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full-maude.maude
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full-maude.maude
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---- To be run on Maude 2.7 (alpha 106)
---- author: Francisco Duran
---- printSyntaxError functionality by Peter Olveczky
---- narrowing search by Santiago Escobar
set show loop stats off .
set show loop timing off .
set show advisories off .
fmod BANNER is
pr STRING .
op banner : -> String .
eq banner = "Full Maude 2.7 March 10th 2015" .
endfm
***(
This file is part of the Maude 2 interpreter.
Copyright 1997-2003 SRI International, Menlo Park, CA 94025, USA.
This program is free software; you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation; either version 2 inclof the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNSS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public Leicense
along with this program; if not, write to the Free Software
Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307, USA.
)
---- to do:
---- - continue .
---- - show search graph .
---- - show path <number> .
---- - show path labels <number> .
---- - show components .
---- Main changes and bugs fixed:
----
---- - Feb 18th, 2015
---- - An operator <_[,_]*> was added to the modules for narrowing. It has been
---- renamed as @<@_[,_]*@>@ to avoid clashes with user-defined operators.
---- - acu coherence completion has been renamed to ax coherence completion.
---- This applies to the acu coherence completion [<module-name>] ., to the
---- metalevel operation axCohComplete and to the module AX-COHERENCE-COMPLETION.
---- The completion was already performed for the different combinations of
---- attributes, but the name was the original one.
---- - Nov 12th, 2014
---- - Classes without attributes may be defined as class Foo . or class Foo | .
---- Requested by A. Riesco.
---- - Parameter sorts used in sort constraints were not appropriately instantiated.
---- Reported by A. Riesco.
---- - July 14th, 2014
---- - Fixed bug in the parsing of terms with operators '=' or '=>'. Although the first-level
---- parsing was done correctly, to solve bubbles an operator = (resp. =>) was introduced
---- to handle equations (resp. rules). Reported by Adrian Riesco.
---- - Fixed bug on the pretty printing of views. Typical error on structures with id elements.
---- Probably due to changes in the definion of map sets. Reported by Adrian Riesco.
---- - September 12th, 2013
---- - Bug in ACU completion when handling modules with explicit use of kinds. Reported
---- by Luis Aguirre
---- - December 12th, 2013
---- - Bug in the renaming of operators with explicit arity where parameterized sorts
---- are used.
---- - Bug in the renaming of ac operators fixed. Given an acu operator __, a term
---- card(E E S, C) was not renamed.
---- - July 24th, 2012
---- - commands remove ids and remove non-handled ids available
---- - July 7th, 2012
---- - A bug in the removal of identity attributes has been fixed. A metadata("variant")
---- was expected in all equations to be used to generate the variants. To be consistent
---- to the new built-in getVariants function I'm using the attribute variant instead
---- of the metadata.
---- - March 20th, 2012
---- - Core Maude views are now accessible from Full Maude. Full Maude do not require
---- explicit sort maps any more.
---- - The set of more general eqs and rls (moreGeneralEqs and moreGeneralRls ops)
---- is now correctly calculated. These functions are used in several places, for
---- example, in the functions and commands to eliminate identity attributes and in
---- the completion procedures.
---- Reported by Santiago Escobar.
---- - October 24th, 2011
---- - format attribute was not correctly handled. Equation missing in the downAttr op.
---- - July 13th, 2011
---- - A bug on the load metamodule command making it fail when loading a metamodule
---- with a metadata attribute has been fixed.
---- Reported by Tobias Muhlbauer and Jonas Eckhardt.
---- - December 5th, 2009
---- - New command (remove id attributes [<module-expr.>] .) that shows the
---- module with the id attributes removed using variants.
---- - New command (remove assoc attributes [<module-expr.>] .) that shows the
---- module with the assoc (if not with comm) attributes removed using variants.
---- - November 22nd, 2009
---- - A new version of the narrowing/unification stuff by S. Escobar fixing a bug in the
---- getVariants function and incorporating some other changes.
---- To integrate it into Full Maude:
---- - The TERMSET module is moved, so that now Full Maude uses it instead of its
---- definition of term sets. In the original module by Santiago this module imported
---- the SUBSTITUTION-HANDLING module; this importation is now commented out.
---- - October 4th, 2009
---- - New (acu coherence completion .) / (acu coherence completion <Module> .) command.
---- It shows result of completing the flatten version of the module for acu coherence.
---- - Setember 11th, 2009
---- - sort Set<List<Type>> replaced by the TypeListSet sort from META-MODULE
---- - sort List<Set<Type>> renamed as TypeSetList
---- - MAYBE removed, DEFAULT-VALUE used instead. MAYBE{TERM} replaced by DEFAULT-VALUE{Term}
---- - July 28th, 2009
---- - Some cleaning up. Some of the changes may break other applications.
---- - April 18th, 2009
---- - The metadata attribute is now available for operation declarations. Reported by A. Riesco.
---- - Fixed bug in the handling of ditto. ctor and metadata attributes were copied.
---- - March 9th, 2009
---- - Bug in the search command. The number of solutions argument was used as depth bound. Reported by P. Olveczky.
---- - New (remove id attributes .) / (remove id attributes <Module> .) command
---- It shows an equivalent version of the flatten module without ids using variants.
---- - March 9th, 2009
---- - Bug in the handling of mbs/cmbs. Sorts in bubbles were not handled correctly. Reported by T. Serbanuta.
---- - February 12th, 2009
---- - The summation module expression now generates a module
---- fmod A + B + C is
---- inc A .
---- inc B .
---- inc C .
---- endfm
---- for a module expression A + B + C.
---- - February 6th, 2009
---- - Fixed a bug in the id-unify command. Fixed by Santiago Escobar
---- - February 3rd, 2009
---- - Missing equation for downAttr, for the case of nonexec
---- - Missing declaration in the CONFIGURATION+ module to handle class declarations with no attributes
---- - January 29th, 2009
---- - The downModule operation has been extended to be able to handle oo metamodules.
---- Note that omod metamodules are defined in the UNIT Full Maude module. Therefore,
---- to be able to do things like
---- (load omod ... endm .)
---- the current module must be the FM UNIT module or one extending it.
---- - January 28th, 2009
---- - A bug in downAttr. Found thanks to a problem with metamodule load. Reported by Peter Olveczky.
---- - January 8th, 2009
---- - A bug in the narrowing functionality. It was narrowing on frozen positions.
---- (fixed by Santiago Escobar)
---- - December 20th, 2008
---- - Fixed a bug in the handling of the such-that part of search commands.
---- Reported by Enrique Martin.
---- - December 17th, 2008
---- - A new search_~>_ family of commands (as for search_=>_) is now available.
---- The commands are implemented by Santiago Escobar.
---- - December 8th, 2008
---- - A new meta-module load command is available.
---- It enters a metamodule into Full Maude's database of modules.
---- Asked by Peter Olveczky and Jose Meseguer.
---- The syntax for the new command is (load <meta-module> .), where <meta-module is any term of sort
---- Module, either a term of the form fmod...endfm or any other expression reducing to a module.
---- Thus, you can write things like
----
---- (select META-LEVEL .)
----
---- (load fmod 'FOO is
---- including 'BOOL .
---- sorts 'Foo .
---- none
---- op 'f : nil -> 'Foo [none] .
---- op 'g : nil -> 'Foo [none] .
---- none
---- eq 'f.Foo = 'g.Foo [none] .
---- endfm .)
----
---- or
----
---- (load upModule('NAT, true) .)
----
---- - September 18th, 2008
---- The search command now supports its complete generality (maximum depth couln't be given). Bug reported by Zhang Min.
---- The unify command is now supported.
---- Bug in the renaming of partial operations fixed. Reported by Edu Rivera.
---- - April 2nd, 2008
---- Bug in the application of views (and renamings) with kinds in the specification
---- of op renamings. It appears in an example in which the sort was coming from a theory.
---- Reported by A. Boronat.
---- - March 24th, 2008
---- Bug in the application of renamings to op hooks. Reported by A. Boronat
---- - March 17th, 2008
---- Bug in the instantiation of parameterized sorts in sort memberships.
---- Reported by A. Boronat
---- - March 14th, 2008
---- Bug in the handling of parameterized module expressions. When the parameterers
---- are not right, the system hangs. Reported by A. Verdejo.
---- - March 9th, 2008
---- Statement attributes of membership axioms were not correctly handled.
---- Reported by A. Riesco & A. Verdejo
---- - Feb 18th, 2008
---- Bug in the renaming of operators
---- - Feb 14th, 2008
---- Statement attributes of membership axioms were not correctly handled.
---- Reported by A. Riesco & A. Verdejo
---- - Dec 17th, 2007
---- Rule in CONFIGURATION+ was causing non-termination
---- - Dec 13th, 2007
---- Change in the specification of the transform function to allow new types of modules
---- - Nov 23rd, 2007
---- Bug in the evaluation of expressions in commands (red in FOO + BAR : ...)
---- - Oct 5th, 2007
---- Bug in down of modules (reported by Pedro Ojeda)
---- - July 31st, 2007
---- bug in the application of maps to terms
---- - July 31st, 2007
---- bug in getThClasses
---- (reported by Marisol)
---- - (october 17th, 2006)
---- Changes in Alpha88a's prelude are now correctly handled
---- - (july 22nd, 2006)
---- Bug in the meta-pretty-print of types.
---- - (july 21st, 2006)
---- Object-oriented messages where not given the attribute msg
---- (from a comment by Peter).
---- - (reported by Radestock)
---- getSort was not handling parameterized sorts appropriately.
---- - the set protect/extend/include off commands didn't work if the
---- module not importing was not among the imported ones
----
---- Last changes:
----
---- - May 21st, 2007
---- GRAMMAR now extends a module BUBBLES with all bubble delcarations.
---- This BUBBLES module is also used to define the GRAMMAR-RED, GRAMMAR-REW, ...
---- modules.
----
---- - May 19th, 2007
---- procCommand changed. It now returns a Tuple{Database, QidList} instead of
---- just a QidList. Since some modules may need to be compiled for the
---- execution of a command, the resulting database is returned and used as
---- new database.
----
---- - May 19th, 2007
---- proRew takes now one argument less. The Bound (4th arg.) was unnecessary.
----
---- - BOOL is included, instead of protected, into any entered module.
----
---- - A new module expression POWER[n] is now available. A module expression
---- POWER[n]{Nat} produces a module
----
---- fmod POWER[n]{X :: TRIV} is
---- inc TUPLE[n]{X, X, ..., X} .
---- endfm
----
---- which is then instantiated by the Nat view.
---- - (July 18th, 2006)
---- The summation module expression now generates a module
---- that includes (instead of protect) its summands.
----
---- - All sorts declared in modules used for parsing have been renamed.
---- Any sort S in one of these modules is nos called @S@.
---- Since some of these modules where added to the user defined modules
---- for dealing with ups, conditions, etc., he was getting error when
---- using sorts like Token or OpDecl in his specs.
----
---- - Syntax for parameterization has been changed (again) !!! :
---- - module definition: FOO{X :: TRIV, Y :: TRIV}
---- - module instantiation: FOO{Bar,Baz}
---- - parameterized sorts: Foo{Bar,Baz}
----
---- - Any module loaded in Core Maude can be used in Full Maude.
---- This may be particularly useful in the case of using the model checker.
----
---- (mod CHECK-RESP is
---- protecting MODEL-CHECKER .
---- ...
---- endm)
----
---- (red p(0) |= (<> Qstate) .)
----
---- - Module renaming and summation consistent with Core Maude's. Built-ins
---- are now handled at the metalevel, instead of leaving the inclusions to
---- Core Maude. In this way, they can be renamed and redefined, as in
---- Core Maude. This makes Full Maude slower.
----
---- - The lazy evaluation of modules is working. When a module is redefined
---- its dependent modules are removed only if generated internally. Those
---- introduced by the user save their term representation, from which the
---- whole processing can take place. They will be recompiled by need.
----
---- - The form of qualifying sorts coming from the parameters in
---- parameterized modules has changed AGAIN: The sort Elt coming from
---- X :: TRIV is now written as X$Elt (Note that sort names cannot contain
---- dots anymore).
----
---- - Tuples are built with the syntax
---- TUPLE[size]{comma_separated_list_of_views}
---- For example, given a view Nat from TRIV to NAT we can define pairs of
---- nats with TUPLE[2]{Nat, Nat}.
----
---- - The model-checker is loaded before the full maude modules, so that
---- it can be used.
----
---- - Object-oriented modules include a module CONFIGURATION+, which
---- imports CONFIGURATION, defines a function
---- op class : Object -> Cid .
---- returning the actual class of the given object, and add syntax
---- for objects with no attributes <_:_| >. Classes without attributes
---- are defined with syntax class CLASS-NAME .
----
---- Things to come:
----
---- - Commands missing: continue ...
----
---- - On parameterized theories and views: linked parameters, composed and
---- lifted views, and default views.
----
---- - ops names in op declarations
----
---- known bugs:
----
---- - error messages could be given in down commands
----
---- - Check: perhaps we need to convert constants back into vbles in
---- procViewAux
----
---- - Parameterized sorts don't work in sort constraints (nor by themselves,
---- nor in the conditions of axioms. They are accepted in their equivalent
---- single token form but do not get instantiated
---- cmb (A, B) S : PFun(X, Y) if not(A in dom(S)) /\ S : PFun`(X`,Y`) .
----
set include BOOL off .
set include TRUTH-VALUE on .
set show advisories off .
mod CONFIGURATION is
sorts Attribute AttributeSet .
subsort Attribute < AttributeSet .
op none : -> AttributeSet [ctor] .
op _,_ : AttributeSet AttributeSet -> AttributeSet [ctor assoc comm id: none] .
sorts Oid Cid Object Msg Portal Configuration .
subsort Object Msg Portal < Configuration .
op <_:_|_> : Oid Cid AttributeSet -> Object [ctor object] .
op none : -> Configuration [ctor] .
op __ : Configuration Configuration -> Configuration [ctor config assoc comm id: none] .
op <> : -> Portal [ctor] .
endm
mod CONFIGURATION+ is
including CONFIGURATION .
op <_:_|`> : Oid Cid -> Object .
op class : Object -> Cid .
---- eq < O:Oid : C:Cid | > = < O:Oid : C:Cid | none > .
eq class(< O:Oid : C:Cid | A:AttributeSet >) = C:Cid .
endm
set include BOOL on .
set include TRUTH-VALUE off .
*******************************************************************************
*******************************************************************************
***
*** Narrowing and Equational Unification
*** by Santiago Escobar
***
fmod META-LEVEL-MNPA is
pr META-LEVEL * (op `{_`,_`} : Term Nat -> SmtResult to `{_`,_`}Smt ) .
endfm
fmod UNIFICATIONTRIPLE is
protecting META-LEVEL-MNPA .
protecting INT .
--- UnificationPair --------------------------------------------
---sorts UnificationPair UnificationPair? .
---op {_,_} : Substitution Nat -> UnificationPair [ctor] .
---subsort UnificationPair < UnificationPair? .
---op noUnifier : -> UnificationPair? [ctor] .
op getSubst : UnificationPair -> Substitution .
eq getSubst({S1:Substitution, N:Nat}) = S1:Substitution .
op getNextVar : UnificationPair -> Nat .
eq getNextVar({S1:Substitution, N:Nat}) = N:Nat .
--- UnificationTriple --------------------------------------------
---sorts UnificationTriple UnificationTriple? .
---op {_,_,_} : Substitution Substitution Nat -> UnificationTriple [ctor] .
---subsort UnificationTriple < UnificationTriple? .
---op noUnifier : -> UnificationTriple? [ctor] .
op getLSubst : UnificationTriple -> Substitution .
eq getLSubst({S1:Substitution, S2:Substitution, N:Nat}) = S1:Substitution .
op getRSubst : UnificationTriple -> Substitution .
eq getRSubst({S1:Substitution, S2:Substitution, N:Nat}) = S2:Substitution .
op getNextVar : UnificationTriple -> Nat .
eq getNextVar({S1:Substitution, S2:Substitution, N:Nat}) = N:Nat .
endfm
fmod TERM-HANDLING is
protecting META-TERM .
protecting META-LEVEL-MNPA .
protecting EXT-BOOL . *** For and-then
var T T' T'' : Term .
var C C' : Constant .
var QIL : QidList .
var N N' : Nat .
var NL NL' : NatList .
var Q F F' : Qid .
var AtS : AttrSet .
var EqS : EquationSet .
var Eq : Equation .
var Cond : Condition .
var TP : Type .
var TPL TPL' : TypeList .
var TL TL' TL'' : TermList .
var B : Bool .
var V V' : Variable .
var Ct : Context .
var CtL : NeCTermList .
var NeTL : NeTermList .
var M : Module .
*** root ******************************
op root : Term -> Qid .
eq root(V) = V .
eq root(C) = C .
eq root(F[TL]) = F .
*** size ******************************
op size : TermList -> Nat .
eq size(empty) = 0 .
eq size((T,TL)) = s(size(TL)) .
*** elem_of_ *****************************************************
op elem_of_ : Nat TermList ~> Term .
eq elem 1 of (T,TL) = T .
eq elem s(s(N)) of (T,TL) = elem s(N) of TL .
*** subTerm_of_ *****************************************************
op subTerm_of_ : NatList Term ~> Term .
eq subTerm NL of T = subTerm* NL of T .
op subTerm*_of_ : NatList Term ~> Term .
eq subTerm* nil of T = T .
eq subTerm* N NL of (F[TL]) = subTerm* NL of (elem N of TL) .
*** ToDo: UPGRADE THIS NOTION TO MODULO AC *********************
*** is_subTermOf_ *****************************************************
op is_subTermOf_ : Term TermList -> Bool .
eq is T subTermOf (T',NeTL) = is T subTermOf T'
or-else is T subTermOf NeTL .
eq is T subTermOf T = true .
eq is T subTermOf T' = is T subTermOf* T' [owise] .
op is_subTermOf*_ : Term TermList -> Bool .
eq is T subTermOf* (F[TL]) = is T subTermOf TL .
eq is T subTermOf* T' = false [owise] .
*** noVarOfSort_In_ *****************************************************
op noVarOfSort_In_ : Type TermList -> Bool .
eq noVarOfSort T:Type In V = getType(V) =/= T:Type .
eq noVarOfSort T:Type In (F[TL]) = noVarOfSort T:Type In TL .
eq noVarOfSort T:Type In (T',NeTL)
= noVarOfSort T:Type In T' and noVarOfSort T:Type In NeTL .
eq noVarOfSort T:Type In X:TermList = true [owise] .
*** findSubTermOf_In_ ***********************************************
op findSubTermOf_In_ : NeCTermList TermList ~> Term .
eq findSubTermOf (TL, [], TL') In (TL, T, TL') = T .
eq findSubTermOf (TL, F[CtL], TL'') In (TL, F[TL'], TL'')
= findSubTermOf CtL In TL' .
*** replaceElem_of_by_ ****************************************************
op replaceElem_of_by_ : Nat TermList Term ~> TermList .
eq replaceElem 1 of (T,TL) by T' = (T',TL) .
eq replaceElem s(s(N)) of (T,TL) by T' = (T,replaceElem s(N) of TL by T') .
*** replaceSubTerm_of_by_ *************************************************
op replaceSubTerm_of_by_ : NatList TermList Term ~> TermList .
eq replaceSubTerm nil of T by T' = T' .
eq replaceSubTerm N NL of (F[TL]) by T'
= F[replaceSubTermL N NL of TL by T'] .
op replaceSubTermL_of_by_ : NatList TermList Term ~> TermList .
eq replaceSubTermL 1 NL of (T,TL) by T'
= (replaceSubTerm NL of T by T', TL) .
eq replaceSubTermL s(s(N)) NL of (T,TL) by T'
= (T,replaceSubTermL s(N) NL of TL by T') .
op replaceTerm_by_in_ : Term Term TermList ~> TermList .
eq replaceTerm T by T' in T = T' .
eq replaceTerm T by T' in (F[TL]) = F[replaceTerm T by T' in TL] .
eq replaceTerm T by T' in T'' = T'' [owise] .
eq replaceTerm T by T' in (T'',NeTL)
= (replaceTerm T by T' in T'',replaceTerm T by T' in NeTL) .
*** context replacement **************************************************
op _[_] : Context Context -> Context .
op _[_] : NeCTermList Context -> NeCTermList .
eq [] [ Ct ] = Ct .
eq (F[CtL])[ Ct ] = F[ CtL [ Ct ] ] .
eq (CtL,NeTL) [Ct] = (CtL [Ct] ), NeTL .
eq (NeTL,CtL) [Ct] = NeTL, (CtL [Ct] ) .
op _[_] : Context Term -> Term .
op _[_] : NeCTermList Term -> TermList .
eq [] [ T ] = T .
eq (F[CtL])[ T ] = F[ CtL [ T ] ] .
eq (CtL,NeTL) [T] = (CtL [T] ), NeTL .
eq (NeTL,CtL) [T] = NeTL, (CtL [T] ) .
*** is_substring_ *****************************************
op is_substring_ : Qid Qid -> Bool [memo] .
eq is F:Qid substring F':Qid
= rfind(string(F':Qid), string(F:Qid), length(string(F':Qid))) =/= notFound .
*** addprefix_To_ addsufix_To_ *****************************************
op addprefix_To_ : Qid Variable -> Variable [memo] .
eq addprefix Q To V
= qid(string(Q) + string(getName(V)) + ":" + string(getType(V))) .
op addprefix_To_ : Qid Constant -> Constant [ditto] .
eq addprefix Q To F
= if noUnderBar(F) and getName(F) :: Qid then
if getType(F) :: Type then
qid(string(Q) + string(getName(F)) + "." + string(getType(F)))
else
qid(string(Q) + string(getName(F)))
fi
else
qid(string(Q) + string(F))
fi .
op addsufix_To_ : Qid Variable -> Variable [memo] .
eq addsufix Q To V
= qid(string(getName(V)) + string(Q) + ":" + string(getType(V))) .
op addsufix_To_ : Qid Constant -> Constant [ditto] .
eq addsufix Q To F
= if noUnderBar(F) and getName(F) :: Qid then
if getType(F) :: Type then
qid(string(getName(F)) + string(Q) + "." + string(getType(F)))
else
qid(string(getName(F)) + string(Q))
fi
else
qid(string(F) + string(Q))
fi .
op addType_ToVar_ : Type Qid -> Variable [memo] .
eq addType TP:Qid ToVar V:Qid
= qid(string(V:Qid) + ":" + string(TP:Qid)) .
*** noUnderBar (auxiliary) ****************************
op noUnderBar : Qid -> Bool .
eq noUnderBar(F)
= rfind(string(F), "_", length(string(F))) == notFound .
*** addType ******************************
op addType : Qid Type -> Qid .
eq addType(F,TP)
= if noUnderBar(F) and getName(F) :: Qid then
qid( string(getName(F)) + "." + string(TP) )
else
qid( string(F) + "." + string(TP) )
fi .
*** addTypeVar ******************************
op addTypeVar : Qid Type -> Qid .
eq addTypeVar(F,TP)
= qid( string(F) + ":" + string(TP) ) .
endfm
fmod SUBSTITUTION-HANDLING is
protecting META-TERM .
protecting META-LEVEL-MNPA .
protecting TERM-HANDLING .
var S S' Subst Subst' : Substitution .
var V V' : Variable .
var C C' : Constant .
var Ct : Context .
var T T' T1 T2 T1' T2' T1'' T2'' : Term .
var F F' : Qid .
var TL TL' TL1 TL2 TL1' TL2' : TermList .
var Att : AttrSet .
var RLS : RuleSet .
var Rl : Rule .
var TP : Type .
var N : Nat .
var NeTL : NeTermList .
var CtL : NeCTermList .
--- Apply Substitution to Term --------------------------------------------
op _<<_ : Term Substitution -> Term .
eq TL << none = TL .
eq C << Subst = C .
eq V << ((V <- T) ; Subst) = T .
eq V << Subst = V [owise] .
eq F[TL] << Subst = F[TL << Subst] .
op _<<_ : TermList Substitution -> TermList .
eq (T, NeTL) << Subst = (T << Subst, NeTL << Subst) .
eq empty << Subst = empty .
op _<<_ : Context Substitution -> Context .
eq Ct << none = Ct .
eq [] << Subst = [] .
eq F[CtL,NeTL] << Subst = F[CtL << Subst,NeTL << Subst] .
eq F[NeTL,CtL] << Subst = F[NeTL << Subst, CtL << Subst] .
eq F[Ct] << Subst = F[Ct << Subst] .
op _<<_ : Substitution Substitution -> Substitution .
eq S << (none).Substitution = S .
eq (none).Substitution << S = (none).Substitution .
eq ((V' <- T) ; S') << S
= (V' <- (T << S))
;
(S' << S) .
--- Combine Substitutions -------------------------------------------------
op _.._ : Substitution Substitution -> Substitution .
eq S .. S' = (S << S') ; S' .
--- Restrict Assignments to Variables in a Term ----------------------
op _|>_ : Substitution TermList -> Substitution .
eq Subst |> TL = Subst |>* Vars(TL) .
op _|>*_ : Substitution TermList -> Substitution .
--- eq noMatch |>* TL = noMatch .
eq Subst |>* TL = Subst |>** TL [none] .
op _|>**_[_] : Substitution TermList
Substitution -> Substitution .
eq none |>** TL [Subst']
= Subst' .
eq ((V <- V) ; Subst) |>** TL [Subst']
= Subst |>** TL [Subst'] .
eq ((V <- T') ; Subst) |>** TL [Subst']
= Subst |>** TL
[Subst' ; if any V in TL then (V <- T') else none fi] .
--- Remove Variables from list ----------------------
op _intersect_ : TermList TermList -> TermList .
eq (TL1,T,TL2) intersect (TL1',T,TL2')
= (T,((TL1,TL2) intersect (TL1',TL2'))) .
eq TL intersect TL' = empty [owise] .
op _intersectVar_ : TermList TermList -> TermList .
eq TL1 intersectVar TL2
= TL1 intersectVar* Vars(TL2) .
op _intersectVar*_ : TermList TermList -> TermList .
eq (T,TL1) intersectVar* TL2
= (if any Vars(T) in TL2 then T else empty fi,TL1 intersectVar* TL2) .
eq empty intersectVar* TL2
= empty .
--- Remove Variables from list ----------------------
op _setMinus_ : TermList TermList -> TermList .
eq (TL1,T,TL2) setMinus (TL1',T,TL2')
= (TL1,TL2) setMinus (TL1',TL2') .
eq TL setMinus TL' = TL [owise] .
--- Variables ---
op Vars : GTermList -> TermList .
eq Vars((T,TL:GTermList)) = VarsTerm(T),Vars(TL:GTermList) .
eq Vars((Ct,TL:GTermList)) = VarsTerm(Ct),Vars(TL:GTermList) .
eq Vars(empty) = empty .
op VarsTerm : Term -> TermList . ---warning memo
eq VarsTerm(V) = V .
eq VarsTerm(F[TL:TermList]) = Vars(TL:TermList) .
eq VarsTerm(C) = empty .
op VarsTerm : Context -> TermList . ---warning memo
eq VarsTerm(F[TL:GTermList]) = Vars(TL:GTermList) .
--- membership ---
op _in_ : Term TermList -> Bool .
eq T in (TL,T,TL') = true .
eq T in TL = false [owise] .
--- membership ---
op any_in_ : TermList TermList -> Bool . --- [memo] .
eq any empty in TL = false .
eq any (TL1,T,TL2) in (TL1',T,TL2') = true .
eq any TL in TL' = false [owise] .
--- membership ---
op all_in_ : TermList TermList -> Bool . --- [memo] .
eq all empty in TL = true .
eq all (TL1,T,TL2) in (TL1',T,TL2') = all (TL1,TL2) in (TL1',T,TL2') .
eq all TL in TL' = false [owise] .
--- Occur check ---
op allVars_inVars_ : GTermList GTermList -> Bool .
eq allVars TL:GTermList inVars TL':GTermList
= all Vars(TL:GTermList) in Vars(TL':GTermList) .
op anyVars_inVars_ : GTermList GTermList -> Bool .
eq anyVars TL:GTermList inVars TL':GTermList
= any Vars(TL:GTermList) in Vars(TL':GTermList) .
op rangeVars : Substitution -> TermList .
eq rangeVars(V <- T ; Subst) = (Vars(T),rangeVars(Subst)) .
eq rangeVars(none) = empty .
op dom_inVars_ : Substitution TermList -> Bool .
eq dom Subst inVars TL = dom Subst in Vars(TL) .
op dom_in_ : Substitution TermList -> Bool .
eq dom (V <- T ; Subst) in (TL1,V,TL2) = true .
eq dom Subst in TL = false [owise] .
op dom_notInVars_ : Substitution TermList -> Bool .
eq dom Subst notInVars TL = dom Subst notIn Vars(TL) .
op dom_notIn_ : Substitution TermList -> Bool .
eq dom none notIn TL = true .
ceq dom (V <- T ; Subst) notIn TL = true if not (V in TL) .
eq dom Subst notIn TL = false [owise] .
op range_inVars_ : Substitution TermList -> Bool .
eq range Subst inVars TL = range Subst in Vars(TL) .
op range_in_ : Substitution TermList -> Bool .
eq range (V <- T ; Subst) in TL
= any Vars(T) in TL or-else range Subst in TL .
eq range none in TL
= false .
op valid-occur-check? : Substitution -> Bool .
eq valid-occur-check?(Subst)
= not (dom Subst inVars (rangeVars(Subst))) .
endfm
fmod TERMSET is
protecting META-LEVEL-MNPA .
protecting SUBSTITUTION-HANDLING .
sort TermSet .
subsort Term < TermSet .
op emptyTermSet : -> TermSet [ctor] .
op _|_ : TermSet TermSet -> TermSet
[ctor assoc comm id: emptyTermSet format (d n d d)] .
eq X:Term | X:Term = X:Term .
op _in_ : Term TermSet -> Bool .
eq T:Term in (T:Term | TS:TermSet) = true .
eq T:Term in TS:TermSet = false [owise] .
op TermSet : TermList -> TermSet .
eq TermSet(empty)
= emptyTermSet .
eq TermSet((T:Term,TL:TermList))
= T:Term | TermSet(TL:TermList) .
endfm
fmod RENAMING is
protecting META-TERM .
protecting META-LEVEL-MNPA .
protecting TERM-HANDLING .
protecting SUBSTITUTION-HANDLING .
protecting TERMSET .
protecting CONVERSION .
protecting QID .
protecting INT .
protecting UNIFICATIONTRIPLE .
var S S' Subst Subst' : Substitution .
var V V' : Variable .
var C C' : Constant .
var CtL : NeCTermList .
var Ct : Context .
var T T' T1 T2 T1' T2' T1'' T2'' : Term .
var F F' : Qid .
var TL TL' TL'' TL''' : TermList .
var Att : AttrSet .
var RLS : RuleSet .
var Rl : Rule .
var TP : Type .
var N N' : Nat .
var NeTL : NeTermList .
var Q Q' : Qid .
var IL : ImportList .
var SS : SortSet .
var SSDS : SubsortDeclSet .
var OPDS : OpDeclSet .
var MAS : MembAxSet .
var EQS : EquationSet .
var TPL : TypeList .
--- Extra filter for substitutions ------
op _|>_ : Substitution Nat -> Substitution .
eq Subst |> N
= Subst |>* N [none] .
op _|>*_[_] : Substitution Nat Substitution -> Substitution .
eq none |>* N [Subst']
= Subst' .
eq ((V <- T') ; Subst) |>* N [Subst']
= Subst |>* N
[Subst' ; if highestVar(V) < N then (V <- T') else none fi ] .
--- instantiatesAbove -----------------------------------
op _instantiatesAbove_ : Substitution Nat -> Bool .
eq none instantiatesAbove N = false .
eq ((V <- T') ; Subst) instantiatesAbove N
= highestVar(V) >= N
or-else
Subst instantiatesAbove N .
----------------------------------------------
--- New Renaming Utilities -------------------
op highestVar : GTermList -> Nat .
eq highestVar(TL:GTermList)
= highestVar(TL:GTermList,0) .
op highestVarTerm : Term -> Nat . ---warning memo
op highestVarTerm : Context -> Nat . ---warning memo
eq highestVarTerm([]) = 0 .
eq highestVarTerm(C) = 0 .
eq highestVarTerm(V)
= if rfind(string(V), "#", length(string(V))) =/= notFound
and
rfind(string(V), ":", length(string(V))) =/= notFound
and
rat(substr(string(V),
rfind(string(V), "#", length(string(V))) + 1,
rfind(string(V), ":", length(string(V))) + (- 1))
,10)
:: Nat
then rat(substr(string(V),
rfind(string(V), "#", length(string(V))) + 1,
rfind(string(V), ":", length(string(V))) + (- 1))
,10)
else
if rfind(string(V), "%", length(string(V))) =/= notFound
and
rfind(string(V), ":", length(string(V))) =/= notFound
and
rat(substr(string(V),
rfind(string(V), "%", length(string(V))) + 1,
rfind(string(V), ":", length(string(V))) + (- 1))
,10)
:: Nat
then rat(substr(string(V),
rfind(string(V), "%", length(string(V))) + 1,
rfind(string(V), ":", length(string(V))) + (- 1))
,10)
else 0
fi
fi .
eq highestVarTerm(F[TL:GTermList])
= highestVar(TL:GTermList,0) .
op highestVar : GTermList Nat -> Nat .
eq highestVar(empty,N)
= N .
eq highestVar((Ct,TL:GTermList),N)
= highestVar(TL:GTermList,
if highestVarTerm(Ct) > N then highestVarTerm(Ct) else N fi
) .
eq highestVar((T,TL:GTermList),N)
= highestVar(TL:GTermList,
if highestVarTerm(T) > N then highestVarTerm(T) else N fi
) .
--- For substitutions
op highestVar : Substitution -> Nat . --- [memo] .
eq highestVar(Subst)
= highestVar(Subst,0) .
op highestVar : Substitution Nat -> Nat .
eq highestVar((none).Substitution,N) = N .
eq highestVar(V <- T ; Subst,N)
= highestVar(Subst,highestVar((T,V),N)) .
--- Renaming ------------------------------------------------------
op newVar : Nat TypeList -> TermList .
eq newVar(N,nil) = empty .
eq newVar(N,TP TPL) = (newVar*(N,TP),newVar(s(N),TPL)) .
op newVar* : Nat Type -> Variable .
eq newVar*(N,TP)
= qid("#" + string(N,10) + ":" + string(TP)) .
op simplifyVars : TermList -> TermList .
eq simplifyVars(TL) = TL << 0 < .
op _<<`(_`)< : TermList GTermList -> TermList .
eq X:TermList <<(TL:GTermList)<
= X:TermList << highestVar(TL:GTermList) + 1 < .
op _<<_ : TermList UnificationPair -> TermList .
eq TL << {Subst,N} = TL << Subst .
op _<<_ : TermList UnificationTriple -> TermList .
eq TL << {Subst,Subst',N} = TL << (Subst ; Subst') .
op _<<_ : Substitution UnificationTriple -> Substitution .
eq S:Substitution << {Subst,Subst',N} = S:Substitution << (Subst ; Subst') .
op _<<_< : TermList Nat -> TermList .
eq TL << N < = TL << (TL << { none, N } <) .
op _<<_< : TermList UnificationPair -> UnificationPair . ***Huge [memo] .
eq C << {S,N} < = {S,N} .
eq F[TL] << {S,N} < = TL << {S,N} < .
eq V << {S,N} <
= if not (dom S inVars V)
then {S ; V <- newVar(N,getType(V)), N + 1}
else {S,N}
fi .
eq (T,TL:NeTermList) << {S,N} <
= TL:NeTermList << (T << {S,N} < ) < .
eq empty << {S,N} <
= {S,N} .
endfm
fmod SUBSTITUTIONSET is
protecting SUBSTITUTION-HANDLING .
protecting META-LEVEL-MNPA .
protecting TERMSET .
protecting RENAMING .
sort SubstitutionSet NeSubstitutionSet .
subsort Substitution < NeSubstitutionSet < SubstitutionSet .
op empty : -> SubstitutionSet [ctor] .
op _|_ : SubstitutionSet SubstitutionSet -> SubstitutionSet
[ctor assoc comm id: empty format (d n d d)] .
op _|_ : NeSubstitutionSet SubstitutionSet -> NeSubstitutionSet
[ctor ditto] .
eq X:Substitution | X:Substitution = X:Substitution .
vars SS SS' : SubstitutionSet .
vars S S' Subst : Substitution .
vars T T' : Term .
vars TL TL' : TermList .
vars N N' : Nat .
var V : Variable .
op _<<_ : Substitution SubstitutionSet -> SubstitutionSet .
eq S << empty = empty .
ceq S << (S' | SS') = (S << S') | (S << SS') if SS' =/= empty .
op _..._ : SubstitutionSet [SubstitutionSet]
-> SubstitutionSet [strat (1) gather (e E)] .
eq empty ... SS':[SubstitutionSet] = empty .
eq (S | SS) ... SS':[SubstitutionSet]
= (S ...' SS':[SubstitutionSet])
|
(SS ... SS':[SubstitutionSet]) .
op _...'_ : Substitution SubstitutionSet -> SubstitutionSet .
eq S ...' empty
= empty .
eq S ...' (S' | SS')
= (S .. S')
|
(S ...' SS') .
op _|>_ : SubstitutionSet TermList -> SubstitutionSet .
eq (empty).SubstitutionSet |> TL = empty .
eq (S | SS:NeSubstitutionSet) |> TL
= (S |> TL) | (SS:NeSubstitutionSet |> TL) .
op _|>_ : SubstitutionSet Nat -> SubstitutionSet .
eq SS:NeSubstitutionSet |> N
= SS:NeSubstitutionSet |> (0,N) .
op _|>`(_,_`) : SubstitutionSet Nat Nat -> SubstitutionSet .
eq (empty).SubstitutionSet |> (N,N') = empty .
eq (S | SS:NeSubstitutionSet) |> (N,N')
= (S |> (N,N')) | (SS:NeSubstitutionSet |> (N,N')) .
op _|>`(_,_`) : Substitution Nat Nat -> Substitution .
eq none |> (N,N') = none .
eq ((V <- T') ; Subst) |> (N,N')
= if N <= highestVar(V) and highestVar(V) <= N'
then (V <- T')
else none
fi
; (Subst |> (N,N')) .
op filter_by!InVars_ : SubstitutionSet TermList -> SubstitutionSet .