author | oheimb |
Wed, 12 Nov 1997 18:58:50 +0100 | |
changeset 4223 | f60e3d2c81d3 |
parent 4205 | 96632970d203 |
child 4320 | 24d9e6639cd4 |
permissions | -rw-r--r-- |
1465 | 1 |
(* Title: HOL/simpdata.ML |
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ID: $Id$ |
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Author: Tobias Nipkow |
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Copyright 1991 University of Cambridge |
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||
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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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open Simplifier; |
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1984 | 13 |
(*** Addition of rules to simpsets and clasets simultaneously ***) |
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||
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(*Takes UNCONDITIONAL theorems of the form A<->B to |
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the Safe Intr rule B==>A and |
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the Safe Destruct rule A==>B. |
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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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||
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fun addIff th = |
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(case HOLogic.dest_Trueprop (#prop(rep_thm th)) of |
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(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]; |
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1984 | 33 |
Addsimps [th]) |
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handle _ => error ("AddIffs: theorem must be unconditional\n" ^ |
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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 |
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(Const("Not",_) $ A) => |
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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), |
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make_elim (zero_var_indexes (th RS iffD1))] |
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else Delrules [th] |
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| _ => Delrules [th]; |
|
1984 | 47 |
Delsimps [th]) |
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handle _ => warning("DelIffs: ignoring conditional theorem\n" ^ |
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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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||
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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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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; |
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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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|
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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]) |
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in atoms end; |
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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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|
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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$rhs) => |
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(case fst(Logic.rewrite_rule_ok (#sign(rep_thm r)) (prems_of r) lhs rhs) of |
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None => mk_meta_eq r |
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| Some _ => r RS P_imp_P_eq_True) |
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| _$(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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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", |
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"(P | False) = P", "(False | P) = P", |
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"(P | P) = P", "(P | (P | Q)) = (P | Q)", |
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"(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])); |
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fun Addcongs congs = (simpset_ref() := simpset() addcongs congs); |
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fun Delcongs congs = (simpset_ref() := 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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val imp_cong = impI RSN |
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(2, prove_goal HOL.thy "(P=P')--> (P'--> (Q=Q'))--> ((P-->Q) = (P'-->Q'))" |
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(fn _=> [blast_tac HOL_cs 1]) RS mp RS mp); |
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|
1948
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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))"]; |
|
1948
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|
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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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1948
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|
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(*** Simplification procedures for turning |
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|
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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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|
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and ! x. (... & x = t & ...) --> P x |
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156 |
into ! x. x = t --> (... & ...) --> P x |
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157 |
where the `!x. x=t -->' in the latter formula is eliminated |
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by ordinary simplification. |
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|
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160 |
NB Simproc is only triggered by "!x. P(x) & P'(x) --> Q(x)" |
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161 |
"!x. x=t --> P(x)" and "!x. t=x --> P(x)" |
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162 |
must be taken care of by ordinary rewrite rules. |
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163 |
***) |
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164 |
|
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165 |
local |
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166 |
|
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167 |
fun def(eq as (c as Const("op =",_)) $ s $ t) = |
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168 |
if s = Bound 0 andalso not(loose_bvar1(t,0)) then Some eq else |
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169 |
if t = Bound 0 andalso not(loose_bvar1(s,0)) then Some(c$t$s) |
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170 |
else None |
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171 |
| def _ = None; |
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172 |
|
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173 |
fun extract(Const("op &",_) $ P $ Q) = |
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174 |
(case def P of |
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175 |
Some eq => Some(eq,Q) |
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176 |
| None => (case def Q of |
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177 |
Some eq => Some(eq,P) |
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178 |
| None => |
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179 |
(case extract P of |
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180 |
Some(eq,P') => Some(eq, HOLogic.conj $ P' $ Q) |
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| None => (case extract Q of |
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182 |
Some(eq,Q') => Some(eq,HOLogic.conj $ P $ Q') |
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183 |
| None => None)))) |
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184 |
| extract _ = None; |
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185 |
|
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186 |
fun prove_ex_eq(ceqt) = |
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187 |
let val tac = rtac eq_reflection 1 THEN rtac iffI 1 THEN |
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188 |
ALLGOALS(EVERY'[etac exE, REPEAT o (etac conjE), |
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189 |
rtac exI, REPEAT o (ares_tac [conjI] ORELSE' etac sym)]) |
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190 |
in rule_by_tactic tac (trivial ceqt) end; |
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191 |
|
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192 |
fun rearrange_ex sg _ (F as ex $ Abs(x,T,P)) = |
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193 |
(case extract P of |
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194 |
None => None |
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195 |
| Some(eq,Q) => |
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196 |
let val ceqt = cterm_of sg |
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197 |
(Logic.mk_equals(F,ex $ Abs(x,T,HOLogic.conj$eq$Q))) |
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198 |
in Some(prove_ex_eq ceqt) end) |
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199 |
| rearrange_ex _ _ _ = None; |
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200 |
|
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201 |
val ex_pattern = |
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202 |
read_cterm (sign_of HOL.thy) ("? x. P(x) & Q(x)",HOLogic.boolT) |
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203 |
|
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204 |
fun prove_all_eq(ceqt) = |
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|
205 |
let fun tac _ = [EVERY1[rtac eq_reflection, rtac iffI, |
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206 |
rtac allI, etac allE, rtac impI, rtac impI, etac mp, |
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|
207 |
REPEAT o (etac conjE), |
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|
208 |
REPEAT o (ares_tac [conjI] ORELSE' etac sym), |
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|
209 |
rtac allI, etac allE, rtac impI, REPEAT o (etac conjE), |
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|
210 |
etac impE, atac ORELSE' etac sym, etac mp, |
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|
211 |
REPEAT o (ares_tac [conjI])]] |
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|
212 |
in prove_goalw_cterm [] ceqt tac end; |
4b1c69d8b767
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|
213 |
|
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|
214 |
fun rearrange_all sg _ (F as all $ Abs(x,T,Const("op -->",_)$P$Q)) = |
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|
215 |
(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 |
|
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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" "(P|Q) = (Q|P)"; |
261 |
prove "disj_left_commute" "(P|(Q|R)) = (Q|(P|R))"; |
|
262 |
val disj_comms = [disj_commute, disj_left_commute]; |
|
2134 | 263 |
prove "disj_assoc" "((P|Q)|R) = (P|(Q|R))"; |
1922 | 264 |
|
923 | 265 |
prove "conj_disj_distribL" "(P&(Q|R)) = (P&Q | P&R)"; |
266 |
prove "conj_disj_distribR" "((P|Q)&R) = (P&R | Q&R)"; |
|
1485
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|
267 |
|
1892 | 268 |
prove "disj_conj_distribL" "(P|(Q&R)) = ((P|Q) & (P|R))"; |
269 |
prove "disj_conj_distribR" "((P&Q)|R) = ((P|R) & (Q|R))"; |
|
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" "((P|Q) --> 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--> Q|R)"; |
280 |
prove "imp_disj2" "(Q|(P-->R)) = (P--> Q|R)"; |
|
281 |
||
1485
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|
282 |
prove "de_Morgan_disj" "(~(P | Q)) = (~P & ~Q)"; |
240cc98b94a7
Added qed_spec_mp to avoid renaming of bound vars in 'th RS spec'
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|
283 |
prove "de_Morgan_conj" "(~(P & Q)) = (~P | ~Q)"; |
3446
a14e5451f613
Addition of not_imp (which pushes negation into implication) as a default
paulson
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changeset
|
284 |
prove "not_imp" "(~(P --> Q)) = (P & ~Q)"; |
1922 | 285 |
prove "not_iff" "(P~=Q) = (P = (~Q))"; |
1485
240cc98b94a7
Added qed_spec_mp to avoid renaming of bound vars in 'th RS spec'
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changeset
|
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'))--> ((P|Q) = (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 |
|
4205
96632970d203
simpdata.ML: renamed split_prem_tac to split_asm_tac, added split_if_asm
oheimb
parents:
4189
diff
changeset
|
343 |
"P(if Q then x else y) = ((Q --> P(x)) & (~Q --> P(y)))" (K [ |
96632970d203
simpdata.ML: renamed split_prem_tac to split_asm_tac, added split_if_asm
oheimb
parents:
4189
diff
changeset
|
344 |
res_inst_tac [("Q","Q")] (excluded_middle RS disjE) 1, |
2134 | 345 |
stac if_P 2, |
346 |
stac if_not_P 1, |
|
4205
96632970d203
simpdata.ML: renamed split_prem_tac to split_asm_tac, added split_if_asm
oheimb
parents:
4189
diff
changeset
|
347 |
ALLGOALS (blast_tac HOL_cs)]); |
96632970d203
simpdata.ML: renamed split_prem_tac to split_asm_tac, added split_if_asm
oheimb
parents:
4189
diff
changeset
|
348 |
|
96632970d203
simpdata.ML: renamed split_prem_tac to split_asm_tac, added split_if_asm
oheimb
parents:
4189
diff
changeset
|
349 |
qed_goal "split_if_asm" HOL.thy |
96632970d203
simpdata.ML: renamed split_prem_tac to split_asm_tac, added split_if_asm
oheimb
parents:
4189
diff
changeset
|
350 |
"P(if Q then x else y) = (~((Q & ~P x) | (~Q & ~P y)))" (K [ |
96632970d203
simpdata.ML: renamed split_prem_tac to split_asm_tac, added split_if_asm
oheimb
parents:
4189
diff
changeset
|
351 |
stac expand_if 1, |
96632970d203
simpdata.ML: renamed split_prem_tac to split_asm_tac, added split_if_asm
oheimb
parents:
4189
diff
changeset
|
352 |
blast_tac HOL_cs 1]); |
2134 | 353 |
|
354 |
qed_goal "if_bool_eq" HOL.thy |
|
355 |
"(if P then Q else R) = ((P-->Q) & (~P-->R))" |
|
356 |
(fn _ => [rtac expand_if 1]); |
|
357 |
||
3913 | 358 |
|
359 |
||
360 |
(** Case splitting **) |
|
361 |
||
2263 | 362 |
local val mktac = mk_case_split_tac (meta_eq_to_obj_eq RS iffD2) |
363 |
in |
|
364 |
fun split_tac splits = mktac (map mk_meta_eq splits) |
|
365 |
end; |
|
366 |
||
367 |
local val mktac = mk_case_split_inside_tac (meta_eq_to_obj_eq RS iffD2) |
|
368 |
in |
|
369 |
fun split_inside_tac splits = mktac (map mk_meta_eq splits) |
|
370 |
end; |
|
371 |
||
4205
96632970d203
simpdata.ML: renamed split_prem_tac to split_asm_tac, added split_if_asm
oheimb
parents:
4189
diff
changeset
|
372 |
val split_asm_tac = mk_case_split_asm_tac split_tac |
96632970d203
simpdata.ML: renamed split_prem_tac to split_asm_tac, added split_if_asm
oheimb
parents:
4189
diff
changeset
|
373 |
(disjE,conjE,exE,contrapos,contrapos2,notnotD); |
4189 | 374 |
|
3919 | 375 |
infix 4 addsplits; |
376 |
fun ss addsplits splits = ss addloop (split_tac splits); |
|
377 |
||
2263 | 378 |
|
2251 | 379 |
qed_goal "if_cancel" HOL.thy "(if c then x else x) = x" |
2935 | 380 |
(fn _ => [split_tac [expand_if] 1, blast_tac HOL_cs 1]); |
2251 | 381 |
|
2134 | 382 |
(** 'if' congruence rules: neither included by default! *) |
383 |
||
384 |
(*Simplifies x assuming c and y assuming ~c*) |
|
385 |
qed_goal "if_cong" HOL.thy |
|
386 |
"[| b=c; c ==> x=u; ~c ==> y=v |] ==>\ |
|
387 |
\ (if b then x else y) = (if c then u else v)" |
|
388 |
(fn rew::prems => |
|
389 |
[stac rew 1, stac expand_if 1, stac expand_if 1, |
|
2935 | 390 |
blast_tac (HOL_cs addDs prems) 1]); |
2134 | 391 |
|
392 |
(*Prevents simplification of x and y: much faster*) |
|
393 |
qed_goal "if_weak_cong" HOL.thy |
|
394 |
"b=c ==> (if b then x else y) = (if c then x else y)" |
|
395 |
(fn [prem] => [rtac (prem RS arg_cong) 1]); |
|
396 |
||
397 |
(*Prevents simplification of t: much faster*) |
|
398 |
qed_goal "let_weak_cong" HOL.thy |
|
399 |
"a = b ==> (let x=a in t(x)) = (let x=b in t(x))" |
|
400 |
(fn [prem] => [rtac (prem RS arg_cong) 1]); |
|
401 |
||
402 |
(*In general it seems wrong to add distributive laws by default: they |
|
403 |
might cause exponential blow-up. But imp_disjL has been in for a while |
|
404 |
and cannot be removed without affecting existing proofs. Moreover, |
|
405 |
rewriting by "(P|Q --> R) = ((P-->R)&(Q-->R))" might be justified on the |
|
406 |
grounds that it allows simplification of R in the two cases.*) |
|
407 |
||
408 |
val mksimps_pairs = |
|
409 |
[("op -->", [mp]), ("op &", [conjunct1,conjunct2]), |
|
410 |
("All", [spec]), ("True", []), ("False", []), |
|
411 |
("If", [if_bool_eq RS iffD1])]; |
|
1758 | 412 |
|
2636
4b30dbe4a020
added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents:
2595
diff
changeset
|
413 |
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
|
414 |
atac, etac FalseE]; |
4b30dbe4a020
added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents:
2595
diff
changeset
|
415 |
(*No premature instantiation of variables during simplification*) |
4b30dbe4a020
added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents:
2595
diff
changeset
|
416 |
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
|
417 |
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
|
418 |
|
2636
4b30dbe4a020
added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents:
2595
diff
changeset
|
419 |
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
|
420 |
setSSolver safe_solver |
4b30dbe4a020
added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents:
2595
diff
changeset
|
421 |
setSolver unsafe_solver |
4b30dbe4a020
added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents:
2595
diff
changeset
|
422 |
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
|
423 |
|
3446
a14e5451f613
Addition of not_imp (which pushes negation into implication) as a default
paulson
parents:
3282
diff
changeset
|
424 |
val HOL_ss = |
a14e5451f613
Addition of not_imp (which pushes negation into implication) as a default
paulson
parents:
3282
diff
changeset
|
425 |
HOL_basic_ss addsimps |
a14e5451f613
Addition of not_imp (which pushes negation into implication) as a default
paulson
parents:
3282
diff
changeset
|
426 |
([triv_forall_equality, (* prunes params *) |
3654 | 427 |
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
|
428 |
if_True, if_False, if_cancel, |
a14e5451f613
Addition of not_imp (which pushes negation into implication) as a default
paulson
parents:
3282
diff
changeset
|
429 |
o_apply, imp_disjL, conj_assoc, disj_assoc, |
3904 | 430 |
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
|
431 |
not_all, not_ex, cases_simp] |
a14e5451f613
Addition of not_imp (which pushes negation into implication) as a default
paulson
parents:
3282
diff
changeset
|
432 |
@ 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
|
433 |
addsimprocs [defALL_regroup,defEX_regroup] |
3446
a14e5451f613
Addition of not_imp (which pushes negation into implication) as a default
paulson
parents:
3282
diff
changeset
|
434 |
addcongs [imp_cong]; |
2082 | 435 |
|
1655 | 436 |
qed_goal "if_distrib" HOL.thy |
437 |
"f(if c then x else y) = (if c then f x else f y)" |
|
438 |
(fn _ => [simp_tac (HOL_ss setloop (split_tac [expand_if])) 1]); |
|
439 |
||
2097 | 440 |
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
|
441 |
(fn _ => [rtac ext 1, rtac refl 1]); |
1984 | 442 |
|
443 |
||
2948
f18035b1d531
Moved expand_case_tac from Auth/Message.ML to simpdata.ML
paulson
parents:
2935
diff
changeset
|
444 |
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
|
445 |
by (case_tac "P" 1); |
f18035b1d531
Moved expand_case_tac from Auth/Message.ML to simpdata.ML
paulson
parents:
2935
diff
changeset
|
446 |
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
|
447 |
val expand_case = result(); |
f18035b1d531
Moved expand_case_tac from Auth/Message.ML to simpdata.ML
paulson
parents:
2935
diff
changeset
|
448 |
|
f18035b1d531
Moved expand_case_tac from Auth/Message.ML to simpdata.ML
paulson
parents:
2935
diff
changeset
|
449 |
fun expand_case_tac P i = |
f18035b1d531
Moved expand_case_tac from Auth/Message.ML to simpdata.ML
paulson
parents:
2935
diff
changeset
|
450 |
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
|
451 |
Simp_tac (i+1) THEN |
f18035b1d531
Moved expand_case_tac from Auth/Message.ML to simpdata.ML
paulson
parents:
2935
diff
changeset
|
452 |
Simp_tac i; |
f18035b1d531
Moved expand_case_tac from Auth/Message.ML to simpdata.ML
paulson
parents:
2935
diff
changeset
|
453 |
|
f18035b1d531
Moved expand_case_tac from Auth/Message.ML to simpdata.ML
paulson
parents:
2935
diff
changeset
|
454 |
|
4119 | 455 |
(* install implicit simpset *) |
1984 | 456 |
|
4086 | 457 |
simpset_ref() := HOL_ss; |
1984 | 458 |
|
3615
e5322197cfea
Moved some functions which used to be part of thy_data.ML
berghofe
parents:
3577
diff
changeset
|
459 |
|
2636
4b30dbe4a020
added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents:
2595
diff
changeset
|
460 |
(*** Integration of simplifier with classical reasoner ***) |
4b30dbe4a020
added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents:
2595
diff
changeset
|
461 |
|
4b30dbe4a020
added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents:
2595
diff
changeset
|
462 |
(* 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
|
463 |
fails if there is no equaliy or if an equality is already at the front *) |
3538 | 464 |
local |
465 |
fun is_eq (Const ("Trueprop", _) $ (Const("op =" ,_) $ _ $ _)) = true |
|
466 |
| is_eq _ = false; |
|
4188
1025a27b08f9
changed libraray function find to find_index_eq, currying it
oheimb
parents:
4119
diff
changeset
|
467 |
val find_eq = find_index is_eq; |
3538 | 468 |
in |
469 |
val rot_eq_tac = |
|
4188
1025a27b08f9
changed libraray function find to find_index_eq, currying it
oheimb
parents:
4119
diff
changeset
|
470 |
SUBGOAL (fn (Bi,i) => let val n = find_eq (Logic.strip_assums_hyp Bi) in |
1025a27b08f9
changed libraray function find to find_index_eq, currying it
oheimb
parents:
4119
diff
changeset
|
471 |
if n>0 then rotate_tac n i else no_tac end) |
3538 | 472 |
end; |
2636
4b30dbe4a020
added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents:
2595
diff
changeset
|
473 |
|
4b30dbe4a020
added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents:
2595
diff
changeset
|
474 |
(*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
|
475 |
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
|
476 |
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
|
477 |
premises to all the premises *) |
4b30dbe4a020
added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents:
2595
diff
changeset
|
478 |
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
|
479 |
safe_asm_full_simp_tac ss; |
4b30dbe4a020
added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents:
2595
diff
changeset
|
480 |
|
4b30dbe4a020
added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents:
2595
diff
changeset
|
481 |
(*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
|
482 |
infix 4 addSss addss; |
a3de7f32728c
renamed addss to addSss, unsafe_addss to addss, extended auto_tac
oheimb
parents:
3040
diff
changeset
|
483 |
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
|
484 |
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
|
485 |
|
4086 | 486 |
fun Addss ss = (claset_ref() := claset() addss ss); |
2636
4b30dbe4a020
added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents:
2595
diff
changeset
|
487 |
|
4b30dbe4a020
added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents:
2595
diff
changeset
|
488 |
(*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
|
489 |
in some of the subgoals*) |
4b30dbe4a020
added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents:
2595
diff
changeset
|
490 |
|
4b30dbe4a020
added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents:
2595
diff
changeset
|
491 |
type clasimpset = (claset * simpset); |
4b30dbe4a020
added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents:
2595
diff
changeset
|
492 |
|
4b30dbe4a020
added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents:
2595
diff
changeset
|
493 |
val HOL_css = (HOL_cs, HOL_ss); |
4b30dbe4a020
added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents:
2595
diff
changeset
|
494 |
|
4b30dbe4a020
added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents:
2595
diff
changeset
|
495 |
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
|
496 |
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
|
497 |
|
4b30dbe4a020
added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents:
2595
diff
changeset
|
498 |
infix 4 addSIs2 addSEs2 addSDs2 addIs2 addEs2 addDs2 |
4b30dbe4a020
added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents:
2595
diff
changeset
|
499 |
addsimps2 delsimps2 addcongs2 delcongs2; |
2748
3ae9ccdd701e
Eta-expanded some declarations for compatibility with value polymorphism
paulson
parents:
2718
diff
changeset
|
500 |
fun op addSIs2 arg = pair_upd1 (op addSIs) arg; |
3ae9ccdd701e
Eta-expanded some declarations for compatibility with value polymorphism
paulson
parents:
2718
diff
changeset
|
501 |
fun op addSEs2 arg = pair_upd1 (op addSEs) arg; |
3ae9ccdd701e
Eta-expanded some declarations for compatibility with value polymorphism
paulson
parents:
2718
diff
changeset
|
502 |
fun op addSDs2 arg = pair_upd1 (op addSDs) arg; |
3ae9ccdd701e
Eta-expanded some declarations for compatibility with value polymorphism
paulson
parents:
2718
diff
changeset
|
503 |
fun op addIs2 arg = pair_upd1 (op addIs ) arg; |
3ae9ccdd701e
Eta-expanded some declarations for compatibility with value polymorphism
paulson
parents:
2718
diff
changeset
|
504 |
fun op addEs2 arg = pair_upd1 (op addEs ) arg; |
3ae9ccdd701e
Eta-expanded some declarations for compatibility with value polymorphism
paulson
parents:
2718
diff
changeset
|
505 |
fun op addDs2 arg = pair_upd1 (op addDs ) arg; |
3ae9ccdd701e
Eta-expanded some declarations for compatibility with value polymorphism
paulson
parents:
2718
diff
changeset
|
506 |
fun op addsimps2 arg = pair_upd2 (op addsimps) arg; |
3ae9ccdd701e
Eta-expanded some declarations for compatibility with value polymorphism
paulson
parents:
2718
diff
changeset
|
507 |
fun op delsimps2 arg = pair_upd2 (op delsimps) arg; |
3ae9ccdd701e
Eta-expanded some declarations for compatibility with value polymorphism
paulson
parents:
2718
diff
changeset
|
508 |
fun op addcongs2 arg = pair_upd2 (op addcongs) arg; |
3ae9ccdd701e
Eta-expanded some declarations for compatibility with value polymorphism
paulson
parents:
2718
diff
changeset
|
509 |
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
|
510 |
|
2805 | 511 |
fun auto_tac (cs,ss) = |
512 |
let val cs' = cs addss ss |
|
513 |
in EVERY [TRY (safe_tac cs'), |
|
514 |
REPEAT (FIRSTGOAL (fast_tac cs')), |
|
3206
a3de7f32728c
renamed addss to addSss, unsafe_addss to addss, extended auto_tac
oheimb
parents:
3040
diff
changeset
|
515 |
TRY (safe_tac (cs addSss ss)), |
2805 | 516 |
prune_params_tac] |
517 |
end; |
|
2636
4b30dbe4a020
added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents:
2595
diff
changeset
|
518 |
|
4086 | 519 |
fun Auto_tac () = auto_tac (claset(), simpset()); |
2636
4b30dbe4a020
added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents:
2595
diff
changeset
|
520 |
|
4b30dbe4a020
added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents:
2595
diff
changeset
|
521 |
fun auto () = by (Auto_tac ()); |