diff -r 000000000000 -r 7949f97df77a 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;