{- |

Module : $Header$

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@tzi.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

, removeEL

, extAxType

, fixMRec

, newConstTab

, getTermName

, extRightH

, IsaSort

, IsaType

, IsaPattern

, IsaTerm

, IsaName(..)

, xDummy

, termMAbs

, termMAppl

, PrExp

, PrPat

, renVars

, remove_duplicates

, HsType

, HsScheme

, HsId

, getInstClass

, getInstType

, repVarClass

, constrVarClass

, getLitName

, transTN

, transPath

, showIsaS

, funFliftbin

, VaMap

, AConstTab

, liftMapByListD

, nothingFiOut

, IsaTypeInsts

, IsaVT(..)

, TyMap

, liftMapByList

, HsTypeInfo

, HsInstance

, HsInstances

, extClassInfo

, extAbbrsInfo

, groupInst

, getMainInstType

, prepInst

, checkTyCons

, getDepDoms

, getDomType

, getFieldTypes

, isCont

) 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

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

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

type HsInstance = TiInstanceDB.Instance PNT

type HsInstances = [TiInstanceDB.Instance PNT]

type HsPred = TiTypes.Pred PNT

type HsType = TiTypes.Type PNT

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 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

_ -> error "Hs2HOLCFaux.getInstType"

getInstClass :: HsPred -> HsType

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

_ -> error "Hs2HOLCFaux.getInstClass"

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

extClassInfo :: HsTypeInfo -> [HsClass]

extClassInfo p = case p of

TiTypes.Class a _ _ _ -> map getInstType 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"

----------- getting 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 ---------------------------

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

xDummy :: IsaTerm

xDummy = conDouble "dummy"

holEq :: IsaTerm -> IsaTerm -> IsaTerm

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

getTermName :: Term -> String

getTermName a = case a of

Const x _ -> new x

Free x -> new x

_ -> "_"

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

-- Translating to strings compatible with Isabelle

class IsaName a where

showIsaName :: a -> String

showIsaString :: a -> String

showIsaS :: String -> String

showIsaS = transConstStringT HOLCF_thy

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 (inessentially) depending on IsaSign ----

joinNames :: [String] -> String

joinNames = concatMap (++ "_X")

isCont :: Continuity -> Bool

isCont = (== IsCont)

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

"Bool" -> if ic then "tr" else "bool"

"Int" -> if ic then "dInt" else "int"

"Integer" -> if ic then "dInt" else "int"

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

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

"(,)" -> "*"

_ -> d

else d

transPath :: String -> String -> String

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

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

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

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

typTuple c ts = case ts of

[] -> noType

[a] -> a

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

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

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

typEq t1 t2 = t1 == noType || t2 == noType || 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

------------------------------- 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 varibles 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

------------------ more extraction and replacement functions ------------------

unifyTVars :: [IsaType] -> (IsaType,[IsaType])

unifyTVars ls = case chkTHead ls of

False -> error "Hs2HOLCFaux.unifyTVars"

True -> case ls of

IsaSign.Type "=>" _ [i, _] : _ ->

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

_ -> error "Hs2HOLCFaux.uTV"

chkTHead :: [IsaType] -> Bool

chkTHead ls = case ls of

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

if typEq x y then

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

[IsaSign.Type "=>" _ _] -> True

_ -> False

renTVars :: [Typ] -> [Typ]

renTVars ls = [renTVar b a | (a, b) <- listEnum ls]

where

renTVar n t =

case t of

TFree x s -> if take 2 x == "vX" then t else

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

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

_ -> t

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

groupInst :: [IsaTypeInsts] -> [IsaTypeInsts]

groupInst db =

remove_duplicates [(y,

remove_duplicates $ concat

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

------------------------- 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

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

quickSort f ls = case ls of

[] -> []

a:as -> let

(xs,ys) = compF f a as

xxs = quickSort f xs

yys = quickSort f ys

in xxs ++ a:yys

where

compF g c bs =

([ b | b <- bs, g c b == True],[ b | b <- bs, g c b == False])

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]

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

_ -> []

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

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

funFliftbin :: Term -> Term

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

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_"

, "fromInteger"

, "derived__Prelude_"]

in case (t, ts) of

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

(_, []) -> t

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

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

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

----------------------- 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 (conDouble (if isCont c then "cfst" else "fst"))

$ [tupleSelect (n - 1) t c]

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

tupleSelect n t c = case n of

0 -> t

_ -> tupleSelect (n - 1)

(termMAppl c (conDouble $ if isCont c then "csnd" else "snd") [t]) c

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

isDicConst :: Term -> Bool

isDicConst t = case t of

Const 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 x y

_ -> False

{- this functions was actually meant to compare only constructors -

check out, there might be bugs -}

simTerms :: Term -> Term -> Bool

simTerms t1 t2 = case (t1, t2) of

(IsaSign.Const x _, IsaSign.Const y _) -> x == y

(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 = senName s

extAxType :: Named Sentence -> Typ

extAxType s = case s of

NamedSen _ True _ (ConstDef (IsaEq (Const _ t) _)) -> t

NamedSen _ True _

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

_ -> noType

extFunTerm :: Named Sentence -> Term

extFunTerm s = case s of

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

_ -> error "Hs2HOLCFaux.extFunTerm"

extLeftH :: Named Sentence -> Term

extLeftH s = case s of

NamedSen _ _ _ (ConstDef (IsaEq t _)) -> t

_ -> error "Hs2HOLCFaux.extLeftH"

extRightH :: Named Sentence -> Term

extRightH s = case s of

NamedSen _ _ _ (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 s of

NamedSen _ True _ (ConstDef (IsaEq l r)) -> (l, constFilter r)

_ -> error "Hs2HOLCFaux.sentAna"

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

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

getDepSent ls = abGetDep sentDepOn ls

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

sentDepOn x y =

depOn (\ u v -> simTerms u v && typEq (termType u) (termType v))

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

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

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

fixMRec c ls = addFixPoints c $ getDepSent ls

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 case a of

NamedSen l m n (ConstDef (IsaEq lh rh)) -> case c of

IsCont ->

[NamedSen l m n $ RecDef fixrecS [[holEq lh rh]]]

NotCont -> [NamedSen l m n $ RecDef primrecS

[destCaseS c lh rh]]

_ -> error "Hs2HOLCFaux.fixPoint"

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 [NamedSen jn True False $ RecDef fixrecS ys]

NotCont -> let

jj = joinNames (map extAxName xs)

jn = mkVName jj

jt1 = unifyTVars (map extAxType xs)

jta = fst jt1

jtls = snd jt1

jt = mkFunType jta

(typTuple NotCont (renTVars jtls))

jl = Const jn 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 jtls jta | (x,m) <- listEnum xs]

ps = (NamedSen jj True False $ makeRecDef jl zs):os

in ps

[] -> []

typeTupleTrivInst :: Int -> [Typ] -> Typ -> Typ

typeTupleTrivInst n tls t = mkFunType t

(typTuple NotCont (renTrivTVars n tls))

renTrivTVars :: Int -> [Typ] -> [Typ]

renTrivTVars m tls = [renTVar m b a | (a, b) <- listEnum tls]

where

renTVar x n t = if x == n then t else

case t of

TFree y s -> if (take 2 y == "vX") then t else

IsaSign.Type "unit" s []

IsaSign.Type a b cs -> IsaSign.Type a b (map (renTVar x n) cs)

_ -> t

mkNewDef :: Named Sentence -> String -> Int -> Int -> [Typ] -> Typ

-> Named Sentence

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

a = NotCont

zt = IsaSign.Type "!!!" [] [typeTupleTrivInst y tls t]

in case s of

NamedSen l m n (ConstDef (IsaEq lh rh)) -> case (lh, extFBody rh) of

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

NamedSen l m n (ConstDef (IsaEq lh $

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

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

_ -> error "Hs2HOLCFaux.mkNewDef1"

_ -> error "Hs2HOLCFaux.mkNewDef2"

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] -- [(b, [c])]

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