simpdata.ML

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/simpdata.ML	Thu Sep 16 12:21:07 1993 +0200
@@ -0,0 +1,100 @@
+open Simplifier;
+
+local
+
+fun prover s = prove_goal HOL.thy s (fn _ => [fast_tac HOL_cs 1]);
+
+val P_imp_P_iff_True = prover "P --> (P = True)" RS mp;
+val P_imp_P_eq_True = P_imp_P_iff_True RS eq_reflection;
+
+val not_P_imp_P_iff_F = prover "~P --> (P = False)" RS mp;
+val not_P_imp_P_eq_False = not_P_imp_P_iff_F RS eq_reflection;
+
+fun atomize r =
+  case concl_of r of
+    Const("Trueprop",_) $ p =>
+      (case p of
+	 Const("op -->",_)$_$_ => atomize(r RS mp)
+       | Const("op &",_)$_$_ => atomize(r RS conjunct1) @
+	  		        atomize(r RS conjunct2)
+       | Const("All",_)$_ => atomize(r RS spec)
+       | Const("True",_) => []
+       | Const("False",_) => []
+       | _ => [r])
+  | _ => [r];
+
+fun mk_eq r = case concl_of r of
+	Const("==",_)$_$_ => r
+    |	_$(Const("op =",_)$_$_) => r RS eq_reflection
+    |	_$(Const("not",_)$_) => r RS not_P_imp_P_eq_False
+    |   _ => r RS P_imp_P_eq_True;
+(* last 2 lines requires all formulae to be of the from Trueprop(.) *)
+
+fun gen_all th = forall_elim_vars (#maxidx(rep_thm th)+1) th;
+
+fun mk_rews thm = map mk_eq (atomize(gen_all thm));
+
+val imp_cong_lemma = impI RSN
+    (2, prove_goal HOL.thy "(P=P')--> (P'--> (Q=Q'))--> ((P-->Q) = (P'-->Q'))"
+	(fn _=> [fast_tac HOL_cs 1]) RS mp RS mp);
+val imp_meta_cong = imp_cong_lemma RS eq_reflection;
+
+val o_apply = prove_goal HOL.thy "(f o g)(x) = f(g(x))"
+ (fn _ => [ (stac o_def 1), (rtac refl 1) ]);
+
+val simp_thms = map prover
+ [ "(x=x) = True",
+   "(~True) = False", "(~False) = True", "(~ ~ P) = P",
+   "(True=P) = P", "(P=True) = P",
+   "(True --> P) = P", "(False --> P) = True", 
+   "(P --> True) = True", "(P --> P) = True",
+   "(P & True) = P", "(True & P) = P", 
+   "(P & False) = False", "(False & P) = False", "(P & P) = P",
+   "(P | True) = True", "(True | P) = True", 
+   "(P | False) = P", "(False | P) = P", "(P | P) = P",
+   "(!x.P) = P",
+   "(P|Q --> R) = ((P-->R)&(Q-->R))" ];
+
+val meta_obj_reflection = prove_goal HOL.thy "x==y ==> x=y"
+  (fn [prem] => [rewtac prem, rtac refl 1]);
+
+in
+
+
+val if_True = prove_goal HOL.thy "if(True,x,y) = x"
+ (fn _=>[stac if_def 1,  fast_tac (HOL_cs addIs [select_equality]) 1]);
+
+val if_False = prove_goal HOL.thy "if(False,x,y) = y"
+ (fn _=>[stac if_def 1,  fast_tac (HOL_cs addIs [select_equality]) 1]);
+
+val if_P = prove_goal HOL.thy "P ==> if(P,x,y) = x"
+ (fn [prem] => [ stac (prem RS eqTrueI) 1, rtac if_True 1 ]);
+
+val if_not_P = prove_goal HOL.thy "~P ==> if(P,x,y) = y"
+ (fn [prem] => [ stac (prem RS not_P_imp_P_iff_F) 1, rtac if_False 1 ]);
+
+val expand_if = prove_goal HOL.thy
+    "P(if(Q,x,y)) = ((Q --> P(x)) & (~Q --> P(y)))"
+ (fn _=> [ (res_inst_tac [("Q","Q")] (excluded_middle RS disjE) 1),
+	 rtac (if_P RS ssubst) 2,
+	 rtac (if_not_P RS ssubst) 1,
+	 REPEAT(fast_tac HOL_cs 1) ]);
+
+val if_cong = prove_goal HOL.thy
+  "[| b=c; c ==> x=u; ~c ==> y=v |] ==> if(b,x,y) = if(c,u,v)"
+  (fn rew::prems =>
+   [stac rew 1, stac expand_if 1, stac expand_if 1,
+    fast_tac (HOL_cs addDs prems) 1]) RS eq_reflection;
+
+
+val HOL_ss = empty_ss
+      setmksimps mk_rews
+      setsolver (fn prems => resolve_tac (TrueI::refl::prems))
+      setsubgoaler asm_simp_tac
+      addsimps ([if_True, if_False, o_apply] @ simp_thms)
+      addcongs [imp_meta_cong];
+
+fun split_tac splits =
+  mk_case_split_tac (meta_obj_reflection RS iffD2) (map mk_eq splits);
+
+end;