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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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mengj@17998
|
276 |
in
|
mengj@17998
|
277 |
(v'',ts)
|
mengj@17998
|
278 |
end
|
mengj@17998
|
279 |
| combterm_of (Const("op =",T) $ P $ Q) = (*FIXME: allow equal between bools?*)
|
mengj@17998
|
280 |
let val (P',tsP) = combterm_of P
|
mengj@17998
|
281 |
val (Q',tsQ) = combterm_of Q
|
mengj@17998
|
282 |
in
|
mengj@17998
|
283 |
(Equal(P',Q'),tsP union tsQ)
|
mengj@17998
|
284 |
end
|
mengj@17998
|
285 |
| combterm_of (t as (P $ Q)) =
|
mengj@17998
|
286 |
let val (P',tsP) = combterm_of P
|
mengj@17998
|
287 |
val (Q',tsQ) = combterm_of Q
|
mengj@17998
|
288 |
val tp = Term.type_of t
|
mengj@17998
|
289 |
val (tp',is_bool) = simp_type_of tp
|
mengj@17998
|
290 |
val t' = CombApp(P',Q',tp')
|
mengj@17998
|
291 |
val t'' = if is_bool then Bool(t') else t'
|
mengj@17998
|
292 |
in
|
mengj@17998
|
293 |
(t'',tsP union tsQ)
|
mengj@17998
|
294 |
end;
|
mengj@17998
|
295 |
|
mengj@17998
|
296 |
fun predicate_of ((Const("Not",_) $ P), polarity) =
|
mengj@17998
|
297 |
predicate_of (P, not polarity)
|
mengj@17998
|
298 |
| predicate_of (term,polarity) = (combterm_of term,polarity);
|
mengj@17998
|
299 |
|
mengj@17998
|
300 |
|
mengj@17998
|
301 |
fun literals_of_term1 args (Const("Trueprop",_) $ P) = literals_of_term1 args P
|
mengj@17998
|
302 |
| literals_of_term1 args (Const("op |",_) $ P $ Q) =
|
mengj@17998
|
303 |
let val args' = literals_of_term1 args P
|
mengj@17998
|
304 |
in
|
mengj@17998
|
305 |
literals_of_term1 args' Q
|
mengj@17998
|
306 |
end
|
mengj@17998
|
307 |
| literals_of_term1 (lits,ts) P =
|
mengj@17998
|
308 |
let val ((pred,ts'),pol) = predicate_of (P,true)
|
mengj@17998
|
309 |
val lits' = Literal(pol,pred)::lits
|
mengj@17998
|
310 |
in
|
mengj@17998
|
311 |
(lits',ts union ts')
|
mengj@17998
|
312 |
end;
|
mengj@17998
|
313 |
|
mengj@17998
|
314 |
|
mengj@17998
|
315 |
fun literals_of_term P = literals_of_term1 ([],[]) P;
|
mengj@17998
|
316 |
|
mengj@17998
|
317 |
|
mengj@17998
|
318 |
(* making axiom and conjecture clauses *)
|
mengj@17998
|
319 |
fun make_axiom_clause term (ax_name,cls_id) =
|
mengj@17998
|
320 |
let val term' = comb_of term
|
mengj@17998
|
321 |
val (lits,ctypes_sorts) = literals_of_term term'
|
mengj@17998
|
322 |
val (ctvar_lits,ctfree_lits) = ResClause.add_typs_aux2 ctypes_sorts
|
mengj@17998
|
323 |
in
|
mengj@17998
|
324 |
make_clause(cls_id,ax_name,Axiom,
|
mengj@17998
|
325 |
lits,ctypes_sorts,ctvar_lits,ctfree_lits)
|
mengj@17998
|
326 |
end;
|
mengj@17998
|
327 |
|
mengj@17998
|
328 |
|
mengj@17998
|
329 |
fun make_conjecture_clause n t =
|
mengj@17998
|
330 |
let val t' = comb_of t
|
mengj@17998
|
331 |
val (lits,ctypes_sorts) = literals_of_term t'
|
mengj@17998
|
332 |
val (ctvar_lits,ctfree_lits) = ResClause.add_typs_aux2 ctypes_sorts
|
mengj@17998
|
333 |
in
|
mengj@17998
|
334 |
make_clause(n,"conjecture",Conjecture,lits,ctypes_sorts,ctvar_lits,ctfree_lits)
|
mengj@17998
|
335 |
end;
|
mengj@17998
|
336 |
|
mengj@17998
|
337 |
|
mengj@17998
|
338 |
|
mengj@17998
|
339 |
fun make_conjecture_clauses_aux _ [] = []
|
mengj@17998
|
340 |
| make_conjecture_clauses_aux n (t::ts) =
|
mengj@17998
|
341 |
make_conjecture_clause n t :: make_conjecture_clauses_aux (n+1) ts;
|
mengj@17998
|
342 |
|
mengj@17998
|
343 |
val make_conjecture_clauses = make_conjecture_clauses_aux 0;
|
mengj@17998
|
344 |
|
mengj@17998
|
345 |
|
mengj@17998
|
346 |
(**********************************************************************)
|
mengj@17998
|
347 |
(* convert clause into ATP specific formats: *)
|
mengj@17998
|
348 |
(* TPTP used by Vampire and E *)
|
mengj@17998
|
349 |
(**********************************************************************)
|
mengj@17998
|
350 |
|
mengj@17998
|
351 |
val keep_types = ref true;
|
mengj@17998
|
352 |
|
mengj@17998
|
353 |
val type_wrapper = "typeinfo";
|
mengj@17998
|
354 |
|
mengj@17998
|
355 |
fun put_type (c,t) =
|
mengj@17998
|
356 |
if !keep_types then type_wrapper ^ (ResClause.paren_pack [c,t])
|
mengj@17998
|
357 |
else c;
|
mengj@17998
|
358 |
|
mengj@17998
|
359 |
|
mengj@17998
|
360 |
val bool_tp = ResClause.make_fixed_type_const "bool";
|
mengj@17998
|
361 |
|
mengj@17998
|
362 |
val app_str = "hAPP";
|
mengj@17998
|
363 |
|
mengj@17998
|
364 |
val bool_str = "hBOOL";
|
mengj@17998
|
365 |
|
mengj@17998
|
366 |
|
mengj@17998
|
367 |
(* convert literals of clauses into strings *)
|
mengj@17998
|
368 |
fun string_of_combterm (CombConst(c,tp)) =
|
mengj@17998
|
369 |
if tp = bool_tp then c else put_type(c,tp)
|
mengj@17998
|
370 |
| string_of_combterm (CombFree(v,tp)) =
|
mengj@17998
|
371 |
if tp = bool_tp then v else put_type(v,tp)
|
mengj@17998
|
372 |
| string_of_combterm (CombVar(v,tp)) =
|
mengj@17998
|
373 |
if tp = bool_tp then v else put_type(v,tp)
|
mengj@17998
|
374 |
| string_of_combterm (CombApp(t1,t2,tp)) =
|
mengj@17998
|
375 |
let val s1 = string_of_combterm t1
|
mengj@17998
|
376 |
val s2 = string_of_combterm t2
|
mengj@17998
|
377 |
val app = app_str ^ (ResClause.paren_pack [s1,s2])
|
mengj@17998
|
378 |
in
|
mengj@17998
|
379 |
if tp = bool_tp then app else put_type(app,tp)
|
mengj@17998
|
380 |
end
|
mengj@17998
|
381 |
| string_of_combterm (Bool(t)) =
|
mengj@17998
|
382 |
let val t' = string_of_combterm t
|
mengj@17998
|
383 |
in
|
mengj@17998
|
384 |
bool_str ^ (ResClause.paren_pack [t'])
|
mengj@17998
|
385 |
end
|
mengj@17998
|
386 |
| string_of_combterm (Equal(t1,t2)) =
|
mengj@17998
|
387 |
let val s1 = string_of_combterm t1
|
mengj@17998
|
388 |
val s2 = string_of_combterm t2
|
mengj@17998
|
389 |
in
|
mengj@17998
|
390 |
"equal" ^ (ResClause.paren_pack [s1,s2])
|
mengj@17998
|
391 |
end;
|
mengj@17998
|
392 |
|
mengj@17998
|
393 |
fun string_of_clausename (cls_id,ax_name) =
|
mengj@17998
|
394 |
ResClause.clause_prefix ^ ResClause.ascii_of ax_name ^ "_" ^ Int.toString cls_id;
|
mengj@17998
|
395 |
|
mengj@17998
|
396 |
fun string_of_type_clsname (cls_id,ax_name,idx) =
|
mengj@17998
|
397 |
string_of_clausename (cls_id,ax_name) ^ "_tcs" ^ (Int.toString idx);
|
mengj@17998
|
398 |
|
mengj@17998
|
399 |
|
mengj@17998
|
400 |
fun tptp_literal (Literal(pol,pred)) =
|
mengj@17998
|
401 |
let val pred_string = string_of_combterm pred
|
mengj@17998
|
402 |
val pol_str = if pol then "++" else "--"
|
mengj@17998
|
403 |
in
|
mengj@17998
|
404 |
pol_str ^ pred_string
|
mengj@17998
|
405 |
end;
|
mengj@17998
|
406 |
|
mengj@17998
|
407 |
|
mengj@17998
|
408 |
fun tptp_type_lits (Clause cls) =
|
mengj@17998
|
409 |
let val lits = map tptp_literal (#literals cls)
|
mengj@17998
|
410 |
val ctvar_lits_strs =
|
mengj@17998
|
411 |
if !keep_types
|
mengj@17998
|
412 |
then (map ResClause.tptp_of_typeLit (#ctvar_type_literals cls))
|
mengj@17998
|
413 |
else []
|
mengj@17998
|
414 |
val ctfree_lits =
|
mengj@17998
|
415 |
if !keep_types
|
mengj@17998
|
416 |
then (map ResClause.tptp_of_typeLit (#ctfree_type_literals cls))
|
mengj@17998
|
417 |
else []
|
mengj@17998
|
418 |
in
|
mengj@17998
|
419 |
(ctvar_lits_strs @ lits, ctfree_lits)
|
mengj@17998
|
420 |
end;
|
mengj@17998
|
421 |
|
mengj@17998
|
422 |
|
mengj@17998
|
423 |
fun clause2tptp cls =
|
mengj@17998
|
424 |
let val (lits,ctfree_lits) = tptp_type_lits cls
|
mengj@17998
|
425 |
val cls_id = get_clause_id cls
|
mengj@17998
|
426 |
val ax_name = get_axiomName cls
|
mengj@17998
|
427 |
val knd = string_of_kind cls
|
mengj@17998
|
428 |
val lits_str = ResClause.bracket_pack lits
|
mengj@17998
|
429 |
val cls_str = ResClause.gen_tptp_cls(cls_id,ax_name,knd,lits_str)
|
mengj@17998
|
430 |
in
|
mengj@17998
|
431 |
(cls_str,ctfree_lits)
|
mengj@17998
|
432 |
end;
|
mengj@17998
|
433 |
|
mengj@17998
|
434 |
|
mengj@17998
|
435 |
end |