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(***********************************************************************)
(* v * The Coq Proof Assistant / The Coq Development Team *)
(* <O___,, * INRIA-Rocquencourt & LRI-CNRS-Orsay *)
(* \VV/ *************************************************************)
(* // * This file is distributed under the terms of the *)
(* * GNU Lesser General Public License Version 2.1 *)
(***********************************************************************)
(* $Id$: *)
Declare ML Module "setoid_replace".
Grammar tactic simple_tactic : ast :=
setoid_replace [ "Setoid_replace" constrarg($c1) "with" constrarg($c2) ] -> [(Setoid_replace $c1 $c2)]
.
Grammar tactic simple_tactic : ast :=
setoid_rewriteLR [ "Setoid_rewrite" "->" constrarg($c) ] -> [(Setoid_rewriteLR $c)]
| setoid_rewriteRL [ "Setoid_rewrite" "<-" constrarg($c) ] -> [(Setoid_rewriteRL $c)]
| setoid_rewrite [ "Setoid_rewrite" constrarg($c) ] -> [(Setoid_rewriteLR $c)]
.
Syntax tactic level 0 :
setoid_replace [<<(Setoid_replace $c1 $c2)>>] -> [[<hov 0>"Setoid_replace " $c1 [1 1] "with " $c2]]
| setoid_rewritelr [<<(Setoid_rewriteLR $c)>>] -> ["Setoid_rewrite " $c]
| setoid_rewriterl [<<(Setoid_rewriteRL $c)>>] -> ["Setoid_rewrite <- " $c]
.
Grammar vernac vernac : ast :=
add_setoid [ "Add" "Setoid" constrarg($a) constrarg($aeq) constrarg($t) "." ]
-> [(AddSetoid $a $aeq $t)]
| new_morphism [ "Add" "Morphism" constrarg($m) ":" identarg($s) "." ] -> [(NamedNewMorphism $s $m)]
.
Section Setoid.
Variable A : Type.
Variable Aeq : A -> A -> Prop.
Record Setoid_Theory : Prop :=
{ Seq_refl : (x:A) (Aeq x x);
Seq_sym : (x,y:A) (Aeq x y) -> (Aeq y x);
Seq_trans : (x,y,z:A) (Aeq x y) -> (Aeq y z) -> (Aeq x z)
}.
End Setoid.
Definition Prop_S : (Setoid_Theory Prop ([x,y:Prop] x<->y)).
Split; Tauto.
Save.
Add Setoid Prop iff Prop_S.
Hint prop_set : setoid := Resolve (Seq_refl Prop iff Prop_S).
Hint prop_set : setoid := Resolve (Seq_sym Prop iff Prop_S).
Hint prop_set : setoid := Resolve (Seq_trans Prop iff Prop_S).
Add Morphism or : or_ext.
Tauto.
Save.
Add Morphism and : and_ext.
Tauto.
Save.
Add Morphism not : not_ext.
Tauto.
Save.
Definition fleche [A,B:Prop] := A -> B.
Add Morphism fleche : fleche_ext.
Tauto.
Save.
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