src/Pure/conv.ML
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abs_conv/forall_conv: proper context (avoid gensym); removed unused cache_conv;
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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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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: (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: int -> (Proof.context -> conv) -> Proof.context -> conv
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  val concl_conv: int -> conv -> conv
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  val prems_conv: int -> conv -> conv
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  val fconv_rule: conv -> thm -> thm
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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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      | 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 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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(* logic *)
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(*rewrite B in !!x1 ... xn. B*)
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fun forall_conv n cv ctxt ct =
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  if n <> 0 andalso can Logic.dest_all (Thm.term_of ct)
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  then arg_conv (abs_conv (forall_conv (n - 1) cv) ctxt) ct
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  else cv ctxt 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 _ 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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(* conversions as 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;