module Agda.TypeChecking.Primitive where
import Control.Monad
import Control.Monad.Error
import Data.Map (Map)
import qualified Data.Map as Map
import Data.Char
import Agda.Interaction.Options
import Agda.Syntax.Position
import Agda.Syntax.Common hiding (Nat)
import Agda.Syntax.Internal
import Agda.Syntax.Literal
import Agda.Syntax.Concrete.Pretty ()
import Agda.Syntax.Abstract.Name
import qualified Agda.Syntax.Concrete.Name as C
import Agda.TypeChecking.Monad
import Agda.TypeChecking.Monad.Builtin
import Agda.TypeChecking.Reduce
import Agda.TypeChecking.Substitute
import Agda.TypeChecking.Errors
import Agda.TypeChecking.Quote (quoteType, quotingKit)
import Agda.TypeChecking.Pretty ()
import Agda.TypeChecking.Conversion
import Agda.TypeChecking.Constraints
import Agda.TypeChecking.Level
import Agda.Utils.Monad
import Agda.Utils.Pretty (pretty)
#include "../undefined.h"
import Agda.Utils.Impossible
constructorForm :: Term -> TCM Term
constructorForm v = case ignoreSharing v of
Lit (LitInt r n) -> cons primZero primSuc (Lit . LitInt r) n
_ -> return v
where
cons pZero pSuc lit n
| n == 0 = pZero
| n > 0 = do
s <- pSuc
return $ s `apply` [defaultArg $ lit $ n 1]
| otherwise = return v
data PrimitiveImpl = PrimImpl Type PrimFun
newtype Str = Str { unStr :: String }
deriving (Eq, Ord)
newtype Nat = Nat { unNat :: Integer }
deriving (Eq, Ord, Num, Integral, Enum, Real)
newtype Lvl = Lvl { unLvl :: Integer }
deriving (Eq, Ord)
instance Show Lvl where
show = show . unLvl
instance Show Nat where
show = show . unNat
class PrimType a where
primType :: a -> TCM Type
instance (PrimType a, PrimType b) => PrimTerm (a -> b) where
primTerm _ = unEl <$> (primType (undefined :: a) --> primType (undefined :: b))
instance PrimTerm a => PrimType a where
primType _ = el $ primTerm (undefined :: a)
class PrimTerm a where primTerm :: a -> TCM Term
instance PrimTerm Integer where primTerm _ = primInteger
instance PrimTerm Bool where primTerm _ = primBool
instance PrimTerm Char where primTerm _ = primChar
instance PrimTerm Double where primTerm _ = primFloat
instance PrimTerm Str where primTerm _ = primString
instance PrimTerm Nat where primTerm _ = primNat
instance PrimTerm Lvl where primTerm _ = primLevel
instance PrimTerm QName where primTerm _ = primQName
instance PrimTerm Type where primTerm _ = primAgdaType
instance PrimTerm a => PrimTerm [a] where
primTerm _ = list (primTerm (undefined :: a))
instance PrimTerm a => PrimTerm (IO a) where
primTerm _ = io (primTerm (undefined :: a))
class ToTerm a where
toTerm :: TCM (a -> Term)
instance ToTerm Integer where toTerm = return $ Lit . LitInt noRange
instance ToTerm Nat where toTerm = return $ Lit . LitInt noRange . unNat
instance ToTerm Lvl where toTerm = return $ Level . Max . (:[]) . ClosedLevel . unLvl
instance ToTerm Double where toTerm = return $ Lit . LitFloat noRange
instance ToTerm Char where toTerm = return $ Lit . LitChar noRange
instance ToTerm Str where toTerm = return $ Lit . LitString noRange . unStr
instance ToTerm QName where toTerm = return $ Lit . LitQName noRange
instance ToTerm Bool where
toTerm = do
true <- primTrue
false <- primFalse
return $ \b -> if b then true else false
instance ToTerm Type where
toTerm = snd <$> quotingKit
buildList :: TCM ([Term] -> Term)
buildList = do
nil' <- primNil
cons' <- primCons
let nil = nil'
cons x xs = cons' `apply` [defaultArg x, defaultArg xs]
return $ foldr cons nil
instance (PrimTerm a, ToTerm a) => ToTerm [a] where
toTerm = do
mkList <- buildList
fromA <- toTerm
return $ mkList . map fromA
type FromTermFunction a = Arg Term -> TCM (Reduced (MaybeReduced (Arg Term)) a)
class FromTerm a where
fromTerm :: TCM (FromTermFunction a)
instance FromTerm Integer where
fromTerm = fromLiteral $ \l -> case l of
LitInt _ n -> Just n
_ -> Nothing
instance FromTerm Nat where
fromTerm = fromLiteral $ \l -> case l of
LitInt _ n -> Just $ Nat n
_ -> Nothing
instance FromTerm Lvl where
fromTerm = fromReducedTerm $ \l -> case l of
Level (Max [ClosedLevel n]) -> Just $ Lvl n
_ -> Nothing
instance FromTerm Double where
fromTerm = fromLiteral $ \l -> case l of
LitFloat _ x -> Just x
_ -> Nothing
instance FromTerm Char where
fromTerm = fromLiteral $ \l -> case l of
LitChar _ c -> Just c
_ -> Nothing
instance FromTerm Str where
fromTerm = fromLiteral $ \l -> case l of
LitString _ s -> Just $ Str s
_ -> Nothing
instance FromTerm QName where
fromTerm = fromLiteral $ \l -> case l of
LitQName _ x -> Just x
_ -> Nothing
instance FromTerm Bool where
fromTerm = do
true <- primTrue
false <- primFalse
fromReducedTerm $ \t -> case t of
_ | t === true -> Just True
| t === false -> Just False
| otherwise -> Nothing
where
Def x [] === Def y [] = x == y
Con x [] === Con y [] = x == y
Var n [] === Var m [] = n == m
_ === _ = False
instance (ToTerm a, FromTerm a) => FromTerm [a] where
fromTerm = do
nil' <- primNil
cons' <- primCons
nil <- isCon nil'
cons <- isCon cons'
toA <- fromTerm
fromA <- toTerm
return $ mkList nil cons toA fromA
where
isCon (Lam _ b) = isCon $ absBody b
isCon (Con c _) = return c
isCon (Shared p) = isCon (derefPtr p)
isCon v = do
d <- prettyTCM v
typeError $ GenericError $ "expected constructor in built-in binding to " ++ show d
mkList nil cons toA fromA t = do
b <- reduceB t
let t = ignoreBlocking b
let arg = Arg (argHiding t) (argRelevance t)
case unArg t of
Con c []
| c == nil -> return $ YesReduction []
Con c [x,xs]
| c == cons ->
redBind (toA x)
(\x' -> notReduced $ arg $ Con c [ignoreReduced x',xs]) $ \y ->
redBind
(mkList nil cons toA fromA xs)
(fmap $ \xs' -> arg $ Con c [defaultArg $ fromA y, xs']) $ \ys ->
redReturn (y : ys)
_ -> return $ NoReduction (reduced b)
redBind :: TCM (Reduced a a') -> (a -> b) ->
(a' -> TCM (Reduced b b')) -> TCM (Reduced b b')
redBind ma f k = do
r <- ma
case r of
NoReduction x -> return $ NoReduction $ f x
YesReduction y -> k y
redReturn :: a -> TCM (Reduced a' a)
redReturn = return . YesReduction
fromReducedTerm :: (Term -> Maybe a) -> TCM (FromTermFunction a)
fromReducedTerm f = return $ \t -> do
b <- reduceB t
case f $ ignoreSharing $ unArg (ignoreBlocking b) of
Just x -> return $ YesReduction x
Nothing -> return $ NoReduction (reduced b)
fromLiteral :: (Literal -> Maybe a) -> TCM (FromTermFunction a)
fromLiteral f = fromReducedTerm $ \t -> case t of
Lit lit -> f lit
_ -> Nothing
primTrustMe :: TCM PrimitiveImpl
primTrustMe = do
clo <- commandLineOptions
when (optSafe clo) (typeError SafeFlagPrimTrustMe)
t <- hPi "a" (el primLevel) $
hPi "A" (return $ sort $ varSort 0) $
hPi "x" (El (varSort 1) <$> varM 0) $
hPi "y" (El (varSort 2) <$> varM 1) $
El (varSort 3) <$>
primEquality <#> varM 3 <#> varM 2 <@> varM 1 <@> varM 0
Con rf [] <- ignoreSharing <$> primRefl
n <- conPars . theDef <$> getConstInfo rf
let refl x | n == 2 = Con rf [Arg Hidden Forced x]
| n == 3 = Con rf []
| otherwise = __IMPOSSIBLE__
return $ PrimImpl t $ PrimFun __IMPOSSIBLE__ 4 $ \ts ->
case ts of
[a, t, x, y] -> liftTCM $ do
noConstraints $
equalTerm (El (Type $ lvlView $ unArg a) (unArg t))
(unArg x) (unArg y)
redReturn (refl $ unArg x)
`catchError` \_ -> return (NoReduction $ map notReduced [a, t, x, y])
_ -> __IMPOSSIBLE__
primQNameType :: TCM PrimitiveImpl
primQNameType = mkPrimFun1TCM (el primQName --> el primAgdaType) typeOfConst
primQNameDefinition :: TCM PrimitiveImpl
primQNameDefinition = do
let argQName qn = [defaultArg (Lit (LitQName noRange qn))]
app mt xs = do t <- mt
return $ apply t xs
con qn Function{} = app primAgdaDefinitionFunDef (argQName qn)
con qn Datatype{} = app primAgdaDefinitionDataDef (argQName qn)
con qn Record{} = app primAgdaDefinitionRecordDef (argQName qn)
con _ Axiom{} = app primAgdaDefinitionPostulate []
con _ Primitive{} = app primAgdaDefinitionPrimitive []
con _ Constructor{} = app primAgdaDefinitionDataConstructor []
unquoteQName <- fromTerm
t <- el primQName --> el primAgdaDefinition
return $ PrimImpl t $ PrimFun __IMPOSSIBLE__ 1 $ \ts ->
case ts of
[v] -> liftTCM $
redBind (unquoteQName v)
(\v' -> [v']) $ \x ->
redReturn =<< con x . theDef =<< getConstInfo x
_ -> __IMPOSSIBLE__
primDataConstructors :: TCM PrimitiveImpl
primDataConstructors = mkPrimFun1TCM (el primAgdaDataDef --> el (list primQName))
(fmap (dataCons . theDef) . getConstInfo)
mkPrimLevelZero :: TCM PrimitiveImpl
mkPrimLevelZero = do
t <- primType (undefined :: Lvl)
return $ PrimImpl t $ PrimFun __IMPOSSIBLE__ 0 $ \_ -> redReturn $ Level $ Max []
mkPrimLevelSuc :: TCM PrimitiveImpl
mkPrimLevelSuc = do
t <- primType (id :: Lvl -> Lvl)
return $ PrimImpl t $ PrimFun __IMPOSSIBLE__ 1 $ \ ~[a] -> liftTCM $ do
l <- levelView $ unArg a
redReturn $ Level $ levelSuc l
mkPrimLevelMax :: TCM PrimitiveImpl
mkPrimLevelMax = do
t <- primType (max :: Op Lvl)
return $ PrimImpl t $ PrimFun __IMPOSSIBLE__ 2 $ \ ~[a, b] -> liftTCM $ do
Max as <- levelView $ unArg a
Max bs <- levelView $ unArg b
redReturn $ Level $ levelMax $ as ++ bs
mkPrimFun1TCM :: (FromTerm a, ToTerm b) => TCM Type -> (a -> TCM b) -> TCM PrimitiveImpl
mkPrimFun1TCM mt f = do
toA <- fromTerm
fromB <- toTerm
t <- mt
return $ PrimImpl t $ PrimFun __IMPOSSIBLE__ 1 $ \ts ->
case ts of
[v] -> liftTCM $
redBind (toA v)
(\v' -> [v']) $ \x ->
redReturn . fromB =<< f x
_ -> __IMPOSSIBLE__
mkPrimFun1 :: (PrimType a, PrimType b, FromTerm a, ToTerm b) =>
(a -> b) -> TCM PrimitiveImpl
mkPrimFun1 f = do
toA <- fromTerm
fromB <- toTerm
t <- primType f
return $ PrimImpl t $ PrimFun __IMPOSSIBLE__ 1 $ \ts ->
case ts of
[v] -> liftTCM $
redBind (toA v)
(\v' -> [v']) $ \x ->
redReturn $ fromB $ f x
_ -> __IMPOSSIBLE__
mkPrimFun2 :: (PrimType a, PrimType b, PrimType c, FromTerm a, ToTerm a, FromTerm b, ToTerm c) =>
(a -> b -> c) -> TCM PrimitiveImpl
mkPrimFun2 f = do
toA <- fromTerm
fromA <- toTerm
toB <- fromTerm
fromC <- toTerm
t <- primType f
return $ PrimImpl t $ PrimFun __IMPOSSIBLE__ 2 $ \ts ->
case ts of
[v,w] -> liftTCM $
redBind (toA v)
(\v' -> [v', notReduced w]) $ \x ->
redBind (toB w)
(\w' -> [ reduced $ notBlocked $ Arg (argHiding v) (argRelevance v) (fromA x)
, w']) $ \y ->
redReturn $ fromC $ f x y
_ -> __IMPOSSIBLE__
mkPrimFun4 :: ( PrimType a, FromTerm a, ToTerm a
, PrimType b, FromTerm b, ToTerm b
, PrimType c, FromTerm c, ToTerm c
, PrimType d, FromTerm d
, PrimType e, ToTerm e) =>
(a -> b -> c -> d -> e) -> TCM PrimitiveImpl
mkPrimFun4 f = do
(toA, fromA) <- (,) <$> fromTerm <*> toTerm
(toB, fromB) <- (,) <$> fromTerm <*> toTerm
(toC, fromC) <- (,) <$> fromTerm <*> toTerm
toD <- fromTerm
fromE <- toTerm
t <- primType f
return $ PrimImpl t $ PrimFun __IMPOSSIBLE__ 4 $ \ts ->
let argFrom fromX a x =
reduced $ notBlocked $ Arg (argHiding a) (argRelevance a) (fromX x)
in case ts of
[a,b,c,d] -> liftTCM $
redBind (toA a)
(\a' -> a' : map notReduced [b,c,d]) $ \x ->
redBind (toB b)
(\b' -> [argFrom fromA a x, b', notReduced c, notReduced d]) $ \y ->
redBind (toC c)
(\c' -> [ argFrom fromA a x
, argFrom fromB b y
, c', notReduced d]) $ \z ->
redBind (toD d)
(\d' -> [ argFrom fromA a x
, argFrom fromB b y
, argFrom fromC c z
, d']) $ \w ->
redReturn $ fromE $ f x y z w
_ -> __IMPOSSIBLE__
infixr 4 -->
(-->) :: TCM Type -> TCM Type -> TCM Type
a --> b = do
a' <- a
b' <- b
return $ El (getSort a' `sLub` getSort b') $ Pi (Dom NotHidden Relevant a') (NoAbs "_" b')
infixr 4 .-->
(.-->) :: TCM Type -> TCM Type -> TCM Type
a .--> b = do
a' <- a
b' <- b
return $ El (getSort a' `sLub` getSort b') $ Pi (Dom NotHidden Irrelevant a') (NoAbs "_" b')
gpi :: Hiding -> Relevance -> String -> TCM Type -> TCM Type -> TCM Type
gpi h r name a b = do
a <- a
x <- freshName_ name
b <- addCtx x (Dom h r a) b
return $ El (getSort a `dLub` Abs name (getSort b))
(Pi (Dom h r a) (Abs name b))
hPi, nPi :: String -> TCM Type -> TCM Type -> TCM Type
hPi = gpi Hidden Relevant
nPi = gpi NotHidden Relevant
varM :: Int -> TCM Term
varM = return . var
infixl 9 <@>, <#>
gApply :: Hiding -> TCM Term -> TCM Term -> TCM Term
gApply h a b = do
x <- a
y <- b
return $ x `apply` [Arg h Relevant y]
(<@>),(<#>) :: TCM Term -> TCM Term -> TCM Term
(<@>) = gApply NotHidden
(<#>) = gApply Hidden
list :: TCM Term -> TCM Term
list t = primList <@> t
io :: TCM Term -> TCM Term
io t = primIO <@> t
el :: TCM Term -> TCM Type
el t = El (mkType 0) <$> t
tset :: TCM Type
tset = return $ sort (mkType 0)
argN = Arg NotHidden Relevant
domN = Dom NotHidden Relevant
argH = Arg Hidden Relevant
domH = Dom Hidden Relevant
type Op a = a -> a -> a
type Fun a = a -> a
type Rel a = a -> a -> Bool
type Pred a = a -> Bool
primitiveFunctions :: Map String (TCM PrimitiveImpl)
primitiveFunctions = Map.fromList
[ "primIntegerPlus" |-> mkPrimFun2 ((+) :: Op Integer)
, "primIntegerMinus" |-> mkPrimFun2 (() :: Op Integer)
, "primIntegerTimes" |-> mkPrimFun2 ((*) :: Op Integer)
, "primIntegerDiv" |-> mkPrimFun2 (div :: Op Integer)
, "primIntegerMod" |-> mkPrimFun2 (mod :: Op Integer)
, "primIntegerEquality" |-> mkPrimFun2 ((==) :: Rel Integer)
, "primIntegerLess" |-> mkPrimFun2 ((<) :: Rel Integer)
, "primIntegerAbs" |-> mkPrimFun1 (Nat . abs :: Integer -> Nat)
, "primNatToInteger" |-> mkPrimFun1 (unNat :: Nat -> Integer)
, "primShowInteger" |-> mkPrimFun1 (Str . show :: Integer -> Str)
, "primNatPlus" |-> mkPrimFun2 ((+) :: Op Nat)
, "primNatMinus" |-> mkPrimFun2 ((\x y -> max 0 (x y)) :: Op Nat)
, "primNatTimes" |-> mkPrimFun2 ((*) :: Op Nat)
, "primNatDivSucAux" |-> mkPrimFun4 ((\k m n j -> k + div (max 0 $ n + m j) (m + 1)) :: Nat -> Nat -> Nat -> Nat -> Nat)
, "primNatModSucAux" |->
let aux :: Nat -> Nat -> Nat -> Nat -> Nat
aux k m n j | n > j = mod (n j 1) (m + 1)
| otherwise = k + n
in mkPrimFun4 aux
, "primNatEquality" |-> mkPrimFun2 ((==) :: Rel Nat)
, "primNatLess" |-> mkPrimFun2 ((<) :: Rel Nat)
, "primLevelZero" |-> mkPrimLevelZero
, "primLevelSuc" |-> mkPrimLevelSuc
, "primLevelMax" |-> mkPrimLevelMax
, "primIntegerToFloat" |-> mkPrimFun1 (fromIntegral :: Integer -> Double)
, "primFloatPlus" |-> mkPrimFun2 ((+) :: Op Double)
, "primFloatMinus" |-> mkPrimFun2 (() :: Op Double)
, "primFloatTimes" |-> mkPrimFun2 ((*) :: Op Double)
, "primFloatDiv" |-> mkPrimFun2 ((/) :: Op Double)
, "primFloatLess" |-> mkPrimFun2 ((<) :: Rel Double)
, "primRound" |-> mkPrimFun1 (round :: Double -> Integer)
, "primFloor" |-> mkPrimFun1 (floor :: Double -> Integer)
, "primCeiling" |-> mkPrimFun1 (ceiling :: Double -> Integer)
, "primExp" |-> mkPrimFun1 (exp :: Fun Double)
, "primLog" |-> mkPrimFun1 (log :: Fun Double)
, "primSin" |-> mkPrimFun1 (sin :: Fun Double)
, "primShowFloat" |-> mkPrimFun1 (Str . show :: Double -> Str)
, "primCharEquality" |-> mkPrimFun2 ((==) :: Rel Char)
, "primIsLower" |-> mkPrimFun1 isLower
, "primIsDigit" |-> mkPrimFun1 isDigit
, "primIsAlpha" |-> mkPrimFun1 isAlpha
, "primIsSpace" |-> mkPrimFun1 isSpace
, "primIsAscii" |-> mkPrimFun1 isAscii
, "primIsLatin1" |-> mkPrimFun1 isLatin1
, "primIsPrint" |-> mkPrimFun1 isPrint
, "primIsHexDigit" |-> mkPrimFun1 isHexDigit
, "primToUpper" |-> mkPrimFun1 toUpper
, "primToLower" |-> mkPrimFun1 toLower
, "primCharToNat" |-> mkPrimFun1 (fromIntegral . fromEnum :: Char -> Nat)
, "primNatToChar" |-> mkPrimFun1 (toEnum . fromIntegral :: Nat -> Char)
, "primShowChar" |-> mkPrimFun1 (Str . show . pretty . LitChar noRange)
, "primStringToList" |-> mkPrimFun1 unStr
, "primStringFromList" |-> mkPrimFun1 Str
, "primStringAppend" |-> mkPrimFun2 (\s1 s2 -> Str $ unStr s1 ++ unStr s2)
, "primStringEquality" |-> mkPrimFun2 ((==) :: Rel Str)
, "primShowString" |-> mkPrimFun1 (Str . show . pretty . LitString noRange . unStr)
, "primQNameType" |-> primQNameType
, "primQNameDefinition" |-> primQNameDefinition
, "primDataConstructors"|-> primDataConstructors
, "primTrustMe" |-> primTrustMe
, "primQNameEquality" |-> mkPrimFun2 ((==) :: Rel QName)
]
where
(|->) = (,)
lookupPrimitiveFunction :: String -> TCM PrimitiveImpl
lookupPrimitiveFunction x =
case Map.lookup x primitiveFunctions of
Just p -> liftTCM p
Nothing -> typeError $ NoSuchPrimitiveFunction x
lookupPrimitiveFunctionQ :: QName -> TCM (String, PrimitiveImpl)
lookupPrimitiveFunctionQ q = do
let s = case qnameName q of
Name _ x _ _ -> show x
PrimImpl t pf <- lookupPrimitiveFunction s
return (s, PrimImpl t $ pf { primFunName = q })