author | blanchet |
Fri, 17 Sep 2010 01:56:19 +0200 | |
changeset 39501 | aaa7078fff55 |
parent 39444 | beabb8443ee4 |
child 39502 | cffceed8e7fa |
permissions | -rw-r--r-- |
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(* ========================================================================= *) |
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(* FIRST ORDER LOGIC FORMULAS *) |
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39501
aaa7078fff55
updated source files with Metis 2.3 (timestamp: 16 Sept. 2010)
blanchet
parents:
39444
diff
changeset
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(* Copyright (c) 2001 Joe Hurd, distributed under the MIT license *) |
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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 |