From 577d275822c7a266f865952bdcf2dd41861b5b21 Mon Sep 17 00:00:00 2001 From: msozeau Date: Wed, 13 Feb 2008 18:19:32 +0000 Subject: Debugging of the class_setoid tactic and eauto. Prepare for move from class_setoid to class_tactics... git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@10563 85f007b7-540e-0410-9357-904b9bb8a0f7 --- theories/Classes/Relations.v | 22 ++++++++++++++++++++++ theories/Program/Basics.v | 32 +++++++++++++++++--------------- 2 files changed, 39 insertions(+), 15 deletions(-) (limited to 'theories') diff --git a/theories/Classes/Relations.v b/theories/Classes/Relations.v index 9cc78a970..c05a4b1e1 100644 --- a/theories/Classes/Relations.v +++ b/theories/Classes/Relations.v @@ -184,6 +184,12 @@ Ltac relation_refl := | [ |- ?R ?A ?B ?C ?D ?X ?X ] => apply (reflexive (R:=R A B C D) X) | [ H : ?R ?A ?B ?C ?D ?X ?X |- _ ] => apply (irreflexive (R:=R A B C D) H) + + | [ |- ?R ?A ?B ?C ?D ?E ?X ?X ] => apply (reflexive (R:=R A B C D E) X) + | [ H : ?R ?A ?B ?C ?D ?E ?X ?X |- _ ] => apply (irreflexive (R:=R A B C D E) H) + + | [ |- ?R ?A ?B ?C ?D ?E ?F ?X ?X ] => apply (reflexive (R:=R A B C D E F) X) + | [ H : ?R ?A ?B ?C ?D ?E ?F ?X ?X |- _ ] => apply (irreflexive (R:=R A B C D E F) H) end. Ltac refl := relation_refl. @@ -200,6 +206,9 @@ Ltac relation_sym := | [ H : ?R ?A ?B ?C ?D ?X ?Y |- ?R ?A ?B ?C ?D ?Y ?X ] => apply (symmetric (R:=R A B C D) (x:=X) (y:=Y) H) + | [ H : ?R ?A ?B ?C ?D ?E ?X ?Y |- ?R ?A ?B ?C ?D ?E ?Y ?X ] => apply (symmetric (R:=R A B C D E) (x:=X) (y:=Y) H) + + | [ H : ?R ?A ?B ?C ?D ?E ?F ?X ?Y |- ?R ?A ?B ?C ?D ?E ?F ?Y ?X ] => apply (symmetric (R:=R A B C D E F) (x:=X) (y:=Y) H) end. Ltac relation_symmetric := @@ -213,6 +222,10 @@ Ltac relation_symmetric := | [ |- ?R ?A ?B ?C ?Y ?X ] => apply (symmetric (R:=R A B C) (x:=X) (y:=Y)) | [ |- ?R ?A ?B ?C ?D ?Y ?X ] => apply (symmetric (R:=R A B C D) (x:=X) (y:=Y)) + + | [ |- ?R ?A ?B ?C ?D ?E ?Y ?X ] => apply (symmetric (R:=R A B C D E) (x:=X) (y:=Y)) + + | [ |- ?R ?A ?B ?C ?D ?E ?F ?Y ?X ] => apply (symmetric (R:=R A B C D E F) (x:=X) (y:=Y)) end. Ltac sym := relation_symmetric. @@ -236,6 +249,9 @@ Ltac relation_trans := | [ H : ?R ?A ?B ?C ?D ?E ?X ?Y, H' : ?R ?A ?B ?C ?D ?E ?Y ?Z |- ?R ?A ?B ?C ?D ?E ?X ?Z ] => apply (transitive (R:=R A B C D E) (x:=X) (y:=Y) (z:=Z) H H') + + | [ H : ?R ?A ?B ?C ?D ?E ?F ?X ?Y, H' : ?R ?A ?B ?C ?D ?E ?F ?Y ?Z |- ?R ?A ?B ?C ?D ?E ?F ?X ?Z ] => + apply (transitive (R:=R A B C D E F) (x:=X) (y:=Y) (z:=Z) H H') end. Ltac relation_transitive Y := @@ -254,6 +270,12 @@ Ltac relation_transitive Y := | [ |- ?R ?A ?B ?C ?D ?X ?Z ] => apply (transitive (R:=R A B C D) (x:=X) (y:=Y) (z:=Z)) + + | [ |- ?R ?A ?B ?C ?D ?E ?X ?Z ] => + apply (transitive (R:=R A B C D E) (x:=X) (y:=Y) (z:=Z)) + + | [ |- ?R ?A ?B ?C ?D ?E ?F ?X ?Z ] => + apply (transitive (R:=R A B C D E F) (x:=X) (y:=Y) (z:=Z)) end. Ltac trans Y := relation_transitive Y. diff --git a/theories/Program/Basics.v b/theories/Program/Basics.v index 014ff3a01..3040dd04b 100644 --- a/theories/Program/Basics.v +++ b/theories/Program/Basics.v @@ -1,4 +1,3 @@ -(* -*- coq-prog-args: ("-emacs-U" "-nois") -*- *) (************************************************************************) (* v * The Coq Proof Assistant / The Coq Development Team *) (* C) (f : A -> B) := fun x : A => g (f x). +Notation "'λ' x : T , y" := (fun x:T => y) (at level 1, x,T,y at level 10) : program_scope. -Definition arrow (A B : Type) := A -> B. +Open Scope program_scope. -Definition impl (A B : Prop) : Prop := A -> B. +Definition id `A` := λ x : A, x. -Definition id `A` := fun x : A => x. +Definition compose `A B C` (g : B -> C) (f : A -> B) := λ x : A , g (f x). Hint Unfold compose. -Notation " g 'o' f " := (compose g f) (at level 50, left associativity) : program_scope. - -Open Scope program_scope. +Notation " g ∘ f " := (compose g f) (at level 50, left associativity) : program_scope. -Lemma compose_id_left : forall A B (f : A -> B), id o f = f. +Lemma compose_id_left : forall A B (f : A -> B), id ∘ f = f. Proof. intros. unfold id, compose. symmetry ; apply eta_expansion. Qed. -Lemma compose_id_right : forall A B (f : A -> B), f o id = f. +Lemma compose_id_right : forall A B (f : A -> B), f ∘ id = f. Proof. intros. unfold id, compose. @@ -48,13 +45,18 @@ Proof. Qed. Lemma compose_assoc : forall A B C D (f : A -> B) (g : B -> C) (h : C -> D), - h o (g o f) = h o g o f. + h ∘ (g ∘ f) = h ∘ g ∘ f. Proof. + intros. reflexivity. Qed. Hint Rewrite @compose_id_left @compose_id_right @compose_assoc : core. +Definition arrow (A B : Type) := A -> B. + +Definition impl (A B : Prop) : Prop := A -> B. + Notation " f '#' x " := (f x) (at level 100, x at level 200, only parsing). Definition const `A B` (a : A) := fun x : B => a. @@ -126,13 +128,13 @@ Notation " [ x ; .. ; y ] " := (cons x .. (cons y nil) ..). (** n-ary exists ! *) -Notation "'exists' x y , p" := (ex (fun x => (ex (fun y => p)))) +Notation " 'exists' x y , p" := (ex (fun x => (ex (fun y => p)))) (at level 200, x ident, y ident, right associativity) : type_scope. -Notation "'exists' x y z , p" := (ex (fun x => (ex (fun y => (ex (fun z => p)))))) +Notation " 'exists' x y z , p" := (ex (fun x => (ex (fun y => (ex (fun z => p)))))) (at level 200, x ident, y ident, z ident, right associativity) : type_scope. -Notation "'exists' x y z w , p" := (ex (fun x => (ex (fun y => (ex (fun z => (ex (fun w => p)))))))) +Notation " 'exists' x y z w , p" := (ex (fun x => (ex (fun y => (ex (fun z => (ex (fun w => p)))))))) (at level 200, x ident, y ident, z ident, w ident, right associativity) : type_scope. Tactic Notation "exist" constr(x) := exists x. -- cgit v1.2.3