From d513d6872096bfe51f8fa3ced917131e954130e1 Mon Sep 17 00:00:00 2001
From: Ferruccio Guidi <ferruccio.guidi@unibo.it>
Date: Wed, 15 Jun 2005 12:42:21 +0000
Subject: [PATCH] support for the new tactics lapply and fwd used in forward
 reasoning

---
 helm/matita/matitaEngine.ml | 15 ++++++
 helm/matita/tests/fguidi.ma | 94 +++++++++++++++++++++++++++++++++++++
 2 files changed, 109 insertions(+)
 create mode 100644 helm/matita/tests/fguidi.ma

diff --git a/helm/matita/matitaEngine.ml b/helm/matita/matitaEngine.ml
index 2ac69a575..d9297bce5 100644
--- a/helm/matita/matitaEngine.ml
+++ b/helm/matita/matitaEngine.ml
@@ -123,6 +123,11 @@ let tactic_of_ast = function
         EqualityTactics.rewrite_tac ~term:t 
       else
         EqualityTactics.rewrite_back_tac ~term:t
+  | TacticAst.FwdSimpl (_, name) -> 
+     Tactics.fwd_simpl ~hyp:(Cic.Name name) ~dbd:(MatitaDb.instance ())
+  | TacticAst.LApply (_, term, substs) ->
+     let f (name, term) = Cic.Name name, term in
+     Tactics.lapply ~substs:(List.map f substs) term
   | _ -> assert false
 
 let eval_tactical status tac =
@@ -488,6 +493,16 @@ let disambiguate_tactic status = function
   | TacticAst.Split loc -> status, TacticAst.Split loc
   | TacticAst.Symmetry loc -> status, TacticAst.Symmetry loc
   | TacticAst.Goal (loc, g) -> status, TacticAst.Goal (loc, g)
+  | TacticAst.FwdSimpl (loc, name) -> status, TacticAst.FwdSimpl (loc, name)  
+  | TacticAst.LApply (loc, term, substs) ->
+     let f (status, substs) (name, term) =
+        let status, term = disambiguate_term status term in
+	status, (name, term) :: substs
+     in
+     let status, term = disambiguate_term status term in
+     let status, substs = List.fold_left f (status, []) substs in 
+     status, TacticAst.LApply (loc, term, substs)
+  
   | x -> 
       print_endline ("Not yet implemented:" ^ TacticAstPp.pp_tactic x);
       assert false
diff --git a/helm/matita/tests/fguidi.ma b/helm/matita/tests/fguidi.ma
new file mode 100644
index 000000000..623e327f9
--- /dev/null
+++ b/helm/matita/tests/fguidi.ma
@@ -0,0 +1,94 @@
+alias id "O" = "cic:/Coq/Init/Datatypes/nat.ind#xpointer(1/1/1)".
+alias id "nat" = "cic:/Coq/Init/Datatypes/nat.ind#xpointer(1/1)".
+alias id "S" = "cic:/Coq/Init/Datatypes/nat.ind#xpointer(1/1/2)".
+alias id "le" = "cic:/matita/fguidi/le.ind#xpointer(1/1)".
+alias id "False_ind" = "cic:/Coq/Init/Logic/False_ind.con".
+alias id "I" = "cic:/Coq/Init/Logic/True.ind#xpointer(1/1/1)". 
+alias id "ex_intro" = "cic:/Coq/Init/Logic/ex.ind#xpointer(1/1/1)".
+
+alias symbol "and" (instance 0) = "logical and".
+alias symbol "eq" (instance 0) = "leibnitz's equality".
+alias symbol "exists" (instance 0) = "exists".
+alias id "False" = "cic:/Coq/Init/Logic/False.ind#xpointer(1/1)".
+alias id "True" = "cic:/Coq/Init/Logic/True.ind#xpointer(1/1)".
+
+definition is_S: nat \to Prop \def
+   \lambda n. match n with 
+      [ O     \Rightarrow False
+      | (S n) \Rightarrow True
+      ].
+
+definition pred: nat \to nat \def
+   \lambda n. match n with
+      [ O     \Rightarrow O
+      | (S n) \Rightarrow n
+      ]. 
+
+theorem eq_gen_S_O: \forall x. (S x = O) \to \forall P:Prop. P.
+intros. apply False_ind. cut (is_S O). auto. elim H. exact I.
+qed.
+
+theorem eq_gen_S_O_cc: (\forall P:Prop. P) \to \forall x. (S x = O).
+intros. auto.
+qed.
+
+theorem eq_gen_S_S: \forall m,n. (S m) = (S n) \to m = n. 
+intros. cut (pred (S m)) = (pred (S n)). 
+assumption. elim H. auto.
+qed.
+
+theorem eq_gen_S_S_cc: \forall m,n. m = n \to (S m) = (S n).
+intros. elim H. auto.
+qed.
+
+inductive le: nat \to nat \to Prop \def
+     le_zero: \forall n. (le O n)
+   | le_succ: \forall m, n. (le m n) \to (le (S m) (S n)).
+
+theorem le_refl: \forall x. (le x x).
+intros. elim x. auto. auto.
+qed.
+
+theorem le_gen_x_O_aux: \forall x, y. (le x y) \to (y =O) \to 
+                        (x = O).
+intros 3. elim H. auto. apply eq_gen_S_O. exact x2. auto.
+qed.
+
+theorem le_gen_x_O: \forall x. (le x O) \to (x = O).
+intros. apply le_gen_x_O_aux. exact O. auto. auto.
+qed.
+
+theorem le_gen_x_O_cc: \forall x. (x = O) \to (le x O).
+intros. elim H. auto.
+qed.
+
+theorem le_gen_S_x_aux: \forall m,x,y. (le y x) \to (y = S m) \to 
+                        (\exists n. x = (S n) \land (le m n)).
+intros 4. elim H. 
+apply eq_gen_S_O. exact m. elim H1. auto. 
+cut x1 = m. elim Hcut. apply ex_intro. exact x2. auto. auto.
+qed.
+
+theorem le_gen_S_x: \forall m,x. (le (S m) x) \to 
+                    (\exists n. x = (S n) \land (le m n)).
+intros. apply le_gen_S_x_aux. exact (S m). auto. auto.
+qed.
+
+theorem le_gen_S_x_cc: \forall m,x. (\exists n. x = (S n) \land (le m n)) \to
+                       (le (S m) x).
+intros. elim H. elim H1. cut (S x1) = x. elim Hcut. auto. elim H2. auto.
+qed.
+
+theorem le_gen_S_S: \forall m,n. (le (S m) (S n)) \to (le m n).
+intros. cut (\exists p. (S n) = (S p) \land (le m p)).
+elim Hcut. elim H1. cut x = n. 
+elim Hcut1. auto. symmetry. auto. auto.
+qed.
+
+theorem le_gen_S_S_cc: \forall m,n. (le m n) \to (le (S m) (S n)).
+intros. auto.
+qed.
+
+theorem pippo: \forall m,n. (le (S m) (S n)) \to (le m n).
+intros.
+lapply le_gen_S_x.
\ No newline at end of file
-- 
2.39.2