author  clasohm 
Tue, 30 Jan 1996 13:42:57 +0100  
changeset 1461  6bcb44e4d6e5 
parent 1036  0d28f4bc8a44 
child 1612  f9f0145e1c7e 
permissions  rwrr 
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(* Title: ZF/simpdata 
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ID: $Id$ 

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Author: Lawrence C Paulson, Cambridge University Computer Laboratory 

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Copyright 1991 University of Cambridge 

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Rewriting for ZF set theory  based on FOL rewriting 

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*) 

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(** Tactics for type checking  from CTT **) 

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fun is_rigid_elem (Const("Trueprop",_) $ (Const("op :",_) $ a $ _)) = 

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not (is_Var (head_of a)) 

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 is_rigid_elem _ = false; 

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(*Try solving a:A by assumption provided a is rigid!*) 

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val test_assume_tac = SUBGOAL(fn (prem,i) => 

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if is_rigid_elem (Logic.strip_assums_concl prem) 

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then assume_tac i else eq_assume_tac i); 
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(*Type checking solves a:?A (a rigid, ?A maybe flexible). 

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match_tac is too strict; would refuse to instantiate ?A*) 

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fun typechk_step_tac tyrls = 

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FIRSTGOAL (test_assume_tac ORELSE' filt_resolve_tac tyrls 3); 

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fun typechk_tac tyrls = REPEAT (typechk_step_tac tyrls); 

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val ZF_typechecks = 
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[if_type, lam_type, SigmaI, apply_type, split_type, consI1]; 
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(*Instantiates variables in typing conditions. 
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drawback: does not simplify conjunctions*) 

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fun type_auto_tac tyrls hyps = SELECT_GOAL 
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(DEPTH_SOLVE (typechk_step_tac (tyrls@hyps) 

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ORELSE ares_tac [TrueI,refl,iff_refl,ballI,allI,conjI,impI] 1)); 
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(** New version of mk_rew_rules **) 

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(*Should False yield False<>True, or should it solve goals some other way?*) 

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(*Analyse a theorem to atomic rewrite rules*) 
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fun atomize (conn_pairs, mem_pairs) th = 

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let fun tryrules pairs t = 

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case head_of t of 
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Const(a,_) => 

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(case assoc(pairs,a) of 

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Some rls => flat (map (atomize (conn_pairs, mem_pairs)) 

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([th] RL rls)) 

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 None => [th]) 

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 _ => [th] 

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

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Const("op :",_) $ a $ b => tryrules mem_pairs b 

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 Const("True",_) => [] 

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 Const("False",_) => [] 

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 A => tryrules conn_pairs A) 

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 _ => [th] 
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end; 

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(*Analyse a rigid formula*) 
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val ZF_conn_pairs = 
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[("Ball", [bspec]), 
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("All", [spec]), 

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("op >", [mp]), 

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("op &", [conjunct1,conjunct2])]; 

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(*Analyse a:b, where b is rigid*) 

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val ZF_mem_pairs = 
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[("Collect", [CollectD1,CollectD2]), 
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("op ", [DiffD1,DiffD2]), 

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("op Int", [IntD1,IntD2])]; 

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val ZF_simps = 
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[empty_subsetI, consI1, succI1, ball_simp, if_true, if_false, 
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beta, eta, restrict, fst_conv, snd_conv, split, Pair_iff, singleton_iff, 
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Sigma_empty1, Sigma_empty2, triv_RepFun, subset_refl]; 
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(*Sigma_cong, Pi_cong NOT included by default since they cause 
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flexflex pairs and the "Check your prover" error  because most 
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Sigma's and Pi's are abbreviated as * or > *) 
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val ZF_congs = 
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[ball_cong, bex_cong, Replace_cong, RepFun_cong, Collect_cong, lam_cong]; 
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val ZF_atomize = atomize (ZF_conn_pairs, ZF_mem_pairs); 
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val ZF_ss = FOL_ss 
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setmksimps (map mk_meta_eq o ZF_atomize o gen_all) 
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addsimps (ZF_simps @ mem_simps @ bquant_simps @ 
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Collect_simps @ UnInt_simps) 
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addcongs ZF_congs; 