author | blanchet |
Thu, 16 Sep 2010 07:24:04 +0200 | |
changeset 39443 | e330437cd22a |
parent 39353 | 7f11d833d65b |
child 39444 | beabb8443ee4 |
permissions | -rw-r--r-- |
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(* ========================================================================= *) |
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(* FIRST ORDER LOGIC SUBSTITUTIONS *) |
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39443
e330437cd22a
copied the unmodified official Metis 2.3 (15 Sept. 2010) sources into Isabelle
blanchet
parents:
39353
diff
changeset
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(* Copyright (c) 2002 Joe Hurd, distributed under the MIT license *) |
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(* ========================================================================= *) |
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signature Subst = |
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sig |
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(* ------------------------------------------------------------------------- *) |
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(* A type of first order logic substitutions. *) |
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(* ------------------------------------------------------------------------- *) |
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type subst |
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(* ------------------------------------------------------------------------- *) |
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(* Basic operations. *) |
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(* ------------------------------------------------------------------------- *) |
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val empty : subst |
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val null : subst -> bool |
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val size : subst -> int |
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val peek : subst -> Term.var -> Term.term option |
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val insert : subst -> Term.var * Term.term -> subst |
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val singleton : Term.var * Term.term -> subst |
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val toList : subst -> (Term.var * Term.term) list |
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val fromList : (Term.var * Term.term) list -> subst |
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val foldl : (Term.var * Term.term * 'a -> 'a) -> 'a -> subst -> 'a |
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val foldr : (Term.var * Term.term * 'a -> 'a) -> 'a -> subst -> 'a |
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val pp : subst Print.pp |
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val toString : subst -> string |
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(* ------------------------------------------------------------------------- *) |
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(* Normalizing removes identity substitutions. *) |
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(* ------------------------------------------------------------------------- *) |
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val normalize : subst -> subst |
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(* ------------------------------------------------------------------------- *) |
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(* Applying a substitution to a first order logic term. *) |
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(* ------------------------------------------------------------------------- *) |
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val subst : subst -> Term.term -> Term.term |
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(* ------------------------------------------------------------------------- *) |
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(* Restricting a substitution to a smaller set of variables. *) |
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(* ------------------------------------------------------------------------- *) |
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val restrict : subst -> NameSet.set -> subst |
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val remove : subst -> NameSet.set -> subst |
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(* ------------------------------------------------------------------------- *) |
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(* Composing two substitutions so that the following identity holds: *) |
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(* *) |
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(* subst (compose sub1 sub2) tm = subst sub2 (subst sub1 tm) *) |
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(* ------------------------------------------------------------------------- *) |
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val compose : subst -> subst -> subst |
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(* ------------------------------------------------------------------------- *) |
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(* Creating the union of two compatible substitutions. *) |
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(* ------------------------------------------------------------------------- *) |
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val union : subst -> subst -> subst (* raises Error *) |
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(* ------------------------------------------------------------------------- *) |
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(* Substitutions can be inverted iff they are renaming substitutions. *) |
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(* ------------------------------------------------------------------------- *) |
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val invert : subst -> subst (* raises Error *) |
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val isRenaming : subst -> bool |
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(* ------------------------------------------------------------------------- *) |
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(* Creating a substitution to freshen variables. *) |
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(* ------------------------------------------------------------------------- *) |
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val freshVars : NameSet.set -> subst |
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(* ------------------------------------------------------------------------- *) |
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(* Free variables. *) |
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(* ------------------------------------------------------------------------- *) |
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val redexes : subst -> NameSet.set |
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val residueFreeVars : subst -> NameSet.set |
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val freeVars : subst -> NameSet.set |
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(* ------------------------------------------------------------------------- *) |
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(* Functions. *) |
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(* ------------------------------------------------------------------------- *) |
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val functions : subst -> NameAritySet.set |
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(* ------------------------------------------------------------------------- *) |
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(* Matching for first order logic terms. *) |
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(* ------------------------------------------------------------------------- *) |
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val match : subst -> Term.term -> Term.term -> subst (* raises Error *) |
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(* ------------------------------------------------------------------------- *) |
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(* Unification for first order logic terms. *) |
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(* ------------------------------------------------------------------------- *) |
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val unify : subst -> Term.term -> Term.term -> subst (* raises Error *) |
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end |