author  nipkow 
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child 4086  958806f7e840 
permissions  rwrr 
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(* Title: HOL/simpdata.ML 
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ID: $Id$ 
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Author: Tobias Nipkow 
923  4 
Copyright 1991 University of Cambridge 
5 

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Instantiation of the generic simplifier 

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*) 

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1984  9 
section "Simplifier"; 
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923  11 
open Simplifier; 
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1984  13 
(*** Addition of rules to simpsets and clasets simultaneously ***) 
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(*Takes UNCONDITIONAL theorems of the form A<>B to 

2031  16 
the Safe Intr rule B==>A and 
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the Safe Destruct rule A==>B. 

1984  18 
Also ~A goes to the Safe Elim rule A ==> ?R 
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Failing other cases, A is added as a Safe Intr rule*) 

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local 

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val iff_const = HOLogic.eq_const HOLogic.boolT; 

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fun addIff th = 

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(case HOLogic.dest_Trueprop (#prop(rep_thm th)) of 

2718  25 
(Const("Not",_) $ A) => 
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AddSEs [zero_var_indexes (th RS notE)] 
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 (con $ _ $ _) => 

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if con=iff_const 

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then (AddSIs [zero_var_indexes (th RS iffD2)]; 

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AddSDs [zero_var_indexes (th RS iffD1)]) 

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else AddSIs [th] 

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 _ => AddSIs [th]; 

1984  33 
Addsimps [th]) 
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handle _ => error ("AddIffs: theorem must be unconditional\n" ^ 

2031  35 
string_of_thm th) 
1984  36 

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fun delIff th = 

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(case HOLogic.dest_Trueprop (#prop(rep_thm th)) of 

2718  39 
(Const("Not",_) $ A) => 
2031  40 
Delrules [zero_var_indexes (th RS notE)] 
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 (con $ _ $ _) => 

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if con=iff_const 

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then Delrules [zero_var_indexes (th RS iffD2), 

3518  44 
make_elim (zero_var_indexes (th RS iffD1))] 
2031  45 
else Delrules [th] 
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 _ => Delrules [th]; 

1984  47 
Delsimps [th]) 
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handle _ => warning("DelIffs: ignoring conditional theorem\n" ^ 

2031  49 
string_of_thm th) 
1984  50 
in 
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val AddIffs = seq addIff 

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val DelIffs = seq delIff 

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end; 

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local 
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fun prover s = prove_goal HOL.thy s (fn _ => [blast_tac HOL_cs 1]); 
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1922  60 
val P_imp_P_iff_True = prover "P > (P = True)" RS mp; 
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val P_imp_P_eq_True = P_imp_P_iff_True RS eq_reflection; 

923  62 

1922  63 
val not_P_imp_P_iff_F = prover "~P > (P = False)" RS mp; 
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val not_P_imp_P_eq_False = not_P_imp_P_iff_F RS eq_reflection; 

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1922  66 
fun atomize pairs = 
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let fun atoms th = 

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(case concl_of th of 
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Const("Trueprop",_) $ p => 

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(case head_of p of 

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Const(a,_) => 

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(case assoc(pairs,a) of 

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Some(rls) => flat (map atoms ([th] RL rls)) 

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 None => [th]) 

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 _ => [th]) 

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 _ => [th]) 

1922  77 
in atoms end; 
923  78 

2134  79 
fun gen_all th = forall_elim_vars (#maxidx(rep_thm th)+1) th; 
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in 

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fun mk_meta_eq r = r RS eq_reflection; 
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fun mk_meta_eq_simp r = case concl_of r of 
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Const("==",_)$_$_ => r 
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 _$(Const("op =",_)$lhs$rhs) => 
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(case fst(Logic.loops (#sign(rep_thm r)) (prems_of r) lhs rhs) of 
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None => mk_meta_eq r 
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 Some _ => r RS P_imp_P_eq_True) 
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 _$(Const("Not",_)$_) => r RS not_P_imp_P_eq_False 
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 _ => r RS P_imp_P_eq_True; 
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(* last 2 lines requires all formulae to be of the from Trueprop(.) *) 

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2082  95 
val simp_thms = map prover 
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[ "(x=x) = True", 

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"(~True) = False", "(~False) = True", "(~ ~ P) = P", 

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"(~P) ~= P", "P ~= (~P)", "(P ~= Q) = (P = (~Q))", 

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"(True=P) = P", "(P=True) = P", 

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"(True > P) = P", "(False > P) = True", 

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"(P > True) = True", "(P > P) = True", 

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"(P > False) = (~P)", "(P > ~P) = (~P)", 

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"(P & True) = P", "(True & P) = P", 

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"(P & False) = False", "(False & P) = False", 
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"(P & P) = P", "(P & (P & Q)) = (P & Q)", 

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"(P & ~P) = False", "(~P & P) = False", 
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"(P  True) = True", "(True  P) = True", 
2800  108 
"(P  False) = P", "(False  P) = P", 
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"(P  P) = P", "(P  (P  Q)) = (P  Q)", 

3913  110 
"(P  ~P) = True", "(~P  P) = True", 
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"((~P) = (~Q)) = (P=Q)", 
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"(!x. P) = P", "(? x. P) = P", "? x. x=t", "? x. t=x", 
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"(? x. x=t & P(x)) = P(t)", 
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"(! x. t=x > P(x)) = P(t)" ]; 
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988  116 
(*Add congruence rules for = (instead of ==) *) 
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infix 4 addcongs delcongs; 
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fun ss addcongs congs = ss addeqcongs (map standard (congs RL [eq_reflection])); 
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fun ss delcongs congs = ss deleqcongs (map standard (congs RL [eq_reflection])); 

923  120 

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fun Addcongs congs = (simpset := !simpset addcongs congs); 
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fun Delcongs congs = (simpset := !simpset delcongs congs); 
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fun mksimps pairs = map mk_meta_eq_simp o atomize pairs o gen_all; 
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1922  126 
val imp_cong = impI RSN 
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(2, prove_goal HOL.thy "(P=P')> (P'> (Q=Q'))> ((P>Q) = (P'>Q'))" 

2935  128 
(fn _=> [blast_tac HOL_cs 1]) RS mp RS mp); 
1922  129 

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(*Miniscoping: pushing in existential quantifiers*) 
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val ex_simps = map prover 
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["(EX x. P x & Q) = ((EX x. P x) & Q)", 
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"(EX x. P & Q x) = (P & (EX x. Q x))", 

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"(EX x. P x  Q) = ((EX x. P x)  Q)", 

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"(EX x. P  Q x) = (P  (EX x. Q x))", 

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"(EX x. P x > Q) = ((ALL x. P x) > Q)", 

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"(EX x. P > Q x) = (P > (EX x. Q x))"]; 

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(*Miniscoping: pushing in universal quantifiers*) 
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val all_simps = map prover 
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["(ALL x. P x & Q) = ((ALL x. P x) & Q)", 
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"(ALL x. P & Q x) = (P & (ALL x. Q x))", 

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"(ALL x. P x  Q) = ((ALL x. P x)  Q)", 

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"(ALL x. P  Q x) = (P  (ALL x. Q x))", 

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"(ALL x. P x > Q) = ((EX x. P x) > Q)", 

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"(ALL x. P > Q x) = (P > (ALL x. Q x))"]; 

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(*** Simplification procedures for turning 
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? x. ... & x = t & ... 
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into ? x. x = t & ... & ... 
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where the `? x. x = t &' in the latter formula is eliminated 
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by ordinary simplification. 
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and ! x. (... & x = t & ...) > P x 
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into ! x. x = t > (... & ...) > P x 
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where the `!x. x=t >' in the latter formula is eliminated 
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by ordinary simplification. 
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NB Simproc is only triggered by "!x. P(x) & P'(x) > Q(x)" 
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"!x. x=t > P(x)" and "!x. t=x > P(x)" 
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must be taken care of by ordinary rewrite rules. 
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***) 
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local 
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fun def(eq as (c as Const("op =",_)) $ s $ t) = 
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if s = Bound 0 andalso not(loose_bvar1(t,0)) then Some eq else 
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if t = Bound 0 andalso not(loose_bvar1(s,0)) then Some(c$t$s) 
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else None 
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 def _ = None; 
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fun extract(Const("op &",_) $ P $ Q) = 
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(case def P of 
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Some eq => Some(eq,Q) 
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 None => (case def Q of 
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Some eq => Some(eq,P) 
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 None => 
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(case extract P of 
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Some(eq,P') => Some(eq, HOLogic.conj $ P' $ Q) 
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 None => (case extract Q of 
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Some(eq,Q') => Some(eq,HOLogic.conj $ P $ Q') 
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 None => None)))) 
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 extract _ = None; 
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fun prove_ex_eq(ceqt) = 
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let val tac = rtac eq_reflection 1 THEN rtac iffI 1 THEN 
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ALLGOALS(EVERY'[etac exE, REPEAT o (etac conjE), 
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rtac exI, REPEAT o (ares_tac [conjI] ORELSE' etac sym)]) 
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in rule_by_tactic tac (trivial ceqt) end; 
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fun rearrange_ex sg _ (F as ex $ Abs(x,T,P)) = 
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(case extract P of 
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None => None 
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 Some(eq,Q) => 
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let val ceqt = cterm_of sg 
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(Logic.mk_equals(F,ex $ Abs(x,T,HOLogic.conj$eq$Q))) 
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in Some(prove_ex_eq ceqt) end) 
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 rearrange_ex _ _ _ = None; 
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val ex_pattern = 
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read_cterm (sign_of HOL.thy) ("? x. P(x) & Q(x)",HOLogic.boolT) 
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fun prove_all_eq(ceqt) = 
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let fun tac _ = [EVERY1[rtac eq_reflection, rtac iffI, 
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rtac allI, etac allE, rtac impI, rtac impI, etac mp, 
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REPEAT o (etac conjE), 
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REPEAT o (ares_tac [conjI] ORELSE' etac sym), 
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rtac allI, etac allE, rtac impI, REPEAT o (etac conjE), 
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etac impE, atac ORELSE' etac sym, etac mp, 
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REPEAT o (ares_tac [conjI])]] 
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in prove_goalw_cterm [] ceqt tac end; 
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fun rearrange_all sg _ (F as all $ Abs(x,T,Const("op >",_)$P$Q)) = 
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(case extract P of 
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216 
None => None 
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217 
 Some(eq,P') => 
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218 
let val R = HOLogic.imp $ eq $ (HOLogic.imp $ P' $ Q) 
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219 
val ceqt = cterm_of sg (Logic.mk_equals(F,all$Abs(x,T,R))) 
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220 
in Some(prove_all_eq ceqt) end) 
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221 
 rearrange_all _ _ _ = None; 
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222 

4b1c69d8b767
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223 
val all_pattern = 
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224 
read_cterm (sign_of HOL.thy) ("! x. P(x) & P'(x) > Q(x)",HOLogic.boolT) 
3568
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225 

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226 
in 
4032
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227 
val defEX_regroup = mk_simproc "defined EX" [ex_pattern] rearrange_ex; 
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228 
val defALL_regroup = mk_simproc "defined ALL" [all_pattern] rearrange_all; 
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229 
end; 
1722  230 

923  231 

2022  232 
(* elimination of existential quantifiers in assumptions *) 
923  233 

234 
val ex_all_equiv = 

235 
let val lemma1 = prove_goal HOL.thy 

236 
"(? x. P(x) ==> PROP Q) ==> (!!x. P(x) ==> PROP Q)" 

237 
(fn prems => [resolve_tac prems 1, etac exI 1]); 

238 
val lemma2 = prove_goalw HOL.thy [Ex_def] 

239 
"(!!x. P(x) ==> PROP Q) ==> (? x. P(x) ==> PROP Q)" 

240 
(fn prems => [REPEAT(resolve_tac prems 1)]) 

241 
in equal_intr lemma1 lemma2 end; 

242 

243 
end; 

244 

3654  245 
(* Elimination of True from asumptions: *) 
246 

247 
val True_implies_equals = prove_goal HOL.thy 

248 
"(True ==> PROP P) == PROP P" 

249 
(fn _ => [rtac equal_intr_rule 1, atac 2, 

250 
METAHYPS (fn prems => resolve_tac prems 1) 1, 

251 
rtac TrueI 1]); 

252 

2935  253 
fun prove nm thm = qed_goal nm HOL.thy thm (fn _ => [blast_tac HOL_cs 1]); 
923  254 

255 
prove "conj_commute" "(P&Q) = (Q&P)"; 

256 
prove "conj_left_commute" "(P&(Q&R)) = (Q&(P&R))"; 

257 
val conj_comms = [conj_commute, conj_left_commute]; 

2134  258 
prove "conj_assoc" "((P&Q)&R) = (P&(Q&R))"; 
923  259 

1922  260 
prove "disj_commute" "(PQ) = (QP)"; 
261 
prove "disj_left_commute" "(P(QR)) = (Q(PR))"; 

262 
val disj_comms = [disj_commute, disj_left_commute]; 

2134  263 
prove "disj_assoc" "((PQ)R) = (P(QR))"; 
1922  264 

923  265 
prove "conj_disj_distribL" "(P&(QR)) = (P&Q  P&R)"; 
266 
prove "conj_disj_distribR" "((PQ)&R) = (P&R  Q&R)"; 

1485
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267 

1892  268 
prove "disj_conj_distribL" "(P(Q&R)) = ((PQ) & (PR))"; 
269 
prove "disj_conj_distribR" "((P&Q)R) = ((PR) & (QR))"; 

270 

2134  271 
prove "imp_conjR" "(P > (Q&R)) = ((P>Q) & (P>R))"; 
272 
prove "imp_conjL" "((P&Q) >R) = (P > (Q > R))"; 

273 
prove "imp_disjL" "((PQ) > R) = ((P>R)&(Q>R))"; 

1892  274 

3448  275 
(*These two are specialized, but imp_disj_not1 is useful in Auth/Yahalom.ML*) 
276 
prove "imp_disj_not1" "((P > Q  R)) = (~Q > P > R)"; 

277 
prove "imp_disj_not2" "((P > Q  R)) = (~R > P > Q)"; 

278 

3904  279 
prove "imp_disj1" "((P>Q)R) = (P> QR)"; 
280 
prove "imp_disj2" "(Q(P>R)) = (P> QR)"; 

281 

1485
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282 
prove "de_Morgan_disj" "(~(P  Q)) = (~P & ~Q)"; 
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283 
prove "de_Morgan_conj" "(~(P & Q)) = (~P  ~Q)"; 
3446
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284 
prove "not_imp" "(~(P > Q)) = (P & ~Q)"; 
1922  285 
prove "not_iff" "(P~=Q) = (P = (~Q))"; 
1485
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286 

2134  287 
(*Avoids duplication of subgoals after expand_if, when the true and false 
288 
cases boil down to the same thing.*) 

289 
prove "cases_simp" "((P > Q) & (~P > Q)) = Q"; 

290 

3842  291 
prove "not_all" "(~ (! x. P(x))) = (? x.~P(x))"; 
1922  292 
prove "imp_all" "((! x. P x) > Q) = (? x. P x > Q)"; 
3842  293 
prove "not_ex" "(~ (? x. P(x))) = (! x.~P(x))"; 
1922  294 
prove "imp_ex" "((? x. P x) > Q) = (! x. P x > Q)"; 
1660  295 

1655  296 
prove "ex_disj_distrib" "(? x. P(x)  Q(x)) = ((? x. P(x))  (? x. Q(x)))"; 
297 
prove "all_conj_distrib" "(!x. P(x) & Q(x)) = ((! x. P(x)) & (! x. Q(x)))"; 

298 

2134  299 
(* '&' congruence rule: not included by default! 
300 
May slow rewrite proofs down by as much as 50% *) 

301 

302 
let val th = prove_goal HOL.thy 

303 
"(P=P')> (P'> (Q=Q'))> ((P&Q) = (P'&Q'))" 

2935  304 
(fn _=> [blast_tac HOL_cs 1]) 
2134  305 
in bind_thm("conj_cong",standard (impI RSN (2, th RS mp RS mp))) end; 
306 

307 
let val th = prove_goal HOL.thy 

308 
"(Q=Q')> (Q'> (P=P'))> ((P&Q) = (P'&Q'))" 

2935  309 
(fn _=> [blast_tac HOL_cs 1]) 
2134  310 
in bind_thm("rev_conj_cong",standard (impI RSN (2, th RS mp RS mp))) end; 
311 

312 
(* '' congruence rule: not included by default! *) 

313 

314 
let val th = prove_goal HOL.thy 

315 
"(P=P')> (~P'> (Q=Q'))> ((PQ) = (P'Q'))" 

2935  316 
(fn _=> [blast_tac HOL_cs 1]) 
2134  317 
in bind_thm("disj_cong",standard (impI RSN (2, th RS mp RS mp))) end; 
318 

319 
prove "eq_sym_conv" "(x=y) = (y=x)"; 

320 

321 
qed_goalw "o_apply" HOL.thy [o_def] "(f o g) x = f (g x)" 

322 
(fn _ => [rtac refl 1]); 

323 

324 
qed_goal "meta_eq_to_obj_eq" HOL.thy "x==y ==> x=y" 

325 
(fn [prem] => [rewtac prem, rtac refl 1]); 

326 

327 
qed_goalw "if_True" HOL.thy [if_def] "(if True then x else y) = x" 

2935  328 
(fn _=>[blast_tac (HOL_cs addIs [select_equality]) 1]); 
2134  329 

330 
qed_goalw "if_False" HOL.thy [if_def] "(if False then x else y) = y" 

2935  331 
(fn _=>[blast_tac (HOL_cs addIs [select_equality]) 1]); 
2134  332 

333 
qed_goal "if_P" HOL.thy "P ==> (if P then x else y) = x" 

334 
(fn [prem] => [ stac (prem RS eqTrueI) 1, rtac if_True 1 ]); 

335 
(* 

336 
qed_goal "if_not_P" HOL.thy "~P ==> (if P then x else y) = y" 

337 
(fn [prem] => [ stac (prem RS not_P_imp_P_iff_F) 1, rtac if_False 1 ]); 

338 
*) 

339 
qed_goalw "if_not_P" HOL.thy [if_def] "!!P. ~P ==> (if P then x else y) = y" 

2935  340 
(fn _ => [blast_tac (HOL_cs addIs [select_equality]) 1]); 
2134  341 

342 
qed_goal "expand_if" HOL.thy 

343 
"P(if Q then x else y) = ((Q > P(x)) & (~Q > P(y)))" 

344 
(fn _=> [ (res_inst_tac [("Q","Q")] (excluded_middle RS disjE) 1), 

345 
stac if_P 2, 

346 
stac if_not_P 1, 

2935  347 
REPEAT(blast_tac HOL_cs 1) ]); 
2134  348 

349 
qed_goal "if_bool_eq" HOL.thy 

350 
"(if P then Q else R) = ((P>Q) & (~P>R))" 

351 
(fn _ => [rtac expand_if 1]); 

352 

3913  353 

354 

355 
(** Case splitting **) 

356 

2263  357 
local val mktac = mk_case_split_tac (meta_eq_to_obj_eq RS iffD2) 
358 
in 

359 
fun split_tac splits = mktac (map mk_meta_eq splits) 

360 
end; 

361 

362 
local val mktac = mk_case_split_inside_tac (meta_eq_to_obj_eq RS iffD2) 

363 
in 

364 
fun split_inside_tac splits = mktac (map mk_meta_eq splits) 

365 
end; 

366 

3919  367 
infix 4 addsplits; 
368 
fun ss addsplits splits = ss addloop (split_tac splits); 

369 

2263  370 

2251  371 
qed_goal "if_cancel" HOL.thy "(if c then x else x) = x" 
2935  372 
(fn _ => [split_tac [expand_if] 1, blast_tac HOL_cs 1]); 
2251  373 

2134  374 
(** 'if' congruence rules: neither included by default! *) 
375 

376 
(*Simplifies x assuming c and y assuming ~c*) 

377 
qed_goal "if_cong" HOL.thy 

378 
"[ b=c; c ==> x=u; ~c ==> y=v ] ==>\ 

379 
\ (if b then x else y) = (if c then u else v)" 

380 
(fn rew::prems => 

381 
[stac rew 1, stac expand_if 1, stac expand_if 1, 

2935  382 
blast_tac (HOL_cs addDs prems) 1]); 
2134  383 

384 
(*Prevents simplification of x and y: much faster*) 

385 
qed_goal "if_weak_cong" HOL.thy 

386 
"b=c ==> (if b then x else y) = (if c then x else y)" 

387 
(fn [prem] => [rtac (prem RS arg_cong) 1]); 

388 

389 
(*Prevents simplification of t: much faster*) 

390 
qed_goal "let_weak_cong" HOL.thy 

391 
"a = b ==> (let x=a in t(x)) = (let x=b in t(x))" 

392 
(fn [prem] => [rtac (prem RS arg_cong) 1]); 

393 

394 
(*In general it seems wrong to add distributive laws by default: they 

395 
might cause exponential blowup. But imp_disjL has been in for a while 

396 
and cannot be removed without affecting existing proofs. Moreover, 

397 
rewriting by "(PQ > R) = ((P>R)&(Q>R))" might be justified on the 

398 
grounds that it allows simplification of R in the two cases.*) 

399 

400 
val mksimps_pairs = 

401 
[("op >", [mp]), ("op &", [conjunct1,conjunct2]), 

402 
("All", [spec]), ("True", []), ("False", []), 

403 
("If", [if_bool_eq RS iffD1])]; 

1758  404 

2636
4b30dbe4a020
added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents:
2595
diff
changeset

405 
fun unsafe_solver prems = FIRST'[resolve_tac (TrueI::refl::prems), 
4b30dbe4a020
added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents:
2595
diff
changeset

406 
atac, etac FalseE]; 
4b30dbe4a020
added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents:
2595
diff
changeset

407 
(*No premature instantiation of variables during simplification*) 
4b30dbe4a020
added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents:
2595
diff
changeset

408 
fun safe_solver prems = FIRST'[match_tac (TrueI::refl::prems), 
4b30dbe4a020
added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents:
2595
diff
changeset

409 
eq_assume_tac, ematch_tac [FalseE]]; 
2443
a81d4c219c3c
factored out HOL_base_ss and val HOL_min_ss, added HOL_safe_min_ss
oheimb
parents:
2263
diff
changeset

410 

2636
4b30dbe4a020
added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents:
2595
diff
changeset

411 
val HOL_basic_ss = empty_ss setsubgoaler asm_simp_tac 
4b30dbe4a020
added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents:
2595
diff
changeset

412 
setSSolver safe_solver 
4b30dbe4a020
added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents:
2595
diff
changeset

413 
setSolver unsafe_solver 
4b30dbe4a020
added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents:
2595
diff
changeset

414 
setmksimps (mksimps mksimps_pairs); 
2443
a81d4c219c3c
factored out HOL_base_ss and val HOL_min_ss, added HOL_safe_min_ss
oheimb
parents:
2263
diff
changeset

415 

3446
a14e5451f613
Addition of not_imp (which pushes negation into implication) as a default
paulson
parents:
3282
diff
changeset

416 
val HOL_ss = 
a14e5451f613
Addition of not_imp (which pushes negation into implication) as a default
paulson
parents:
3282
diff
changeset

417 
HOL_basic_ss addsimps 
a14e5451f613
Addition of not_imp (which pushes negation into implication) as a default
paulson
parents:
3282
diff
changeset

418 
([triv_forall_equality, (* prunes params *) 
3654  419 
True_implies_equals, (* prune asms `True' *) 
3446
a14e5451f613
Addition of not_imp (which pushes negation into implication) as a default
paulson
parents:
3282
diff
changeset

420 
if_True, if_False, if_cancel, 
a14e5451f613
Addition of not_imp (which pushes negation into implication) as a default
paulson
parents:
3282
diff
changeset

421 
o_apply, imp_disjL, conj_assoc, disj_assoc, 
3904  422 
de_Morgan_conj, de_Morgan_disj, imp_disj1, imp_disj2, not_imp, 
3446
a14e5451f613
Addition of not_imp (which pushes negation into implication) as a default
paulson
parents:
3282
diff
changeset

423 
not_all, not_ex, cases_simp] 
a14e5451f613
Addition of not_imp (which pushes negation into implication) as a default
paulson
parents:
3282
diff
changeset

424 
@ ex_simps @ all_simps @ simp_thms) 
4032
4b1c69d8b767
For each datatype `t' there is now a theorem `split_t_case' of the form
nipkow
parents:
3919
diff
changeset

425 
addsimprocs [defALL_regroup,defEX_regroup] 
3446
a14e5451f613
Addition of not_imp (which pushes negation into implication) as a default
paulson
parents:
3282
diff
changeset

426 
addcongs [imp_cong]; 
2082  427 

1655  428 
qed_goal "if_distrib" HOL.thy 
429 
"f(if c then x else y) = (if c then f x else f y)" 

430 
(fn _ => [simp_tac (HOL_ss setloop (split_tac [expand_if])) 1]); 

431 

2097  432 
qed_goalw "o_assoc" HOL.thy [o_def] "f o (g o h) = f o g o h" 
2098
2bfc0675c92f
corrected `correction` of o_assoc (of version 1.14),
oheimb
parents:
2097
diff
changeset

433 
(fn _ => [rtac ext 1, rtac refl 1]); 
1984  434 

435 

2948
f18035b1d531
Moved expand_case_tac from Auth/Message.ML to simpdata.ML
paulson
parents:
2935
diff
changeset

436 
val prems = goal HOL.thy "[ P ==> Q(True); ~P ==> Q(False) ] ==> Q(P)"; 
f18035b1d531
Moved expand_case_tac from Auth/Message.ML to simpdata.ML
paulson
parents:
2935
diff
changeset

437 
by (case_tac "P" 1); 
f18035b1d531
Moved expand_case_tac from Auth/Message.ML to simpdata.ML
paulson
parents:
2935
diff
changeset

438 
by (ALLGOALS (asm_simp_tac (HOL_ss addsimps prems))); 
f18035b1d531
Moved expand_case_tac from Auth/Message.ML to simpdata.ML
paulson
parents:
2935
diff
changeset

439 
val expand_case = result(); 
f18035b1d531
Moved expand_case_tac from Auth/Message.ML to simpdata.ML
paulson
parents:
2935
diff
changeset

440 

f18035b1d531
Moved expand_case_tac from Auth/Message.ML to simpdata.ML
paulson
parents:
2935
diff
changeset

441 
fun expand_case_tac P i = 
f18035b1d531
Moved expand_case_tac from Auth/Message.ML to simpdata.ML
paulson
parents:
2935
diff
changeset

442 
res_inst_tac [("P",P)] expand_case i THEN 
f18035b1d531
Moved expand_case_tac from Auth/Message.ML to simpdata.ML
paulson
parents:
2935
diff
changeset

443 
Simp_tac (i+1) THEN 
f18035b1d531
Moved expand_case_tac from Auth/Message.ML to simpdata.ML
paulson
parents:
2935
diff
changeset

444 
Simp_tac i; 
f18035b1d531
Moved expand_case_tac from Auth/Message.ML to simpdata.ML
paulson
parents:
2935
diff
changeset

445 

f18035b1d531
Moved expand_case_tac from Auth/Message.ML to simpdata.ML
paulson
parents:
2935
diff
changeset

446 

1984  447 

448 

449 
(*** Install simpsets and datatypes in theory structure ***) 

450 

2251  451 
simpset := HOL_ss; 
1984  452 

453 
exception SS_DATA of simpset; 

454 

455 
let fun merge [] = SS_DATA empty_ss 

456 
 merge ss = let val ss = map (fn SS_DATA x => x) ss; 

457 
in SS_DATA (foldl merge_ss (hd ss, tl ss)) end; 

458 

459 
fun put (SS_DATA ss) = simpset := ss; 

460 

461 
fun get () = SS_DATA (!simpset); 

462 
in add_thydata "HOL" 

463 
("simpset", ThyMethods {merge = merge, put = put, get = get}) 

464 
end; 

465 

3615
e5322197cfea
Moved some functions which used to be part of thy_data.ML
berghofe
parents:
3577
diff
changeset

466 
fun simpset_of tname = 
e5322197cfea
Moved some functions which used to be part of thy_data.ML
berghofe
parents:
3577
diff
changeset

467 
case get_thydata tname "simpset" of 
e5322197cfea
Moved some functions which used to be part of thy_data.ML
berghofe
parents:
3577
diff
changeset

468 
None => empty_ss 
e5322197cfea
Moved some functions which used to be part of thy_data.ML
berghofe
parents:
3577
diff
changeset

469 
 Some (SS_DATA ss) => ss; 
e5322197cfea
Moved some functions which used to be part of thy_data.ML
berghofe
parents:
3577
diff
changeset

470 

3040
7d48671753da
Introduced a generic "induct_tac" which picks up the right induction scheme
nipkow
parents:
2948
diff
changeset

471 
type dtype_info = {case_const:term, 
7d48671753da
Introduced a generic "induct_tac" which picks up the right induction scheme
nipkow
parents:
2948
diff
changeset

472 
case_rewrites:thm list, 
7d48671753da
Introduced a generic "induct_tac" which picks up the right induction scheme
nipkow
parents:
2948
diff
changeset

473 
constructors:term list, 
7d48671753da
Introduced a generic "induct_tac" which picks up the right induction scheme
nipkow
parents:
2948
diff
changeset

474 
induct_tac: string > int > tactic, 
3282
c31e6239d4c9
Added exhaustion thm and exhaust_tac for each datatype.
nipkow
parents:
3206
diff
changeset

475 
nchotomy: thm, 
c31e6239d4c9
Added exhaustion thm and exhaust_tac for each datatype.
nipkow
parents:
3206
diff
changeset

476 
exhaustion: thm, 
c31e6239d4c9
Added exhaustion thm and exhaust_tac for each datatype.
nipkow
parents:
3206
diff
changeset

477 
exhaust_tac: string > int > tactic, 
3040
7d48671753da
Introduced a generic "induct_tac" which picks up the right induction scheme
nipkow
parents:
2948
diff
changeset

478 
case_cong:thm}; 
1984  479 

480 
exception DT_DATA of (string * dtype_info) list; 

481 
val datatypes = ref [] : (string * dtype_info) list ref; 

482 

483 
let fun merge [] = DT_DATA [] 

484 
 merge ds = 

485 
let val ds = map (fn DT_DATA x => x) ds; 

486 
in DT_DATA (foldl (gen_union eq_fst) (hd ds, tl ds)) end; 

487 

488 
fun put (DT_DATA ds) = datatypes := ds; 

489 

490 
fun get () = DT_DATA (!datatypes); 

491 
in add_thydata "HOL" 

492 
("datatypes", ThyMethods {merge = merge, put = put, get = get}) 

493 
end; 

494 

495 

2636
4b30dbe4a020
added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents:
2595
diff
changeset

496 

4b30dbe4a020
added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents:
2595
diff
changeset

497 
(*** Integration of simplifier with classical reasoner ***) 
4b30dbe4a020
added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents:
2595
diff
changeset

498 

4b30dbe4a020
added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents:
2595
diff
changeset

499 
(* rot_eq_tac rotates the first equality premise of subgoal i to the front, 
4b30dbe4a020
added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents:
2595
diff
changeset

500 
fails if there is no equaliy or if an equality is already at the front *) 
3538  501 
local 
502 
fun is_eq (Const ("Trueprop", _) $ (Const("op =" ,_) $ _ $ _)) = true 

503 
 is_eq _ = false; 

504 
fun find_eq n [] = None 

505 
 find_eq n (t :: ts) = if (is_eq t) then Some n 

506 
else find_eq (n + 1) ts; 

507 
in 

508 
val rot_eq_tac = 

509 
SUBGOAL (fn (Bi,i) => 

510 
case find_eq 0 (Logic.strip_assums_hyp Bi) of 

2805  511 
None => no_tac 
512 
 Some 0 => no_tac 

3538  513 
 Some n => rotate_tac n i) 
514 
end; 

2636
4b30dbe4a020
added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents:
2595
diff
changeset

515 

4b30dbe4a020
added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents:
2595
diff
changeset

516 
(*an unsatisfactory fix for the incomplete asm_full_simp_tac! 
4b30dbe4a020
added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents:
2595
diff
changeset

517 
better: asm_really_full_simp_tac, a yet to be implemented version of 
4b30dbe4a020
added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents:
2595
diff
changeset

518 
asm_full_simp_tac that applies all equalities in the 
4b30dbe4a020
added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents:
2595
diff
changeset

519 
premises to all the premises *) 
4b30dbe4a020
added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents:
2595
diff
changeset

520 
fun safe_asm_more_full_simp_tac ss = TRY o rot_eq_tac THEN' 
4b30dbe4a020
added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents:
2595
diff
changeset

521 
safe_asm_full_simp_tac ss; 
4b30dbe4a020
added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents:
2595
diff
changeset

522 

4b30dbe4a020
added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents:
2595
diff
changeset

523 
(*Add a simpset to a classical set!*) 
3206
a3de7f32728c
renamed addss to addSss, unsafe_addss to addss, extended auto_tac
oheimb
parents:
3040
diff
changeset

524 
infix 4 addSss addss; 
a3de7f32728c
renamed addss to addSss, unsafe_addss to addss, extended auto_tac
oheimb
parents:
3040
diff
changeset

525 
fun cs addSss ss = cs addSaltern (CHANGED o (safe_asm_more_full_simp_tac ss)); 
a3de7f32728c
renamed addss to addSss, unsafe_addss to addss, extended auto_tac
oheimb
parents:
3040
diff
changeset

526 
fun cs addss ss = cs addbefore asm_full_simp_tac ss; 
2636
4b30dbe4a020
added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents:
2595
diff
changeset

527 

4b30dbe4a020
added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents:
2595
diff
changeset

528 
fun Addss ss = (claset := !claset addss ss); 
4b30dbe4a020
added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents:
2595
diff
changeset

529 

4b30dbe4a020
added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents:
2595
diff
changeset

530 
(*Designed to be idempotent, except if best_tac instantiates variables 
4b30dbe4a020
added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents:
2595
diff
changeset

531 
in some of the subgoals*) 
4b30dbe4a020
added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents:
2595
diff
changeset

532 

4b30dbe4a020
added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents:
2595
diff
changeset

533 
type clasimpset = (claset * simpset); 
4b30dbe4a020
added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents:
2595
diff
changeset

534 

4b30dbe4a020
added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents:
2595
diff
changeset

535 
val HOL_css = (HOL_cs, HOL_ss); 
4b30dbe4a020
added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents:
2595
diff
changeset

536 

4b30dbe4a020
added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents:
2595
diff
changeset

537 
fun pair_upd1 f ((a,b),x) = (f(a,x), b); 
4b30dbe4a020
added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents:
2595
diff
changeset

538 
fun pair_upd2 f ((a,b),x) = (a, f(b,x)); 
4b30dbe4a020
added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents:
2595
diff
changeset

539 

4b30dbe4a020
added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents:
2595
diff
changeset

540 
infix 4 addSIs2 addSEs2 addSDs2 addIs2 addEs2 addDs2 
4b30dbe4a020
added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents:
2595
diff
changeset

541 
addsimps2 delsimps2 addcongs2 delcongs2; 
2748
3ae9ccdd701e
Etaexpanded some declarations for compatibility with value polymorphism
paulson
parents:
2718
diff
changeset

542 
fun op addSIs2 arg = pair_upd1 (op addSIs) arg; 
3ae9ccdd701e
Etaexpanded some declarations for compatibility with value polymorphism
paulson
parents:
2718
diff
changeset

543 
fun op addSEs2 arg = pair_upd1 (op addSEs) arg; 
3ae9ccdd701e
Etaexpanded some declarations for compatibility with value polymorphism
paulson
parents:
2718
diff
changeset

544 
fun op addSDs2 arg = pair_upd1 (op addSDs) arg; 
3ae9ccdd701e
Etaexpanded some declarations for compatibility with value polymorphism
paulson
parents:
2718
diff
changeset

545 
fun op addIs2 arg = pair_upd1 (op addIs ) arg; 
3ae9ccdd701e
Etaexpanded some declarations for compatibility with value polymorphism
paulson
parents:
2718
diff
changeset

546 
fun op addEs2 arg = pair_upd1 (op addEs ) arg; 
3ae9ccdd701e
Etaexpanded some declarations for compatibility with value polymorphism
paulson
parents:
2718
diff
changeset

547 
fun op addDs2 arg = pair_upd1 (op addDs ) arg; 
3ae9ccdd701e
Etaexpanded some declarations for compatibility with value polymorphism
paulson
parents:
2718
diff
changeset

548 
fun op addsimps2 arg = pair_upd2 (op addsimps) arg; 
3ae9ccdd701e
Etaexpanded some declarations for compatibility with value polymorphism
paulson
parents:
2718
diff
changeset

549 
fun op delsimps2 arg = pair_upd2 (op delsimps) arg; 
3ae9ccdd701e
Etaexpanded some declarations for compatibility with value polymorphism
paulson
parents:
2718
diff
changeset

550 
fun op addcongs2 arg = pair_upd2 (op addcongs) arg; 
3ae9ccdd701e
Etaexpanded some declarations for compatibility with value polymorphism
paulson
parents:
2718
diff
changeset

551 
fun op delcongs2 arg = pair_upd2 (op delcongs) arg; 
2636
4b30dbe4a020
added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents:
2595
diff
changeset

552 

2805  553 
fun auto_tac (cs,ss) = 
554 
let val cs' = cs addss ss 

555 
in EVERY [TRY (safe_tac cs'), 

556 
REPEAT (FIRSTGOAL (fast_tac cs')), 

3206
a3de7f32728c
renamed addss to addSss, unsafe_addss to addss, extended auto_tac
oheimb
parents:
3040
diff
changeset

557 
TRY (safe_tac (cs addSss ss)), 
2805  558 
prune_params_tac] 
559 
end; 

2636
4b30dbe4a020
added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents:
2595
diff
changeset

560 

4b30dbe4a020
added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents:
2595
diff
changeset

561 
fun Auto_tac () = auto_tac (!claset, !simpset); 
4b30dbe4a020
added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents:
2595
diff
changeset

562 

4b30dbe4a020
added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents:
2595
diff
changeset

563 
fun auto () = by (Auto_tac ()); 