author | immler@in.tum.de |
Thu, 26 Feb 2009 10:13:43 +0100 | |
changeset 30151 | 629f3a92863e |
parent 29606 | fedb8be05f24 |
child 30136 | 6a874aedb964 |
permissions | -rw-r--r-- |
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Conversions: primitive equality reasoning (from drule.ML);
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(* Title: Pure/conv.ML |
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Author: Amine Chaieb and Makarius |
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Conversions: primitive equality reasoning. |
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Conversions: primitive equality reasoning (from drule.ML);
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*) |
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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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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 abs_conv: (cterm * Proof.context -> conv) -> Proof.context -> 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 binop_conv: conv -> conv |
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val forall_conv: (cterm * Proof.context -> conv) -> Proof.context -> conv |
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val implies_conv: conv -> conv -> conv |
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val implies_concl_conv: conv -> conv |
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val rewr_conv: thm -> conv |
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val params_conv: int -> (Proof.context -> conv) -> Proof.context -> conv |
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val prems_conv: int -> conv -> conv |
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val concl_conv: int -> conv -> conv |
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val fconv_rule: conv -> thm -> thm |
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else_conv: only handle THM | CTERM | TERM | TYPE;
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val gconv_rule: conv -> int -> 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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fun no_conv _ = raise CTERM ("no conversion", []); |
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val all_conv = Thm.reflexive; |
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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 Thm.is_reflexive eq1 then eq2 |
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else if Thm.is_reflexive 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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(cv1 ct |
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handle THM _ => cv2 ct |
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else_conv: only handle THM | CTERM | TERM | TYPE;
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| CTERM _ => cv2 ct |
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| TERM _ => cv2 ct |
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| TYPE _ => 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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(** Pure conversions **) |
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(* lambda terms *) |
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fun abs_conv cv ctxt ct = |
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(case Thm.term_of ct of |
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Abs (x, _, _) => |
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let |
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val ([u], ctxt') = Variable.variant_fixes ["u"] ctxt; |
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val (v, ct') = Thm.dest_abs (SOME u) ct; |
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val eq = cv (v, ctxt') ct'; |
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in if Thm.is_reflexive eq then all_conv ct else Thm.abstract_rule x v eq 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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fun binop_conv cv = combination_conv (arg_conv cv) cv; |
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(* primitive logic *) |
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fun forall_conv cv ctxt ct = |
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(case Thm.term_of ct of |
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Const ("all", _) $ Abs _ => arg_conv (abs_conv cv ctxt) ct |
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| _ => raise CTERM ("forall_conv", [ct])); |
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fun implies_conv cv1 cv2 ct = |
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(case Thm.term_of ct of |
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Const ("==>", _) $ _ $ _ => combination_conv (arg_conv cv1) cv2 ct |
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| _ => raise CTERM ("implies_conv", [ct])); |
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fun implies_concl_conv cv ct = |
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(case Thm.term_of ct of |
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Const ("==>", _) $ _ $ _ => arg_conv cv ct |
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| _ => raise CTERM ("implies_concl_conv", [ct])); |
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(* single rewrite step, cf. REWR_CONV in HOL *) |
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fun rewr_conv rule ct = |
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let |
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val rule1 = Thm.incr_indexes (#maxidx (Thm.rep_cterm ct) + 1) rule; |
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val lhs = Thm.lhs_of rule1; |
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val rule2 = Thm.rename_boundvars (Thm.term_of lhs) (Thm.term_of ct) rule1; |
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in |
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Drule.instantiate (Thm.match (lhs, ct)) rule2 |
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handle Pattern.MATCH => raise CTERM ("rewr_conv", [lhs, ct]) |
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end; |
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(* conversions on HHF rules *) |
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(*rewrite B in !!x1 ... xn. B*) |
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fun params_conv n cv ctxt ct = |
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if n <> 0 andalso Logic.is_all (Thm.term_of ct) |
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then arg_conv (abs_conv (params_conv (n - 1) cv o #2) ctxt) ct |
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else cv ctxt ct; |
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(*rewrite the A's in A1 ==> ... ==> An ==> B*) |
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fun prems_conv 0 _ ct = all_conv ct |
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| prems_conv n cv ct = |
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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 A) (prems_conv (n - 1) cv B)); |
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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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(* conversions as inference rules *) |
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(*forward conversion, cf. FCONV_RULE in LCF*) |
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fun fconv_rule cv th = |
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let val eq = cv (Thm.cprop_of th) in |
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if Thm.is_reflexive eq then th |
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else Thm.equal_elim eq th |
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end; |
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(*goal conversion*) |
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fun gconv_rule cv i th = |
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(case try (Thm.cprem_of th) i of |
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SOME ct => |
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let val eq = cv ct in |
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if Thm.is_reflexive eq then th |
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else Drule.with_subgoal i (fconv_rule (arg1_conv (K eq))) th |
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end |
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| NONE => raise THM ("gconv_rule", i, [th])); |
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end; |