curry-frontend-2.0.0: src/Transformations/CurryToIL.hs
{- |
Module : $Header$
Description : Translation of Curry into IL
Copyright : (c) 1999 - 2003 Wolfgang Lux
Martin Engelke
2011 - 2015 Björn Peemöller
2015 Jan Tikovsky
2016 - 2017 Finn Teegen
License : BSD-3-clause
Maintainer : bjp@informatik.uni-kiel.de
Stability : experimental
Portability : portable
After desugaring and lifting have been performed, the source code is
translated into the intermediate language. Besides translating from
source terms and expressions into intermediate language terms and
expressions, this phase in particular has to implement the pattern
matching algorithm for equations and case expressions.
Because of name conflicts between the source and intermediate language
data structures, we can use only a qualified import for the 'IL' module.
-}
{-# LANGUAGE CPP #-}
module Transformations.CurryToIL (ilTrans, transType) where
#if __GLASGOW_HASKELL__ < 710
import Control.Applicative ((<$>), (<*>))
#endif
import Control.Monad.Extra (concatMapM)
import qualified Control.Monad.Reader as R
import qualified Control.Monad.State as S
import Data.List (nub, partition)
import Data.Maybe (fromJust)
import qualified Data.Map as Map
import qualified Data.Set as Set (Set, empty, insert, delete, toList)
import Curry.Base.Ident
import Curry.Syntax hiding (caseAlt)
import Base.Expr
import Base.Messages (internalError)
import Base.Types hiding (polyType)
import Base.Kinds
import Base.Typing
import Base.Utils (foldr2)
import Env.TypeConstructor
import Env.Value (ValueEnv, ValueInfo (..), qualLookupValue)
import qualified IL as IL
ilTrans :: Bool -> ValueEnv -> TCEnv -> Module Type -> IL.Module
ilTrans remIm vEnv tcEnv (Module _ _ _ m _ im ds) = IL.Module m im' ds'
where ds' = R.runReader (concatMapM trDecl ds) (TransEnv m vEnv tcEnv)
im' = preludeMIdent : if remIm then imports m ds' else map moduleImport im
moduleImport (ImportDecl _ mdl _ _ _) = mdl
-- -----------------------------------------------------------------------------
-- Computation of necessary imports
-- -----------------------------------------------------------------------------
-- The list of import declarations in the intermediate language code is
-- determined by collecting all module qualifiers used in the current module.
imports :: ModuleIdent -> [IL.Decl] -> [ModuleIdent]
imports m = Set.toList . Set.delete m . foldr mdlsDecl Set.empty
mdlsDecl :: IL.Decl -> Set.Set ModuleIdent -> Set.Set ModuleIdent
mdlsDecl (IL.DataDecl _ _ cs) ms = foldr mdlsConstrsDecl ms cs
where mdlsConstrsDecl (IL.ConstrDecl _ tys) ms' = foldr mdlsType ms' tys
mdlsDecl (IL.NewtypeDecl _ _ nc) ms = mdlsNewConstrDecl nc
where mdlsNewConstrDecl (IL.NewConstrDecl _ ty) = mdlsType ty ms
mdlsDecl (IL.ExternalDataDecl _ _) ms = ms
mdlsDecl (IL.FunctionDecl _ _ ty e) ms = mdlsType ty (mdlsExpr e ms)
mdlsDecl (IL.ExternalDecl _ _ ty) ms = mdlsType ty ms
mdlsType :: IL.Type -> Set.Set ModuleIdent -> Set.Set ModuleIdent
mdlsType (IL.TypeConstructor tc tys) ms = modules tc (foldr mdlsType ms tys)
mdlsType (IL.TypeVariable _) ms = ms
mdlsType (IL.TypeArrow ty1 ty2) ms = mdlsType ty1 (mdlsType ty2 ms)
mdlsType (IL.TypeForall _ ty) ms = mdlsType ty ms
mdlsExpr :: IL.Expression -> Set.Set ModuleIdent -> Set.Set ModuleIdent
mdlsExpr (IL.Function _ f _) ms = modules f ms
mdlsExpr (IL.Constructor _ c _) ms = modules c ms
mdlsExpr (IL.Apply e1 e2) ms = mdlsExpr e1 (mdlsExpr e2 ms)
mdlsExpr (IL.Case _ e as) ms = mdlsExpr e (foldr mdlsAlt ms as)
where
mdlsAlt (IL.Alt t e') = mdlsPattern t . mdlsExpr e'
mdlsPattern (IL.ConstructorPattern _ c _) = modules c
mdlsPattern _ = id
mdlsExpr (IL.Or e1 e2) ms = mdlsExpr e1 (mdlsExpr e2 ms)
mdlsExpr (IL.Exist _ _ e) ms = mdlsExpr e ms
mdlsExpr (IL.Let b e) ms = mdlsBinding b (mdlsExpr e ms)
mdlsExpr (IL.Letrec bs e) ms = foldr mdlsBinding (mdlsExpr e ms) bs
mdlsExpr _ ms = ms
mdlsBinding :: IL.Binding -> Set.Set ModuleIdent -> Set.Set ModuleIdent
mdlsBinding (IL.Binding _ e) = mdlsExpr e
modules :: QualIdent -> Set.Set ModuleIdent -> Set.Set ModuleIdent
modules x ms = maybe ms (`Set.insert` ms) (qidModule x)
-- -----------------------------------------------------------------------------
-- Internal reader monad
-- -----------------------------------------------------------------------------
data TransEnv = TransEnv
{ moduleIdent :: ModuleIdent
, valueEnv :: ValueEnv
, tyconEnv :: TCEnv
}
type TransM a = R.Reader TransEnv a
getValueEnv :: TransM ValueEnv
getValueEnv = R.asks valueEnv
getTCEnv :: TransM TCEnv
getTCEnv = R.asks tyconEnv
trQualify :: Ident -> TransM QualIdent
trQualify i = flip qualifyWith i <$> R.asks moduleIdent
getArity :: QualIdent -> TransM Int
getArity qid = do
vEnv <- getValueEnv
return $ case qualLookupValue qid vEnv of
[DataConstructor _ a _ _] -> a
[NewtypeConstructor _ _ _] -> 1
[Value _ _ a _] -> a
[Label _ _ _] -> 1
_ ->
internalError $ "CurryToIL.getArity: " ++ show qid
-- Return the type of a constructor
constrType :: QualIdent -> TransM Type
constrType c = do
vEnv <- getValueEnv
case qualLookupValue c vEnv of
[DataConstructor _ _ _ (ForAll _ (PredType _ ty))] -> return ty
[NewtypeConstructor _ _ (ForAll _ (PredType _ ty))] -> return ty
_ -> internalError $ "CurryToIL.constrType: " ++ show c
-- Return the kinds of a type constructor's type variables
tcTVarKinds :: QualIdent -> TransM [Kind]
tcTVarKinds qid = do
tcEnv <- getTCEnv
let mid = fromJust $ qidModule qid
kind = tcKind mid qid tcEnv
return $ kindArgs kind
-- -----------------------------------------------------------------------------
-- Translation
-- -----------------------------------------------------------------------------
-- At the top-level, the compiler has to translate data type, newtype,
-- function, and external declarations. When translating a data type or
-- newtype declaration, we ignore the types in the declaration and lookup
-- the types of the constructors in the type environment instead because
-- these types are already fully expanded, i.e., they do not include any
-- alias types.
trDecl :: Decl Type -> TransM [IL.Decl]
trDecl (DataDecl _ tc tvs cs _) = (:[]) <$> trData tc tvs cs
trDecl (NewtypeDecl _ tc tvs nc _) = (:[]) <$> trNewtype tc tvs nc
trDecl (ExternalDataDecl _ tc tvs) = (:[]) <$> trExternalData tc tvs
trDecl (FunctionDecl _ _ f eqs) = (:[]) <$> trFunction f eqs
trDecl (ExternalDecl _ vs) = mapM trExternal vs
trDecl _ = return []
trData :: Ident -> [Ident] -> [ConstrDecl] -> TransM IL.Decl
trData tc tvs cs = do
tc' <- trQualify tc
ks <- tcTVarKinds tc'
IL.DataDecl tc' (transKind <$> ks) <$> mapM trConstrDecl cs
trNewtype :: Ident -> [Ident] -> NewConstrDecl -> TransM IL.Decl
trNewtype tc tvs nc = do
tc' <- trQualify tc
ks <- tcTVarKinds tc'
IL.NewtypeDecl tc' (transKind <$> ks) <$> trNewConstrDecl nc
trConstrDecl :: ConstrDecl -> TransM IL.ConstrDecl
trConstrDecl d = do
c' <- trQualify (constr d)
ty' <- arrowArgs <$> constrType c'
tcEnv <- getTCEnv
return $ IL.ConstrDecl c' (map (transType tcEnv) ty')
where
constr (ConstrDecl _ c _) = c
constr (ConOpDecl _ _ op _) = op
constr (RecordDecl _ c _) = c
trNewConstrDecl :: NewConstrDecl -> TransM IL.NewConstrDecl
trNewConstrDecl d = do
c' <- trQualify (constr d)
ty' <- arrowArgs <$> constrType c'
tcEnv <- getTCEnv
case ty' of
[ty] -> return $ IL.NewConstrDecl c' (transType tcEnv ty)
_ -> internalError "CurryToIL.trNewConstrDecl: invalid constructor type"
where
constr (NewConstrDecl _ c _) = c
constr (NewRecordDecl _ c _) = c
trExternalData :: Ident -> [Ident] -> TransM IL.Decl
trExternalData tc tvs = do
tc' <- trQualify tc
ks <- tcTVarKinds tc'
return $ IL.ExternalDataDecl tc' (transKind <$> ks)
trExternal :: Var Type -> TransM IL.Decl
trExternal (Var ty f) = do
tcEnv <- getTCEnv
f' <- trQualify f
a <- getArity f'
return $ IL.ExternalDecl f' a (transType tcEnv $ polyType ty)
-- The type representation in the intermediate language does not support
-- types with higher order kinds. Therefore, the type transformations has
-- to transform all types to first order terms. To that end, we assume the
-- existence of a type synonym 'type Apply f a = f a'. In addition, the type
-- representation of the intermediate language does not support constrained
-- type variables and skolem types. The former are fixed and the later are
-- replaced by fresh type constructors.
transType :: TCEnv -> Type -> IL.Type
transType tcEnv ty' = transType' ty' []
where
ks = transTVars tcEnv ty'
transType' (TypeConstructor tc) = IL.TypeConstructor tc
transType' (TypeApply ty1 ty2) = transType' ty1 . (transType' ty2 [] :)
transType' (TypeVariable tv) = foldl applyType' (IL.TypeVariable tv)
transType' (TypeConstrained tys _) = transType' (head tys)
transType' (TypeArrow ty1 ty2) =
foldl applyType' (IL.TypeArrow (transType' ty1 []) (transType' ty2 []))
transType' (TypeForall tvs ty) =
foldl applyType' (IL.TypeForall tvs' (transType' ty []))
where tvs' = filter ((`elem` tvs) . fst) ks
applyType' :: IL.Type -> IL.Type -> IL.Type
applyType' ty1 ty2 =
IL.TypeConstructor (qualifyWith preludeMIdent (mkIdent "Apply")) [ty1, ty2]
-- We need to existentially quantify all variables in some types
polyType :: Type -> Type
polyType (TypeForall _ ty) = polyType ty
polyType ty =
let vs = nub $ typeVars ty
in if null vs then ty else TypeForall vs ty
-- We need to infer kinds for the quantified variables.
-- We already checked the correctness of all Kinds earlier,
-- thus we know that we will be able to unify all the inferred equations.
-- We can also keep a flat environment,
-- as all variables have already been renamed.
data KIS = KIS
{ _nextId :: Int
, kinds :: Map.Map Int IL.Kind
}
freshId :: S.State KIS Int
freshId = do
KIS i ks <- S.get
S.put (KIS (i+1) ks)
return i
transTVars :: TCEnv -> Type -> [(Int, IL.Kind)]
transTVars tcEnv ty' =
Map.toList $ kinds $ S.execState (build ty' IL.KindStar) (KIS 0 Map.empty)
where
build :: Type -> IL.Kind -> S.State KIS ()
build (TypeArrow ty1 ty2) _ =
build ty1 IL.KindStar >> build ty2 IL.KindStar
build (TypeConstrained tys _) k =
build (head tys) k
build (TypeForall _ ty) k =
build ty k
build (TypeVariable tv) k = do
KIS i ks <- S.get
-- get current kind
let k' = Map.findWithDefault k tv ks
-- unify it
let s = unifyKind k k'
-- apply substitution
let ks' = fmap (applyKindSubst s) $ Map.insert tv k' ks
S.put (KIS i ks')
build (TypeConstructor _) _ = return ()
build ta@(TypeApply _ _) k =
let (ty, tys) = unapplyType True ta
in case ty of
TypeConstructor tc -> do
let k' = tcKind (fromJust $ qidModule tc) tc tcEnv
mapM_ (uncurry build) (zip tys $ unarrowKind $ transKind k')
_ -> do -- var of forall
-- construct new kind vars
ks <- mapM (const (freshId >>= return . IL.KindVariable)) tys
-- infer kind for v
build ty (foldr IL.KindArrow k ks)
-- infer kinds for args
mapM_ (uncurry build) (zip tys ks)
type KindSubst = Map.Map Int IL.Kind
transKind :: Kind -> IL.Kind
transKind KindStar = IL.KindStar
transKind (KindVariable _) = IL.KindStar
transKind (KindArrow k1 k2) = IL.KindArrow (transKind k1) (transKind k2)
unarrowKind :: IL.Kind -> [IL.Kind]
unarrowKind (IL.KindArrow k1 k2) = k1 : unarrowKind k2
unarrowKind k = [k]
applyKindSubst :: KindSubst -> IL.Kind -> IL.Kind
applyKindSubst _ IL.KindStar =
IL.KindStar
applyKindSubst s (IL.KindArrow k1 k2) =
IL.KindArrow (applyKindSubst s k1) (applyKindSubst s k2)
applyKindSubst s v@(IL.KindVariable i) =
Map.findWithDefault v i s
composeKindSubst :: KindSubst -> KindSubst -> KindSubst
composeKindSubst s1 s2 = Map.map (applyKindSubst s1) s2 `Map.union` s1
unifyKind :: IL.Kind -> IL.Kind -> KindSubst
unifyKind IL.KindStar IL.KindStar = Map.empty
unifyKind (IL.KindVariable i) k = Map.singleton i k
unifyKind k (IL.KindVariable i) = Map.singleton i k
unifyKind (IL.KindArrow k1 k2) (IL.KindArrow k1' k2') =
let s1 = unifyKind k1 k1'
s2 = unifyKind (applyKindSubst s1 k2) (applyKindSubst s1 k2')
in s1 `composeKindSubst` s2
unifyKind k1 k2 = error $ "Transformation.CurryToIL.unifyKind: " ++ show k1 ++ ", " ++ show k2
-- Each function in the program is translated into a function of the
-- intermediate language. The arguments of the function are renamed such
-- that all variables occurring in the same position (in different
-- equations) have the same name. This is necessary in order to
-- facilitate the translation of pattern matching into a 'case' expression.
-- We use the following simple convention here: The top-level
-- arguments of the function are named from left to right '_1', '_2',
-- and so on. The names of nested arguments are constructed by appending
-- '_1', '_2', etc. from left to right to the name that were assigned
-- to a variable occurring at the position of the constructor term.
-- Some special care is needed for the selector functions introduced by
-- the compiler in place of pattern bindings. In order to generate the
-- code for updating all pattern variables, the equality of names between
-- the pattern variables in the first argument of the selector function
-- and their repeated occurrences in the remaining arguments must be
-- preserved. This means that the second and following arguments of a
-- selector function have to be renamed according to the name mapping
-- computed for its first argument.
trFunction :: Ident -> [Equation Type] -> TransM IL.Decl
trFunction f eqs = do
f' <- trQualify f
tcEnv <- getTCEnv
let tys = map typeOf ts
ty' = transType tcEnv $ polyType $ foldr TypeArrow (typeOf rhs) tys
vs' = zip (map (transType tcEnv) tys) vs
alts <- mapM (trEquation vs ws) eqs
return $ IL.FunctionDecl f' vs' ty' (flexMatch vs' alts)
where
-- vs are the variables needed for the function: _1, _2, etc.
-- ws is an infinite list for introducing additional variables later
Equation _ lhs rhs = head eqs
(_, ts) = flatLhs lhs
(vs, ws) = splitAt (length ts) (argNames (mkIdent ""))
trEquation :: [Ident] -- identifiers for the function's parameters
-> [Ident] -- infinite list of additional identifiers
-> Equation Type -- equation to be translated
-> TransM Match -- nested constructor terms + translated RHS
trEquation vs vs' (Equation _ (FunLhs _ _ ts) rhs) = do
-- construct renaming of variables inside constructor terms
let patternRenaming = foldr2 bindRenameEnv Map.empty vs ts
-- translate right-hand-side
rhs' <- trRhs vs' patternRenaming rhs
-- convert patterns
tcEnv <- getTCEnv
return (zipWith (trPattern tcEnv) vs ts, rhs')
trEquation _ _ _
= internalError "Translation of non-FunLhs euqation not defined"
type RenameEnv = Map.Map Ident Ident
-- Construct a renaming of all variables inside the pattern to fresh identifiers
bindRenameEnv :: Ident -> Pattern a -> RenameEnv -> RenameEnv
bindRenameEnv _ (LiteralPattern _ _ _) env = env
bindRenameEnv v (VariablePattern _ _ v') env = Map.insert v' v env
bindRenameEnv v (ConstructorPattern _ _ _ ts) env
= foldr2 bindRenameEnv env (argNames v) ts
bindRenameEnv v (AsPattern _ v' t) env
= Map.insert v' v (bindRenameEnv v t env)
bindRenameEnv _ _ _
= internalError "CurryToIL.bindRenameEnv"
trRhs :: [Ident] -> RenameEnv -> Rhs Type -> TransM IL.Expression
trRhs vs env (SimpleRhs _ _ e _) = trExpr vs env e
trRhs _ _ (GuardedRhs _ _ _ _) = internalError "CurryToIL.trRhs: GuardedRhs"
-- Note that the case matching algorithm assumes that the matched
-- expression is accessible through a variable. The translation of case
-- expressions therefore introduces a let binding for the scrutinized
-- expression and immediately throws it away after the matching -- except
-- if the matching algorithm has decided to use that variable in the
-- right hand sides of the case expression. This may happen, for
-- instance, if one of the alternatives contains an as-pattern.
trExpr :: [Ident] -> RenameEnv -> Expression Type -> TransM IL.Expression
trExpr _ _ (Literal _ ty l) = do
tcEnv <- getTCEnv
return $ IL.Literal (transType tcEnv ty) (trLiteral l)
trExpr _ env (Variable _ ty v)
| isQualified v = getTCEnv >>= fun
| otherwise = do
tcEnv <- getTCEnv
case Map.lookup (unqualify v) env of
Nothing -> error $ "unexpected variable" ++ show v --TODO: Replace case by fromJust?
Just v' -> return $ IL.Variable (transType tcEnv ty) v' -- apply renaming
where
fun tcEnv = IL.Function (transType tcEnv ty) v <$> getArity v
trExpr _ _ (Constructor _ ty c) = do
tcEnv <- getTCEnv
IL.Constructor (transType tcEnv ty) c <$> getArity c
trExpr vs env (Apply _ e1 e2)
= IL.Apply <$> trExpr vs env e1 <*> trExpr vs env e2
trExpr vs env (Let _ _ ds e) = do
e' <- trExpr vs env' e
case ds of
[FreeDecl _ vs']
-> do tcEnv <- getTCEnv
return $
foldr (\ (Var ty v) -> IL.Exist v (transType tcEnv ty)) e' vs'
[d] | all (`notElem` bv d) (qfv emptyMIdent d)
-> flip IL.Let e' <$> trBinding d
_ -> flip IL.Letrec e' <$> mapM trBinding ds
where
env' = foldr2 Map.insert env bvs bvs
bvs = bv ds
trBinding (PatternDecl _ (VariablePattern _ _ v) rhs)
= IL.Binding v <$> trRhs vs env' rhs
trBinding p = error $ "unexpected binding: " ++ show p
trExpr (v:vs) env (Case _ _ ct e alts) = do
-- the ident v is used for the case expression subject, as this could
-- be referenced in the case alternatives by a variable pattern
e' <- trExpr vs env e
tcEnv <- getTCEnv
let matcher = if ct == Flex then flexMatch else rigidMatch
ty' = transType tcEnv $ typeOf e
expr <- matcher [(ty', v)] <$> mapM (trAlt (v:vs) env) alts
return $ case expr of
IL.Case mode (IL.Variable _ v') alts'
-- subject is not referenced -> forget v and insert subject
| v == v' && v `notElem` fv alts' -> IL.Case mode e' alts'
_
-- subject is referenced -> introduce binding for v as subject
| v `elem` fv expr -> IL.Let (IL.Binding v e') expr
| otherwise -> expr
trExpr vs env (Typed _ e _) = do
tcEnv <- getTCEnv
e' <- trExpr vs env e
return $ IL.Typed e' (transType tcEnv $ typeOf e)
trExpr _ _ _ = internalError "CurryToIL.trExpr"
trAlt :: [Ident] -> RenameEnv -> Alt Type -> TransM Match
trAlt ~(v:vs) env (Alt _ t rhs) = do
tcEnv <- getTCEnv
rhs' <- trRhs vs (bindRenameEnv v t env) rhs
return ([trPattern tcEnv v t], rhs')
trLiteral :: Literal -> IL.Literal
trLiteral (Char c) = IL.Char c
trLiteral (Int i) = IL.Int i
trLiteral (Float f) = IL.Float f
trLiteral _ = internalError "CurryToIL.trLiteral"
-- -----------------------------------------------------------------------------
-- Translation of Patterns
-- -----------------------------------------------------------------------------
data NestedTerm = NestedTerm IL.ConstrTerm [NestedTerm] deriving Show
pattern :: NestedTerm -> IL.ConstrTerm
pattern (NestedTerm t _) = t
arguments :: NestedTerm -> [NestedTerm]
arguments (NestedTerm _ ts) = ts
trPattern :: TCEnv -> Ident -> Pattern Type -> NestedTerm
trPattern tcEnv _ (LiteralPattern _ ty l)
= NestedTerm (IL.LiteralPattern (transType tcEnv ty) $ trLiteral l) []
trPattern tcEnv v (VariablePattern _ ty _)
= NestedTerm (IL.VariablePattern (transType tcEnv ty) v) []
trPattern tcEnv v (ConstructorPattern _ ty c ts)
= NestedTerm (IL.ConstructorPattern (transType tcEnv ty) c vs')
(zipWith (trPattern tcEnv) vs ts)
where vs = argNames v
vs' = zip (map (transType tcEnv . typeOf) ts) vs
trPattern tcEnv v (AsPattern _ _ t)
= trPattern tcEnv v t
trPattern _ _ _
= internalError "CurryToIL.trPattern"
argNames :: Ident -> [Ident]
argNames v = [mkIdent (prefix ++ show i) | i <- [1 :: Integer ..] ]
where prefix = idName v ++ "_"
-- -----------------------------------------------------------------------------
-- Flexible Pattern Matching Algorithm
-- -----------------------------------------------------------------------------
-- The pattern matching code searches for the left-most inductive
-- argument position in the left hand sides of all rules defining an
-- equation. An inductive position is a position where all rules have a
-- constructor rooted term. If such a position is found, a flexible 'case'
-- expression is generated for the argument at that position. The
-- matching code is then computed recursively for all of the alternatives
-- independently. If no inductive position is found, the algorithm looks
-- for the left-most demanded argument position, i.e., a position where
-- at least one of the rules has a constructor rooted term. If such a
-- position is found, an 'or' expression is generated with those
-- cases that have a variable at the argument position in one branch and
-- all other rules in the other branch. If there is no demanded position,
-- the pattern matching is finished and the compiler translates the right
-- hand sides of the remaining rules, eventually combining them using
-- 'or' expressions.
-- Actually, the algorithm below combines the search for inductive and
-- demanded positions. The function 'flexMatch' scans the argument
-- lists for the left-most demanded position. If this turns out to be
-- also an inductive position, the function 'flexMatchInductive' is
-- called in order to generate a flexible 'case' expression. Otherwise, the
-- function 'optFlexMatch' is called that tries to find an inductive
-- position in the remaining arguments. If one is found,
-- 'flexMatchInductive' is called, otherwise the function
-- 'optFlexMatch' uses the demanded argument position found by 'flexMatch'.
-- a @Match@ is a list of patterns and the respective expression.
type Match = ([NestedTerm], IL.Expression)
-- a @Match'@ is a @Match@ with skipped patterns during the search for an
-- inductive position.
type Match' = (FunList NestedTerm, [NestedTerm], IL.Expression)
-- Functional lists
type FunList a = [a] -> [a]
flexMatch :: [(IL.Type, Ident)] -- variables to be matched
-> [Match] -- alternatives
-> IL.Expression -- result expression
flexMatch [] alts = foldl1 IL.Or (map snd alts)
flexMatch (v:vs) alts
| notDemanded = varExp
| isInductive = conExp
| otherwise = optFlexMatch (IL.Or conExp varExp) (v:) vs (map skipPat alts)
where
isInductive = null varAlts
notDemanded = null conAlts
-- separate variable and constructor patterns
(varAlts, conAlts) = partition isVarMatch (map tagAlt alts)
-- match variables
varExp = flexMatch vs (map snd varAlts)
-- match constructors
conExp = flexMatchInductive id v vs (map prep conAlts)
prep (p, (ts, e)) = (p, (id, ts, e))
-- Search for the next inductive position
optFlexMatch :: IL.Expression -- default expression
-> FunList (IL.Type, Ident) -- skipped variables
-> [(IL.Type, Ident)] -- next variables
-> [Match'] -- alternatives
-> IL.Expression
optFlexMatch def _ [] _ = def
optFlexMatch def prefix (v:vs) alts
| isInductive = flexMatchInductive prefix v vs alts'
| otherwise = optFlexMatch def (prefix . (v:)) vs (map skipPat' alts)
where
isInductive = not (any isVarMatch alts')
alts' = map tagAlt' alts
-- Generate a case expression matching the inductive position
flexMatchInductive :: FunList (IL.Type, Ident) -- skipped variables
-> (IL.Type, Ident) -- current variable
-> [(IL.Type, Ident)] -- next variables
-> [(IL.ConstrTerm, Match')] -- alternatives
-> IL.Expression
flexMatchInductive prefix v vs as
= IL.Case IL.Flex (uncurry IL.Variable v) (flexMatchAlts as)
where
-- create alternatives for the different constructors
flexMatchAlts [] = []
flexMatchAlts ((t, e) : alts) = IL.Alt t expr : flexMatchAlts others
where
-- match nested patterns for same constructors
expr = flexMatch (prefix (vars t ++ vs)) (map expandVars (e : map snd same))
expandVars (pref, ts1, e') = (pref ts1, e')
-- split into same and other constructors
(same, others) = partition ((t ==) . fst) alts
-- -----------------------------------------------------------------------------
-- Rigid Pattern Matching Algorithm
-- -----------------------------------------------------------------------------
-- Matching in a 'case'-expression works a little bit differently.
-- In this case, the alternatives are matched from the first to the last
-- alternative and the first matching alternative is chosen. All
-- remaining alternatives are discarded.
-- TODO: The case matching algorithm should use type information in order
-- to detect total matches and immediately discard all alternatives which
-- cannot be reached.
rigidMatch :: [(IL.Type, Ident)] -> [Match] -> IL.Expression
rigidMatch vs alts = rigidOptMatch (snd $ head alts) id vs (map prepare alts)
where prepare (ts, e) = (id, ts, e)
rigidOptMatch :: IL.Expression -- default expression
-> FunList (IL.Type, Ident) -- variables to be matched next
-> [(IL.Type, Ident)] -- variables to be matched afterwards
-> [Match'] -- translated equations
-> IL.Expression
-- if there are no variables left: return the default expression
rigidOptMatch def _ [] _ = def
rigidOptMatch def prefix (v : vs) alts
| isDemanded = rigidMatchDemanded prefix v vs alts'
| otherwise = rigidOptMatch def (prefix . (v:)) vs (map skipPat' alts)
where
isDemanded = not $ isVarMatch (head alts')
alts' = map tagAlt' alts
-- Generate a case expression matching the demanded position.
-- This algorithm constructs a branch for all contained patterns, where
-- the right-hand side then respects the order of the patterns.
-- Thus, the expression
-- case x of
-- [] -> []
-- ys -> ys
-- y:ys -> [y]
-- gets translated to
-- case x of
-- [] -> []
-- y:ys -> x
-- x -> x
rigidMatchDemanded :: FunList (IL.Type, Ident) -- skipped variables
-> (IL.Type, Ident) -- current variable
-> [(IL.Type, Ident)] -- next variables
-> [(IL.ConstrTerm, Match')] -- alternatives
-> IL.Expression
rigidMatchDemanded prefix v vs alts = IL.Case IL.Rigid (uncurry IL.Variable v)
$ map caseAlt (consPats ++ varPats)
where
-- N.B.: @varPats@ is either empty or a singleton list due to nub
(varPats, consPats) = partition isVarPattern $ nub $ map fst alts
caseAlt t = IL.Alt t expr
where
expr = rigidMatch (prefix $ vars t ++ vs) (matchingCases alts)
-- matchingCases selects the matching alternatives
-- and recursively matches the remaining patterns
matchingCases a = map (expandVars (vars t)) $ filter (matches . fst) a
matches t' = t == t' || isVarPattern t'
expandVars vs' (p, (pref, ts1, e)) = (pref ts2, e)
where ts2 | isVarPattern p = map var2Pattern vs' ++ ts1
| otherwise = ts1
var2Pattern v' = NestedTerm (uncurry IL.VariablePattern v') []
-- -----------------------------------------------------------------------------
-- Pattern Matching Auxiliaries
-- -----------------------------------------------------------------------------
isVarPattern :: IL.ConstrTerm -> Bool
isVarPattern (IL.VariablePattern _ _) = True
isVarPattern _ = False
isVarMatch :: (IL.ConstrTerm, a) -> Bool
isVarMatch = isVarPattern . fst
vars :: IL.ConstrTerm -> [(IL.Type, Ident)]
vars (IL.ConstructorPattern _ _ vs) = vs
vars _ = []
-- tagAlt extracts the structure of the first pattern
tagAlt :: Match -> (IL.ConstrTerm, Match)
tagAlt (t:ts, e) = (pattern t, (arguments t ++ ts, e))
tagAlt ([] , _) = error "CurryToIL.tagAlt: empty pattern list"
-- skipPat skips the current pattern position for later matching
skipPat :: Match -> Match'
skipPat (t:ts, e) = ((t:), ts, e)
skipPat ([] , _) = error "CurryToIL.skipPat: empty pattern list"
-- tagAlt' extracts the next pattern
tagAlt' :: Match' -> (IL.ConstrTerm, Match')
tagAlt' (pref, t:ts, e') = (pattern t, (pref, arguments t ++ ts, e'))
tagAlt' (_ , [] , _ ) = error "CurryToIL.tagAlt': empty pattern list"
-- skipPat' skips the current argument for later matching
skipPat' :: Match' -> Match'
skipPat' (pref, t:ts, e') = (pref . (t:), ts, e')
skipPat' (_ , [] , _ ) = error "CurryToIL.skipPat': empty pattern list"