author  wenzelm 
Fri, 11 May 2007 18:46:50 +0200  
changeset 22937  08cf9aaf3aa1 
parent 22926  fb6917e426da 
child 23034  b3a6815754d6 
permissions  rwrr 
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(* Title: Pure/conv.ML 
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ID: $Id$ 
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Author: Amine Chaieb and Makarius 
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Conversions: primitive equality reasoning. 
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*) 
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22937  8 
infix 1 then_conv; 
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infix 0 else_conv; 

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signature CONV = 
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sig 
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type conv = cterm > thm 
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val no_conv: conv 
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val all_conv: conv 
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val then_conv: conv * conv > conv 
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val else_conv: conv * conv > conv 

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val first_conv: conv list > conv 
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val every_conv: conv list > conv 

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val try_conv: conv > conv 
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val repeat_conv: conv > conv 

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val cache_conv: conv > conv 
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val abs_conv: conv > conv 

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val combination_conv: conv > conv > conv 

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val comb_conv: conv > conv 

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val arg_conv: conv > conv 

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val fun_conv: conv > conv 

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val arg1_conv: conv > conv 

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val fun2_conv: conv > conv 

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val forall_conv: int > conv > conv 
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val concl_conv: int > conv > conv 
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val prems_conv: int > (int > conv) > conv 
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val goals_conv: (int > bool) > conv > conv 
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val fconv_rule: conv > thm > thm 
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end; 
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structure Conv: CONV = 
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struct 
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(* conversionals *) 
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type conv = cterm > thm; 
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fun no_conv _ = raise CTERM ("no conversion", []); 
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val all_conv = Thm.reflexive; 
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val is_refl = op aconv o Logic.dest_equals o Thm.prop_of; 
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fun (cv1 then_conv cv2) ct = 
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let 
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val eq1 = cv1 ct; 
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val eq2 = cv2 (Thm.rhs_of eq1); 

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in 
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if is_refl eq1 then eq2 
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else if is_refl eq2 then eq1 
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else Thm.transitive eq1 eq2 
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end; 
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fun (cv1 else_conv cv2) ct = 
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(case try cv1 ct of SOME eq => eq  NONE => cv2 ct); 
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fun first_conv cvs = fold_rev (curry op else_conv) cvs no_conv; 
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fun every_conv cvs = fold_rev (curry op then_conv) cvs all_conv; 

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fun try_conv cv = cv else_conv all_conv; 
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fun repeat_conv cv ct = try_conv (cv then_conv repeat_conv cv) ct; 

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fun cache_conv cv = 

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let 

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val cache = ref Termtab.empty; 

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fun conv ct = 

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(case Termtab.lookup (! cache) (term_of ct) of 

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SOME th => th 

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 NONE => 

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let val th = cv ct 

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in change cache (Termtab.update (term_of ct, th)); th end); 

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in conv end; 

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(** Pure conversions **) 
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(* lambda terms *) 

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fun abs_conv cv ct = 

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(case term_of ct of 

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Abs (x, _, _) => 

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let val (v, ct') = Thm.dest_abs (SOME (gensym "abs_")) ct 

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in Thm.abstract_rule x v (cv ct') end 

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 _ => raise CTERM ("abs_conv", [ct])); 

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fun combination_conv cv1 cv2 ct = 

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let val (ct1, ct2) = Thm.dest_comb ct 

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in Thm.combination (cv1 ct1) (cv2 ct2) end; 

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fun comb_conv cv = combination_conv cv cv; 

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fun arg_conv cv = combination_conv all_conv cv; 

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fun fun_conv cv = combination_conv cv all_conv; 

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val arg1_conv = fun_conv o arg_conv; 

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val fun2_conv = fun_conv o fun_conv; 

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(* logic *) 

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(*rewrite B in !!x1 ... xn. B*) 
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fun forall_conv 0 cv ct = cv ct 
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 forall_conv n cv ct = 
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(case try Thm.dest_comb ct of 
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NONE => cv ct 
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 SOME (A, B) => 
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(case (term_of A, term_of B) of 
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(Const ("all", _), Abs (x, _, _)) => 
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let val (v, B') = Thm.dest_abs (SOME (gensym "all_")) B in 
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Thm.combination (all_conv A) 
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(Thm.abstract_rule x v (forall_conv (n  1) cv B')) 
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end 
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 _ => cv ct)); 
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(*rewrite B in A1 ==> ... ==> An ==> B*) 
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fun concl_conv 0 cv ct = cv ct 
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 concl_conv n cv ct = 
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(case try Thm.dest_implies ct of 
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NONE => cv ct 
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 SOME (A, B) => Drule.imp_cong_rule (all_conv A) (concl_conv (n  1) cv B)); 
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(*rewrite the A's in A1 ==> ... ==> An ==> B*) 
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fun prems_conv 0 _ = all_conv 
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 prems_conv n cv = 
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let 
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fun conv i ct = 
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if i = n + 1 then all_conv ct 
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else 
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(case try Thm.dest_implies ct of 
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NONE => all_conv ct 
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 SOME (A, B) => Drule.imp_cong_rule (cv i A) (conv (i + 1) B)); 
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in conv 1 end; 
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fun goals_conv pred cv = prems_conv ~1 (fn i => if pred i then cv else all_conv); 
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fun fconv_rule cv th = equal_elim (cv (cprop_of th)) th; 
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end; 