diff options
Diffstat (limited to 'test-suite/success/eauto.v')
| -rw-r--r-- | test-suite/success/eauto.v | 136 |
1 files changed, 96 insertions, 40 deletions
diff --git a/test-suite/success/eauto.v b/test-suite/success/eauto.v index 4db547f4e..160f2d9de 100644 --- a/test-suite/success/eauto.v +++ b/test-suite/success/eauto.v @@ -5,7 +5,6 @@ (* // * This file is distributed under the terms of the *) (* * GNU Lesser General Public License Version 2.1 *) (************************************************************************) -Require Import List. Class A (A : Type). Instance an: A nat. @@ -31,6 +30,8 @@ Defined. Hint Extern 0 (_ /\ _) => constructor : typeclass_instances. +Existing Class and. + Goal exists (T : Type) (t : T), A T /\ B T t. Proof. eexists. eexists. typeclasses eauto. @@ -46,7 +47,7 @@ Class C {T} `(a : A T) (t : T). Require Import Classes.Init. Hint Extern 0 { x : ?A & _ } => unshelve class_apply @existT : typeclass_instances. - +Existing Class sigT. Set Typeclasses Debug. Instance can: C an 0. (* Backtrack on instance implementation *) @@ -63,41 +64,6 @@ Proof. Defined. -Parameter in_list : list (nat * nat) -> nat -> Prop. -Definition not_in_list (l : list (nat * nat)) (n : nat) : Prop := - ~ in_list l n. - -(* Hints Unfold not_in_list. *) - -Axiom - lem1 : - forall (l1 l2 : list (nat * nat)) (n : nat), - not_in_list (l1 ++ l2) n -> not_in_list l1 n. - -Axiom - lem2 : - forall (l1 l2 : list (nat * nat)) (n : nat), - not_in_list (l1 ++ l2) n -> not_in_list l2 n. - -Axiom - lem3 : - forall (l : list (nat * nat)) (n p q : nat), - not_in_list ((p, q) :: l) n -> not_in_list l n. - -Axiom - lem4 : - forall (l1 l2 : list (nat * nat)) (n : nat), - not_in_list l1 n -> not_in_list l2 n -> not_in_list (l1 ++ l2) n. - -Hint Resolve lem1 lem2 lem3 lem4: essai. - -Goal -forall (l : list (nat * nat)) (n p q : nat), -not_in_list ((p, q) :: l) n -> not_in_list l n. - intros. - eauto with essai. -Qed. - (* Example from Nicolas Magaud on coq-club - Jul 2000 *) Definition Nat : Set := nat. @@ -126,6 +92,9 @@ Qed. Full backtracking on dependent subgoals. *) Require Import Coq.Classes.Init. + +Module NTabareau. + Set Typeclasses Dependency Order. Unset Typeclasses Iterative Deepening. Notation "x .1" := (projT1 x) (at level 3). @@ -149,7 +118,8 @@ Hint Extern 5 (Bar ?D.1) => Hint Extern 5 (Qux ?D.1) => destruct D; simpl : typeclass_instances. -Hint Extern 1 myType => unshelve refine (fooTobar _ _).1 : typeclass_instances. +Hint Extern 1 myType => + unshelve refine (fooTobar _ _).1 : typeclass_instances. Hint Extern 1 myType => unshelve refine (barToqux _ _).1 : typeclass_instances. @@ -158,8 +128,94 @@ Hint Extern 0 { x : _ & _ } => simple refine (existT _ _ _) : typeclass_instance Unset Typeclasses Debug. Definition trivial a (H : Foo a) : {b : myType & Qux b}. Proof. - Time typeclasses eauto 10. + Time typeclasses eauto 10 with typeclass_instances. Undo. Set Typeclasses Iterative Deepening. - Time typeclasses eauto. + Time typeclasses eauto with typeclass_instances. Defined. +End NTabareau. + +Module NTabareauClasses. + +Set Typeclasses Dependency Order. +Unset Typeclasses Iterative Deepening. +Notation "x .1" := (projT1 x) (at level 3). +Notation "x .2" := (projT2 x) (at level 3). + +Parameter myType: Type. +Existing Class myType. + +Class Foo (a:myType) := {}. + +Class Bar (a:myType) := {}. + +Class Qux (a:myType) := {}. + +Parameter fooTobar : forall a (H : Foo a), {b: myType & Bar b}. + +Parameter barToqux : forall a (H : Bar a), {b: myType & Qux b}. + +Hint Extern 5 (Bar ?D.1) => + destruct D; simpl : typeclass_instances. + +Hint Extern 5 (Qux ?D.1) => + destruct D; simpl : typeclass_instances. + +Hint Extern 1 myType => + unshelve notypeclasses refine (fooTobar _ _).1 : typeclass_instances. + +Hint Extern 1 myType => + unshelve notypeclasses refine (barToqux _ _).1 : typeclass_instances. + +Hint Extern 0 { x : _ & _ } => + unshelve notypeclasses refine (existT _ _ _) : typeclass_instances. + +Unset Typeclasses Debug. + +Definition trivial a (H : Foo a) : {b : myType & Qux b}. +Proof. + Time typeclasses eauto 10 with typeclass_instances. + Undo. Set Typeclasses Iterative Deepening. + (* Much faster in iteratove deepening mode *) + Time typeclasses eauto with typeclass_instances. +Defined. + +End NTabareauClasses. + + +Require Import List. + +Parameter in_list : list (nat * nat) -> nat -> Prop. +Definition not_in_list (l : list (nat * nat)) (n : nat) : Prop := + ~ in_list l n. + +(* Hints Unfold not_in_list. *) + +Axiom + lem1 : + forall (l1 l2 : list (nat * nat)) (n : nat), + not_in_list (l1 ++ l2) n -> not_in_list l1 n. + +Axiom + lem2 : + forall (l1 l2 : list (nat * nat)) (n : nat), + not_in_list (l1 ++ l2) n -> not_in_list l2 n. + +Axiom + lem3 : + forall (l : list (nat * nat)) (n p q : nat), + not_in_list ((p, q) :: l) n -> not_in_list l n. + +Axiom + lem4 : + forall (l1 l2 : list (nat * nat)) (n : nat), + not_in_list l1 n -> not_in_list l2 n -> not_in_list (l1 ++ l2) n. + +Hint Resolve lem1 lem2 lem3 lem4: essai. + +Goal +forall (l : list (nat * nat)) (n p q : nat), +not_in_list ((p, q) :: l) n -> not_in_list l n. + intros. + eauto with essai. +Qed. |