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(* ========================================================================= *)
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(* FIRST ORDER LOGIC FORMULAS *)
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39349
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(* Copyright (c) 2001-2006 Joe Hurd, distributed under the BSD License *)
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39348
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(* ========================================================================= *)
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signature Formula =
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sig
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(* ------------------------------------------------------------------------- *)
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(* A type of first order logic formulas. *)
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(* ------------------------------------------------------------------------- *)
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datatype formula =
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True
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| False
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| Atom of Atom.atom
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| Not of formula
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| And of formula * formula
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| Or of formula * formula
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| Imp of formula * formula
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| Iff of formula * formula
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| Forall of Term.var * formula
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| Exists of Term.var * formula
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(* ------------------------------------------------------------------------- *)
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(* Constructors and destructors. *)
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(* ------------------------------------------------------------------------- *)
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(* Booleans *)
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val mkBoolean : bool -> formula
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val destBoolean : formula -> bool
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val isBoolean : formula -> bool
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val isTrue : formula -> bool
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val isFalse : formula -> bool
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(* Functions *)
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val functions : formula -> NameAritySet.set
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val functionNames : formula -> NameSet.set
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(* Relations *)
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val relations : formula -> NameAritySet.set
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val relationNames : formula -> NameSet.set
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(* Atoms *)
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val destAtom : formula -> Atom.atom
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val isAtom : formula -> bool
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(* Negations *)
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val destNeg : formula -> formula
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val isNeg : formula -> bool
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val stripNeg : formula -> int * formula
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(* Conjunctions *)
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val listMkConj : formula list -> formula
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val stripConj : formula -> formula list
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val flattenConj : formula -> formula list
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(* Disjunctions *)
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val listMkDisj : formula list -> formula
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val stripDisj : formula -> formula list
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val flattenDisj : formula -> formula list
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(* Equivalences *)
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val listMkEquiv : formula list -> formula
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val stripEquiv : formula -> formula list
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val flattenEquiv : formula -> formula list
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(* Universal quantification *)
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val destForall : formula -> Term.var * formula
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val isForall : formula -> bool
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val listMkForall : Term.var list * formula -> formula
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val setMkForall : NameSet.set * formula -> formula
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val stripForall : formula -> Term.var list * formula
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(* Existential quantification *)
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val destExists : formula -> Term.var * formula
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val isExists : formula -> bool
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val listMkExists : Term.var list * formula -> formula
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val setMkExists : NameSet.set * formula -> formula
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val stripExists : formula -> Term.var list * formula
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(* ------------------------------------------------------------------------- *)
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(* The size of a formula in symbols. *)
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(* ------------------------------------------------------------------------- *)
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val symbols : formula -> int
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(* ------------------------------------------------------------------------- *)
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(* A total comparison function for formulas. *)
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(* ------------------------------------------------------------------------- *)
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val compare : formula * formula -> order
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val equal : formula -> formula -> bool
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(* ------------------------------------------------------------------------- *)
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(* Free variables. *)
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(* ------------------------------------------------------------------------- *)
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val freeIn : Term.var -> formula -> bool
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val freeVars : formula -> NameSet.set
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val freeVarsList : formula list -> NameSet.set
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val specialize : formula -> formula
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val generalize : formula -> formula
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(* ------------------------------------------------------------------------- *)
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(* Substitutions. *)
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(* ------------------------------------------------------------------------- *)
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val subst : Subst.subst -> formula -> formula
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(* ------------------------------------------------------------------------- *)
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(* The equality relation. *)
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(* ------------------------------------------------------------------------- *)
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val mkEq : Term.term * Term.term -> formula
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val destEq : formula -> Term.term * Term.term
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val isEq : formula -> bool
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val mkNeq : Term.term * Term.term -> formula
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val destNeq : formula -> Term.term * Term.term
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val isNeq : formula -> bool
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val mkRefl : Term.term -> formula
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val destRefl : formula -> Term.term
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val isRefl : formula -> bool
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val sym : formula -> formula (* raises Error if given a refl *)
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val lhs : formula -> Term.term
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val rhs : formula -> Term.term
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(* ------------------------------------------------------------------------- *)
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(* Splitting goals. *)
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(* ------------------------------------------------------------------------- *)
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val splitGoal : formula -> formula list
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(* ------------------------------------------------------------------------- *)
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(* Parsing and pretty-printing. *)
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(* ------------------------------------------------------------------------- *)
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type quotation = formula Parse.quotation
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val pp : formula Print.pp
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val toString : formula -> string
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val fromString : string -> formula
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val parse : quotation -> formula
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end
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