--- a/simpdata.ML Tue Oct 24 14:59:17 1995 +0100
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,170 +0,0 @@
-(* Title: HOL/simpdata.ML
- ID: $Id$
- Author: Tobias Nipkow
- Copyright 1991 University of Cambridge
-
-Instantiation of the generic simplifier
-*)
-
-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 pairs =
- let fun atoms th =
- (case concl_of th of
- Const("Trueprop",_) $ p =>
- (case head_of p of
- Const(a,_) =>
- (case assoc(pairs,a) of
- Some(rls) => flat (map atoms ([th] RL rls))
- | None => [th])
- | _ => [th])
- | _ => [th])
- in atoms end;
-
-fun mk_meta_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;
-
-val imp_cong = 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 o_apply = prove_goalw HOL.thy [o_def] "(f o g)(x) = f(g(x))"
- (fn _ => [rtac refl 1]);
-
-val simp_thms = map prover
- [ "(x=x) = True",
- "(~True) = False", "(~False) = True", "(~ ~ P) = P",
- "(~P) ~= P", "P ~= (~P)", "(P ~= Q) = (P = (~Q))",
- "(True=P) = P", "(P=True) = P",
- "(True --> P) = P", "(False --> P) = True",
- "(P --> True) = True", "(P --> P) = True",
- "(P --> False) = (~P)", "(P --> ~P) = (~P)",
- "(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", "(? x.P) = P", "? x. x=t", "(? x. x=t & P(x)) = P(t)",
- "(P|Q --> R) = ((P-->R)&(Q-->R))" ];
-
-in
-
-val meta_eq_to_obj_eq = prove_goal HOL.thy "x==y ==> x=y"
- (fn [prem] => [rewtac prem, rtac refl 1]);
-
-val eq_sym_conv = prover "(x=y) = (y=x)";
-
-val conj_assoc = prover "((P&Q)&R) = (P&(Q&R))";
-
-val if_True = prove_goalw HOL.thy [if_def] "if(True,x,y) = x"
- (fn _=>[fast_tac (HOL_cs addIs [select_equality]) 1]);
-
-val if_False = prove_goalw HOL.thy [if_def] "if(False,x,y) = y"
- (fn _=>[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_bool_eq = prove_goal HOL.thy "if(P,Q,R) = ((P-->Q) & (~P-->R))"
- (fn _ => [rtac expand_if 1]);
-
-(*Add congruence rules for = (instead of ==) *)
-infix 4 addcongs;
-fun ss addcongs congs = ss addeqcongs (congs RL [eq_reflection]);
-
-(*Add a simpset to a classical set!*)
-infix 4 addss;
-fun cs addss ss = cs addbefore asm_full_simp_tac ss 1;
-
-val mksimps_pairs =
- [("op -->", [mp]), ("op &", [conjunct1,conjunct2]),
- ("All", [spec]), ("True", []), ("False", []),
- ("if", [if_bool_eq RS iffD1])];
-
-fun mksimps pairs = map mk_meta_eq o atomize pairs o gen_all;
-
-val HOL_ss = empty_ss
- setmksimps (mksimps mksimps_pairs)
- setsolver (fn prems => resolve_tac (TrueI::refl::prems) ORELSE' atac
- ORELSE' etac FalseE)
- setsubgoaler asm_simp_tac
- addsimps ([if_True, if_False, o_apply, conj_assoc] @ simp_thms)
- addcongs [imp_cong];
-
-local val mktac = mk_case_split_tac (meta_eq_to_obj_eq RS iffD2)
-in
-fun split_tac splits = mktac (map mk_meta_eq splits)
-end;
-
-(* eliminiation of existential quantifiers in assumptions *)
-
-val ex_all_equiv =
- let val lemma1 = prove_goal HOL.thy
- "(? x. P(x) ==> PROP Q) ==> (!!x. P(x) ==> PROP Q)"
- (fn prems => [resolve_tac prems 1, etac exI 1]);
- val lemma2 = prove_goalw HOL.thy [Ex_def]
- "(!!x. P(x) ==> PROP Q) ==> (? x. P(x) ==> PROP Q)"
- (fn prems => [REPEAT(resolve_tac prems 1)])
- in equal_intr lemma1 lemma2 end;
-
-(* '&' congruence rule: not included by default!
- May slow rewrite proofs down by as much as 50% *)
-
-val conj_cong = 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);
-
-(** 'if' congruence rules: neither included by default! *)
-
-(*Simplifies x assuming c and y assuming ~c*)
-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]);
-
-(*Prevents simplification of x and y: much faster*)
-val if_weak_cong = prove_goal HOL.thy
- "b=c ==> if(b,x,y) = if(c,x,y)"
- (fn [prem] => [rtac (prem RS arg_cong) 1]);
-
-(*Prevents simplification of t: much faster*)
-val let_weak_cong = prove_goal HOL.thy
- "a = b ==> (let x=a in t(x)) = (let x=b in t(x))"
- (fn [prem] => [rtac (prem RS arg_cong) 1]);
-
-end;
-
-fun prove nm thm = qed_goal nm HOL.thy thm (fn _ => [fast_tac HOL_cs 1]);
-
-prove "conj_commute" "(P&Q) = (Q&P)";
-prove "conj_left_commute" "(P&(Q&R)) = (Q&(P&R))";
-val conj_comms = [conj_commute, conj_left_commute];
-
-prove "conj_disj_distribL" "(P&(Q|R)) = (P&Q | P&R)";
-prove "conj_disj_distribR" "((P|Q)&R) = (P&R | Q&R)";