src/HOL/Tools/res_hol_clause.ML
author paulson
Wed Nov 01 15:49:43 2006 +0100 (2006-11-01)
changeset 21135 07549f79d19c
parent 21108 04d8e6eb9a2e
child 21254 d53f76357f41
permissions -rw-r--r--
Numerous cosmetic changes.
Use of ---> notation for types.
Added rules for the introduction of the iff connective, but they are too prolific to be useful.
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(* ID: $Id$ 
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   Author: Jia Meng, NICTA
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FOL clauses translated from HOL formulae.  Combinators are used to represent lambda terms.
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*)
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structure ResHolClause =
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struct
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(* theorems for combinators and function extensionality *)
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val ext = thm "HOL.ext";
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val comb_I = thm "Reconstruction.COMBI_def";
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val comb_K = thm "Reconstruction.COMBK_def";
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val comb_B = thm "Reconstruction.COMBB_def";
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val comb_C = thm "Reconstruction.COMBC_def";
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val comb_S = thm "Reconstruction.COMBS_def";
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val comb_B' = thm "Reconstruction.COMBB'_def";
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val comb_C' = thm "Reconstruction.COMBC'_def";
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val comb_S' = thm "Reconstruction.COMBS'_def";
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val fequal_imp_equal = thm "Reconstruction.fequal_imp_equal";
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val equal_imp_fequal = thm "Reconstruction.equal_imp_fequal";
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(*A flag to set if we use the Turner optimizations. Currently FALSE, as the 5 standard
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  combinators appear to work best.*)
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val use_Turner = ref false;
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(*FIXME: these refs should probaby replaced by code to count the combinators in the 
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  translated form of the term.*)
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val combI_count = ref 0;
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val combK_count = ref 0;
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val combB_count = ref 0;
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val combC_count = ref 0;
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val combS_count = ref 0;
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val combB'_count = ref 0;
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val combC'_count = ref 0;
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val combS'_count = ref 0; 
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fun increI count_comb =  if count_comb then combI_count := !combI_count + 1 else ();
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fun increK count_comb =  if count_comb then combK_count := !combK_count + 1 else ();
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fun increB count_comb =  if count_comb then combB_count := !combB_count + 1 else ();
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fun increC count_comb =  if count_comb then combC_count := !combC_count + 1 else ();
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fun increS count_comb =  if count_comb then combS_count := !combS_count + 1 else (); 
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fun increB' count_comb =  if count_comb then combB'_count := !combB'_count + 1 else (); 
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fun increC' count_comb =  if count_comb then combC'_count := !combC'_count + 1 else ();
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fun increS' count_comb =  if count_comb then combS'_count := !combS'_count + 1 else (); 
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exception DECRE_COMB of string;
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fun decreB count_comb n = 
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  if count_comb then 
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    if !combB_count >= n then combB_count := !combB_count - n else raise DECRE_COMB "COMBB"
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  else ();
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fun decreC count_comb n =
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  if count_comb then 
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    if !combC_count >= n then combC_count := !combC_count - n else raise DECRE_COMB "COMBC"
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  else ();
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fun decreS count_comb n = 
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  if count_comb then 
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    if !combS_count >= n then combS_count := !combS_count - n else raise DECRE_COMB "COMBS"
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  else ();
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val const_typargs = ref (Library.K [] : (string*typ -> typ list));
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fun init thy = (combI_count:=0; combK_count:=0;combB_count:=0;combC_count:=0;combS_count:=0;combB'_count:=0;combC'_count:=0;combS'_count:=0;
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                const_typargs := Sign.const_typargs thy);
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(**********************************************************************)
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(* convert a Term.term with lambdas into a Term.term with combinators *) 
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(**********************************************************************)
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fun is_free (Bound(a)) n = (a = n)
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  | is_free (Abs(x,_,b)) n = (is_free b (n+1))
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  | is_free (P $ Q) n = ((is_free P n) orelse (is_free Q n))
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  | is_free _ _ = false;
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(*******************************************)
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fun mk_compact_comb (tm as (Const("Reconstruction.COMBB",_)$p) $ (Const("Reconstruction.COMBB",_)$q$r)) Bnds count_comb =
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    let val tp_p = Term.type_of1(Bnds,p)
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	val tp_q = Term.type_of1(Bnds,q)
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	val tp_r = Term.type_of1(Bnds,r)
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	val typ = Term.type_of1(Bnds,tm)
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	val typ_B' = [tp_p,tp_q,tp_r] ---> typ
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	val _ = increB' count_comb
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	val _ = decreB count_comb 2
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    in
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	Const("Reconstruction.COMBB'",typ_B') $ p $ q $ r
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    end
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  | mk_compact_comb (tm as (Const("Reconstruction.COMBC",_) $ (Const("Reconstruction.COMBB",_)$p$q) $ r)) Bnds count_comb =
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    let val tp_p = Term.type_of1(Bnds,p)
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	val tp_q = Term.type_of1(Bnds,q)
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	val tp_r = Term.type_of1(Bnds,r)
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	val typ = Term.type_of1(Bnds,tm)
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	val typ_C' = [tp_p,tp_q,tp_r] ---> typ
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	val _ = increC' count_comb
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	val _ = decreC count_comb 1
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	val _ = decreB count_comb 1
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    in
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	Const("Reconstruction.COMBC'",typ_C') $ p $ q $ r
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    end
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  | mk_compact_comb (tm as (Const("Reconstruction.COMBS",_) $ (Const("Reconstruction.COMBB",_)$p$q) $ r)) Bnds count_comb =
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    let val tp_p = Term.type_of1(Bnds,p)
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	val tp_q = Term.type_of1(Bnds,q)
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	val tp_r = Term.type_of1(Bnds,r)
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	val typ = Term.type_of1(Bnds,tm)
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	val typ_S' = [tp_p,tp_q,tp_r] ---> typ
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	val _ = increS' count_comb
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	val _ = decreS count_comb 1
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	val _ = decreB count_comb 1
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    in
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	Const("Reconstruction.COMBS'",typ_S') $ p $ q $ r
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    end
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  | mk_compact_comb tm _ _ = tm;
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fun compact_comb t Bnds count_comb = 
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  if !use_Turner then mk_compact_comb t Bnds count_comb else t;
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fun lam2comb (Abs(x,tp,Bound 0)) _ count_comb = 
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      let val _ = increI count_comb
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      in 
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	  Const("Reconstruction.COMBI",tp-->tp) 
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      end
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  | lam2comb (Abs(x,tp,Bound n)) Bnds count_comb = 
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      let val tb = List.nth(Bnds,n-1)
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	  val _ = increK count_comb 
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      in
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	  Const("Reconstruction.COMBK", [tb,tp] ---> tb) $ (Bound (n-1))
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      end
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  | lam2comb (Abs(x,t1,Const(c,t2))) _ count_comb = 
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      let val _ = increK count_comb 
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      in 
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	  Const("Reconstruction.COMBK",[t2,t1] ---> t2) $ Const(c,t2) 
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      end
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  | lam2comb (Abs(x,t1,Free(v,t2))) _ count_comb =
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      let val _ = increK count_comb
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      in
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	  Const("Reconstruction.COMBK",[t2,t1] ---> t2) $ Free(v,t2)
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      end
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  | lam2comb (Abs(x,t1,Var(ind,t2))) _ count_comb =
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      let val _ = increK count_comb 
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      in
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	  Const("Reconstruction.COMBK", [t2,t1] ---> t2) $ Var(ind,t2)
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      end
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  | lam2comb (t as (Abs(x,t1,P$(Bound 0)))) Bnds count_comb =
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      let val tr = Term.type_of1(t1::Bnds,P)
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      in
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	  if not(is_free P 0) then (incr_boundvars ~1 P)
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	  else 
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	  let val tI = [t1] ---> t1
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	      val P' = lam2comb (Abs(x,t1,P)) Bnds count_comb
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	      val tp' = Term.type_of1(Bnds,P')
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	      val tS = [tp',tI] ---> tr
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	      val _ = increI count_comb
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	      val _ = increS count_comb
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	  in
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	      compact_comb (Const("Reconstruction.COMBS",tS) $ P' $ 
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	                     Const("Reconstruction.COMBI",tI)) Bnds count_comb
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	  end
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      end	    
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  | lam2comb (t as (Abs(x,t1,P$Q))) Bnds count_comb =
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      let val nfreeP = not(is_free P 0)
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	  and nfreeQ = not(is_free Q 0)
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	  val tpq = Term.type_of1(t1::Bnds, P$Q) 
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      in
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	  if nfreeP andalso nfreeQ 
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	  then 
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	    let val tK = [tpq,t1] ---> tpq
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		val PQ' = incr_boundvars ~1(P $ Q)
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		val _ = increK count_comb
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	    in 
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		Const("Reconstruction.COMBK",tK) $ PQ'
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	    end
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	  else if nfreeP then 
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	    let val Q' = lam2comb (Abs(x,t1,Q)) Bnds count_comb
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		val P' = incr_boundvars ~1 P
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		val tp = Term.type_of1(Bnds,P')
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		val tq' = Term.type_of1(Bnds, Q')
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		val tB = [tp,tq',t1] ---> tpq
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		val _ = increB count_comb
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	    in
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		compact_comb (Const("Reconstruction.COMBB",tB) $ P' $ Q') Bnds count_comb 
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	    end
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	  else if nfreeQ then 
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	    let val P' = lam2comb (Abs(x,t1,P)) Bnds count_comb
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		val Q' = incr_boundvars ~1 Q
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		val tq = Term.type_of1(Bnds,Q')
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		val tp' = Term.type_of1(Bnds, P')
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		val tC = [tp',tq,t1] ---> tpq
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		val _ = increC count_comb
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	    in
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		compact_comb (Const("Reconstruction.COMBC",tC) $ P' $ Q') Bnds count_comb
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	    end
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          else
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	    let val P' = lam2comb (Abs(x,t1,P)) Bnds count_comb
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		val Q' = lam2comb (Abs(x,t1,Q)) Bnds count_comb 
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		val tp' = Term.type_of1(Bnds,P')
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		val tq' = Term.type_of1(Bnds,Q')
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		val tS = [tp',tq',t1] ---> tpq
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		val _ = increS count_comb
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	    in
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		compact_comb (Const("Reconstruction.COMBS",tS) $ P' $ Q') Bnds count_comb
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	    end
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      end
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  | lam2comb (t as (Abs(x,t1,_))) _ _ = raise ResClause.CLAUSE("HOL CLAUSE",t);
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(*********************)
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fun to_comb (Abs(x,tp,b)) Bnds count_comb =
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    let val b' = to_comb b (tp::Bnds) count_comb
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    in lam2comb (Abs(x,tp,b')) Bnds count_comb end
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  | to_comb (P $ Q) Bnds count_comb = ((to_comb P Bnds count_comb) $ (to_comb Q Bnds count_comb))
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  | to_comb t _ _ = t;
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fun comb_of t count_comb = to_comb t [] count_comb;
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(* print a term containing combinators, used for debugging *)
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exception TERM_COMB of term;
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fun string_of_term (Const(c,t)) = c
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  | string_of_term (Free(v,t)) = v
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  | string_of_term (Var((x,n),t)) = x ^ "_" ^ (string_of_int n)
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  | string_of_term (P $ Q) =
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      "(" ^ string_of_term P ^ " " ^ string_of_term Q ^ ")" 
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  | string_of_term t =  raise TERM_COMB (t);
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(******************************************************)
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(* data types for typed combinator expressions        *)
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(******************************************************)
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datatype type_level = T_FULL | T_PARTIAL | T_CONST | T_NONE;
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val typ_level = ref T_CONST;
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fun full_types () = (typ_level:=T_FULL);
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fun partial_types () = (typ_level:=T_PARTIAL);
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fun const_types_only () = (typ_level:=T_CONST);
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fun no_types () = (typ_level:=T_NONE);
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fun find_typ_level () = !typ_level;
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type axiom_name = string;
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datatype kind = Axiom | Conjecture;
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fun name_of_kind Axiom = "axiom"
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  | name_of_kind Conjecture = "conjecture";
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type polarity = bool;
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type indexname = Term.indexname;
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type clause_id = int;
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type csort = Term.sort;
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type ctyp = ResClause.fol_type;
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val string_of_ctyp = ResClause.string_of_fol_type;
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type ctyp_var = ResClause.typ_var;
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type ctype_literal = ResClause.type_literal;
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datatype combterm = CombConst of string * ctyp * ctyp list
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		  | CombFree of string * ctyp
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		  | CombVar of string * ctyp
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		  | CombApp of combterm * combterm * ctyp
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		  | Bool of combterm;
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datatype literal = Literal of polarity * combterm;
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datatype clause = 
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	 Clause of {clause_id: clause_id,
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		    axiom_name: axiom_name,
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		    th: thm,
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		    kind: kind,
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		    literals: literal list,
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		    ctypes_sorts: (ctyp_var * csort) list, 
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                    ctvar_type_literals: ctype_literal list, 
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                    ctfree_type_literals: ctype_literal list};
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fun string_of_kind (Clause cls) = name_of_kind (#kind cls);
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fun get_axiomName (Clause cls) = #axiom_name cls;
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fun get_clause_id (Clause cls) = #clause_id cls;
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fun get_literals (c as Clause(cls)) = #literals cls;
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(*********************************************************************)
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(* convert a clause with type Term.term to a clause with type clause *)
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(*********************************************************************)
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fun isFalse (Literal(pol,Bool(CombConst(c,_,_)))) =
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      (pol andalso c = "c_False") orelse
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      (not pol andalso c = "c_True")
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  | isFalse _ = false;
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fun isTrue (Literal (pol,Bool(CombConst(c,_,_)))) =
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      (pol andalso c = "c_True") orelse
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      (not pol andalso c = "c_False")
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  | isTrue _ = false;
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fun isTaut (Clause {literals,...}) = exists isTrue literals;  
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mengj@18440
   314
fun type_of (Type (a, Ts)) =
mengj@18440
   315
    let val (folTypes,ts) = types_of Ts
mengj@17998
   316
	val t = ResClause.make_fixed_type_const a
mengj@17998
   317
    in
mengj@18440
   318
	(ResClause.mk_fol_type("Comp",t,folTypes),ts)
mengj@18440
   319
    end
mengj@18440
   320
  | type_of (tp as (TFree(a,s))) =
mengj@18440
   321
    let val t = ResClause.make_fixed_type_var a
mengj@18440
   322
    in
mengj@18440
   323
	(ResClause.mk_fol_type("Fixed",t,[]),[ResClause.mk_typ_var_sort tp])
mengj@17998
   324
    end
mengj@18440
   325
  | type_of (tp as (TVar(v,s))) =
mengj@18440
   326
    let val t = ResClause.make_schematic_type_var v
mengj@18440
   327
    in
mengj@18440
   328
	(ResClause.mk_fol_type("Var",t,[]),[ResClause.mk_typ_var_sort tp])
mengj@18440
   329
    end
mengj@18356
   330
mengj@18440
   331
and types_of Ts =
mengj@18440
   332
    let val foltyps_ts = map type_of Ts
mengj@18440
   333
	val (folTyps,ts) = ListPair.unzip foltyps_ts
mengj@18440
   334
    in
mengj@18440
   335
	(folTyps,ResClause.union_all ts)
mengj@18440
   336
    end;
mengj@17998
   337
mengj@17998
   338
(* same as above, but no gathering of sort information *)
mengj@18440
   339
fun simp_type_of (Type (a, Ts)) = 
mengj@18356
   340
    let val typs = map simp_type_of Ts
mengj@17998
   341
	val t = ResClause.make_fixed_type_const a
mengj@17998
   342
    in
mengj@18440
   343
	ResClause.mk_fol_type("Comp",t,typs)
mengj@17998
   344
    end
mengj@18440
   345
  | simp_type_of (TFree (a,s)) = ResClause.mk_fol_type("Fixed",ResClause.make_fixed_type_var a,[])
mengj@18440
   346
  | simp_type_of (TVar (v,s)) = ResClause.mk_fol_type("Var",ResClause.make_schematic_type_var v,[]);
mengj@18440
   347
mengj@18356
   348
mengj@20865
   349
fun const_type_of (c,t) =
mengj@18356
   350
    let val (tp,ts) = type_of t
mengj@18356
   351
	val tvars = !const_typargs(c,t)
mengj@18356
   352
	val tvars' = map simp_type_of tvars
mengj@18356
   353
    in
mengj@18356
   354
	(tp,ts,tvars')
mengj@18356
   355
    end;
mengj@18356
   356
mengj@20644
   357
mengj@18356
   358
fun is_bool_type (Type("bool",[])) = true
mengj@18356
   359
  | is_bool_type _ = false;
mengj@17998
   360
mengj@17998
   361
mengj@17998
   362
(* convert a Term.term (with combinators) into a combterm, also accummulate sort info *)
mengj@17998
   363
fun combterm_of (Const(c,t)) =
mengj@18356
   364
    let val (tp,ts,tvar_list) = const_type_of (c,t)
mengj@18356
   365
	val is_bool = is_bool_type t
mengj@18356
   366
	val c' = CombConst(ResClause.make_fixed_const c,tp,tvar_list)
mengj@17998
   367
	val c'' = if is_bool then Bool(c') else c'
mengj@17998
   368
    in
mengj@17998
   369
	(c'',ts)
mengj@17998
   370
    end
mengj@17998
   371
  | combterm_of (Free(v,t)) =
mengj@18356
   372
    let val (tp,ts) = type_of t
mengj@18356
   373
	val is_bool = is_bool_type t
mengj@17998
   374
	val v' = if ResClause.isMeta v then CombVar(ResClause.make_schematic_var(v,0),tp)
mengj@17998
   375
		 else CombFree(ResClause.make_fixed_var v,tp)
mengj@17998
   376
	val v'' = if is_bool then Bool(v') else v'
mengj@17998
   377
    in
mengj@17998
   378
	(v'',ts)
mengj@17998
   379
    end
mengj@17998
   380
  | combterm_of (Var(v,t)) =
mengj@18356
   381
    let val (tp,ts) = type_of t
mengj@18356
   382
	val is_bool = is_bool_type t
mengj@17998
   383
	val v' = CombVar(ResClause.make_schematic_var v,tp)
mengj@17998
   384
	val v'' = if is_bool then Bool(v') else v'
mengj@17998
   385
    in
mengj@17998
   386
	(v'',ts)
mengj@17998
   387
    end
mengj@17998
   388
  | combterm_of (t as (P $ Q)) =
mengj@17998
   389
    let val (P',tsP) = combterm_of P
mengj@17998
   390
	val (Q',tsQ) = combterm_of Q
mengj@17998
   391
	val tp = Term.type_of t
mengj@18356
   392
	val tp' = simp_type_of tp
mengj@18356
   393
	val is_bool = is_bool_type tp
mengj@17998
   394
	val t' = CombApp(P',Q',tp')
mengj@17998
   395
	val t'' = if is_bool then Bool(t') else t'
mengj@17998
   396
    in
mengj@17998
   397
	(t'',tsP union tsQ)
mengj@17998
   398
    end;
mengj@17998
   399
mengj@17998
   400
fun predicate_of ((Const("Not",_) $ P), polarity) =
mengj@17998
   401
    predicate_of (P, not polarity)
mengj@17998
   402
  | predicate_of (term,polarity) = (combterm_of term,polarity);
mengj@17998
   403
mengj@17998
   404
mengj@17998
   405
fun literals_of_term1 args (Const("Trueprop",_) $ P) = literals_of_term1 args P
mengj@17998
   406
  | literals_of_term1 args (Const("op |",_) $ P $ Q) = 
mengj@17998
   407
    let val args' = literals_of_term1 args P
mengj@17998
   408
    in
mengj@17998
   409
	literals_of_term1 args' Q
mengj@17998
   410
    end
mengj@17998
   411
  | literals_of_term1 (lits,ts) P =
mengj@17998
   412
    let val ((pred,ts'),pol) = predicate_of (P,true)
mengj@17998
   413
	val lits' = Literal(pol,pred)::lits
mengj@17998
   414
    in
mengj@17998
   415
	(lits',ts union ts')
mengj@17998
   416
    end;
mengj@17998
   417
mengj@17998
   418
mengj@17998
   419
fun literals_of_term P = literals_of_term1 ([],[]) P;
mengj@17998
   420
mengj@20274
   421
fun occurs a (CombVar(b,_)) = a = b
mengj@20274
   422
  | occurs a (CombApp(t1,t2,_)) = (occurs a t1) orelse (occurs a t2)
mengj@20274
   423
  | occurs _ _ = false
mengj@20274
   424
mengj@20274
   425
fun too_general_terms (CombVar(v,_), t) = not (occurs v t)
mengj@20274
   426
  | too_general_terms _ = false;
mengj@20274
   427
paulson@21135
   428
fun too_general_equality (Literal(true,(Bool(CombApp(CombApp(CombConst("equal",tp,tps),t1,tp1),t2,tp2))))) =
paulson@20360
   429
      too_general_terms (t1,t2) orelse too_general_terms (t2,t1)
paulson@21135
   430
  | too_general_equality _ = false;
mengj@20274
   431
paulson@21135
   432
(* forbid the literal hBOOL(V) *)
paulson@21135
   433
fun too_general_bool (Literal(_,Bool(CombVar _))) = true
paulson@21135
   434
  | too_general_bool _ = false;
mengj@20130
   435
mengj@17998
   436
(* making axiom and conjecture clauses *)
mengj@20274
   437
exception MAKE_CLAUSE
mengj@20130
   438
fun make_clause(clause_id,axiom_name,kind,thm,is_user) =
mengj@19444
   439
    let val term = prop_of thm
mengj@20130
   440
	val term' = comb_of term is_user
mengj@20016
   441
	val (lits,ctypes_sorts) = literals_of_term term'
paulson@18856
   442
	val (ctvar_lits,ctfree_lits) = ResClause.add_typs_aux ctypes_sorts
mengj@17998
   443
    in
mengj@20016
   444
	if forall isFalse lits
mengj@20016
   445
	then error "Problem too trivial for resolution (empty clause)"
paulson@21135
   446
	else if (!typ_level <> T_FULL) andalso kind=Axiom andalso 
paulson@21135
   447
	        (forall too_general_equality lits orelse exists too_general_bool lits)
paulson@21135
   448
	    then (Output.debug ("Omitting " ^ axiom_name ^ ": clause is too prolific"); 
paulson@20360
   449
	          raise MAKE_CLAUSE) 
mengj@20016
   450
	else
mengj@20016
   451
	    Clause {clause_id = clause_id, axiom_name = axiom_name, th = thm, kind = kind,
mengj@20016
   452
		    literals = lits, ctypes_sorts = ctypes_sorts, 
mengj@20016
   453
		    ctvar_type_literals = ctvar_lits,
mengj@20016
   454
		    ctfree_type_literals = ctfree_lits}
mengj@17998
   455
    end;
mengj@17998
   456
mengj@20016
   457
paulson@20360
   458
fun make_axiom_clause thm (ax_name,cls_id,is_user) = 
paulson@20360
   459
      make_clause(cls_id,ax_name,Axiom,thm,is_user);
mengj@20016
   460
 
mengj@20130
   461
fun make_axiom_clauses [] user_lemmas = []
mengj@20130
   462
  | make_axiom_clauses ((thm,(name,id))::thms) user_lemmas =
mengj@20130
   463
    let val is_user = name mem user_lemmas
paulson@20360
   464
	val cls = SOME (make_axiom_clause thm (name,id,is_user)) 
paulson@20360
   465
	          handle MAKE_CLAUSE => NONE
mengj@20130
   466
	val clss = make_axiom_clauses thms user_lemmas
mengj@19354
   467
    in
mengj@20130
   468
	case cls of NONE => clss
paulson@20360
   469
		  | SOME(cls') => if isTaut cls' then clss 
paulson@20360
   470
		                  else (name,cls')::clss
mengj@19354
   471
    end;
mengj@19354
   472
mengj@19354
   473
mengj@17998
   474
fun make_conjecture_clauses_aux _ [] = []
paulson@20421
   475
  | make_conjecture_clauses_aux n (th::ths) =
paulson@20421
   476
      make_clause(n,"conjecture",Conjecture,th,true) ::
paulson@20421
   477
      make_conjecture_clauses_aux (n+1) ths;
mengj@17998
   478
mengj@17998
   479
val make_conjecture_clauses = make_conjecture_clauses_aux 0;
mengj@17998
   480
mengj@17998
   481
mengj@17998
   482
(**********************************************************************)
mengj@17998
   483
(* convert clause into ATP specific formats:                          *)
mengj@17998
   484
(* TPTP used by Vampire and E                                         *)
mengj@19720
   485
(* DFG used by SPASS                                                  *)
mengj@17998
   486
(**********************************************************************)
mengj@17998
   487
mengj@17998
   488
val type_wrapper = "typeinfo";
mengj@17998
   489
mengj@18356
   490
fun wrap_type (c,t) = 
paulson@21135
   491
    case !typ_level of T_FULL => type_wrapper ^ ResClause.paren_pack [c,t]
mengj@18356
   492
		     | _ => c;
mengj@18356
   493
    
mengj@17998
   494
mengj@17998
   495
val bool_tp = ResClause.make_fixed_type_const "bool";
mengj@17998
   496
mengj@17998
   497
val app_str = "hAPP";
mengj@17998
   498
mengj@17998
   499
val bool_str = "hBOOL";
mengj@17998
   500
mengj@18356
   501
exception STRING_OF_COMBTERM of int;
mengj@17998
   502
mengj@17998
   503
(* convert literals of clauses into strings *)
mengj@18440
   504
fun string_of_combterm1_aux _ (CombConst(c,tp,_)) = 
mengj@18440
   505
    let val tp' = string_of_ctyp tp
paulson@20864
   506
	val c' = if c = "equal" then "c_fequal" else c
mengj@18440
   507
    in
mengj@19452
   508
	(wrap_type (c',tp'),tp')
mengj@18440
   509
    end
mengj@18440
   510
  | string_of_combterm1_aux _ (CombFree(v,tp)) = 
mengj@18440
   511
    let val tp' = string_of_ctyp tp
mengj@18440
   512
    in
mengj@18440
   513
	(wrap_type (v,tp'),tp')
mengj@18440
   514
    end
mengj@18440
   515
  | string_of_combterm1_aux _ (CombVar(v,tp)) = 
mengj@18440
   516
    let val tp' = string_of_ctyp tp
mengj@18440
   517
    in
mengj@18440
   518
	(wrap_type (v,tp'),tp')
mengj@18440
   519
    end
mengj@18356
   520
  | string_of_combterm1_aux is_pred (CombApp(t1,t2,tp)) =
mengj@18356
   521
    let val (s1,tp1) = string_of_combterm1_aux is_pred t1
mengj@18356
   522
	val (s2,tp2) = string_of_combterm1_aux is_pred t2
mengj@18440
   523
	val tp' = ResClause.string_of_fol_type tp
paulson@21135
   524
	val r =	case !typ_level of
paulson@21135
   525
	            T_FULL => type_wrapper ^ ResClause.paren_pack [(app_str ^ ResClause.paren_pack [s1,s2]),tp']
paulson@21135
   526
		  | T_PARTIAL => app_str ^ ResClause.paren_pack [s1,s2,tp1]
paulson@21135
   527
		  | T_NONE => app_str ^ ResClause.paren_pack [s1,s2]
paulson@21135
   528
		  | T_CONST => raise STRING_OF_COMBTERM 1 (*should not happen, if happened may be a bug*)
paulson@21135
   529
    in	(r,tp')   end
mengj@19452
   530
  | string_of_combterm1_aux is_pred (Bool(CombApp(CombApp(CombConst("equal",tp,tps),t1,tp1),t2,tp2))) =
mengj@19452
   531
    if is_pred then 
mengj@19452
   532
	let val (s1,_) = string_of_combterm1_aux false t1
mengj@19452
   533
	    val (s2,_) = string_of_combterm1_aux false t2
mengj@19452
   534
	in
paulson@21135
   535
	    ("equal" ^ ResClause.paren_pack [s1,s2], bool_tp)
mengj@19452
   536
	end
mengj@19452
   537
    else
mengj@19452
   538
	let val (t,_) = string_of_combterm1_aux false (CombApp(CombApp(CombConst("equal",tp,tps),t1,tp1),t2,tp2))
mengj@19452
   539
	in
mengj@19452
   540
	    (t,bool_tp)
mengj@19452
   541
	end
mengj@18356
   542
  | string_of_combterm1_aux is_pred (Bool(t)) = 
mengj@18356
   543
    let val (t',_) = string_of_combterm1_aux false t
paulson@21135
   544
	val r = if is_pred then bool_str ^ ResClause.paren_pack [t']
mengj@18356
   545
		else t'
mengj@17998
   546
    in
mengj@18356
   547
	(r,bool_tp)
mengj@18356
   548
    end;
mengj@18356
   549
mengj@18356
   550
fun string_of_combterm1 is_pred term = fst (string_of_combterm1_aux is_pred term);
mengj@18356
   551
mengj@18440
   552
fun string_of_combterm2 _ (CombConst(c,tp,tvars)) = 
mengj@18440
   553
    let val tvars' = map string_of_ctyp tvars
paulson@20864
   554
	val c' = if c = "equal" then "c_fequal" else c
mengj@18440
   555
    in
paulson@21135
   556
	c' ^ ResClause.paren_pack tvars'
mengj@18440
   557
    end
mengj@18356
   558
  | string_of_combterm2 _ (CombFree(v,tp)) = v
mengj@18356
   559
  | string_of_combterm2 _ (CombVar(v,tp)) = v
mengj@18356
   560
  | string_of_combterm2 is_pred (CombApp(t1,t2,tp)) =
mengj@18356
   561
    let val s1 = string_of_combterm2 is_pred t1
mengj@18356
   562
	val s2 = string_of_combterm2 is_pred t2
mengj@18356
   563
    in
paulson@21135
   564
	app_str ^ ResClause.paren_pack [s1,s2]
mengj@18356
   565
    end
mengj@19452
   566
  | string_of_combterm2 is_pred (Bool(CombApp(CombApp(CombConst("equal",tp,tps),t1,tp1),t2,tp2))) =
mengj@19452
   567
    if is_pred then 
mengj@19452
   568
	let val s1 = string_of_combterm2 false t1
mengj@19452
   569
	    val s2 = string_of_combterm2 false t2
mengj@19452
   570
	in
paulson@21135
   571
	    ("equal" ^ ResClause.paren_pack [s1,s2])
mengj@19452
   572
	end
mengj@19452
   573
    else
mengj@19452
   574
	string_of_combterm2 false (CombApp(CombApp(CombConst("equal",tp,tps),t1,tp1),t2,tp2))
mengj@19452
   575
 
mengj@18356
   576
  | string_of_combterm2 is_pred (Bool(t)) = 
mengj@18356
   577
    let val t' = string_of_combterm2 false t
mengj@17998
   578
    in
paulson@21135
   579
	if is_pred then bool_str ^ ResClause.paren_pack [t']
mengj@18200
   580
	else t'
mengj@17998
   581
    end;
mengj@17998
   582
mengj@18356
   583
fun string_of_combterm is_pred term = 
mengj@18356
   584
    case !typ_level of T_CONST => string_of_combterm2 is_pred term
mengj@18356
   585
		     | _ => string_of_combterm1 is_pred term;
mengj@18356
   586
mengj@17998
   587
fun string_of_clausename (cls_id,ax_name) = 
mengj@17998
   588
    ResClause.clause_prefix ^ ResClause.ascii_of ax_name ^ "_" ^ Int.toString cls_id;
mengj@17998
   589
mengj@17998
   590
fun string_of_type_clsname (cls_id,ax_name,idx) = 
mengj@17998
   591
    string_of_clausename (cls_id,ax_name) ^ "_tcs" ^ (Int.toString idx);
mengj@17998
   592
mengj@17998
   593
mengj@19720
   594
(* tptp format *)
mengj@19720
   595
mengj@17998
   596
fun tptp_literal (Literal(pol,pred)) =
mengj@18200
   597
    let val pred_string = string_of_combterm true pred
mengj@17998
   598
	val pol_str = if pol then "++" else "--"
mengj@17998
   599
    in
mengj@17998
   600
	pol_str ^ pred_string
mengj@17998
   601
    end;
mengj@17998
   602
mengj@17998
   603
 
mengj@17998
   604
fun tptp_type_lits (Clause cls) = 
mengj@17998
   605
    let val lits = map tptp_literal (#literals cls)
mengj@17998
   606
	val ctvar_lits_strs =
mengj@18356
   607
	    case !typ_level of T_NONE => []
paulson@20360
   608
	      | _ => map ResClause.tptp_of_typeLit (#ctvar_type_literals cls)
mengj@17998
   609
	val ctfree_lits = 
mengj@18356
   610
	    case !typ_level of T_NONE => []
paulson@20360
   611
	      | _ => map ResClause.tptp_of_typeLit (#ctfree_type_literals cls)
mengj@17998
   612
    in
mengj@17998
   613
	(ctvar_lits_strs @ lits, ctfree_lits)
mengj@17998
   614
    end; 
mengj@18356
   615
    
mengj@18356
   616
    
mengj@17998
   617
fun clause2tptp cls =
mengj@17998
   618
    let val (lits,ctfree_lits) = tptp_type_lits cls
mengj@17998
   619
	val cls_id = get_clause_id cls
mengj@17998
   620
	val ax_name = get_axiomName cls
mengj@17998
   621
	val knd = string_of_kind cls
mengj@17998
   622
	val lits_str = ResClause.bracket_pack lits
mengj@17998
   623
	val cls_str = ResClause.gen_tptp_cls(cls_id,ax_name,knd,lits_str)
mengj@17998
   624
    in
mengj@17998
   625
	(cls_str,ctfree_lits)
mengj@17998
   626
    end;
mengj@17998
   627
mengj@17998
   628
mengj@19720
   629
(* dfg format *)
mengj@19720
   630
fun dfg_literal (Literal(pol,pred)) = ResClause.dfg_sign pol (string_of_combterm true pred);
mengj@19720
   631
mengj@19720
   632
fun dfg_clause_aux (Clause{literals, ctypes_sorts, ...}) = 
mengj@19720
   633
  let val lits = map dfg_literal literals
mengj@19720
   634
      val (tvar_lits,tfree_lits) = ResClause.add_typs_aux ctypes_sorts
mengj@19720
   635
      val tvar_lits_strs = 
mengj@19720
   636
	  case !typ_level of T_NONE => [] 
paulson@20360
   637
	      | _ => map ResClause.dfg_of_typeLit tvar_lits
mengj@19720
   638
      val tfree_lits =
mengj@19720
   639
          case !typ_level of T_NONE => []
paulson@20360
   640
	      | _ => map ResClause.dfg_of_typeLit tfree_lits 
mengj@19720
   641
  in
mengj@19720
   642
      (tvar_lits_strs @ lits, tfree_lits)
mengj@19720
   643
  end; 
mengj@19720
   644
mengj@19720
   645
fun get_uvars (CombConst(_,_,_)) vars = vars
mengj@19720
   646
  | get_uvars (CombFree(_,_)) vars = vars
mengj@19720
   647
  | get_uvars (CombVar(v,tp)) vars = (v::vars)
mengj@19720
   648
  | get_uvars (CombApp(P,Q,tp)) vars = get_uvars P (get_uvars Q vars)
mengj@19720
   649
  | get_uvars (Bool(c)) vars = get_uvars c vars;
mengj@19720
   650
mengj@19720
   651
mengj@19720
   652
fun get_uvars_l (Literal(_,c)) = get_uvars c [];
mengj@19720
   653
mengj@19720
   654
fun dfg_vars (Clause {literals,...}) = ResClause.union_all (map get_uvars_l literals);
mengj@19720
   655
 
mengj@19720
   656
fun clause2dfg (cls as Clause{axiom_name,clause_id,kind,ctypes_sorts,...}) =
mengj@19720
   657
    let val (lits,tfree_lits) = dfg_clause_aux cls 
mengj@19720
   658
        val vars = dfg_vars cls
mengj@19720
   659
        val tvars = ResClause.get_tvar_strs ctypes_sorts
mengj@19720
   660
	val knd = name_of_kind kind
mengj@19720
   661
	val lits_str = commas lits
mengj@19720
   662
	val cls_str = ResClause.gen_dfg_cls(clause_id, axiom_name, knd, lits_str, tvars@vars) 
mengj@19720
   663
    in (cls_str, tfree_lits) end;
mengj@19720
   664
mengj@19720
   665
mengj@19720
   666
fun init_funcs_tab funcs = 
mengj@19724
   667
    let val tp = !typ_level
mengj@20865
   668
	val funcs1 = case tp of T_PARTIAL => Symtab.update ("hAPP",3) funcs
mengj@20865
   669
				      | _ => Symtab.update ("hAPP",2) funcs
mengj@19724
   670
	val funcs2 = case tp of T_FULL => Symtab.update ("typeinfo",2) funcs1
mengj@19724
   671
				      | _ => funcs1
mengj@19724
   672
    in
mengj@20865
   673
	funcs2
mengj@19724
   674
    end;
mengj@19720
   675
mengj@19720
   676
mengj@19725
   677
fun add_funcs (CombConst(c,_,tvars),funcs) =
mengj@19725
   678
    if c = "equal" then foldl ResClause.add_foltype_funcs funcs tvars
mengj@19725
   679
    else
mengj@19725
   680
	(case !typ_level of T_CONST => foldl ResClause.add_foltype_funcs (Symtab.update(c,length tvars) funcs) tvars
mengj@19725
   681
			  | _ => foldl ResClause.add_foltype_funcs (Symtab.update(c,0) funcs) tvars)
mengj@19724
   682
  | add_funcs (CombFree(v,ctp),funcs) = ResClause.add_foltype_funcs (ctp,Symtab.update (v,0) funcs) 
mengj@19720
   683
  | add_funcs (CombVar(_,ctp),funcs) = ResClause.add_foltype_funcs (ctp,funcs)
mengj@19720
   684
  | add_funcs (CombApp(P,Q,_),funcs) = add_funcs(P,add_funcs (Q,funcs))
mengj@19720
   685
  | add_funcs (Bool(t),funcs) = add_funcs (t,funcs);
mengj@19720
   686
mengj@19720
   687
mengj@19720
   688
fun add_literal_funcs (Literal(_,c), funcs) = add_funcs (c,funcs);
mengj@19720
   689
mengj@19720
   690
fun add_clause_funcs (Clause {literals, ...}, funcs) =
mengj@19720
   691
    foldl add_literal_funcs funcs literals
mengj@19720
   692
    handle Symtab.DUP a => raise ERROR ("function " ^ a ^ " has multiple arities")
mengj@19720
   693
mengj@19720
   694
fun funcs_of_clauses clauses arity_clauses =
mengj@19720
   695
    Symtab.dest (foldl ResClause.add_arityClause_funcs 
mengj@19720
   696
                       (foldl add_clause_funcs (init_funcs_tab Symtab.empty) clauses)
mengj@19720
   697
                       arity_clauses)
mengj@19720
   698
mengj@19720
   699
fun preds_of clsrel_clauses arity_clauses = 
mengj@19720
   700
    Symtab.dest
mengj@19720
   701
	(foldl ResClause.add_classrelClause_preds 
mengj@19720
   702
	       (foldl ResClause.add_arityClause_preds
mengj@19720
   703
		      (Symtab.update ("hBOOL",1) Symtab.empty)
mengj@19720
   704
		      arity_clauses)
mengj@19720
   705
	       clsrel_clauses)
mengj@19720
   706
mengj@18440
   707
mengj@18440
   708
(**********************************************************************)
mengj@19198
   709
(* write clauses to files                                             *)
mengj@19198
   710
(**********************************************************************)
mengj@19198
   711
mengj@20791
   712
val cnf_helper_thms = ResAxioms.cnf_rules_pairs o (map ResAxioms.pairname)
mengj@20644
   713
paulson@21135
   714
(*Simulate the result of conversion to CNF*)
paulson@21135
   715
fun pretend_cnf s = (thm s, (s,0));
paulson@21135
   716
paulson@21135
   717
(*These theorems allow the proof of P=Q from P-->Q and Q-->P, so they are necessary for
paulson@21135
   718
  completeness. Unfortunately, they are very prolific, causing greatly increased runtimes.
paulson@21135
   719
  They also lead to many unsound proofs. Thus it is well that the "exists too_general_bool"
paulson@21135
   720
  test deletes them except with the full-typed translation.*)
paulson@21135
   721
val iff_thms = [pretend_cnf "Reconstruction.iff_positive", 
paulson@21135
   722
                pretend_cnf "Reconstruction.iff_negative"];
mengj@20644
   723
mengj@20791
   724
fun get_helper_clauses () =
paulson@21135
   725
    let val IK = if !combI_count > 0 orelse !combK_count > 0 
paulson@21135
   726
                 then (Output.debug "Include combinator I K"; cnf_helper_thms [comb_I,comb_K]) 
paulson@21135
   727
                 else []
paulson@21135
   728
	val BC = if !combB_count > 0 orelse !combC_count > 0 
paulson@21135
   729
	         then (Output.debug "Include combinator B C"; cnf_helper_thms [comb_B,comb_C]) 
paulson@21135
   730
	         else []
paulson@21135
   731
	val S = if !combS_count > 0 
paulson@21135
   732
	        then (Output.debug "Include combinator S"; cnf_helper_thms [comb_S]) 
paulson@21135
   733
	        else []
paulson@21135
   734
	val B'C' = if !combB'_count > 0 orelse !combC'_count > 0 
paulson@21135
   735
	           then (Output.debug "Include combinator B' C'"; cnf_helper_thms [comb_B', comb_C']) 
paulson@21135
   736
	           else []
paulson@21135
   737
	val S' = if !combS'_count > 0 
paulson@21135
   738
	         then (Output.debug "Include combinator S'"; cnf_helper_thms [comb_S']) 
paulson@21135
   739
	         else []
mengj@20791
   740
	val other = cnf_helper_thms [ext,fequal_imp_equal,equal_imp_fequal]
mengj@20791
   741
    in
paulson@21135
   742
	make_axiom_clauses (iff_thms @ other @ IK @ BC @ S @ B'C' @ S') []
mengj@20791
   743
    end
mengj@20791
   744
mengj@20791
   745
mengj@20791
   746
(* tptp format *)
mengj@19491
   747
						  
mengj@19198
   748
(* write TPTP format to a single file *)
mengj@19198
   749
(* when "get_helper_clauses" is called, "include_combS" and "include_min_comb" should have correct values already *)
mengj@20130
   750
fun tptp_write_file thms filename (axclauses,classrel_clauses,arity_clauses) user_lemmas=
mengj@19444
   751
    let val clss = make_conjecture_clauses thms
mengj@20130
   752
        val (clnames,axclauses') = ListPair.unzip (make_axiom_clauses axclauses user_lemmas)
mengj@19198
   753
	val (tptp_clss,tfree_litss) = ListPair.unzip (map clause2tptp clss)
mengj@19198
   754
	val tfree_clss = map ResClause.tptp_tfree_clause (foldl (op union_string) [] tfree_litss)
mengj@19198
   755
	val out = TextIO.openOut filename
mengj@20791
   756
	val helper_clauses = (#2 o ListPair.unzip o get_helper_clauses) ()
mengj@19198
   757
    in
mengj@19198
   758
	List.app (curry TextIO.output out o #1 o clause2tptp) axclauses';
mengj@19198
   759
	ResClause.writeln_strs out tfree_clss;
mengj@19198
   760
	ResClause.writeln_strs out tptp_clss;
mengj@19198
   761
	List.app (curry TextIO.output out o ResClause.tptp_classrelClause) classrel_clauses;
mengj@19198
   762
	List.app (curry TextIO.output out o ResClause.tptp_arity_clause) arity_clauses;
mengj@20791
   763
	List.app (curry TextIO.output out o #1 o clause2tptp) helper_clauses;
paulson@20022
   764
	TextIO.closeOut out;
paulson@20022
   765
	clnames
mengj@19198
   766
    end;
mengj@19198
   767
mengj@19720
   768
mengj@20644
   769
mengj@19720
   770
(* dfg format *)
mengj@19720
   771
mengj@20130
   772
fun dfg_write_file  thms filename (axclauses,classrel_clauses,arity_clauses) user_lemmas =
mengj@19720
   773
    let val _ = Output.debug ("Preparing to write the DFG file " ^ filename) 
mengj@19720
   774
	val conjectures = make_conjecture_clauses thms
mengj@20130
   775
        val (clnames,axclauses') = ListPair.unzip (make_axiom_clauses axclauses user_lemmas)
mengj@19720
   776
	val (dfg_clss,tfree_litss) = ListPair.unzip (map clause2dfg conjectures)
mengj@19720
   777
	and probname = Path.pack (Path.base (Path.unpack filename))
mengj@19720
   778
	val (axstrs,_) =  ListPair.unzip (map clause2dfg axclauses')
mengj@19720
   779
	val tfree_clss = map ResClause.dfg_tfree_clause (ResClause.union_all tfree_litss)
mengj@19720
   780
	val out = TextIO.openOut filename
mengj@20791
   781
	val helper_clauses = (#2 o ListPair.unzip o get_helper_clauses) ()
mengj@20791
   782
	val helper_clauses_strs = (#1 o ListPair.unzip o (map clause2dfg)) helper_clauses
paulson@20864
   783
	val funcs = funcs_of_clauses (helper_clauses @ conjectures @ axclauses') arity_clauses
paulson@20864
   784
	and preds = preds_of classrel_clauses arity_clauses
mengj@19720
   785
    in
mengj@19720
   786
	TextIO.output (out, ResClause.string_of_start probname); 
mengj@19720
   787
	TextIO.output (out, ResClause.string_of_descrip probname); 
mengj@19720
   788
	TextIO.output (out, ResClause.string_of_symbols (ResClause.string_of_funcs funcs) (ResClause.string_of_preds preds)); 
mengj@19720
   789
	TextIO.output (out, "list_of_clauses(axioms,cnf).\n");
mengj@19720
   790
	ResClause.writeln_strs out axstrs;
mengj@19720
   791
	List.app (curry TextIO.output out o ResClause.dfg_classrelClause) classrel_clauses;
mengj@19720
   792
	List.app (curry TextIO.output out o ResClause.dfg_arity_clause) arity_clauses;
mengj@20791
   793
	ResClause.writeln_strs out helper_clauses_strs;
mengj@19720
   794
	TextIO.output (out, "end_of_list.\n\nlist_of_clauses(conjectures,cnf).\n");
mengj@19720
   795
	ResClause.writeln_strs out tfree_clss;
mengj@19720
   796
	ResClause.writeln_strs out dfg_clss;
paulson@20953
   797
	TextIO.output (out, "end_of_list.\n\n");
paulson@20953
   798
	(*VarWeight=3 helps the HO problems, probably by counteracting the presence of hAPP*)
paulson@20953
   799
	TextIO.output (out, "list_of_settings(SPASS).\n{*\nset_flag(VarWeight,3).\n*}\nend_of_list.\n\n");
paulson@20953
   800
	TextIO.output (out, "end_problem.\n");
paulson@20022
   801
	TextIO.closeOut out;
paulson@20022
   802
	clnames
mengj@19720
   803
    end;
mengj@19720
   804
mengj@17998
   805
end