src/HOL/Tools/res_hol_clause.ML
author mengj
Fri Nov 18 07:10:00 2005 +0100 (2005-11-18)
changeset 18200 9d476d1054d7
parent 17998 0a869029ca58
child 18276 c62ec94e326e
permissions -rw-r--r--
-- terms are fully typed.
-- only the top-level boolean terms are predicates.
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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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(**********************************************************************)
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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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exception LAM2COMB of term;
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exception BND of term;
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fun decre_bndVar (Bound n) = Bound (n-1)
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  | decre_bndVar (P $ Q) = (decre_bndVar P) $ (decre_bndVar Q)
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  | decre_bndVar t =
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    case t of Const(_,_) => t
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	    | Free(_,_) => t
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	    | Var(_,_) => t
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	    | Abs(_,_,_) => raise BND(t); (*should not occur*)
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(*******************************************)
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fun lam2comb (Abs(x,tp,Bound 0)) _ = 
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    let val tpI = Type("fun",[tp,tp])
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    in 
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	Const("COMBI",tpI) 
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    end
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  | lam2comb (Abs(x,t1,Const(c,t2))) _ = 
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    let val tK = Type("fun",[t2,Type("fun",[t1,t2])])
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    in 
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	Const("COMBK",tK) $ Const(c,t2) 
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    end
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  | lam2comb (Abs(x,t1,Free(v,t2))) _ =
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    let val tK = Type("fun",[t2,Type("fun",[t1,t2])])
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    in
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	Const("COMBK",tK) $ Free(v,t2)
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    end
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  | lam2comb (Abs(x,t1,Var(ind,t2))) _=
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    let val tK = Type("fun",[t2,Type("fun",[t1,t2])])
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    in
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	Const("COMBK",tK) $ Var(ind,t2)
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    end
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  | lam2comb (t as (Abs(x,t1,P$(Bound 0)))) Bnds =
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    let val nfreeP = not(is_free P 0)
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	val tr = Term.type_of1(t1::Bnds,P)
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    in
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	if nfreeP then (decre_bndVar P)
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	else (
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	      let val tI = Type("fun",[t1,t1])
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		  val P' = lam2comb (Abs(x,t1,P)) Bnds
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		  val tp' = Term.type_of1(Bnds,P')
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		  val tS = Type("fun",[tp',Type("fun",[tI,tr])])
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	      in
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		  Const("COMBS",tS) $ P' $ Const("COMBI",tI)
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	      end)
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    end
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  | lam2comb (t as (Abs(x,t1,P$Q))) Bnds =
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    let val (nfreeP,nfreeQ) = (not(is_free P 0),not(is_free Q 0))
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	val tpq = Term.type_of1(t1::Bnds, P$Q) 
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    in
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	if(nfreeP andalso nfreeQ) then (
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	    let val tK = Type("fun",[tpq,Type("fun",[t1,tpq])])
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		val PQ' = decre_bndVar(P $ Q)
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	    in 
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		Const("COMBK",tK) $ PQ'
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	    end)
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	else (
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	      if nfreeP then (
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			       let val Q' = lam2comb (Abs(x,t1,Q)) Bnds
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				   val P' = decre_bndVar 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 = Type("fun",[tp,Type("fun",[tq',Type("fun",[t1,tpq])])])
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			       in
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				   Const("COMBB",tB) $ P' $ Q' 
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			       end)
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	      else (
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		    if nfreeQ then (
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				    let val P' = lam2comb (Abs(x,t1,P)) Bnds
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					val Q' = decre_bndVar 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 = Type("fun",[tp',Type("fun",[tq,Type("fun",[t1,tpq])])])
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				    in
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					Const("COMBC",tC) $ P' $ Q'
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				    end)
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		    else(
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			 let val P' = lam2comb (Abs(x,t1,P)) Bnds
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			     val Q' = lam2comb (Abs(x,t1,Q)) Bnds
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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 = Type("fun",[tp',Type("fun",[tq',Type("fun",[t1,tpq])])])
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			 in
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			     Const("COMBS",tS) $ P' $ Q'
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			 end)))
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    end
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  | lam2comb (t as (Abs(x,t1,_))) _ = raise LAM2COMB (t);
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(*********************)
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fun to_comb (Abs(x,tp,b)) Bnds =
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    let val b' = to_comb b (tp::Bnds)
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    in lam2comb (Abs(x,tp,b')) Bnds end
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  | to_comb (P $ Q) Bnds = ((to_comb P Bnds) $ (to_comb Q Bnds))
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  | to_comb t _ = t;
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fun comb_of t = to_comb t [];
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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)) =
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    let val xn = x ^ "_" ^ (string_of_int n)
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    in xn end
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  | string_of_term (P $ Q) =
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    let val P' = string_of_term P
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	val Q' = string_of_term Q
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    in
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	"(" ^ P' ^ " " ^ Q' ^ ")" end
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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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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 = string;
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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
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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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		  | Equal of combterm * 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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		    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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(*********************************************************************)
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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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fun make_clause(clause_id,axiom_name,kind,literals,ctypes_sorts,ctvar_type_literals,ctfree_type_literals) =
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    if forall isFalse literals
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    then error "Problem too trivial for resolution (empty clause)"
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    else
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	Clause {clause_id = clause_id, axiom_name = axiom_name, kind = kind,
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		literals = literals, ctypes_sorts = ctypes_sorts, 
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		ctvar_type_literals = ctvar_type_literals,
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		ctfree_type_literals = ctfree_type_literals};
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(* convert a Term.type to a string; gather sort information of type variables; also check if the type is a bool type *)
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fun type_of (Type (a, [])) = ((ResClause.make_fixed_type_const a,[]),a ="bool")
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  | type_of (Type (a, Ts)) = 
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    let val typbs = map type_of Ts
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	val (types,_) = ListPair.unzip typbs
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	val (ctyps,tvarSorts) = ListPair.unzip types
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	val ts = ResClause.union_all tvarSorts
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	val t = ResClause.make_fixed_type_const a
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    in
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	(((t ^ ResClause.paren_pack ctyps),ts),false)
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    end
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  | type_of (tp as (TFree (a,s))) = ((ResClause.make_fixed_type_var a,[ResClause.mk_typ_var_sort tp]),false)
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  | type_of (tp as (TVar (v,s))) = ((ResClause.make_schematic_type_var v,[ResClause.mk_typ_var_sort tp]),false);
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(* same as above, but no gathering of sort information *)
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fun simp_type_of (Type (a, [])) = (ResClause.make_fixed_type_const a,a ="bool")
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  | simp_type_of (Type (a, Ts)) = 
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    let val typbs = map simp_type_of Ts
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	val (types,_) = ListPair.unzip typbs
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	val t = ResClause.make_fixed_type_const a
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    in
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	((t ^ ResClause.paren_pack types),false)
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    end
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  | simp_type_of (TFree (a,s)) = (ResClause.make_fixed_type_var a,false)
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  | simp_type_of (TVar (v,s)) = (ResClause.make_schematic_type_var v,false);
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(* convert a Term.term (with combinators) into a combterm, also accummulate sort info *)
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fun combterm_of (Const(c,t)) =
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    let val ((tp,ts),is_bool) = type_of t
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	val c' = CombConst(ResClause.make_fixed_const c,tp)
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	val c'' = if is_bool then Bool(c') else c'
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    in
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	(c'',ts)
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    end
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  | combterm_of (Free(v,t)) =
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    let val ((tp,ts),is_bool) = type_of t
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	val v' = if ResClause.isMeta v then CombVar(ResClause.make_schematic_var(v,0),tp)
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		 else CombFree(ResClause.make_fixed_var v,tp)
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	val v'' = if is_bool then Bool(v') else v'
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    in
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	(v'',ts)
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    end
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  | combterm_of (Var(v,t)) =
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    let val ((tp,ts),is_bool) = type_of t
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	val v' = CombVar(ResClause.make_schematic_var v,tp)
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	val v'' = if is_bool then Bool(v') else v'
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    in
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	(v'',ts)
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    end
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  | combterm_of (Const("op =",T) $ P $ Q) = (*FIXME: allow equal between bools?*)
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    let val (P',tsP) = combterm_of P        
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	val (Q',tsQ) = combterm_of Q
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    in
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	(Equal(P',Q'),tsP union tsQ)
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    end
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  | combterm_of (t as (P $ Q)) =
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    let val (P',tsP) = combterm_of P
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	val (Q',tsQ) = combterm_of Q
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	val tp = Term.type_of t
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	val (tp',is_bool) = simp_type_of tp
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	val t' = CombApp(P',Q',tp')
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	val t'' = if is_bool then Bool(t') else t'
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    in
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	(t'',tsP union tsQ)
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    end;
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fun predicate_of ((Const("Not",_) $ P), polarity) =
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    predicate_of (P, not polarity)
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  | predicate_of (term,polarity) = (combterm_of term,polarity);
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fun literals_of_term1 args (Const("Trueprop",_) $ P) = literals_of_term1 args P
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  | literals_of_term1 args (Const("op |",_) $ P $ Q) = 
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    let val args' = literals_of_term1 args P
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    in
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	literals_of_term1 args' Q
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    end
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  | literals_of_term1 (lits,ts) P =
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    let val ((pred,ts'),pol) = predicate_of (P,true)
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	val lits' = Literal(pol,pred)::lits
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    in
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	(lits',ts union ts')
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    end;
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fun literals_of_term P = literals_of_term1 ([],[]) P;
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(* making axiom and conjecture clauses *)
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fun make_axiom_clause term (ax_name,cls_id) =
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    let val term' = comb_of term
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	val (lits,ctypes_sorts) = literals_of_term term'
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	val (ctvar_lits,ctfree_lits) = ResClause.add_typs_aux2 ctypes_sorts
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    in
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	make_clause(cls_id,ax_name,Axiom,
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		    lits,ctypes_sorts,ctvar_lits,ctfree_lits)
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    end;
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fun make_conjecture_clause n t =
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    let val t' = comb_of t
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	val (lits,ctypes_sorts) = literals_of_term t'
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	val (ctvar_lits,ctfree_lits) = ResClause.add_typs_aux2 ctypes_sorts
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    in
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	make_clause(n,"conjecture",Conjecture,lits,ctypes_sorts,ctvar_lits,ctfree_lits)
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    end;
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fun make_conjecture_clauses_aux _ [] = []
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  | make_conjecture_clauses_aux n (t::ts) =
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    make_conjecture_clause n t :: make_conjecture_clauses_aux (n+1) ts;
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val make_conjecture_clauses = make_conjecture_clauses_aux 0;
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(**********************************************************************)
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(* convert clause into ATP specific formats:                          *)
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(* TPTP used by Vampire and E                                         *)
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(**********************************************************************)
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val keep_types = ref true;
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val include_combS = ref false;
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val type_wrapper = "typeinfo";
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fun put_type (c,t) = 
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    if !keep_types then type_wrapper ^ (ResClause.paren_pack [c,t])
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    else c;
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val bool_tp = ResClause.make_fixed_type_const "bool";
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val app_str = "hAPP";
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val bool_str = "hBOOL";
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(* convert literals of clauses into strings *)
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fun string_of_combterm _ (CombConst(c,tp)) = put_type(c,tp)
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  | string_of_combterm _ (CombFree(v,tp)) = put_type(v,tp)
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  | string_of_combterm _ (CombVar(v,tp)) = put_type(v,tp)
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  | string_of_combterm is_pred (CombApp(t1,t2,tp)) = 
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    let val s1 = string_of_combterm is_pred t1
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	val s2 = string_of_combterm is_pred t2
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	val app = app_str ^ (ResClause.paren_pack [s1,s2])
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    in
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	put_type(app,tp)
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    end
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  | string_of_combterm is_pred (Bool(t)) = 
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    let val t' = string_of_combterm false t
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    in
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	if is_pred then bool_str ^ (ResClause.paren_pack [t'])
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	else t'
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    end
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  | string_of_combterm _ (Equal(t1,t2)) =
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    let val s1 = string_of_combterm false t1
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	val s2 = string_of_combterm false t2
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    in
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	"equal" ^ (ResClause.paren_pack [s1,s2]) 
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    end;
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fun string_of_clausename (cls_id,ax_name) = 
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    ResClause.clause_prefix ^ ResClause.ascii_of ax_name ^ "_" ^ Int.toString cls_id;
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fun string_of_type_clsname (cls_id,ax_name,idx) = 
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    string_of_clausename (cls_id,ax_name) ^ "_tcs" ^ (Int.toString idx);
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fun tptp_literal (Literal(pol,pred)) =
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    let val pred_string = string_of_combterm true pred
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	val pol_str = if pol then "++" else "--"
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    in
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   404
	pol_str ^ pred_string
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   405
    end;
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mengj@17998
   407
 
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fun tptp_type_lits (Clause cls) = 
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    let val lits = map tptp_literal (#literals cls)
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	val ctvar_lits_strs =
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   411
	      if !keep_types 
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   412
	      then (map ResClause.tptp_of_typeLit (#ctvar_type_literals cls)) 
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	      else []
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	val ctfree_lits = 
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   415
	      if !keep_types
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	      then (map ResClause.tptp_of_typeLit (#ctfree_type_literals cls)) 
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	      else []
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    in
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	(ctvar_lits_strs @ lits, ctfree_lits)
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    end; 
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   422
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   423
fun clause2tptp cls =
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    let val (lits,ctfree_lits) = tptp_type_lits cls
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   425
	val cls_id = get_clause_id cls
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   426
	val ax_name = get_axiomName cls
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   427
	val knd = string_of_kind cls
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   428
	val lits_str = ResClause.bracket_pack lits
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   429
	val cls_str = ResClause.gen_tptp_cls(cls_id,ax_name,knd,lits_str)
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   430
    in
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   431
	(cls_str,ctfree_lits)
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   432
    end;
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   433
mengj@17998
   434
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   435
end