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{- |
Module : $Header$
Description : Utilities for CspCASLProver related to the actual
construction of Isabelle theories.
Copyright : (c) Liam O'Reilly and Markus Roggenbach,
Swansea University 2009
License : similar to LGPL, see HetCATS/LICENSE.txt or LIZENZ.txt
Maintainer : csliam@swansea.ac.uk
Stability : provisional
Portability : portable
Utilities for CspCASLProver related to the actual construction of
Isabelle theories.
-}
module CspCASLProver.Utils
( addAlphabetType
, addAllBarTypes
, addAllChooseFunctions
, addAllCompareWithFun
, addAllIntegrationTheorems
, addEqFun
, addInstansanceOfEquiv
, addJustificationTheorems
, addPreAlphabet
, addProcMap
, addProcNameDatatype
) where
import CASL.AS_Basic_CASL (SORT, OpKind(..))
import qualified CASL.Sign as CASLSign
import qualified CASL.Inject as CASLInject
import Common.AS_Annotation (makeNamed, Named, SenAttr(..))
import qualified Common.Lib.Rel as Rel
import Comorphisms.CFOL2IsabelleHOL (IsaTheory)
import CspCASL.AS_CspCASL_Process (PROCESS_NAME)
import CspCASL.SignCSP (CspSign(..), ProcProfile(..), CspCASLSen(..)
, isProcessEq)
import CspCASLProver.Consts
import CspCASLProver.IsabelleUtils
import CspCASLProver.TransProcesses (transProcess)
import qualified Data.List as List
import qualified Data.Map as Map
import qualified Data.Set as Set
import Isabelle.IsaConsts
import Isabelle.IsaSign
-------------------------------------------------------------------------
-- Functions for adding the PreAlphabet datatype to an Isabelle theory --
-------------------------------------------------------------------------
-- | Add the PreAlphabet (built from a list of sorts) to an Isabelle
-- theory.
addPreAlphabet :: [SORT] -> IsaTheory -> IsaTheory
addPreAlphabet sortList isaTh =
let preAlphabetDomainEntry = mkPreAlphabetDE sortList
-- Add to the isabelle signature the new domain entry
in updateDomainTab preAlphabetDomainEntry isaTh
-- | Make a Domain Entry for the PreAlphabet from a list of sorts.
mkPreAlphabetDE :: [SORT] -> DomainEntry
mkPreAlphabetDE sorts =
(Type {typeId = preAlphabetS, typeSort = [isaTerm], typeArgs = []},
map (\sort ->
(mkVName (mkPreAlphabetConstructor sort),
[Type {typeId = convertSort2String sort,
typeSort = [isaTerm],
typeArgs = []}])
) sorts
)
----------------------------------------------------------------
-- Functions for adding the eq functions and the compare_with --
-- functions to an Isabelle theory --
----------------------------------------------------------------
-- | Add the eq function to an Isabelle theory using a list of sorts
addEqFun :: [SORT] -> IsaTheory -> IsaTheory
addEqFun sortList isaTh =
let eqtype = mkFunType preAlphabetType $ mkFunType preAlphabetType boolType
isaThWithConst = addConst eq_PreAlphabetS eqtype isaTh
mkEq sort =
let x = mkFree "x"
y = mkFree "y"
lhs = binEq_PreAlphabet lhs_a y
lhs_a = termAppl (conDouble (mkPreAlphabetConstructor sort)) x
rhs = termAppl rhs_a y
rhs_a = termAppl (conDouble (mkCompareWithFunName sort)) x
in binEq lhs rhs
eqs = map mkEq sortList
in addPrimRec eqs isaThWithConst
-- | Add all compare_with functions for a given list of sorts to an
-- Isabelle theory. We need to know about the casl signature (data
-- part of a CspCASL spec) so that we can pass it on to the
-- addCompareWithFun function
addAllCompareWithFun :: CASLSign.CASLSign -> IsaTheory -> IsaTheory
addAllCompareWithFun caslSign isaTh =
let sortList = Set.toList(CASLSign.sortSet caslSign)
in foldl (addCompareWithFun caslSign) isaTh sortList
-- | Add a single compare_with function for a given sort to an
-- Isabelle theory. We need to know about the casl signature (data
-- part of a CspCASL spec) to work out the RHS of the equations.
addCompareWithFun :: CASLSign.CASLSign -> IsaTheory -> SORT -> IsaTheory
addCompareWithFun caslSign isaTh sort =
let sortList = Set.toList(CASLSign.sortSet caslSign)
sortType = Type {typeId = convertSort2String sort, typeSort = [],
typeArgs =[]}
funName = mkCompareWithFunName sort
funType = mkFunType sortType $ mkFunType preAlphabetType boolType
isaThWithConst = addConst funName funType isaTh
sortSuperSet = CASLSign.supersortsOf sort caslSign
mkEq sort' =
let x = mkFree "x"
y = mkFree "y"
sort'Constructor = mkPreAlphabetConstructor sort'
lhs = termAppl lhs_a lhs_b
lhs_a = termAppl (conDouble funName) x
lhs_b = termAppl (conDouble (sort'Constructor)) y
sort'SuperSet =CASLSign.supersortsOf sort' caslSign
commonSuperList = Set.toList (Set.intersection
sortSuperSet
sort'SuperSet)
-- If there are no tests then the rhs=false else
-- combine all tests using binConj
rhs = if (null allTests)
then false
else foldr1 binConj allTests
-- The tests produce a list of equations for each test
-- Test 1 = test equality at: current sort vs current sort
-- Test 2 = test equality at: current sort vs super sorts
-- Test 3 = test equality at: super sorts vs current sort
-- Test 4 = test equality at: super sorts vs super sorts
allTests = concat [test1, test2, test3, test4]
test1 = if (sort == sort') then [binEq x y] else []
test2 = if (Set.member sort sort'SuperSet)
then [binEq x (mkInjection sort' sort y)]
else []
test3 = if (Set.member sort' sortSuperSet)
then [binEq (mkInjection sort sort' x) y]
else []
test4 = if (null commonSuperList)
then []
else map test4_atSort commonSuperList
test4_atSort s = binEq (mkInjection sort s x)
(mkInjection sort' s y)
in binEq lhs rhs
eqs = map mkEq sortList
in addPrimRec eqs isaThWithConst
--------------------------------------------------------
-- Functions for producing the Justification theorems --
--------------------------------------------------------
-- | Add all justification theorems to an Isabelle Theory. We need to
-- the CASL signature (from the datapart) and the PFOL Signature to
-- pass it on. We could recalculate the PFOL signature from the CASL
-- signature here, but we dont as it can be passed in. We need the
-- PFOL signature which is the data part CASL signature afetr
-- translation to PCFOL (i.e. without subsorting)
addJustificationTheorems :: CASLSign.CASLSign -> CASLSign.CASLSign ->
IsaTheory -> IsaTheory
addJustificationTheorems caslSign pfolSign isaTh =
let sortRel = Rel.toList(CASLSign.sortRel caslSign)
sorts = Set.toList(CASLSign.sortSet caslSign)
in addTransitivityTheorem sorts sortRel
$ addAllInjectivityTheorems pfolSign sorts sortRel
$ addAllDecompositionTheorem pfolSign sorts sortRel
$ addSymmetryTheorem sorts
$ addReflexivityTheorem
$ isaTh
-- | Add the reflexivity theorem and proof to an Isabelle Theory
addReflexivityTheorem :: IsaTheory -> IsaTheory
addReflexivityTheorem isaTh =
let name = reflexivityTheoremS
x = mkFree "x"
thmConds = []
thmConcl = binEq_PreAlphabet x x
proof' = IsaProof {
proof = [Apply (Induct x),
Apply Auto],
end = Done
}
in addTheoremWithProof name thmConds thmConcl proof' isaTh
-- | Add the symmetry theorem and proof to an Isabelle Theory. We need
-- to know the number of sorts, but instead we are given a list of
-- all sorts
addSymmetryTheorem :: [SORT] -> IsaTheory -> IsaTheory
addSymmetryTheorem sorts isaTh =
let numSorts = length(sorts)
name = symmetryTheoremS
x = mkFree "x"
y = mkFree "y"
thmConds = [binEq_PreAlphabet x y]
thmConcl = binEq_PreAlphabet y x
inductY = concat $ map (\i -> [Prefer (i*numSorts+1),
Apply (Induct y)])
[0..(numSorts-1)]
proof' = IsaProof {
proof = [Apply (Induct x)] ++ inductY ++ [Apply Auto],
end = Done
}
in addTheoremWithProof name thmConds thmConcl proof' isaTh
-- | Add all the decoposition theorems and proofs
addAllDecompositionTheorem :: CASLSign.CASLSign -> [SORT] -> [(SORT,SORT)] ->
IsaTheory -> IsaTheory
addAllDecompositionTheorem pfolSign sorts sortRel isaTh =
let tripples = [(s1,s2,s3) |
(s1,s2) <- sortRel, (s2',s3) <- sortRel, s2==s2']
in foldl (addDecompositionTheorem pfolSign sorts sortRel) isaTh tripples
-- | Add the decomposition theorem and proof which should be deduced
-- from the transitivity axioms from the translation CASL2PCFOL;
-- CASL2SubCFOL for a pair of injections represented as a tripple of
-- sorts. e.g. (S,T,U) means produce the lemma and proof for
-- inj_T_U(inj_S_T(x)) = inj_S_U(x). As a work around, we need to
-- know all sorts to pass them on.
addDecompositionTheorem :: CASLSign.CASLSign -> [SORT] -> [(SORT,SORT)] ->
IsaTheory -> (SORT,SORT,SORT) -> IsaTheory
addDecompositionTheorem pfolSign sorts sortRel isaTh (s1,s2,s3) =
let x = mkFree "x"
-- These 5 lines make use of currying
injOp_s1_s2 = mkInjection s1 s2
injOp_s2_s3 = mkInjection s2 s3
injOp_s1_s3 = mkInjection s1 s3
inj_s1_s2_s3_x = injOp_s2_s3 (injOp_s1_s2 x)
inj_s1_s3_x = injOp_s1_s3 x
definedOp_s1 = getDefinedOp sorts s1
definedOp_s3 = getDefinedOp sorts s3
collectionTransAx = getCollectionTransAx sortRel
collectionTotAx = getCollectionTotAx pfolSign
collectionNotDefBotAx = getCollectionNotDefBotAx sorts
name = getDecompositionThmName(s1, s2, s3)
conds = []
concl = binEq inj_s1_s2_s3_x inj_s1_s3_x
proof' = IsaProof [Apply(CaseTac (definedOp_s3 inj_s1_s2_s3_x)),
-- Case 1
Apply(SubgoalTac(definedOp_s1 x)),
Apply(Insert collectionTransAx),
Apply(Simp),
Apply(SimpAdd Nothing collectionTotAx),
-- Case 2
Apply(SubgoalTac(
termAppl notOp(definedOp_s3 inj_s1_s3_x))),
Apply(SimpAdd Nothing collectionNotDefBotAx),
Apply(SimpAdd Nothing collectionTotAx)]
Done
in addTheoremWithProof name conds concl proof' isaTh
-- | Add all the injectivity theorems and proofs
addAllInjectivityTheorems :: CASLSign.CASLSign -> [SORT] -> [(SORT,SORT)] ->
IsaTheory -> IsaTheory
addAllInjectivityTheorems pfolSign sorts sortRel isaTh =
foldl (addInjectivityTheorem pfolSign sorts sortRel) isaTh sortRel
-- | Add the injectivity theorem and proof which should be deduced
-- from the embedding_Injectivity axioms from the translation
-- CASL2PCFOL; CASL2SubCFOL for a single injection represented as a
-- pair of sorts. As a work around, we need to know all sorts to
-- pass them on
addInjectivityTheorem :: CASLSign.CASLSign -> [SORT] -> [(SORT,SORT)] ->
IsaTheory -> (SORT,SORT) -> IsaTheory
addInjectivityTheorem pfolSign sorts sortRel isaTh (s1,s2) =
let x = mkFree "x"
y = mkFree "y"
injX = mkInjection s1 s2 x
injY = mkInjection s1 s2 y
definedOp_s1 = getDefinedOp sorts s1
definedOp_s2 = getDefinedOp sorts s2
collectionEmbInjAx = getCollectionEmbInjAx sortRel
collectionTotAx = getCollectionTotAx pfolSign
collectionNotDefBotAx = getCollectionNotDefBotAx sorts
name = getInjectivityThmName(s1, s2)
conds = [binEq injX injY]
concl = binEq x y
proof' = IsaProof [Apply(CaseTac (definedOp_s2 injX)),
-- Case 1
Apply(SubgoalTac(definedOp_s1 x)),
Apply(SubgoalTac(definedOp_s1 y)),
Apply(Insert collectionEmbInjAx),
Apply(Simp),
Apply(SimpAdd Nothing collectionTotAx),
Apply(SimpAdd (Just No_asm_use) collectionTotAx),
-- Case 2
Apply(SubgoalTac(termAppl notOp (definedOp_s1 x))),
Apply(SubgoalTac(termAppl notOp(definedOp_s1 y))),
Apply(SimpAdd Nothing collectionNotDefBotAx),
Apply(SimpAdd Nothing collectionTotAx),
Apply(SimpAdd (Just No_asm_use) collectionTotAx)]
Done
in addTheoremWithProof name conds concl proof' isaTh
-- | Add the transitivity theorem and proof to an Isabelle Theory. We
-- need to know the number of sorts to know how much induction to
-- perfom and also the sub-sort relation to build the collection of
-- injectivity theorem names
addTransitivityTheorem :: [SORT] -> [(SORT,SORT)] -> IsaTheory -> IsaTheory
addTransitivityTheorem sorts sortRel isaTh =
let colInjThmNames = getColInjectivityThmName sortRel
colDecompThmNames = getColDecompositionThmName sortRel
numSorts = length(sorts)
name = transitivityS
x = mkFree "x"
y = mkFree "y"
z = mkFree "z"
thmConds = [binEq_PreAlphabet x y, binEq_PreAlphabet y z]
thmConcl = binEq_PreAlphabet x z
inductY = concat $ map (\i -> [Prefer (i*numSorts+1),
Apply (Induct y)])
[0..(numSorts-1)]
inductZ = concat $ map (\i -> [Prefer (i*numSorts+1),
Apply (Induct z)])
[0..((numSorts^(2::Int))-1)]
proof' = IsaProof {
proof = [Apply (Induct x)] ++
inductY ++
inductZ ++
[Apply (AutoSimpAdd Nothing
(colDecompThmNames ++ colInjThmNames))],
end = Done
}
in addTheoremWithProof name thmConds thmConcl proof' isaTh
--------------------------------------------------------------
-- Functions for producing instances of equivalence classes --
--------------------------------------------------------------
-- | Function to add preAlphabet as an equivalence relation to an
-- Isabelle theory
addInstansanceOfEquiv :: IsaTheory -> IsaTheory
addInstansanceOfEquiv isaTh =
let eqvSort = [IsaClass eqvTypeClassS]
eqvProof = IsaProof [] (By (Other "intro_classes"))
equivSort = [IsaClass equivTypeClassS]
equivProof = IsaProof [Apply (Other "intro_classes"),
Apply (Other ("unfold " ++ preAlphabetSimS
++ "_def")),
Apply (Other ("rule " ++ reflexivityTheoremS)),
Apply (Other ("rule " ++ transitivityS
++", auto")),
Apply (Other ("rule " ++ symmetryTheoremS
++ ", simp"))]
Done
x = mkFree "x"
y = mkFree "y"
defLhs = binEqvSim x y
defRhs = binEq_PreAlphabet x y
in addInstanceOf preAlphabetS [] equivSort equivProof
$ addDef preAlphabetSimS defLhs defRhs
$ addInstanceOf preAlphabetS [] eqvSort eqvProof
$ isaTh
-------------------------------------------------------------
-- Functions for producing the alphabet type --
-------------------------------------------------------------
-- | Function to add the Alphabet type (type synonym) to an Isabelle theory
addAlphabetType :: IsaTheory -> IsaTheory
addAlphabetType isaTh =
let isaTh_sign = fst isaTh
isaTh_sign_tsig = tsig isaTh_sign
myabbrs = abbrs isaTh_sign_tsig
abbrsNew = Map.insert alphabetS ([], preAlphabetQuotType) myabbrs
isaTh_sign_updated = isaTh_sign {
tsig = (isaTh_sign_tsig {abbrs =abbrsNew})
}
in (isaTh_sign_updated, snd isaTh)
-------------------------------------------------------------
-- Functions for producing the bar types --
-------------------------------------------------------------
-- | Function to add all the bar types to an Isabelle theory.
addAllBarTypes :: [SORT] -> IsaTheory -> IsaTheory
addAllBarTypes sorts isaTh = foldl addBarType isaTh sorts
-- | Function to add the bar types of a sort to an Isabelle theory.
addBarType :: IsaTheory -> SORT -> IsaTheory
addBarType isaTh sort =
let sortBarString = mkSortBarString sort
barType = Type {typeId = sortBarString, typeSort = [], typeArgs =[]}
isaTh_sign = fst isaTh
isaTh_sen = snd isaTh
x = mkFree "x"
y = mkFree "y"
rhs = termAppl (conDouble (mkPreAlphabetConstructor sort)) y
bin_eq = binEq x $ termAppl (conDouble classS ) rhs
exist_eq =termAppl (conDouble exS) (Abs y bin_eq NotCont)
subset = SubSet x alphabetType exist_eq
sen = TypeDef barType subset (IsaProof [] (By Auto))
namedSen = (makeNamed sortBarString sen)
in (isaTh_sign, isaTh_sen ++ [namedSen])
-------------------------------------------------------------
-- Functions for producing the choose functions --
-------------------------------------------------------------
-- | Add all choose functions for a given list of sorts to an Isabelle
-- theory.
addAllChooseFunctions :: [SORT] -> IsaTheory -> IsaTheory
addAllChooseFunctions sorts isaTh =
let isaTh' = foldl addChooseFunction isaTh sorts --add function and def
in foldl addChooseFunctionLemma isaTh' sorts --add theorem and proof
-- | Add a single choose function for a given sort to an Isabelle
-- theory. The following Isabelle code is produced by this function:
-- consts choose_Nat :: "Alphabet => Nat"
-- defs choose_Nat_def: "choose_Nat x == contents{y . class(C_Nat y) = x}"
addChooseFunction :: IsaTheory -> SORT -> IsaTheory
addChooseFunction isaTh sort =
let --constant
sortType = Type {typeId = convertSort2String sort,
typeSort = [],
typeArgs =[]}
chooseFunName = mkChooseFunName sort
chooseFunType = mkFunType alphabetType sortType
-- definition
x = mkFree "x"
y = mkFree "y"
contentsOp = termAppl (conDouble "contents")
chooseOp = termAppl (conDouble chooseFunName)
sortConsOp = termAppl (conDouble (mkPreAlphabetConstructor sort))
bin_eq = binEq (classOp $ sortConsOp y) x
subset = SubSet y sortType bin_eq
lhs = chooseOp x
rhs = contentsOp (Set subset)
in addDef chooseFunName lhs rhs -- Add defintion to theory
$ addConst chooseFunName chooseFunType isaTh -- Add constant to theory
-- | Add a single choose function lemma for a given sort to an
-- Isabelle theory. The following Isabelle code is produced by this
-- function: lemma "choose_Nat (class (C_Nat x)) = x". The proof is
-- also produced.
addChooseFunctionLemma :: IsaTheory -> SORT -> IsaTheory
addChooseFunctionLemma isaTh sort =
let sortType = Type {typeId = convertSort2String sort,
typeSort = [],
typeArgs =[]}
chooseFunName = mkChooseFunName sort
x = mkFree "x"
y = mkFree "y"
chooseOp = termAppl (conDouble chooseFunName)
sortConsOp = termAppl (conDouble (mkPreAlphabetConstructor sort))
-- theorm
subgoalTacTermLhsBinEq = binEq (classOp $ sortConsOp y)
(classOp $ sortConsOp x)
subgoalTacTermLhs = Set $ SubSet y sortType subgoalTacTermLhsBinEq
subgoalTacTermRhs = Set $ FixedSet [x]
subgoalTacTerm = binEq subgoalTacTermLhs subgoalTacTermRhs
thmConds = []
thmConcl = binEq (chooseOp $ classOp $ sortConsOp x) x
proof' = IsaProof [Apply (Other ("unfold " ++ chooseFunName ++ "_def")),
Apply (SubgoalTac subgoalTacTerm),
Apply(Simp),
Apply(SimpAdd Nothing [quotEqualityS]),
Apply(Other ("unfold "++ preAlphabetSimS
++ "_def")),
Apply(Auto)]
Done
in addTheoremWithProof chooseFunName thmConds thmConcl proof' isaTh
------------------------------------------------------
-- Functions for producing the integration theorems --
------------------------------------------------------
-- | Add all the integration theorems. We need to know all the sorts
-- to produce all the theorems. We need to know the CASL signature
-- of the data part to pass it on as an argument.
addAllIntegrationTheorems :: [SORT] -> CASLSign.CASLSign -> IsaTheory ->
IsaTheory
addAllIntegrationTheorems sorts caslSign isaTh =
let pairs = [(s1,s2) | s1 <- sorts, s2 <- sorts]
in foldl (addIntegrationTheorem_A caslSign) isaTh pairs
-- | Add Integration theorem A -- Compare to elements of the Alphabet.
-- We add the integration theorem based on the sorts of both
-- elements of the alphabet. We need to know the subsort relation to
-- find the highest common sort, but we pass in the CASL signature
-- for the data part.
addIntegrationTheorem_A :: CASLSign.CASLSign -> IsaTheory -> (SORT,SORT) ->
IsaTheory
addIntegrationTheorem_A caslSign isaTh (s1,s2) =
let sortRel = Rel.toList(CASLSign.sortRel caslSign)
s1SuperSet = CASLSign.supersortsOf s1 caslSign
s2SuperSet = CASLSign.supersortsOf s2 caslSign
commonSuperList = Set.toList (Set.intersection
(Set.insert s1 s1SuperSet)
(Set.insert s2 s2SuperSet))
x = mkFree "x"
y = mkFree "y"
s1ConsOp = termAppl (conDouble (mkPreAlphabetConstructor s1))
s2ConsOp = termAppl (conDouble (mkPreAlphabetConstructor s2))
rhs = binEq (classOp $ s1ConsOp x) (classOp $ s2ConsOp y)
lhs = if (null commonSuperList)
then false
else
-- BUG pick any common sort for now (this does hold
-- and is valid) we should pick the top most one.
let s' = head commonSuperList
in binEq (mkInjection s1 s' x) (mkInjection s2 s' y)
thmConds = []
thmConcl = binEq rhs lhs
-- theorem names for proof
colInjThmNames = getColInjectivityThmName sortRel
colDecompThmNames = getColDecompositionThmName sortRel
proof' = IsaProof [Apply (SimpAdd Nothing [quotEqualityS]),
Apply (Other ("unfold " ++ preAlphabetSimS
++ "_def")),
Apply (AutoSimpAdd Nothing
(colDecompThmNames ++ colInjThmNames))]
Done
in addTheoremWithProof "IntegrationTheorem_A"
thmConds thmConcl proof' isaTh
--------------------------------------------------------------------------
-- Functions for adding the process name datatype to an Isabelle theory --
--------------------------------------------------------------------------
-- | Add process name datatype which has a constructor for each
-- process name (along with the arguments for the process) in the
-- CspCASL Signature to an Isabelle theory
addProcNameDatatype :: CspSign -> IsaTheory -> IsaTheory
addProcNameDatatype cspSign isaTh =
let -- Create a list of pairs of process names and thier profiles
procSetList = Map.toList (procSet cspSign)
procNameDomainEntry = mkProcNameDE procSetList
in updateDomainTab procNameDomainEntry isaTh
-- | Make a proccess name Domain Entry from a list of a Process name and profile
-- pair. This creates a data type for the process names.
mkProcNameDE :: [(PROCESS_NAME, ProcProfile)] -> DomainEntry
mkProcNameDE processes =
let -- The a list of pairs of constructors and their arguments
constructors = map mk_cons processes
-- Take a proccess name and its argument sorts (also its
-- commAlpha - thrown away) and make a pair representing the
-- constructor and the argument types
mk_cons (procName, (ProcProfile sorts _)) =
(mkVName (mkProcNameConstructor procName), map sortToTyp sorts)
-- Turn a sort in to a Typ suitable for the domain entry The
-- processes need to have arguments of the bar variants of
-- the sorts not the original sorts
sortToTyp sort = Type {typeId = mkSortBarString sort,
typeSort = [isaTerm],
typeArgs = []}
in
(procNameType, constructors)
-------------------------------------------------------------------------
-- Functions adding the process map function to an Isabelle theory --
-------------------------------------------------------------------------
-- | Add the function procMap to an Isabelle theory. This function
-- maps process names to real processes build using the same names
-- and the alphabet i.e., ProcName => (ProcName, Alphabet) proc. We
-- need to know the CspCASL sentences and the casl signature (data
-- part)
addProcMap :: [Named CspCASLSen] -> CASLSign.Sign () () -> IsaTheory ->
IsaTheory
addProcMap namedSens caslSign isaTh =
let
-- Extend Isabelle theory with additional constant
isaThWithConst = addConst procMapS procMapType isaTh
-- Get the plain sentences from the named senetences
sens = map (\namedsen -> sentence namedsen) namedSens
-- Filter so we only have proccess equations and no CASL senetences
processEqs = filter isProcessEq sens
-- the term representing the procMap that tajes a term as a
-- parameter
procMapTerm = termAppl (conDouble procMapS)
-- Make a single equation for the primrec from a process equation
-- BUG HERE - this next part is not right - underscore is bad
mkEq (ProcessEq procName _ _ proc) =
let -- Make the name (string) for this process
procNameString = convertProcessName2String procName
-- Change the name to a term
procNameTerm = conDouble procNameString
-- Turn the list of variables into a list of Isabelle
-- free variables
varTerms = [] -- BUG - should be somehting like map (\x -> mkFree (show x)) vars
-- Make a lhs term built of termAppl applied to the
-- proccess name and the variables
lhs = procMapTerm (foldl termAppl (procNameTerm) varTerms)
rhs = transProcess caslSign proc
in binEq lhs rhs
-- Build equations for primrec using process equations
eqs = map mkEq processEqs
in addPrimRec eqs isaThWithConst
----------------------------------------------
-- Function to help keep strings consistent --
----------------------------------------------
-- | Return the list of strings of all gn_totality axiom names. This
-- function is not implemented in a satisfactory way.
getCollectionTotAx :: CASLSign.CASLSign -> [String]
getCollectionTotAx pfolSign =
let opList = Map.toList $ CASLSign.opMap pfolSign
-- This filter is not quite right
totFilter (_,setOpType) = let listOpType = Set.toList setOpType
in CASLSign.opKind (head listOpType) == Total
totList = filter totFilter opList
mkTotAxName = (\i -> "ga_totality"
++ (if (i==0)
then ""
else ("_" ++ show i))
)
in map mkTotAxName [0 .. (length(totList) - 1)]
-- | Return the name of the definedness function for a sort. We need
-- to know all sorts to perform this workaround
-- This function is not implemented in a satisfactory way
getDefinedName :: [SORT] -> SORT -> String
getDefinedName sorts s =
let index = List.elemIndex s sorts
str = case index of
Nothing -> ""
Just i -> show (i + 1)
in "gn_definedX" ++ str
-- | Return the name of the injection as it is used in the alternative
-- syntax of the injection from one sort to another.
-- This function is not implemented in a satisfactory way
getInjectionName :: SORT -> SORT -> String
getInjectionName s s' =
CASLSign.opArgs = [s],
CASLSign.opRes = s'})
injName = show $ CASLInject.uniqueInjName t
in injName
-- | Return the injection name of the injection from one sort to another
-- This function is not implemented in a satisfactory way
getDefinedOp :: [SORT] -> SORT -> Term -> Term
getDefinedOp sorts s t =
termAppl (con $ VName (getDefinedName sorts s) $ Nothing) t
-- | Return the term representing the injection of a term from one sort to another
-- note: the term is returned if both sorts are the same
-- This function is not implemented in a satisfactory way
mkInjection :: SORT -> SORT -> Term -> Term
mkInjection s s' t =
let injName = getInjectionName s s'
replace string c s1 = concat (map (\x -> if x==c
then s1
else [x]) string)
injOp = Const {
termName= VName {
new = ("X_" ++ injName),
altSyn = Just (AltSyntax ((replace injName '_' "'_")
++ "/'(_')") [3] 999)
},
termType = Hide {
typ = Type {
typeId ="dummy",
typeSort = [IsaClass "type"],
typeArgs = []
},
kon = NA,
arit= Nothing
}
}
in if s == s'
then t
else termAppl injOp t
-- | Return the list of string of all embedding_injectivity axioms
-- produced by the translation CASL2PCFOL; CASL2SubCFOL. This
-- function is not implemented in a satisfactory way.
getCollectionEmbInjAx :: [(SORT,SORT)] -> [String]
getCollectionEmbInjAx sortRel =
let mkEmbInjAxName = (\i -> "ga_embedding_injectivity"
++ (if (i==0)
then ""
else ("_" ++ show i))
)
in map mkEmbInjAxName [0 .. (length(sortRel) - 1)]
-- This function is not implemented in a satisfactory way
-- Return the list of strings of all ga_notDefBottom axioms
getCollectionNotDefBotAx :: [SORT] -> [String]
getCollectionNotDefBotAx sorts =
let mkNotDefBotAxName = (\i -> "ga_notDefBottom"
++ (if (i==0)
then ""
else ("_" ++ show i)))
in map mkNotDefBotAxName [0 .. (length(sorts) - 1)]
-- This function is not implemented in a satisfactory way
-- Return the list of string of all decomposition theorem names that we generate
getColDecompositionThmName :: [(SORT,SORT)] -> [String]
getColDecompositionThmName sortRel =
let tripples = [(s1,s2,s3) |
(s1,s2) <- sortRel, (s2',s3) <- sortRel, s2==s2']
in map getDecompositionThmName tripples
-- Produce the theorem name of the decomposition theorem that we produce
getDecompositionThmName :: (SORT,SORT,SORT) -> String
getDecompositionThmName (s, s', s'') =
"decomposition_" ++ (convertSort2String s) ++ "_" ++ (convertSort2String s')
++ "_" ++ (convertSort2String s'')
-- This function is not implemented in a satisfactory way
-- Return the list of strings of the injectivity theorem names
-- that we generate
getColInjectivityThmName :: [(SORT,SORT)] -> [String]
getColInjectivityThmName sortRel = map getInjectivityThmName sortRel
-- Produce the theorem name of the injectivity theorem that we produce
getInjectivityThmName :: (SORT,SORT) -> String
getInjectivityThmName (s, s') =
"injectivity_" ++ (convertSort2String s) ++ "_" ++ (convertSort2String s')
-- This function is not implemented in a satisfactory way. Return the
-- list of strings of all transitivity axioms produced by the
-- translation CASL2PCFOL; CASL2SubCFOL
getCollectionTransAx :: [(SORT,SORT)] -> [String]
getCollectionTransAx sortRel =
let tripples = [(s1,s2,s3) |
(s1,s2) <- sortRel, (s2',s3) <- sortRel, s2==s2']
mkEmbInjAxName = (\i -> "ga_transitivity"
++ (if (i==0)
then ""
else ("_" ++ show i))
)
in map mkEmbInjAxName [0 .. (length(tripples) - 1)]