src/FOLP/simpdata.ML

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/FOLP/simpdata.ML	Thu Sep 16 12:20:38 1993 +0200
@@ -0,0 +1,135 @@
+(*  Title: 	FOL/simpdata
+    ID:         $Id$
+    Author: 	Lawrence C Paulson, Cambridge University Computer Laboratory
+    Copyright   1991  University of Cambridge
+
+Simplification data for FOL
+*)
+
+(*** Rewrite rules ***)
+
+fun int_prove_fun_raw s = 
+    (writeln s;  prove_goal IFOLP.thy s
+       (fn prems => [ (cut_facts_tac prems 1), (Int.fast_tac 1) ]));
+
+fun int_prove_fun s = int_prove_fun_raw ("?p : "^s);
+
+val conj_rews = map int_prove_fun
+ ["P & True <-> P", 	"True & P <-> P",
+  "P & False <-> False", "False & P <-> False",
+  "P & P <-> P",
+  "P & ~P <-> False", 	"~P & P <-> False",
+  "(P & Q) & R <-> P & (Q & R)"];
+
+val disj_rews = map int_prove_fun
+ ["P | True <-> True", 	"True | P <-> True",
+  "P | False <-> P", 	"False | P <-> P",
+  "P | P <-> P",
+  "(P | Q) | R <-> P | (Q | R)"];
+
+val not_rews = map int_prove_fun
+ ["~ False <-> True",	"~ True <-> False"];
+
+val imp_rews = map int_prove_fun
+ ["(P --> False) <-> ~P",	"(P --> True) <-> True",
+  "(False --> P) <-> True",	"(True --> P) <-> P", 
+  "(P --> P) <-> True",		"(P --> ~P) <-> ~P"];
+
+val iff_rews = map int_prove_fun
+ ["(True <-> P) <-> P", 	"(P <-> True) <-> P",
+  "(P <-> P) <-> True",
+  "(False <-> P) <-> ~P", 	"(P <-> False) <-> ~P"];
+
+val quant_rews = map int_prove_fun
+ ["(ALL x.P) <-> P",	"(EX x.P) <-> P"];
+
+(*These are NOT supplied by default!*)
+val distrib_rews  = map int_prove_fun
+ ["~(P|Q) <-> ~P & ~Q",
+  "P & (Q | R) <-> P&Q | P&R", "(Q | R) & P <-> Q&P | R&P",
+  "(P | Q --> R) <-> (P --> R) & (Q --> R)",
+  "~(EX x.NORM(P(x))) <-> (ALL x. ~NORM(P(x)))",
+  "((EX x.NORM(P(x))) --> Q) <-> (ALL x. NORM(P(x)) --> Q)",
+  "(EX x.NORM(P(x))) & NORM(Q) <-> (EX x. NORM(P(x)) & NORM(Q))",
+  "NORM(Q) & (EX x.NORM(P(x))) <-> (EX x. NORM(Q) & NORM(P(x)))"];
+
+val P_Imp_P_iff_T = int_prove_fun_raw "p:P ==> ?p:(P <-> True)";
+
+fun make_iff_T th = th RS P_Imp_P_iff_T;
+
+val refl_iff_T = make_iff_T refl;
+
+val norm_thms = [(norm_eq RS sym, norm_eq),
+		 (NORM_iff RS iff_sym, NORM_iff)];
+
+
+(* Conversion into rewrite rules *)
+
+val not_P_imp_P_iff_F = int_prove_fun_raw "p:~P ==> ?p:(P <-> False)";
+
+fun mk_eq th = case concl_of th of
+      _ $ (Const("op <->",_)$_$_) $ _ => th
+    | _ $ (Const("op =",_)$_$_) $ _ => th
+    | _ $ (Const("Not",_)$_) $ _ => th RS not_P_imp_P_iff_F 
+    | _ => make_iff_T th;
+
+fun atomize th = case concl_of th of (*The operator below is "Proof $ P $ p"*)
+      _ $ (Const("op -->",_) $ _ $ _) $ _ => atomize(th RS mp)
+    | _ $ (Const("op &",_) $ _ $ _) $ _ => atomize(th RS conjunct1) @
+				       atomize(th RS conjunct2)
+    | _ $ (Const("All",_) $ _) $ _ => atomize(th RS spec)
+    | _ $ (Const("True",_)) $ _ => []
+    | _ $ (Const("False",_)) $ _ => []
+    | _ => [th];
+
+fun mk_rew_rules th = map mk_eq (atomize th);
+
+(*destruct function for analysing equations*)
+fun dest_red(_ $ (red $ lhs $ rhs) $ _) = (red,lhs,rhs)
+  | dest_red t = raise TERM("FOL/dest_red", [t]);
+
+structure FOLP_SimpData : SIMP_DATA =
+  struct
+  val refl_thms		= [refl, iff_refl]
+  val trans_thms	= [trans, iff_trans]
+  val red1		= iffD1
+  val red2		= iffD2
+  val mk_rew_rules	= mk_rew_rules
+  val case_splits	= []         (*NO IF'S!*)
+  val norm_thms		= norm_thms
+  val subst_thms	= [subst];
+  val dest_red		= dest_red
+  end;
+
+structure FOLP_Simp = SimpFun(FOLP_SimpData);
+structure Induction = InductionFun(struct val spec=IFOLP.spec end);
+
+(*not a component of SIMP_DATA, but an argument of SIMP_TAC *)
+val FOLP_congs = 
+   [all_cong,ex_cong,eq_cong,
+    conj_cong,disj_cong,imp_cong,iff_cong,not_cong] @ pred_congs;
+
+val IFOLP_rews =
+   [refl_iff_T] @ conj_rews @ disj_rews @ not_rews @ 
+    imp_rews @ iff_rews @ quant_rews;
+
+open FOLP_Simp Induction;
+
+val auto_ss = empty_ss setauto ares_tac [TrueI];
+
+val IFOLP_ss = auto_ss addcongs FOLP_congs addrews IFOLP_rews;
+
+(*Classical version...*)
+fun prove_fun s = 
+    (writeln s;  prove_goal FOLP.thy s
+       (fn prems => [ (cut_facts_tac prems 1), (Cla.fast_tac FOLP_cs 1) ]));
+
+val cla_rews = map prove_fun
+ ["?p:P | ~P", 		"?p:~P | P",
+  "?p:~ ~ P <-> P",	"?p:(~P --> P) <-> P"];
+
+val FOLP_rews = IFOLP_rews@cla_rews;
+
+val FOLP_ss = auto_ss addcongs FOLP_congs addrews FOLP_rews;
+
+