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(* ========================================================================= *)
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(* FIRST ORDER LOGIC LITERALS *)
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72004
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(* Copyright (c) 2001 Joe Leslie-Hurd, distributed under the BSD License *)
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39348
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(* ========================================================================= *)
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structure Literal :> Literal =
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struct
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open Useful;
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(* ------------------------------------------------------------------------- *)
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(* A type for storing first order logic literals. *)
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(* ------------------------------------------------------------------------- *)
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type polarity = bool;
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type literal = polarity * Atom.atom;
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(* ------------------------------------------------------------------------- *)
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(* Constructors and destructors. *)
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(* ------------------------------------------------------------------------- *)
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fun polarity ((pol,_) : literal) = pol;
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fun atom ((_,atm) : literal) = atm;
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fun name lit = Atom.name (atom lit);
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fun arguments lit = Atom.arguments (atom lit);
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fun arity lit = Atom.arity (atom lit);
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fun positive lit = polarity lit;
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fun negative lit = not (polarity lit);
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fun negate (pol,atm) : literal = (not pol, atm)
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fun relation lit = Atom.relation (atom lit);
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fun functions lit = Atom.functions (atom lit);
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fun functionNames lit = Atom.functionNames (atom lit);
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(* Binary relations *)
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fun mkBinop rel (pol,a,b) : literal = (pol, Atom.mkBinop rel (a,b));
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fun destBinop rel ((pol,atm) : literal) =
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case Atom.destBinop rel atm of (a,b) => (pol,a,b);
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fun isBinop rel = can (destBinop rel);
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(* Formulas *)
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fun toFormula (true,atm) = Formula.Atom atm
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| toFormula (false,atm) = Formula.Not (Formula.Atom atm);
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fun fromFormula (Formula.Atom atm) = (true,atm)
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| fromFormula (Formula.Not (Formula.Atom atm)) = (false,atm)
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| fromFormula _ = raise Error "Literal.fromFormula";
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(* ------------------------------------------------------------------------- *)
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(* The size of a literal in symbols. *)
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(* ------------------------------------------------------------------------- *)
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fun symbols ((_,atm) : literal) = Atom.symbols atm;
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(* ------------------------------------------------------------------------- *)
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(* A total comparison function for literals. *)
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(* ------------------------------------------------------------------------- *)
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val compare = prodCompare boolCompare Atom.compare;
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fun equal (p1,atm1) (p2,atm2) = p1 = p2 andalso Atom.equal atm1 atm2;
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(* ------------------------------------------------------------------------- *)
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(* Subterms. *)
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(* ------------------------------------------------------------------------- *)
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fun subterm lit path = Atom.subterm (atom lit) path;
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fun subterms lit = Atom.subterms (atom lit);
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fun replace (lit as (pol,atm)) path_tm =
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let
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val atm' = Atom.replace atm path_tm
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in
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if Portable.pointerEqual (atm,atm') then lit else (pol,atm')
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end;
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(* ------------------------------------------------------------------------- *)
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(* Free variables. *)
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(* ------------------------------------------------------------------------- *)
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fun freeIn v lit = Atom.freeIn v (atom lit);
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fun freeVars lit = Atom.freeVars (atom lit);
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(* ------------------------------------------------------------------------- *)
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(* Substitutions. *)
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(* ------------------------------------------------------------------------- *)
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fun subst sub (lit as (pol,atm)) : literal =
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let
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val atm' = Atom.subst sub atm
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in
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if Portable.pointerEqual (atm',atm) then lit else (pol,atm')
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end;
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(* ------------------------------------------------------------------------- *)
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(* Matching. *)
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(* ------------------------------------------------------------------------- *)
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fun match sub ((pol1,atm1) : literal) (pol2,atm2) =
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let
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val _ = pol1 = pol2 orelse raise Error "Literal.match"
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in
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Atom.match sub atm1 atm2
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end;
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(* ------------------------------------------------------------------------- *)
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(* Unification. *)
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(* ------------------------------------------------------------------------- *)
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fun unify sub ((pol1,atm1) : literal) (pol2,atm2) =
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let
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val _ = pol1 = pol2 orelse raise Error "Literal.unify"
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in
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Atom.unify sub atm1 atm2
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end;
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(* ------------------------------------------------------------------------- *)
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(* The equality relation. *)
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(* ------------------------------------------------------------------------- *)
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fun mkEq l_r : literal = (true, Atom.mkEq l_r);
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fun destEq ((true,atm) : literal) = Atom.destEq atm
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| destEq (false,_) = raise Error "Literal.destEq";
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val isEq = can destEq;
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fun mkNeq l_r : literal = (false, Atom.mkEq l_r);
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fun destNeq ((false,atm) : literal) = Atom.destEq atm
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| destNeq (true,_) = raise Error "Literal.destNeq";
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val isNeq = can destNeq;
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fun mkRefl tm = (true, Atom.mkRefl tm);
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fun destRefl (true,atm) = Atom.destRefl atm
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| destRefl (false,_) = raise Error "Literal.destRefl";
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val isRefl = can destRefl;
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fun mkIrrefl tm = (false, Atom.mkRefl tm);
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fun destIrrefl (true,_) = raise Error "Literal.destIrrefl"
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| destIrrefl (false,atm) = Atom.destRefl atm;
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val isIrrefl = can destIrrefl;
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fun sym (pol,atm) : literal = (pol, Atom.sym atm);
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fun lhs ((_,atm) : literal) = Atom.lhs atm;
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fun rhs ((_,atm) : literal) = Atom.rhs atm;
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(* ------------------------------------------------------------------------- *)
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(* Special support for terms with type annotations. *)
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(* ------------------------------------------------------------------------- *)
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fun typedSymbols ((_,atm) : literal) = Atom.typedSymbols atm;
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fun nonVarTypedSubterms ((_,atm) : literal) = Atom.nonVarTypedSubterms atm;
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(* ------------------------------------------------------------------------- *)
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(* Parsing and pretty-printing. *)
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(* ------------------------------------------------------------------------- *)
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val pp = Print.ppMap toFormula Formula.pp;
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val toString = Print.toString pp;
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fun fromString s = fromFormula (Formula.fromString s);
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val parse = Parse.parseQuotation Term.toString fromString;
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end
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structure LiteralOrdered =
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struct type t = Literal.literal val compare = Literal.compare end
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structure LiteralMap = KeyMap (LiteralOrdered);
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structure LiteralSet =
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struct
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local
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structure S = ElementSet (LiteralMap);
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in
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open S;
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end;
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fun negateMember lit set = member (Literal.negate lit) set;
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val negate =
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let
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fun f (lit,set) = add set (Literal.negate lit)
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in
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foldl f empty
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end;
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val relations =
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let
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fun f (lit,set) = NameAritySet.add set (Literal.relation lit)
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in
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foldl f NameAritySet.empty
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end;
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val functions =
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let
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fun f (lit,set) = NameAritySet.union set (Literal.functions lit)
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in
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foldl f NameAritySet.empty
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end;
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fun freeIn v = exists (Literal.freeIn v);
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val freeVars =
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let
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fun f (lit,set) = NameSet.union set (Literal.freeVars lit)
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in
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foldl f NameSet.empty
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end;
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val freeVarsList =
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let
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fun f (lits,set) = NameSet.union set (freeVars lits)
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in
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List.foldl f NameSet.empty
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end;
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val symbols =
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let
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fun f (lit,z) = Literal.symbols lit + z
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in
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foldl f 0
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end;
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val typedSymbols =
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let
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fun f (lit,z) = Literal.typedSymbols lit + z
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in
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foldl f 0
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end;
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fun subst sub lits =
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let
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fun substLit (lit,(eq,lits')) =
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let
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val lit' = Literal.subst sub lit
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val eq = eq andalso Portable.pointerEqual (lit,lit')
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in
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(eq, add lits' lit')
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end
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val (eq,lits') = foldl substLit (true,empty) lits
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in
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if eq then lits else lits'
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end;
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fun conjoin set =
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Formula.listMkConj (List.map Literal.toFormula (toList set));
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fun disjoin set =
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Formula.listMkDisj (List.map Literal.toFormula (toList set));
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val pp =
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Print.ppMap
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toList
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(Print.ppBracket "{" "}" (Print.ppOpList "," Literal.pp));
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end
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structure LiteralSetOrdered =
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struct type t = LiteralSet.set val compare = LiteralSet.compare end
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structure LiteralSetMap = KeyMap (LiteralSetOrdered);
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structure LiteralSetSet = ElementSet (LiteralSetMap);
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