the 0 and the equality translated *) - -Goal 0 = 0. -simplify. -Qed. - -(* Examples in the Propositional Calculus - and theory of equality *) - -Parameter A C : Prop. - -Goal A -> A. -simplify. -Qed. - - -Goal A -> (A \/ C). - -simplify. -Qed. - - -Parameter x y z : Z. - -Goal x = y -> y = z -> x = z. -ergo. -Qed. - - -Goal ((((A -> C) -> A) -> A) -> C) -> C. - -ergo. -Qed. - -(* Arithmetic *) -Open Scope Z_scope. - -Goal 1 + 1 = 2. -yices. -Qed. - - -Goal 2*x + 10 = 18 -> x = 4. - -simplify. -Qed. - - -(* Universal quantifier *) - -Goal (forall (x y : Z), x = y) -> 0=1. -try zenon. -ergo. -Qed. - -Goal forall (x: nat), (x + 0 = x)%nat. - -induction x0; ergo. -Qed. - - -(* No decision procedure can solve this problem - Goal forall (x a b : Z), a * x + b = 0 -> x = - b/a. -*) - - -(* Functions definitions *) - -Definition fst (x y : Z) : Z := x. - -Goal forall (g : Z -> Z) (x y : Z), g (fst x y) = g x. - -simplify. -Qed. - - -(* Eta-expansion example *) - -Definition snd_of_3 (x y z : Z) : Z := y. - -Definition f : Z -> Z -> Z := snd_of_3 0. - -Goal forall (x y z z1 : Z), snd_of_3 x y z = f y z1. - -simplify. -Qed. - - -(* Inductive types definitions - call to dp/injection function *) - -Inductive even : Z -> Prop := -| even_0 : even 0 -| even_plus2 : forall z : Z, even z -> even (z + 2). - - -(* Simplify and Zenon can't prove this goal before the timeout - unlike CVC Lite *) - -Goal even 4. -ergo. -Qed. - - -Definition skip_z (z : Z) (n : nat) := n. - -Definition skip_z1 := skip_z. - -Goal forall (z : Z) (n : nat), skip_z z n = skip_z1 z n. -yices. -Qed. - - -(* Axioms definitions and dp_hint *) - -Parameter add : nat -> nat -> nat. -Axiom add_0 : forall (n : nat), add 0%nat n = n. -Axiom add_S : forall (n1 n2 : nat), add (S n1) n2 = S (add n1 n2). - -Dp_hint add_0. -Dp_hint add_S. - -(* Simplify can't prove this goal before the timeout - unlike zenon *) - -Goal forall n : nat, add n 0 = n. -induction n ; yices. -Qed. - - -Definition pred (n : nat) : nat := match n with - | 0%nat => 0%nat - | S n' => n' -end. - -Goal forall n : nat, n <> 0%nat -> pred (S n) <> 0%nat. -yices. -(*zenon.*) -Qed. - - -Fixpoint plus (n m : nat) {struct n} : nat := - match n with - | 0%nat => m - | S n' => S (plus n' m) -end. - -Goal forall n : nat, plus n 0%nat = n. - -induction n; ergo. -Qed. - - -(* Mutually recursive functions *) - -Fixpoint even_b (n : nat) : bool := match n with - | O => true - | S m => odd_b m -end -with odd_b (n : nat) : bool := match n with - | O => false - | S m => even_b m -end. - -Goal even_b (S (S O)) = true. -ergo. -(* -simplify. -zenon. -*) -Qed. - - -(* sorts issues *) - -Parameter foo : Set. -Parameter ff : nat -> foo -> foo -> nat. -Parameter g : foo -> foo. -Goal (forall x:foo, ff 0 x x = O) -> forall y, ff 0 (g y) (g y) = O. -yices. -(*zenon.*) -Qed. - - - -(* abstractions *) - -Parameter poly_f : forall A:Set, A->A. - -Goal forall x:nat, poly_f nat x = poly_f nat x. -ergo. -(*zenon.*) -Qed. - - - -(* Anonymous mutually recursive functions : no equations are produced - -Definition mrf := - fix even2 (n : nat) : bool := match n with - | O => true - | S m => odd2 m - end - with odd2 (n : nat) : bool := match n with - | O => false - | S m => even2 m - end for even. - - Thus this goal is unsolvable - -Goal mrf (S (S O)) = true. - -zenon. - -*) -- cgit v1.2.3