{- |

Module : $Header: /repository/HetCATS/Comorphisms/Hs2HOLCFaux.hs,v 1.26 2007/05/28 09:05:49 paolot Exp $

Copyright : (c) Paolo Torrini and Till Mossakowski and Uni Bremen 2004-2005

License : Asimilar to LGPL, see HetCATS/LICENSE.txt or LIZENZ.txt

Maintainer : paolot@informatik.uni-bremen.de

Stability : provisional

Portability : non-portable (depends on programatica using MPTC)

auxiliary functions for the embedding comorphism from Haskell to Isabelle

-}

module Comorphisms.Hs2HOLCFaux

( PrDecl

, aweLits

, mthEq

, removeEL

, extAxType

, extTBody

, fixMRec

, newConstTab

, getTermName

, extRightH

, ExpRole(..)

, ISign

, IsaSort

, IsaType

, IsaPattern

, IsaTerm

, IsaName(..)

, xDummy

, termMAbs

, termMAppl

, termBAppl

, PrExp

, PrPat

, renVars

, remove_duplicates

, HsType

, HsScheme

, HsId

, listEnum

, getInstClass

, getInstType

, repVarClass

, constrVarClass

, getLitName

, transTN

, transPath

, showIsaS

, funFliftbin

, funFlift2

, VaMap

, AConstTab

, liftMapByListD

, nothingFiOut

, IsaTypeInsts

, IsaVT(..)

, TyMap

, liftMapByList

, HsTypeInfo

, HsInstance

, HsInstances

, extClassInfo

, extAbbrsInfo

, groupInst

, getMainInstType

, prepInst

, checkTyCons

, getDepDoms

, getDomType

, getFieldTypes

, isCont

, replaceTyVar

, varDouble

) where

import Data.List

import qualified Data.Map as Map

import Common.AS_Annotation

-- Haskell (Programatica)

import SourceNames

import TiTypes

import TiKinds

import TiInstanceDB -- as TiInst

import PNT

import PosName

import UniqueNames

import SyntaxRec

import TiPropDecorate

import PropSyntaxStruct as HsName

import TiDecorate

-- Isabelle

import Isabelle.IsaSign as IsaSign

import Isabelle.IsaConsts as IsaConsts

import Isabelle.Translate as Translate

import Debug.Trace

------------------------------- TYPE synonyms ------------------------------

------------------ Haskell -------------------------------------------------

type HsInstance = TiInstanceDB.Instance PNT

type HsInstances = [TiInstanceDB.Instance PNT]

type HsPred = TiTypes.Pred PNT

type HsType = TiTypes.Type PNT -- same as HsPred

type HsClass = TiTypes.Type PNT

type HsScheme = TiTypes.Scheme PNT

type HsId = HsIdentI PNT

type HsTypeInfo = TiTypes.TypeInfo PNT

type PrDecl = TiPropDecorate.TiDecl PNT

type PrExp = TiPropDecorate.TiExp PNT

type PrPat = TiDecorate.TiPat PNT

type HId i = HsIdentI i

type VaMap = Map.Map HsId HsScheme

type TyMap = Map.Map HsId (Kind, HsTypeInfo)

------------------ Isabelle ------------------------------------------------

type ISign = IsaSign.Sign

type IsaSort = IsaSign.Sort

type IsaType = IsaSign.Typ

type IsaTerm = IsaSign.Term

type IsaPattern = IsaSign.Term

type IsaTypeInsts = (TName, [(IsaClass, [(IsaType, [IsaClass])])])

-------------------------- list functions ----------------------------------

removeEL :: [[a]] -> [[a]]

removeEL = filter (not . null)

remove_duplicates :: Eq a => [a] -> [a]

remove_duplicates = nub . reverse

listEnum :: [a] -> [(a, Int)]

listEnum l = zip l [1..]

------------------------------- filters -----------------------------------

nothingFiOut :: [(a, (Maybe b, c))] -> [(a, (b, c))]

nothingFiOut ls = [(x, (y, w)) | (x, (Just y, w)) <- ls]

------------------------------ lifting function ---------------------------

liftMapByList :: (x -> [(a, b)]) -> ([(c, d)] -> y)

-> (a -> c) -> (b -> d) -> x -> y

liftMapByList ma mb h k f = mb [(h a, k b) | (a, b) <- ma f]

liftMapByListD :: (x -> [a]) -> ([c] -> y) -> (a -> b1)

-> (a -> b2) -> ([(b1, b2)] -> [c]) -> x -> y

liftMapByListD l1 l2 h k g f = l2 $ g [ (h a, k a) | a <- l1 f]

------------------------ generic checking of mutual dependencies ----------

abGetDep :: Eq a => (a -> a -> Bool) -> [[a]] -> [[a]]

abGetDep f ls = case ls of

x:xs ->

remove_duplicates $

removeEL (map remove_duplicates (checkDep (abCheckDep (mutRel f))

(xs) [x] []))

[] -> []

{- called to check whether, given two lists of elements, one depends

on the other. -}

abCheckDep :: (a -> a -> Bool) -> [a] -> [a] -> Bool

abCheckDep f as bs = any (\x -> any (f x) bs) as

checkDep :: ([x] -> [x] -> Bool) -> [[x]] -> [[x]] -> [[x]] -> [[x]]

checkDep f ls ms cs = case ls of

a:as -> case ms of

b:bs ->

if (f a b) then checkDep f ((a ++ b):as) bs cs else

checkDep f (a:as) bs (b:cs)

[] -> checkDep f as (a:cs) []

[] -> ms

-- mutual dependence

mutRel :: (a -> a -> Bool) -> a -> a -> Bool

mutRel f x y = f x y && f y x

depOn :: (a -> b -> Bool) -> (c -> a) -> (c -> [b]) -> c -> c -> Bool

depOn f g h x y = any (f (g x)) (h y)

-------------------- HASKELL representation -------------------------------

----------------------- check functions -----------------------------------

checkTyCons :: HsId -> Bool

checkTyCons d = case d of

HsCon _ -> True

_ -> False

---------------------------- get functions -------------------------------

----- ------------- getting info from Haskell types ----------------------

getLitName :: HsType -> PNT

getLitName (Typ t) = case t of

HsTyVar x -> x

HsTyCon x -> x

_ -> error "Hs2HOLCFaux.getLitName"

------------------ getting class and type ouf of predicate --------------

getInstType :: HsPred -> HsType

getInstType x = case x of (Typ (HsTyApp _ t)) -> t

_ -> trace ("\n TYPE: " ++ show x) $

error "Hs2HOLCFaux.getInstType"

getInstClass :: HsPred -> HsType

getInstClass x = case x of (Typ (HsTyApp c _)) -> c

_ -> trace ("\n CLASS: " ++ show x) $

error "Hs2HOLCFaux.getInstClass"

----------------------- getting class information -----------------------

extClassInfo :: HsTypeInfo -> [HsClass]

extClassInfo p = case p of

TiTypes.Class a _ _ _ -> map getInstClass a

_ -> error "Hs2HOLCFaux.extClassInfo"

--------------------------- getting info on type syns -------------------

extAbbrsInfo :: HsTypeInfo -> ([PNT], HsType)

extAbbrsInfo p = case p of

TiTypes.Synonym ls t -> (ls, t)

_ -> error "Hs2HOLCFaux.extAbbrsInfo"

----------- get arity information from Haskell instances ------------

getInstPrems :: HsInstance -> [HsPred]

getInstPrems (_, IE _ _ ps) = ps

getMainInstType :: HsInstance -> HsType

getMainInstType (i, _) = getInstType i

getMainInstClass :: HsInstance -> HsClass

getMainInstClass (i, _) = getInstClass i

prepInst :: HsInstance -> (HsClass, [(HsType, [HsClass])])

prepInst i = (getMainInstClass i, prepInst1 i)

prepInst1 :: HsInstance -> [(HsType, [HsClass])]

prepInst1 i =

[(x, [getInstClass y | y <-

getInstPrems i, showIsaHsTypeString (getInstType y)

== showIsaHsTypeString x])

| x <- remove_duplicates $ map getInstType (getInstPrems i)]

----------------------- ISABELLE representation ---------------------------

data ExpRole = FunDef | InstDef -- no PLogic yet

deriving (Ord,Eq,Show)

----------------------------- constants -----------------------------------

xDummy :: IsaTerm

xDummy = conDouble "dummy"

holEq :: IsaTerm -> IsaTerm -> IsaTerm

holEq t1 t2 = termMAppl NotCont (con eqV) [t1, t2]

getTermName :: Term -> Maybe String

getTermName a = case a of

Const x _ -> Just $ new x

Free x -> Just $ new x

_ -> Nothing -- "_"

------------------------ Haskell names --------------------------------

-- method names

mthEq,mthOrd,mthEnum,mthBounded,mthNum,mthIntegral :: [String]

mthMonad,mthFunctor,mthAll,aweLits,mthFractional :: [String]

mthEq = ["==", "/="]

mthOrd = ["compare", "<", "<=", ">", ">=", "max", "min"]

mthEnum = ["succ", "pred", "toEnum", "fromEnum", "enumFrom",

"enumFromThen", "enumFromTo", "enumFromThenTo"]

mthBounded = ["minBound", "maxBound"]

mthNum = ["+", "-", "*", "negate", "abs", "signum", "fromInteger"]

mthIntegral = ["quot", "rem", "div", "mod", "quotRem", "divMod", "toInteger"]

mthMonad = ["return", ">>=", ">>", "fail"]

mthFunctor = ["fmap"]

mthFractional = ["/","recip","fromRational"]

mthAll = mthEq ++ mthOrd ++ mthEnum ++ mthNum

++ mthIntegral ++ mthMonad ++ mthFunctor ++ mthBounded

-- why not mthFractional, too??

aweLits = mthMonad ++ mthFunctor

nameListA, nameListB, nameListC, nameListD :: [String]

nameListE, nameListF, nameListH :: [String]

-- Special translation - operators

nameListA = ["&&", "||", "==", "/=", "<", "<=", ">", ">=", "+",

"*", "-", "^",

"^^", "++", "!!", "/", ".", "$", "$!", ">>=", ">>"]

-- dual translation - constructors

nameListB = ["()","(,)","True","False",":","[]","Just","Nothing"]

-- dual translation operators

nameListC = ["primError","return"]

-- other constructors

nameListD = ["ET","EQ","GT","Left","Right"]

-- Prelude functions

nameListE = -- map (\x -> x ++ "'")

["not","min","max","negate","abs","signum",

"fromInteger","succ","pred","fromEnum","toEnum","enumFrom",

"enumFromThen","enumFromTo","enumFromThenTo",

"minBound","maxBound","toRational","quot","rem","div","mod",

"quotRem","divMod","toInteger","otherwise","either", "maybe",

"fst","snd","id","curry","uncurry","const","until","asTypeOf",

"odd","even","subtract","flip","gcd","lcm","seq","error",

"undefined","fromRational","recip","powAux","powBux"]

-- Prelude list functions

nameListF = -- map (\x -> x ++ "'")

["map","filter","concat","concatMap","head","last","tail",

"init","null","length","foldl","foldl1","scanl","scanl1",

"foldr","foldr1","scanr","scanr1","iterate","repeat",

"replicate","cycle","take","drop","splitAt","takeWhile",

"dropWhile","span","break","lines","words","unlines",

"unwords","reverse","and","or","any","all","elem","notElem",

"lookup","sum","product","maximum","minimum","zip","zip3",

"zipWith","zipWith3","unzip","unzip3"]

-- hidden

nameListH = ["flip","&&","||",conj,disj]

primedS :: String -> String

primedS s = s ++ "'"

trOSym :: String -> String

trOSym s = case s of

"&&" -> "conj"

"||" -> "disj"

"==" -> "eq"

"/=" -> "neq"

"<" -> "less"

"<=" -> "leq"

">" -> "more"

">=" -> "meq"

"+" -> "add"

"*" -> "prod"

"-" -> "diff"

"^" -> "pow"

"^^" -> "fpow"

"++" -> "bconcat"

"!!" -> "nth"

"/" -> "frac"

"." -> "comp"

"$" -> "apply"

"$!" -> "sapply"

">>=" -> "mbind"

">>" -> "mseq"

_ -> error "Hs2HOLCFaux,trOSym"

transPrelude :: (String -> String) -> String -> String

transPrelude f s =

if elem s (nameListB ++ nameListC ++ nameListD) then s

else if elem s (nameListE ++ nameListF) then (s++"H")

else if elem s nameListA then (trOSym s ++ "H")

else if take 9 s == "default__"

then transPrelude f (drop 9 s) ++ "I"

else if take 3 s == "$--"

then transPrelude f (drop 3 s) ++ "I"

else let ns = init s

in if elem ns nameListA && last s == '#'

then (trOSym ns ++

(if elem ns (mthAll ++ nameListH)

then "H" else "U"))

else if elem s (map primedS (nameListE ++ nameListF))

then (ns ++ (if elem ns (mthAll ++ nameListH)

then "H" else "U"))

else f s

---------------------------- Name translation ----------------------------

-- Translating to strings compatible with Isabelle

class IsaName a where

showIsaName :: a -> String

showIsaString :: a -> String

showIsaS :: String -> String

showIsaS s = case s of

_ -> transPrelude (transConstStringT HOLCF_thy) s

instance IsaName String where

showIsaName x = showIsaS x

showIsaString x = x

showIsaHsN :: Show a => (String -> a) -> HsName.HsName -> a

showIsaHsN f t = case t of

Qual _ y -> f y

UnQual w -> f w

instance IsaName PNT.PId where

showIsaName (PN x _) = showIsaS x

showIsaString (PN x _) = x

instance IsaName HsName.HsName where

showIsaName = showIsaHsN showIsaS

showIsaString = showIsaHsN id

instance IsaName PosName.HsName where

showIsaName (SN x _) = showIsaName x

showIsaString (SN x _) = showIsaString x

instance IsaName PNT.PName where

showIsaName (PN x _) = showIsaName x

showIsaString (PN x _) = showIsaString x

instance IsaName PNT where

showIsaName (PNT x _ _) = showIsaName x

showIsaString (PNT x _ _) = showIsaString x

instance IsaName a => IsaName (HId a) where

showIsaName t = case t of

HsVar x -> showIsaName x

HsCon x -> showIsaName x

showIsaString t = case t of

HsVar x -> showIsaString x

HsCon x -> showIsaString x

showIsaHsTypeString :: HsType -> String

showIsaHsTypeString (Typ t) = case t of

HsTyFun _ _ -> "Fun"

HsTyApp _ _ -> "App"

HsTyVar x -> showIsaString x

HsTyCon x -> showIsaString x

HsTyForall _ _ x -> showIsaHsTypeString x

-------- auxiliary name functions depending on IsaSign ---------------------

joinNames :: [String] -> String

joinNames = concatMap (++ "_X")

isCont :: Continuity -> Bool

isCont x = x == IsCont True || x == IsCont False

transTN :: Continuity -> String -> String -> String

transTN c s1 s2 = let d = transPath s1 s2

ic = isCont c

in if s1 == "Prelude" then case s2 of

"()" -> "unitT"

"Bool" -> if ic then "lBool"

else "bool"

"Int" -> "intT"

"Integer" -> "integerT"

"Char" -> "charT"

"[]" -> if ic then "llist"

else "list"

"Either" -> if ic then "lEither"

else "either"

"Ordering" -> "lOrdering"

"String" -> if ic then "lString"

else "string"

"Maybe" -> if ic then "lMaybe"

else "option"

"(,)" -> if ic then "lprod" else "*"

"Rational" -> if ic then "ratT" else "Rat"

_ -> d

else d

transPath :: String -> String -> String

transPath s1 s2 = showIsaName s1 ++ "_" ++ showIsaName s2

---------------------- DATATYPES -------------------------------------------

-------------------- getting mutually recursive domains in Isabelle --------

getDepDoms :: [[IsaSign.DomainEntry]] -> IsaSign.DomainTab

getDepDoms ls = ordDoms $ abGetDep deDepOn ls

ordDoms :: [[IsaSign.DomainEntry]] -> IsaSign.DomainTab

ordDoms ls = quickSort (orLLift deDepOn) ls

orLLift :: (a -> a -> Bool) -> [a] -> [a] -> Bool

orLLift f as bs = case as of

[] -> False

x:xs -> if genOr (f x) bs == True then True

else (orLLift f xs bs)

genOr :: (a -> Bool) -> [a] -> Bool

genOr f ys = case ys of

[] -> False

x:xs -> if (f x) then True

else (genOr f xs)

deDepOn :: DomainEntry -> DomainEntry -> Bool

deDepOn x y = depOn subTypForm fst (concatMap snd . snd) x y

subTypForm :: Typ -> Typ -> Bool

subTypForm t1 t2 = case t2 of

IsaSign.Type a b cs ->

if a == IsaSign.typeId t1 &&

b == IsaSign.typeSort t1 then True

else any (subTypForm t1) cs

_ -> False

--------------------- getting info about domaintab -------------------------

type AConstTab = Map.Map VName (Typ,IsaVT)

data IsaVT = IsaConst | IsaVal deriving (Eq, Show)

getDomType :: AConstTab -> VName -> IsaType

getDomType ctab c = maybe (error "Hs2HOLCFaux.getDomType")

(getHeadType . fst) $ Map.lookup c ctab

isFunArrow :: String -> Bool

isFunArrow name = elem name [funS, cFunS, lFunS]

getHeadType :: IsaType -> IsaType

getHeadType t = case t of

IsaSign.Type name _ [_, t2] | isFunArrow name -> getHeadType t2

_ -> t

getFieldTypes :: AConstTab -> VName -> [IsaType]

getFieldTypes ctab c = maybe [] (argTypes . fst) $ Map.lookup c ctab

argTypes :: IsaType -> [IsaType]

argTypes a = case a of

IsaSign.Type name _ [b, c] | isFunArrow name -> b : argTypes c

_ -> []

------------------------- Instances ----------------------------------------

groupInst :: [IsaTypeInsts] -> [IsaTypeInsts]

groupInst db =

remove_duplicates [(y,

remove_duplicates $ concat

[b | (a, b) <- db, a == y]) | (y, _) <- db]

----------------------- TERMS ----------------------------------------------

----- lifting, tuples, multiple abstractions and applications, fixpoints ---

funFliftbin :: Term -> Term

funFliftbin f = termMAppl NotCont (conDouble lliftbinS) [f]

funFlift2 :: Term -> Term

funFlift2 f = termMAppl NotCont (conDouble flift2S) [f]

varDouble :: String -> Term

varDouble = Free . mkVName

termMAbs :: Continuity -> [Term] -> Term -> Term

termMAbs c ts t =

case ts of

[] -> t

v:vs -> if isDicConst v then (termMAbs c vs t) else

IsaSign.Abs v (termMAbs c vs t) c

termMAppl :: Continuity -> Term -> [Term] -> Term

termMAppl c t ts =

let prelTest vn = any (\x -> isPrefixOf x $ IsaSign.orig vn)

[ "inst__Prelude_"

, "derived__Prelude_"]

in case (t, ts) of

(Const vn _, [a]) | isDicConst t || prelTest vn -> a

(_, []) -> t

(Const _ p, v : vs) -> case v of

Const vn _ | isDicConst v || prelTest vn -> termMAppl c t vs

_ -> case (kon p,c) of

(TCon,IsCont True) -> let ee = IsCont False

in termMAppl ee (App t v ee) vs

_ -> termMAppl c (App t v c) vs

(_, v : vs) -> case v of

Const vn _ | isDicConst v || prelTest vn -> termMAppl c t vs

_ -> termMAppl c (App t v c) vs

termBAppl :: Continuity -> Term -> Term -> Term -> Term

termBAppl c t1 t2 t3 = termMAppl c t1 [t2,t3]

----------------------- connectives ---------------------------------------

tupleSelector :: Int -> Int -> Term -> Continuity -> Term

tupleSelector mx n t c

| mx < 2 = error "Hs2HOLCFaux.tupleSelector1"

| n == 0 = error "Hs2HOLCFaux.tupleSelector2"

| mx < n = error "Hs2HOLCFaux.tupleSelector3"

| n == mx = tupleSelect (n - 1) t c

| True = termMAppl c (fstPT c)

$ [tupleSelect (n - 1) t c]

tupleSelect :: Int -> Term -> Continuity -> Term

tupleSelect n t c = case n of

0 -> t

_ -> tupleSelect (n - 1)

(termMAppl c (sndPT c) [t]) c

--------------------------------- term filters ----------------------------

isDicConst :: Term -> Bool

isDicConst t = case t of

Const vn _ | IsaSign.orig vn == "DIC" -> True

Free vn | IsaSign.orig vn == "DIC" -> True

_ -> False

constFilter :: Term -> [Term]

constFilter t = case t of

IsaSign.Const _ _ -> [t]

IsaSign.Abs _ x _ -> constFilter x

IsaSign.App x y _ -> concatMap constFilter [x, y]

IsaSign.If x y z _ -> concatMap constFilter [x, y, z]

IsaSign.Case x ys -> concatMap constFilter $ x : map snd ys

IsaSign.Let xs y -> concatMap constFilter $ y : map snd xs

IsaSign.IsaEq x y -> concatMap constFilter [x, y]

IsaSign.Tuplex xs _ -> concatMap constFilter xs

_ -> [t]

elPos :: [Term] -> Term -> Maybe Int

elPos ls x = fmap (+ 1) $ findIndex (constEq x) ls

------------------ subterm extraction -------------------------------------

extFBody :: Term -> (Term, [Term])

extFBody t' = extFB t' []

where

extFB t as = case t of

IsaSign.Abs x b _ -> extFB b (x : as)

_ -> (t, reverse as)

extTBody :: Term -> (Term, [Term])

extTBody t' = extTB t' []

where

extTB t as = case t of

IsaSign.App a x _ -> extTB a (x : as)

_ -> (t, reverse as)

------------------ eliminating case expressions ---------------------------

destCaseS :: Continuity -> IsaTerm -> IsaTerm -> [IsaTerm] -- t is def rh

destCaseS c d t =

[holEq (termMAppl c d xs) y | (xs,y) <- destCaseU (extFBody t,[])]

destCaseU :: ((IsaTerm,[IsaPattern]),[IsaPattern]) -> [([IsaPattern],IsaTerm)]

destCaseU ((t,rs),ks) = case (t,rs) of

(Case v ls, vv : vs) -> if v == vv

then [(ks ++ [l], termMAbs NotCont vs m) | (l,m) <- ls]

else destCaseU ((t,vs), ks ++ [vv])

_ -> error "Hs2HOLCFaux.destCaseU"

destCase :: IsaTerm -> (VName -> VName) -> [(IsaPattern,IsaTerm)]

destCase t f = let w = extFBody t in case w of

(Case v ls, _ : vs) -> case v of

Free n ->

[(renVars (Free (f n)) [l] l, -- repl. l if l is a var.

renVars (Free (f n))

[l] (termMAbs NotCont vs m)) | (l, m) <- ls]

_ -> [(l,termMAbs NotCont vs m) | (l, m) <- ls]

_ -> error "Hs2HOLCFaux.destCase"

--------------------------- equivalence on terms ---------------------------

constEq :: Term -> Term -> Bool

constEq t1 t2 = case (t1,t2) of

(Const m x, Const n y) -> n == m && typEq (typ x) (typ y)

_ -> False

simTerms :: Term -> Term -> Bool

simTerms t1 t2 = case (t1, t2) of

(IsaSign.Const x w, IsaSign.Const y z) ->

x == y && typSim (typ w) (typ z)

(IsaSign.Free _, IsaSign.Free _) -> True

(IsaSign.Abs _ _ c, IsaSign.Abs _ _ d) -> c == d

(If _ _ _ c, If _ _ _ d) -> c == d

(Case _ _, Case _ _) -> True

(Let _ _, Let _ _) -> True

(IsaEq _ _, IsaEq _ _) -> True

(Tuplex _ _, Tuplex _ _) -> True

_ -> False

-------------------- replacement functions -------------------------------

{- in term t, replaces variable f for variables in ls -}

renVars :: Term -> [Term] -> Term -> Term

renVars f ls t = case t of

IsaSign.Free _ -> if elem t ls then f else t

IsaSign.Abs v x c -> IsaSign.Abs v (renVars f ls x) c

IsaSign.App x y c -> IsaSign.App (renVars f ls x) (renVars f ls y) c

IsaSign.If x y z c ->

IsaSign.If (renVars f ls x) (renVars f ls y) (renVars f ls z) c

IsaSign.Case x ys ->

IsaSign.Case (renVars f ls x) [(a,renVars f ls b) | (a,b) <- ys]

IsaSign.Let xs y ->

IsaSign.Let [(a,renVars f ls b) | (a,b) <- xs] (renVars f ls y)

IsaSign.IsaEq x y -> IsaSign.IsaEq (renVars f ls x) (renVars f ls y)

IsaSign.Tuplex xs c -> IsaSign.Tuplex (map (renVars f ls) xs) c

_ -> t

renFuns :: (Term -> Maybe Term) -> Term -> Term

renFuns f t = case t of

IsaSign.Abs v x c -> IsaSign.Abs v (renFuns f x) c

IsaSign.App x y c -> maybe (IsaSign.App (renFuns f x) (renFuns f y) c) id

$ f t

IsaSign.If x y z c ->

IsaSign.If (renFuns f x) (renFuns f y) (renFuns f z) c

IsaSign.Case x ys ->

IsaSign.Case (renFuns f x) [(a,renFuns f b) | (a,b) <- ys]

IsaSign.Let xs y ->

IsaSign.Let [(a,renFuns f b) | (a,b) <- xs] (renFuns f y)

IsaSign.IsaEq x y -> IsaSign.IsaEq (renFuns f x) (renFuns f y)

IsaSign.Tuplex xs c -> IsaSign.Tuplex (map (renFuns f) xs) c

_ -> t

---------------------- SENTENCES ------------------------------------------

--------------------- getting info from sentences -------------------------

newConstTab :: Continuity -> [Named IsaSign.Sentence] -> ConstTab

newConstTab c ls = if isCont c then Map.empty else

Map.fromList [(mkVName $ extAxName x, extAxType x) | x <- ls]

extAxName :: Named Sentence -> String

extAxName s = senAttr s

extAxType :: Named Sentence -> Typ

extAxType s = case sentence s of

ConstDef (IsaEq (Const _ t) _) | isAxiom s -> (typ t)

RecDef _ ((App (App _ (App (Const _ t) _ _) _) _ _ : _) : _)

| isAxiom s -> (typ t)

_ -> noTypeT

extFunTerm :: Named Sentence -> Term

extFunTerm s = case sentence s of

ConstDef (IsaEq t _) -> fst $ extTBody t

_ -> error "Hs2HOLCFaux.extFunTerm"

extLeftH :: Named Sentence -> Term

extLeftH s = case sentence s of

ConstDef (IsaEq t _) -> t

_ -> error "Hs2HOLCFaux.extLeftH"

extRightH :: Named Sentence -> Term

extRightH s = case sentence s of

ConstDef (IsaEq _ t) -> t

_ -> error "Hs2HOLCFaux.extRightH"

{- left comp is the def name, right comp are the constants in the def -}

sentAna :: Named Sentence -> (Term, [Term])

sentAna s = case sentence s of

ConstDef (IsaEq l r) | isAxiom s -> (l, constFilter r)

_ -> error "Hs2HOLCFaux.sentAna"

------------------ checking for mutually recursive function defs ----------

getDepSent :: [[Named Sentence]] -> [[Named Sentence]]

getDepSent ls = abGetDep sentDepOn ls

getExpRole :: Named Sentence -> ExpRole

getExpRole n = case (extFunTerm n) of

Const _ x -> case kon x of

TMet -> InstDef

_ -> FunDef

_ -> error "Hs2HOLCFaux, getExpRole"

sentDepOn :: Named Sentence -> Named Sentence -> Bool

sentDepOn x y = case getExpRole x of

InstDef ->

depOn (\ u v -> simTerms u v

&& typEq (typ $ termType u) (typ $ termType v))

(fst . sentAna) (snd . sentAna) x y

FunDef ->

depOn (\ u v -> simTerms u v

&& typSim (typ $ termType u) (typ $ termType v))

(fst . sentAna) (snd . sentAna) x y

------------------- adding fixpoints ---------------------------------------

fixMRec :: Continuity -> [[Named Sentence]] -> [Named Sentence]

fixMRec c ls = let xs = getDepSent ls

in addFixPoints c xs

addFixPoints :: Continuity -> [[Named Sentence]] -> [Named Sentence]

addFixPoints c xs = concatMap (fixPoint c) xs

fixPoint :: Continuity -> [Named Sentence] -> [Named Sentence]

fixPoint c xs = case xs of

[a] -> if sentDepOn a a then [mapNamed ( \ s -> case s of

ConstDef (IsaEq lh rh) -> case c of

IsCont _ ->

RecDef fixrecS [[holEq lh rh]]

NotCont -> RecDef primrecS [destCaseS c lh rh]

_ -> error "Hs2HOLCFaux.fixPoint") a]

else xs

_ : _ -> case c of

IsCont _ -> let

jn = joinNames (map extAxName xs) -- name is ininfluential here

ys = [[holEq (extLeftH x) $ extRightH x] | x <- xs]

in [makeNamed jn $ RecDef fixrecS ys]

NotCont -> let

jj = joinNames (map extAxName xs)

jn = mkVName jj

jt1 = headTailsType (map extAxType xs)

(jta, jts) = headTailsMT jt1

jt = mkFunType jta (typTuple NotCont jts)

jl = Const jn $ dispNN jt

n = length xs

rs = map extRightH xs

ls = map extFunTerm xs

yys = [destCase x (\ _ -> jn) | x <- rs]

yyys = reassemble yys

zs = [(p,Tuplex (map (renFuns (newFCons (Const jn noType) ls)) ts)

NotCont)

| (p,ts) <- Map.toList yyys]

os = [mkNewDef x jj n m jt | (x,m) <- listEnum xs]

ps = makeNamed jj (makeRecDef jl zs) : os

in ps

[] -> []

mkNewDef :: Named Sentence -> String ->

Int -> Int -> Typ -> Named Sentence

mkNewDef s z x y t = let -- x is the max

a = NotCont

zy = typeTupleSel t y

in mapNamed ( \ sen -> case sen of

ConstDef (IsaEq lh rh) -> case (lh, extFBody rh) of

(Const nam _, (_, w : ws)) ->

ConstDef $ IsaEq (Const nam $ dispNN zy) $

termMAbs a (w:ws) $ termMAppl a (tupleSelector x y

(App (Const (mkVName z) noType) w a) a) ws

_ -> error "Hs2HOLCFaux.mkNewDef1"

_ -> error "Hs2HOLCFaux.mkNewDef2") s

makeRecDef :: Term -> [(Term,Term)] -> Sentence

makeRecDef t ls =

RecDef primrecS [map (\ (a, b) -> holEq (App t a NotCont) b) ls]

reassemble :: [[(Term,Term)]] -> Map.Map Term [Term]

reassemble ls = foldr

(\ (ft, sd) ms ->

Map.insert ft (sd : Map.findWithDefault [] ft ms) ms)

Map.empty (concat ls)

newFCons :: Term -> [Term] -> Term -> Maybe Term

newFCons t ls k = case k of

App n w NotCont -> case elPos ls n of

Nothing -> Nothing

Just i ->

Just $ tupleSelector (length ls) i (IsaSign.App t w NotCont) NotCont

_ -> Nothing

-------------------------- TYPES ------------------------------------------

------------------------ tuples, lifting ----------------------------------

typTuple :: Continuity -> [Typ] -> Typ

typTuple c ts = case ts of

[] -> noTypeT

[a] -> a

a : as -> (if isCont c then mkContProduct else prodType) a (typTuple c as)

typeTupleSel :: Typ -> Int -> Typ

typeTupleSel t n = let

(p,c) = splitFunT t

q = (tupleDes c) !! (n-1)

in mkFunType p q

tupleDes :: Typ -> [Typ]

tupleDes t = case t of

IsaSign.Type "*" _ [t1,t2] -> t1:(tupleDes t2)

_ -> [t]

------------------- function types -----------------------------------

headTailsType :: [Typ] -> [(Typ, Typ)]

headTailsType ls = case chkTHead ls of

False -> error "Hs2HOLCFaux.headTailsType"

True -> map splitFunT ls

splitFunT :: Typ -> (Typ, Typ)

splitFunT x = case x of

IsaSign.Type "=>" _ [i, b] -> (i,b)

_ -> error "Hs2HOLCF, headTail"

-- checks that all types in the list are equivalent in the first argument

-- and that all variables occur in that argument

chkTHead :: [IsaType] -> Bool

chkTHead ls = case ls of

IsaSign.Type "=>" _ [x,n] : IsaSign.Type "=>" s [y,m] : ns ->

if typEq x y && mkTVarMap id x == mkTVarMap id n then

chkTHead (IsaSign.Type "=>" s [y, m] : ns) else False

[IsaSign.Type "=>" _ [x,n]] -> if mkTVarMap id x == mkTVarMap id n

then True else False

_ -> False

----------------------- equivalence of types modulo variables name ------

typSim :: Typ -> Typ -> Bool

typSim t1 t2 = case (t1, t2) of

(IsaSign.Type _ _ ls1, IsaSign.Type _ _ ls2) ->

typeId t1 == typeId t2 && typLSim ls1 ls2

(TFree _ _, TFree _ _) -> True

(TVar _ _, TVar _ _) -> True

_ -> False

typLSim :: [Typ] -> [Typ] -> Bool

typLSim ls1 ls2 = case (ls1, ls2) of

([], []) -> True

(a : as, b : bs) -> typSim a b && typLSim as bs

_ -> False

typEq :: Typ -> Typ -> Bool --make some distinction for case noType?

typEq t1 t2 = t1 == noTypeT || t2 == noTypeT || case (t1, t2) of

(IsaSign.Type _ _ ls1, IsaSign.Type _ _ ls2) ->

typeId t1 == typeId t2 && typeSort t1 == typeSort t2 && typLEq ls1 ls2

(TFree _ _, TFree _ _) -> typeSort t1 == typeSort t2

(TVar _ _, TVar _ _) -> typeSort t1 == typeSort t2

_ -> False

typLEq :: [Typ] -> [Typ] -> Bool

typLEq ls1 ls2 = case (ls1, ls2) of

([], []) -> True

(a : as, b : bs) -> typEq a b && typLEq as bs

_ -> False

------------------------ type renaming -----------------------------------

applyTyRen :: Int -> Typ -> Typ

applyTyRen n t = case t of

TFree x s -> TFree (x ++ "XX" ++ show n) s

IsaSign.Type a b cs -> IsaSign.Type a b $ map (applyTyRen n) cs

_ -> t

-------------------------- type var maps ---------------------------------

headTailsMT :: [(Typ,Typ)] -> (Typ, [Typ])

headTailsMT ls = let

ks = [(mkTVarMap (applyTyRen 0) i, (i, b)) | (i, b) <- ls]

in case ks of

[] -> error "Hs2HOLCFaux, headTailsType"

(f,(x,_)):_ -> let

zs = [(renMap f g, y) | (g,(_,y)) <- ks]

zz = [applyTVM g y | (g, y) <- zs]

w = applyTyRen 0 x

in (w, zz)

renMap :: Map.Map Typ Typ -> Map.Map Typ Typ -> Map.Map Typ Typ

renMap f g = if Map.size f == Map.size g then

Map.fromList [(fst $ Map.elemAt n f, snd $ Map.elemAt n g)

| n <- [0..((Map.size f) - 1)]]

else error "HsHOLCFaux, renMap"

mkTVarMap :: (Typ -> Typ) -> Typ -> Map.Map Typ Typ

mkTVarMap f t = case t of

Type _ _ xs -> Map.unions [mkTVarMap f y | y <- xs]

_ -> Map.singleton t (f t)

applyTVM :: Map.Map Typ Typ -> Typ -> Typ

applyTVM f t = case t of

IsaSign.Type n s vs -> IsaSign.Type n s (map (applyTVM f) vs)

IsaSign.TFree _ _ -> maybe t id $ Map.lookup t f

_ -> t

------------------------ replacement functions -------------------------

-- constrains variables in t with sort constraints in cs

constrVarClass :: IsaType -> [(IsaType,Sort)] -> IsaType

constrVarClass t cs = typeVarsRep addSort [(typeId x,y) | (x,y) <- cs] t

addSort :: [(TName,Sort)] -> TName -> Sort -> Maybe Typ

addSort cs n s = do

as <- Map.lookup n (Map.fromList cs)

return $ TFree n $ remove_duplicates $ s ++ as

-- replaces in t variables of class c with nt

repVarClass :: IsaType -> IsaClass -> IsaType -> IsaType

repVarClass t c nt = typeVarsRep repVC (c,nt) t

repVC :: (IsaClass, IsaType) -> TName -> IsaSort -> Maybe IsaType

repVC (c, t) _ s = if elem c s then return t else Nothing

typeVarsRep :: (a -> TName -> Sort -> Maybe IsaType) -> a ->

IsaType -> IsaType

typeVarsRep f ls t = case t of

IsaSign.Type n s vs -> IsaSign.Type n s (map (typeVarsRep f ls) vs)

IsaSign.TFree n s -> maybe t id $ f ls n s

IsaSign.TVar _ _ -> t

-- replace type var in t with type x; used in instantiation; assumed

-- that t has just one variable

replaceTyVar :: IsaType -> IsaType -> IsaType

replaceTyVar x t = if x == noTypeT then t else case t of

IsaSign.Type n s vs -> IsaSign.Type n s (map (replaceTyVar x) vs)

IsaSign.TFree _ _ -> x

IsaSign.TVar _ _ -> x