A bunch of things!

curry-frontend.cabal

@@ -39,54 +39,60 @@ Executable cymake
     , mtl, old-time, containers, pretty
   ghc-options: -Wall
   Other-Modules:
-      Base.Arity
-    , Base.Eval
+      Checks
+    , CompilerEnv
+    , CompilerOpts
+    , CurryBuilder
+    , CurryDeps
+    , Exports
+    , Frontend
+    , Generators
+    , IL
+    , Imports
+    , Interfaces
+    , Modules
+    , ModuleSummary
+    , Records
+    , Transformations
+    , Base.CurryTypes
     , Base.Expr
-    , Base.Import
-    , Base.Module
-    , Base.OpPrec
-    , Base.TypeConstructors
+    , Base.Messages
+    , Base.SCC
+    , Base.Subst
     , Base.Types
-    , Base.Value
-    , Check.InterfaceCheck
+    , Base.TypeSubst
+    , Base.Typing
+    , Base.Utils
     , Check.KindCheck
     , Check.PrecCheck
     , Check.SyntaxCheck
     , Check.TypeCheck
     , Check.WarnCheck
-    , Env.CurryEnv
+    , Env.Arity
+    , Env.Eval
+    , Env.Import
+    , Env.Label
+    , Env.Module
     , Env.NestEnv
     , Env.OldScopeEnv
+    , Env.OpPrec
     , Env.ScopeEnv
     , Env.TopEnv
+    , Env.TypeConstructors
+    , Env.Value
     , Gen.GenAbstractCurry
     , Gen.GenFlatCurry
     , Html.CurryHtml
     , Html.SyntaxColoring
-    , IL
     , IL.Pretty
     , IL.Type
     , IL.XML
-    , CurryBuilder
-    , CompilerOpts
-    , CurryDeps
-    , CurryToIL
-    , Exports
-    , Frontend
-    , Imports
-    , Messages
-    , Modules
-    , SCC
-    , Subst
     , Transform.CaseCompletion
+    , Transform.CurryToIL
     , Transform.Desugar
     , Transform.Lift
     , Transform.Qual
     , Transform.Simplify
-    , Types
-    , TypeSubst
-    , Typing
-    , Utils
 Library
   hs-source-dirs:  src
   Build-Depends:   filepath

src/Base/CurryTypes.lhs

+\paragraph{Types}
+The functions \texttt{toType}, \texttt{toTypes}, and \texttt{fromType}
+convert Curry type expressions into types and vice versa. The
+functions \texttt{qualifyType} and \texttt{unqualifyType} add and
+remove module qualifiers in a type, respectively.
+
+When Curry type expression are converted with \texttt{toType} or
+\texttt{toTypes}, type variables are assigned ascending indices in the
+order of their occurrence. It is possible to pass a list of additional
+type variables to both functions which are assigned indices before
+those variables occurring in the type. This allows preserving the
+order of type variables in the left hand side of a type declaration.
+\begin{verbatim}
+
+> module Base.CurryTypes
+>  ( toQualType, toQualTypes, toType, toTypes, toType', fromQualType, fromType
+>  ) where
+
+> import Data.List (nub)
+> import qualified Data.Map as Map (Map, fromList, lookup)
+
+> import Curry.Base.Ident
+> import qualified Curry.Syntax as CS
+
+> import Base.Expr
+> import Base.Messages (internalError)
+> import Base.Types
+
+> toQualType :: ModuleIdent -> [Ident] -> CS.TypeExpr -> Type
+> toQualType m tvs = qualifyType m . toType tvs
+
+> toQualTypes :: ModuleIdent -> [Ident] -> [CS.TypeExpr] -> [Type]
+> toQualTypes m tvs = map (qualifyType m) . toTypes tvs
+
+> toType :: [Ident] -> CS.TypeExpr -> Type
+> toType tvs ty = toType' (Map.fromList (zip (tvs ++ tvs') [0 ..])) ty
+>   where tvs' = [tv | tv <- nub (fv ty), tv `notElem` tvs]
+
+> toTypes :: [Ident] -> [CS.TypeExpr] -> [Type]
+> toTypes tvs tys = map (toType' (Map.fromList (zip (tvs ++ tvs') [0 ..]))) tys
+>   where tvs' = [tv | tv <- nub (concatMap fv tys), tv `notElem` tvs]
+
+> toType' :: Map.Map Ident Int -> CS.TypeExpr -> Type
+> toType' tvs (CS.ConstructorType tc tys) =
+>   TypeConstructor tc (map (toType' tvs) tys)
+> toType' tvs (CS.VariableType tv) =
+>   maybe (internalError ("toType " ++ show tv)) TypeVariable (Map.lookup tv tvs)
+> toType' tvs (CS.TupleType tys)
+>   | null tys = TypeConstructor (qualify unitId) []
+>   | otherwise = TypeConstructor (qualify (tupleId (length tys'))) tys'
+>   where tys' = map (toType' tvs) tys
+> toType' tvs (CS.ListType ty) = TypeConstructor (qualify listId) [toType' tvs ty]
+> toType' tvs (CS.ArrowType ty1 ty2) =
+>   TypeArrow (toType' tvs ty1) (toType' tvs ty2)
+> toType' tvs (CS.RecordType fs rty) =
+>   TypeRecord (concatMap (\ (ls, ty) -> map (\ l -> (l, toType' tvs ty)) ls) fs)
+>              (maybe Nothing
+>                 (\ ty -> case toType' tvs ty of
+>                           TypeVariable tv -> Just tv
+>                           _ -> internalError ("toType " ++ show ty))
+>                 rty)
+
+> fromQualType :: ModuleIdent -> Type -> CS.TypeExpr
+> fromQualType m = fromType . unqualifyType m
+
+> fromType :: Type -> CS.TypeExpr
+> fromType (TypeConstructor tc tys)
+>   | isTupleId c                    = CS.TupleType tys'
+>   | c == listId && length tys == 1 = CS.ListType (head tys')
+>   | c == unitId && null tys        = CS.TupleType []
+>   | otherwise                      = CS.ConstructorType tc tys'
+>   where c    = unqualify tc
+>         tys' = map fromType tys
+> fromType (TypeVariable tv)         = CS.VariableType
+>    (if tv >= 0 then identSupply !! tv else mkIdent ('_' : show (-tv)))
+> fromType (TypeConstrained tys _)   = fromType (head tys)
+> fromType (TypeArrow ty1 ty2)       = CS.ArrowType (fromType ty1) (fromType ty2)
+> fromType (TypeSkolem k)            = CS.VariableType (mkIdent ("_?" ++ show k))
+> fromType (TypeRecord fs rty)       =  CS.RecordType
+>   (map (\ (l, ty) -> ([l], fromType ty)) fs)
+>   (maybe Nothing (Just . fromType . TypeVariable) rty)

src/Messages.hs → src/Base/Messages.hs

-module Messages
+module Base.Messages
   ( info, status
   , putErrLn, putErrsLn, abortWith
   , internalError, errorAt, errorAt'

src/Base/Module.lhs

-\paragraph{Interfaces}
-The compiler maintains a global environment holding all (directly or
-indirectly) imported interfaces.
-
-The function \texttt{bindFlatInterface} transforms FlatInterface
-information (type \texttt{FlatCurry.Prog} to MCC interface declarations
-(type \texttt{CurrySyntax.IDecl}. This is necessary to process
-FlatInterfaces instead of ".icurry" files when using MCC as frontend
-for PAKCS.
-\begin{verbatim}
-
-> module Base.Module (ModuleEnv, lookupModule) where
-
-> import qualified Data.Map as Map
-
-> import Curry.Base.Ident (ModuleIdent)
-> import qualified Curry.Syntax as CS (IDecl)
-
-> type ModuleEnv = Map.Map ModuleIdent [CS.IDecl]
-
-> lookupModule :: ModuleIdent -> ModuleEnv -> Maybe [CS.IDecl]
-> lookupModule = Map.lookup
-
-\end{verbatim}

src/SCC.lhs → src/Base/SCC.lhs

@@ -20,7 +20,7 @@ unique number. The latter is only used to provide a trivial ordering
 so that the declarations can be used as set elements.
 \begin{verbatim}
 
-> module SCC (scc) where
+> module Base.SCC (scc) where
 
 > import qualified Data.Set as Set (empty, member, insert)
 

src/Subst.lhs → src/Base/Subst.lhs

@@ -12,7 +12,7 @@ In order to implement substitutions efficiently, composed substitutions are
 marked with a boolean flag (see below).
 \begin{verbatim}
 
-> module Subst
+> module Base.Subst
 >   ( Subst (..), IntSubst (..), idSubst, substToList, bindSubst, unbindSubst
 >   , compose,  substVar', isubstVar, restrictSubstTo
 >   )where

src/TypeSubst.lhs → src/Base/TypeSubst.lhs

@@ -9,15 +9,17 @@
 This module implements substitutions on types.
 \begin{verbatim}
 
-> module TypeSubst (module TypeSubst, idSubst, bindSubst, compose) where
+> module Base.TypeSubst (module Base.TypeSubst, idSubst, bindSubst, compose) where
 
-> import Data.Maybe
-> import Data.List
+> import Data.List (nub)
+> import Data.Maybe (fromJust, isJust)
 
-> import Base.Value (ValueInfo (..))
-> import Subst
-> import Types
 > import Env.TopEnv
+> import Env.Value (ValueInfo (..))
+
+> import Base.Subst
+> import Base.Types
+
 
 > type TypeSubst = Subst Int Type
 

src/Base/Types.lhs

-\paragraph{Types}
-The functions \texttt{toType}, \texttt{toTypes}, and \texttt{fromType}
-convert Curry type expressions into types and vice versa. The
-functions \texttt{qualifyType} and \texttt{unqualifyType} add and
-remove module qualifiers in a type, respectively.
-
-When Curry type expression are converted with \texttt{toType} or
-\texttt{toTypes}, type variables are assigned ascending indices in the
-order of their occurrence. It is possible to pass a list of additional
-type variables to both functions which are assigned indices before
-those variables occurring in the type. This allows preserving the
-order of type variables in the left hand side of a type declaration.
+% $Id: Types.lhs,v 1.11 2004/02/08 22:14:02 wlux Exp $
+%
+% Copyright (c) 2002, Wolfgang Lux
+% See LICENSE for the full license.
+%
+% Modified by Martin Engelke (men@informatik.uni-kiel.de)
+%
+\nwfilename{Types.lhs}
+\section{Types}
+This module modules provides the definitions for the internal
+representation of types in the compiler.
 \begin{verbatim}
 
 > module Base.Types
->  ( toQualType, toQualTypes, toType, toTypes, toType', fromQualType, fromType
->  ) where
+>   ( Type (..), DataConstr (..), isArrowType, arrowArity, arrowArgs, arrowBase
+>   , typeVars, typeConstrs, typeSkolems, equTypes, TypeScheme (..)
+>   , ExistTypeScheme (..), monoType, polyType
+>   , unitType, boolType, charType, intType, floatType, stringType
+>   , successType, listType, ioType, tupleType, primType
+>   , typeVar, predefTypes, qualifyType, unqualifyType
+>   ) where
 
-> import Data.List (nub)
-> import qualified Data.Map as Map (Map, fromList, lookup)
+> import Data.Maybe (fromJust, isJust, isNothing)
 
 > import Curry.Base.Ident
-> import qualified Curry.Syntax as CS
-
-> import Base.Expr
-> import Messages (internalError)
-> import Types
-
-> toQualType :: ModuleIdent -> [Ident] -> CS.TypeExpr -> Type
-> toQualType m tvs = qualifyType m . toType tvs
-
-> toQualTypes :: ModuleIdent -> [Ident] -> [CS.TypeExpr] -> [Type]
-> toQualTypes m tvs = map (qualifyType m) . toTypes tvs
-
-> toType :: [Ident] -> CS.TypeExpr -> Type
-> toType tvs ty = toType' (Map.fromList (zip (tvs ++ tvs') [0 ..])) ty
->   where tvs' = [tv | tv <- nub (fv ty), tv `notElem` tvs]
-
-> toTypes :: [Ident] -> [CS.TypeExpr] -> [Type]
-> toTypes tvs tys = map (toType' (Map.fromList (zip (tvs ++ tvs') [0 ..]))) tys
->   where tvs' = [tv | tv <- nub (concatMap fv tys), tv `notElem` tvs]
-
-> toType' :: Map.Map Ident Int -> CS.TypeExpr -> Type
-> toType' tvs (CS.ConstructorType tc tys) =
->   TypeConstructor tc (map (toType' tvs) tys)
-> toType' tvs (CS.VariableType tv) =
->   maybe (internalError ("toType " ++ show tv)) TypeVariable (Map.lookup tv tvs)
-> toType' tvs (CS.TupleType tys)
->   | null tys = TypeConstructor (qualify unitId) []
->   | otherwise = TypeConstructor (qualify (tupleId (length tys'))) tys'
->   where tys' = map (toType' tvs) tys
-> toType' tvs (CS.ListType ty) = TypeConstructor (qualify listId) [toType' tvs ty]
-> toType' tvs (CS.ArrowType ty1 ty2) =
->   TypeArrow (toType' tvs ty1) (toType' tvs ty2)
-> toType' tvs (CS.RecordType fs rty) =
->   TypeRecord (concatMap (\ (ls, ty) -> map (\ l -> (l, toType' tvs ty)) ls) fs)
->              (maybe Nothing
->                 (\ ty -> case toType' tvs ty of
->                           TypeVariable tv -> Just tv
->                           _ -> internalError ("toType " ++ show ty))
->                 rty)
-
-> fromQualType :: ModuleIdent -> Type -> CS.TypeExpr
-> fromQualType m = fromType . unqualifyType m
-
-> fromType :: Type -> CS.TypeExpr
-> fromType (TypeConstructor tc tys)
->   | isTupleId c = CS.TupleType tys'
->   | c == listId && length tys == 1 = CS.ListType (head tys')
->   | c == unitId && null tys = CS.TupleType []
->   | otherwise = CS.ConstructorType tc tys'
->   where c = unqualify tc
->         tys' = map fromType tys
-> fromType (TypeVariable tv) =
->   CS.VariableType (if tv >= 0 then identSupply !! tv
->                            else mkIdent ('_' : show (-tv)))
-> fromType (TypeConstrained tys _) = fromType (head tys)
-> fromType (TypeArrow ty1 ty2) = CS.ArrowType (fromType ty1) (fromType ty2)
-> fromType (TypeSkolem k) = CS.VariableType (mkIdent ("_?" ++ show k))
-> fromType (TypeRecord fs rty) =
->   CS.RecordType (map (\ (l, ty) -> ([l], fromType ty)) fs)
->              (maybe Nothing (Just . fromType . TypeVariable) rty)
+
+\end{verbatim}
+A type is either a type variable, an application of a type constructor
+to a list of arguments, or an arrow type. The \texttt{TypeConstrained}
+case is used for representing type variables that are restricted to a
+particular set of types. At present, this is used for typing guard
+expressions, which are restricted to be either of type \texttt{Bool}
+or of type \texttt{Success}, and integer literals, which are
+restricted to types \texttt{Int} and \texttt{Float}. If the type is
+not restricted, it defaults to the first type from the constraint list.
+The case \texttt{TypeSkolem} is used for handling skolem types, which
+result from the use of existentially quantified data constructors.
+Finally, \texttt{TypeRecord} is used for records.
+
+Type variables are represented with deBruijn style indices. Universally
+quantified type variables are assigned indices in the order of their
+occurrence in the type from left to right. This leads to a canonical
+representation of types where $\alpha$-equivalence of two types
+coincides with equality of the representation.
+
+Note that even though \texttt{TypeConstrained} variables use indices
+as well, these variables must never be quantified.
+\begin{verbatim}
+
+> data Type
+>   = TypeVariable Int
+>   | TypeConstructor QualIdent [Type]
+>   | TypeArrow Type Type
+>   | TypeConstrained [Type] Int
+>   | TypeSkolem Int
+>   | TypeRecord [(Ident,Type)] (Maybe Int)
+>   deriving (Eq, Show)
+
+\end{verbatim}
+The type \texttt{Data} is used to represent value constructors introduced
+by data or newtype declarations.
+\begin{verbatim}
+
+> data DataConstr = DataConstr Ident Int [Type]
+>     deriving (Eq, Show)
+
+\end{verbatim}
+The function \texttt{isArrowType} checks whether a type is a function
+type $t_1 \rightarrow t_2 \rightarrow \dots \rightarrow t_n$ . The
+function \texttt{arrowArity} computes the arity $n$ of a function type,
+\texttt{arrowArgs} computes the types $t_1 \dots t_{n-1}$
+and \texttt{arrowBase} returns the type $t_n$.
+\begin{verbatim}
+
+> isArrowType :: Type -> Bool
+> isArrowType (TypeArrow _ _) = True
+> isArrowType _ = False
+
+> arrowArity :: Type -> Int
+> arrowArity (TypeArrow _ ty) = 1 + arrowArity ty
+> arrowArity _ = 0
+
+> arrowArgs :: Type -> [Type]
+> arrowArgs (TypeArrow ty1 ty2) = ty1 : arrowArgs ty2
+> arrowArgs _ = []
+
+> arrowBase :: Type -> Type
+> arrowBase (TypeArrow _ ty) = arrowBase ty
+> arrowBase ty = ty
+
+\end{verbatim}
+The functions \texttt{typeVars}, \texttt{typeConstrs},
+\texttt{typeSkolems} return a list of all type variables, type
+constructors, or skolems occurring in a type $t$, respectively. Note
+that \texttt{TypeConstrained} variables are not included in the set of
+type variables because they cannot be generalized.
+\begin{verbatim}
+
+> typeVars :: Type -> [Int]
+> typeVars ty = vars ty [] where
+>   vars (TypeConstructor _ tys) tvs = foldr vars tvs tys
+>   vars (TypeVariable tv)       tvs = tv : tvs
+>   vars (TypeConstrained _ _)   tvs = tvs
+>   vars (TypeArrow ty1 ty2)     tvs = vars ty1 (vars ty2 tvs)
+>   vars (TypeSkolem _)          tvs = tvs
+>   vars (TypeRecord fs rtv)     tvs =
+>     foldr vars (maybe tvs (: tvs) rtv) (map snd fs)
+
+> typeConstrs :: Type -> [QualIdent]
+> typeConstrs ty = constrs ty [] where
+>   constrs (TypeConstructor tc tys) tcs = tc : foldr constrs tcs tys
+>   constrs (TypeVariable _)         tcs = tcs
+>   constrs (TypeConstrained _ _)    tcs = tcs
+>   constrs (TypeArrow ty1 ty2)      tcs = constrs ty1 (constrs ty2 tcs)
+>   constrs (TypeSkolem _)           tcs = tcs
+>   constrs (TypeRecord fs _)        tcs = foldr constrs tcs (map snd fs)
+
+> typeSkolems :: Type -> [Int]
+> typeSkolems ty = skolems ty [] where
+>   skolems (TypeConstructor _ tys) sks = foldr skolems sks tys
+>   skolems (TypeVariable _)        sks = sks
+>   skolems (TypeConstrained _ _)   sks = sks
+>   skolems (TypeArrow ty1 ty2)     sks = skolems ty1 (skolems ty2 sks)
+>   skolems (TypeSkolem k)          sks = k : sks
+>   skolems (TypeRecord fs _)       sks = foldr skolems sks (map snd fs)
+
+> equTypes :: Type -> Type -> Bool
+> equTypes t1 t2 = fst (equ [] t1 t2)
+>  where
+>  equ is (TypeConstructor qid1 ts1) (TypeConstructor qid2 ts2)
+>     | qid1 == qid2 = equs is ts1 ts2
+>     | otherwise    = (False, is)
+>  equ is (TypeVariable i1) (TypeVariable i2)
+>     = maybe (True, (i1,i2):is)
+>             (\ i2' -> (i2 == i2', is))
+>             (lookup i1 is)
+>  equ is (TypeConstrained ts1 i1) (TypeConstrained ts2 i2)
+>     = let (res, is') = equs is ts1 ts2
+>       in  maybe (res, (i1,i2):is')
+>                 (\ i2' -> (res && i2 == i2', is'))
+>                 (lookup i1 is')
+>  equ is (TypeArrow tf1 tt1) (TypeArrow tf2 tt2)
+>     = let (res1, is1) = equ is tf1 tf2
+>           (res2, is2) = equ is1 tt1 tt2
+>       in  (res1 && res2, is2)
+>  equ is (TypeSkolem i1) (TypeSkolem i2)
+>     = maybe (True, (i1,i2):is)
+>             (\ i2' -> (i2 == i2', is))
+>             (lookup i1 is)
+>  equ is (TypeRecord fs1 r1) (TypeRecord fs2 r2)
+>     | isJust r1 && isJust r2
+>       = let (res1, is1) = equ is (TypeVariable (fromJust r1))
+>		                   (TypeVariable (fromJust r2))
+>             (res2, is2) = equRecords is1 fs1 fs2
+>         in  (res1 && res2, is2)
+>     | isNothing r1 && isNothing r2 = equRecords is fs1 fs2
+>     | otherwise = (False, is)
+>  equ is _ _ = (False, is)
+>
+>  equRecords is fs1 fs2 | length fs1 == length fs2 = equrec is fs1 fs2
+>		         | otherwise = (False, is)
+>    where
+>    equrec is' [] _ = (True, is')
+>    equrec is' ((l,t):fs1') fs2'
+>       = let (res1, is1) = maybe (False,is') (equ is' t) (lookup l fs2')
+>             (res2, is2) = equrec is1 fs1' fs2'
+>         in  (res1 && res2, is2)
+>
+>  equs is [] [] = (True, is)
+>  equs _  [] _  = error "pattern not defined" -- TODO
+>  equs _  _  [] = error "pattern not defined" -- TODO
+>  equs is (t1':ts1) (t2':ts2)
+>     = let (res1, is1) = equ is t1' t2'
+>           (res2, is2) = equs is1 ts1 ts2
+>       in  (res1 && res2, is2)
+
+\end{verbatim}
+We support two kinds of quantifications of types here, universally
+quantified type schemes $\forall\overline{\alpha} .
+\tau(\overline{\alpha})$ and universally and existentially quantified
+type schemes $\forall\overline{\alpha} \exists\overline{\eta} .
+\tau(\overline{\alpha},\overline{\eta})$.  In both, quantified type
+variables are assigned ascending indices starting from 0. Therefore it
+is sufficient to record the numbers of quantified type variables in
+the \texttt{ForAll} and \texttt{ForAllExist} constructors. In case of
+the latter, the first of the two numbers is the number of universally
+quantified variables and the second the number of existentially
+quantified variables.
+\begin{verbatim}
+
+> data TypeScheme = ForAll Int Type deriving (Show, Eq)
+> data ExistTypeScheme = ForAllExist Int Int Type deriving (Show, Eq)
+
+\end{verbatim}
+The functions \texttt{monoType} and \texttt{polyType} translate a type
+$\tau$ into a monomorphic type scheme $\forall.\tau$ and a polymorphic
+type scheme $\forall\overline{\alpha}.\tau$ where $\overline{\alpha} =
+\textrm{fv}(\tau)$, respectively. \texttt{polyType} assumes that all
+universally quantified variables in the type are assigned indices
+starting with 0 and does not renumber the variables.
+\begin{verbatim}
+
+> monoType :: Type -> TypeScheme
+> monoType ty = ForAll 0 ty
+
+> polyType :: Type -> TypeScheme
+> polyType ty = ForAll (maximum (-1 : typeVars ty) + 1) ty
+
+\end{verbatim}
+There are a few predefined types:
+\begin{verbatim}
+
+> unitType :: Type
+> unitType = primType unitId []
+
+> boolType :: Type
+> boolType = primType boolId []
+
+> charType :: Type
+> charType = primType charId []
+
+> intType :: Type
+> intType = primType intId []
+
+> floatType :: Type
+> floatType = primType floatId []
+
+> stringType :: Type
+> stringType = listType charType
+
+> successType :: Type
+> successType = primType successId []
+
+> listType :: Type -> Type
+> listType ty = primType listId [ty]
+
+> ioType :: Type -> Type
+> ioType ty = primType ioId [ty]
+
+> tupleType :: [Type] -> Type
+> tupleType tys = primType (tupleId (length tys)) tys
+
+> primType :: Ident -> [Type] -> Type
+> primType = TypeConstructor . qualifyWith preludeMIdent
+
+> typeVar :: Int -> Type
+> typeVar = TypeVariable
+
+> predefTypes :: [(Type, [DataConstr])]
+> predefTypes = let a = typeVar 0 in
+>   [ (unitType  , [ DataConstr unitId 0 [] ])
+>   , (listType a, [ DataConstr nilId  0 []
+>                  , DataConstr consId 0 [a, listType a]])
+>   ]
+
+> qualifyType :: ModuleIdent -> Type -> Type
+> qualifyType m (TypeConstructor tc tys)
+>   | isTupleId tc' = tupleType tys'
+>   | tc' == unitId && n == 0 = unitType
+>   | tc' == listId && n == 1 = listType (head tys')
+>   | otherwise = TypeConstructor (qualQualify m tc) tys'
+>   where n = length tys'
+>         tc' = unqualify tc
+>         tys' = map (qualifyType m) tys
+> qualifyType _ (TypeVariable tv) = TypeVariable tv
+> qualifyType m (TypeConstrained tys tv) =
+>   TypeConstrained (map (qualifyType m) tys) tv
+> qualifyType m (TypeArrow ty1 ty2) =
+>   TypeArrow (qualifyType m ty1) (qualifyType m ty2)
+> qualifyType _ (TypeSkolem k) = TypeSkolem k
+> qualifyType m (TypeRecord fs rty) =
+>   TypeRecord (map (\ (l,ty) -> (l, qualifyType m ty)) fs) rty
+
+> unqualifyType :: ModuleIdent -> Type -> Type
+> unqualifyType m (TypeConstructor tc tys) =
+>   TypeConstructor (qualUnqualify m tc) (map (unqualifyType m) tys)
+> unqualifyType _ (TypeVariable tv) = TypeVariable tv
+> unqualifyType m (TypeConstrained tys tv) =
+>   TypeConstrained (map (unqualifyType m) tys) tv
+> unqualifyType m (TypeArrow ty1 ty2) =
+>   TypeArrow (unqualifyType m ty1) (unqualifyType m ty2)
+> unqualifyType _ (TypeSkolem k) = TypeSkolem k