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(* ========================================================================= *)
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(* RANDOM FINITE MODELS *)
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72004
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(* Copyright (c) 2003 Joe Leslie-Hurd, distributed under the BSD License *)
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39348
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(* ========================================================================= *)
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signature Model =
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sig
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(* ------------------------------------------------------------------------- *)
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(* Model size. *)
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(* ------------------------------------------------------------------------- *)
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type size = {size : int}
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(* ------------------------------------------------------------------------- *)
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(* A model of size N has integer elements 0...N-1. *)
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(* ------------------------------------------------------------------------- *)
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type element = int
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val zeroElement : element
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val incrementElement : size -> element -> element option
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(* ------------------------------------------------------------------------- *)
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(* The parts of the model that are fixed. *)
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(* ------------------------------------------------------------------------- *)
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type fixedFunction = size -> element list -> element option
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type fixedRelation = size -> element list -> bool option
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datatype fixed =
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Fixed of
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{functions : fixedFunction NameArityMap.map,
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relations : fixedRelation NameArityMap.map}
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val emptyFixed : fixed
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val unionFixed : fixed -> fixed -> fixed
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val getFunctionFixed : fixed -> NameArity.nameArity -> fixedFunction
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val getRelationFixed : fixed -> NameArity.nameArity -> fixedRelation
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val insertFunctionFixed : fixed -> NameArity.nameArity * fixedFunction -> fixed
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val insertRelationFixed : fixed -> NameArity.nameArity * fixedRelation -> fixed
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val unionListFixed : fixed list -> fixed
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val basicFixed : fixed (* interprets equality and hasType *)
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(* ------------------------------------------------------------------------- *)
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(* Renaming fixed model parts. *)
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(* ------------------------------------------------------------------------- *)
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type fixedMap =
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{functionMap : Name.name NameArityMap.map,
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relationMap : Name.name NameArityMap.map}
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val mapFixed : fixedMap -> fixed -> fixed
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val ppFixedMap : fixedMap Print.pp
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(* ------------------------------------------------------------------------- *)
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(* Standard fixed model parts. *)
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(* ------------------------------------------------------------------------- *)
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(* Projections *)
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val projectionMin : int
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val projectionMax : int
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val projectionName : int -> Name.name
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val projectionFixed : fixed
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(* Arithmetic *)
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val numeralMin : int
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val numeralMax : int
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val numeralName : int -> Name.name
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val addName : Name.name
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val divName : Name.name
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val dividesName : Name.name
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val evenName : Name.name
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val expName : Name.name
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val geName : Name.name
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val gtName : Name.name
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val isZeroName : Name.name
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val leName : Name.name
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val ltName : Name.name
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val modName : Name.name
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val multName : Name.name
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val negName : Name.name
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val oddName : Name.name
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val preName : Name.name
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val subName : Name.name
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val sucName : Name.name
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val modularFixed : fixed
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val overflowFixed : fixed
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(* Sets *)
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val cardName : Name.name
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val complementName : Name.name
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val differenceName : Name.name
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val emptyName : Name.name
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val memberName : Name.name
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val insertName : Name.name
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val intersectName : Name.name
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val singletonName : Name.name
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val subsetName : Name.name
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val symmetricDifferenceName : Name.name
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val unionName : Name.name
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val universeName : Name.name
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val setFixed : fixed
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(* Lists *)
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val appendName : Name.name
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val consName : Name.name
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val lengthName : Name.name
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val nilName : Name.name
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val nullName : Name.name
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val tailName : Name.name
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val listFixed : fixed
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(* ------------------------------------------------------------------------- *)
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(* Valuations. *)
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(* ------------------------------------------------------------------------- *)
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type valuation
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val emptyValuation : valuation
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val zeroValuation : NameSet.set -> valuation
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val constantValuation : element -> NameSet.set -> valuation
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val peekValuation : valuation -> Name.name -> element option
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val getValuation : valuation -> Name.name -> element
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val insertValuation : valuation -> Name.name * element -> valuation
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val randomValuation : {size : int} -> NameSet.set -> valuation
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val incrementValuation :
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{size : int} -> NameSet.set -> valuation -> valuation option
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val foldValuation :
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{size : int} -> NameSet.set -> (valuation * 'a -> 'a) -> 'a -> 'a
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(* ------------------------------------------------------------------------- *)
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(* A type of random finite models. *)
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(* ------------------------------------------------------------------------- *)
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type parameters = {size : int, fixed : fixed}
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type model
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val default : parameters
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val new : parameters -> model
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val size : model -> int
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(* ------------------------------------------------------------------------- *)
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(* Interpreting terms and formulas in the model. *)
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(* ------------------------------------------------------------------------- *)
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val interpretFunction : model -> Term.functionName * element list -> element
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val interpretRelation : model -> Atom.relationName * element list -> bool
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val interpretTerm : model -> valuation -> Term.term -> element
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val interpretAtom : model -> valuation -> Atom.atom -> bool
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val interpretFormula : model -> valuation -> Formula.formula -> bool
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val interpretLiteral : model -> valuation -> Literal.literal -> bool
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val interpretClause : model -> valuation -> Thm.clause -> bool
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(* ------------------------------------------------------------------------- *)
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(* Check whether random groundings of a formula are true in the model. *)
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(* Note: if it's cheaper, a systematic check will be performed instead. *)
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(* ------------------------------------------------------------------------- *)
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val check :
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(model -> valuation -> 'a -> bool) -> {maxChecks : int option} -> model ->
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NameSet.set -> 'a -> {T : int, F : int}
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val checkAtom :
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{maxChecks : int option} -> model -> Atom.atom -> {T : int, F : int}
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val checkFormula :
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{maxChecks : int option} -> model -> Formula.formula -> {T : int, F : int}
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val checkLiteral :
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{maxChecks : int option} -> model -> Literal.literal -> {T : int, F : int}
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val checkClause :
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{maxChecks : int option} -> model -> Thm.clause -> {T : int, F : int}
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(* ------------------------------------------------------------------------- *)
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(* Updating the model. *)
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(* ------------------------------------------------------------------------- *)
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val updateFunction :
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model -> (Term.functionName * element list) * element -> unit
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val updateRelation :
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model -> (Atom.relationName * element list) * bool -> unit
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(* ------------------------------------------------------------------------- *)
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(* Choosing a random perturbation to make a formula true in the model. *)
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(* ------------------------------------------------------------------------- *)
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val perturbTerm : model -> valuation -> Term.term * element list -> unit
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val perturbAtom : model -> valuation -> Atom.atom * bool -> unit
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val perturbLiteral : model -> valuation -> Literal.literal -> unit
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val perturbClause : model -> valuation -> Thm.clause -> unit
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(* ------------------------------------------------------------------------- *)
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(* Pretty printing. *)
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(* ------------------------------------------------------------------------- *)
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val pp : model Print.pp
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end
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