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|
{-# LANGUAGE OverloadedStrings #-}
{-# LANGUAGE LambdaCase #-}
{-# LANGUAGE ViewPatterns #-}
{-# LANGUAGE PatternSynonyms #-}
{-# LANGUAGE FlexibleContexts #-}
{-# LANGUAGE FlexibleInstances #-}
{-# LANGUAGE NoMonomorphismRestriction #-}
{-# LANGUAGE ScopedTypeVariables #-}
{-# LANGUAGE RankNTypes #-}
{-# LANGUAGE MultiParamTypeClasses #-}
--{-# OPTIONS_GHC -fno-warn-overlapping-patterns #-} -- TODO: remove
--{-# OPTIONS_GHC -fno-warn-unused-binds #-} -- TODO: remove
module LambdaCube.Compiler.Core where
import Data.Monoid
import Data.Function
import Data.List
import Control.Arrow hiding ((<+>))
--import LambdaCube.Compiler.Utils
import LambdaCube.Compiler.DeBruijn
import LambdaCube.Compiler.Pretty hiding (braces, parens)
import LambdaCube.Compiler.DesugaredSource
-------------------------------------------------------------------------------- names with infos
data ConName = ConName FName Int{-ordinal number, e.g. Zero:0, Succ:1-} Type
data TyConName = TyConName FName Int{-num of indices-} Type [(ConName, Type)]{-constructors-} CaseFunName
data FunName = FunName FName Int{-num of global vars-} FunDef Type
data CaseFunName = CaseFunName FName Type Int{-num of parameters-}
data TyCaseFunName = TyCaseFunName FName Type
data FunDef
= DeltaDef !Int{-arity-} (FreeVars -> [Exp] -> Exp)
| NoDef
| ExpDef Exp
class HasFName a where getFName :: a -> FName
instance HasFName ConName where getFName (ConName n _ _) = n
instance HasFName TyConName where getFName (TyConName n _ _ _ _) = n
instance HasFName FunName where getFName (FunName n _ _ _) = n
instance HasFName CaseFunName where getFName (CaseFunName n _ _) = n
instance HasFName TyCaseFunName where getFName (TyCaseFunName n _) = n
instance Eq ConName where (==) = (==) `on` getFName
instance Eq TyConName where (==) = (==) `on` getFName
instance Eq FunName where (==) = (==) `on` getFName
instance Eq CaseFunName where (==) = (==) `on` getFName
instance Eq TyCaseFunName where (==) = (==) `on` getFName
instance Show ConName where show (ConName n _ _) = show n
instance PShow ConName where pShow (ConName n _ _) = pShow n
instance Show TyConName where show (TyConName n _ _ _ _) = show n
instance PShow TyConName where pShow (TyConName n _ _ _ _) = pShow n
instance Show FunName where show (FunName n _ _ _) = show n
instance PShow FunName where pShow (FunName n _ _ _) = pShow n
instance Show CaseFunName where show (CaseFunName n _ _) = CaseName $ show n
instance PShow CaseFunName where pShow (CaseFunName n _ _) = text $ CaseName $ show n
instance Show TyCaseFunName where show (TyCaseFunName n _) = MatchName $ show n
instance PShow TyCaseFunName where pShow (TyCaseFunName n _) = text $ MatchName $ show n
-------------------------------------------------------------------------------- core expression representation
data Freq = CompileTime | RunTime -- TODO
deriving (Eq)
data Exp
= ELit Lit
| TType_ Freq
| Lam_ FreeVars Exp
| Con_ FreeVars ConName !Int{-number of ereased arguments applied-} [Exp]
| TyCon_ FreeVars TyConName [Exp]
| Pi_ FreeVars Visibility Exp Exp
| Neut Neutral
| RHS Exp{-always in hnf-}
| Let_ FreeVars ExpType Exp
data Neutral
= Var_ !Int{-De Bruijn index-}
| App__ FreeVars Neutral Exp
| CaseFun__ FreeVars CaseFunName [Exp] Neutral
| TyCaseFun__ FreeVars TyCaseFunName [Exp] Neutral
| Fun_ FreeVars FunName [Exp]{-given parameters, reversed-} Exp{-unfolded expression, in hnf-}
-------------------------------------------------------------------------------- auxiliary functions and patterns
type Type = Exp
data ExpType = ET {expr :: Exp, ty :: Type}
deriving (Eq)
{-
pattern ET a b <- ET_ a b
where ET a b = ET_ a (hnf b)
-}
instance Rearrange ExpType where
rearrange l f (ET e t) = ET (rearrange l f e) (rearrange l f t)
instance HasFreeVars ExpType where
getFreeVars (ET a b) = getFreeVars a <> getFreeVars b
instance PShow ExpType where pShow = mkDoc (False, False)
type SExp2 = SExp' ExpType
setMaxDB db = \case
Neut (Fun_ _ a b c) -> Neut $ Fun_ db a b c
pattern TType = TType_ CompileTime
infixl 2 `App`, `app_`
infixr 1 :~>
pattern NoRHS <- (isRHS -> False)
isRHS RHS{} = True
isRHS _ = False
-- TODO: elim
pattern Reverse xs <- (reverse -> xs)
where Reverse = reverse
pattern Fun f xs n <- Fun_ _ f xs n
where Fun f xs n = Fun_ (foldMap getFreeVars xs) f xs n
pattern CaseFun_ a b c <- CaseFun__ _ a b c
where CaseFun_ a b c = CaseFun__ (getFreeVars c <> foldMap getFreeVars b) a b c
pattern TyCaseFun_ a b c <- TyCaseFun__ _ a b c
where TyCaseFun_ a b c = TyCaseFun__ (foldMap getFreeVars b <> getFreeVars c) a b c
pattern App_ a b <- App__ _ a b
where App_ a b = App__ (getFreeVars a <> getFreeVars b) a b
pattern Con x n y <- Con_ _ x n y
where Con x n y = Con_ (foldMap getFreeVars y) x n y
pattern TyCon x y <- TyCon_ _ x y
where TyCon x y = TyCon_ (foldMap getFreeVars y) x y
pattern Lam y <- Lam_ _ y
where Lam y = Lam_ (lowerFreeVars (getFreeVars y)) y
pattern Pi v x y <- Pi_ _ v x y
where Pi v x y = Pi_ (getFreeVars x <> lowerFreeVars (getFreeVars y)) v x y
pattern Let x y <- Let_ _ x y
where Let x y = Let_ (getFreeVars x <> lowerFreeVars (getFreeVars y)) x y
pattern SubstLet x <- (substLet -> Just x)
substLet (Let x y) = Just $ subst 0 (expr x) y
substLet _ = Nothing
pattern CaseFun a b c = Neut (CaseFun_ a b c)
pattern TyCaseFun a b c = Neut (TyCaseFun_ a b c)
pattern Var a = Neut (Var_ a)
pattern App a b <- Neut (App_ (Neut -> a) b)
pattern DFun a t b = Neut (DFunN a t b)
-- unreducable function application
pattern UFun a b <- Neut (Fun (FunName (FTag a) _ _ t) (reverse -> b) NoRHS)
-- saturated delta function application
pattern DFunN a t xs = DFunN_ (FTag a) t xs
pattern DFunN_ a t xs <- Fun (FunName' a t) (Reverse xs) _
where DFunN_ a t xs = Fun (FunName' a t) (Reverse xs) delta
conParams (conTypeName -> TyConName _ _ _ _ (CaseFunName _ _ pars)) = pars
mkConPars n (snd . getParams . hnf -> TyCon (TyConName _ _ _ _ (CaseFunName _ _ pars)) xs) = take (min n pars) xs
--mkConPars 0 TType = [] -- ?
mkConPars n x@Neut{} = error $ "mkConPars!: " ++ ppShow x
mkConPars n x = error $ "mkConPars: " ++ ppShow (n, x)
pattern ConN s a <- Con (ConName (FTag s) _ _) _ a
tCon s i t a = Con (ConName (FTag s) i t) 0 a
tCon_ k s i t a = Con (ConName (FTag s) i t) k a
pattern TyConN s a <- TyCon (TyConName s _ _ _ _) a
pattern TTyCon s t a <- TyCon (TyConName s _ t _ _) a
pattern TTyCon0 s <- TyCon (TyConName (FTag s) _ _ _ _) []
tTyCon s t a cs = TyCon (TyConName s (error "todo: inum") t (map ((,) (error "tTyCon")) cs) $ CaseFunName (error "TTyCon-A") (error "TTyCon-B") $ length a) a
tTyCon0 s cs = TyCon (TyConName (FTag s) 0 TType (map ((,) (error "tTyCon0")) cs) $ CaseFunName (error "TTyCon0-A") (error "TTyCon0-B") 0) []
pattern a :~> b = Pi Visible a b
delta = ELit (LString "<<delta function>>") -- TODO: build an error call
pattern TConstraint <- TTyCon0 F'Constraint where TConstraint = tTyCon0 F'Constraint $ error "cs 1"
pattern Unit <- TTyCon0 F'Unit where Unit = tTyCon0 F'Unit [Unit]
pattern TInt <- TTyCon0 F'Int where TInt = tTyCon0 F'Int $ error "cs 1"
pattern TNat <- TTyCon0 F'Nat where TNat = tTyCon0 F'Nat $ error "cs 3"
pattern TBool <- TTyCon0 F'Bool where TBool = tTyCon0 F'Bool $ error "cs 4"
pattern TFloat <- TTyCon0 F'Float where TFloat = tTyCon0 F'Float $ error "cs 5"
pattern TString <- TTyCon0 F'String where TString = tTyCon0 F'String $ error "cs 6"
pattern TChar <- TTyCon0 F'Char where TChar = tTyCon0 F'Char $ error "cs 7"
pattern TOrdering <- TTyCon0 F'Ordering where TOrdering = tTyCon0 F'Ordering $ error "cs 8"
pattern TVec a b <- TyConN (FTag F'VecS) [b, a]
pattern Empty s <- TyCon (TyConName (FTag F'Empty) _ _ _ _) [HString{-hnf?-} s]
where Empty s = TyCon (TyConName (FTag F'Empty) (error "todo: inum2_") (TString :~> TType) (error "todo: tcn cons 3_") $ error "Empty") [HString s]
pattern TT <- Con _ _ _
where TT = tCon FTT 0 Unit []
pattern CUnit <- ConN FCUnit _
where CUnit = tCon FCUnit 0 TConstraint []
pattern CEmpty s <- ConN FCEmpty (HString s: _)
where CEmpty s = tCon FCEmpty 1 (TString :~> TConstraint) [HString s]
pattern CstrT t a b = Neut (CstrT' t a b)
pattern CstrT' t a b = DFunN F'EqCT (TType :~> Var 0 :~> Var 1 :~> TConstraint) [t, a, b]
pattern Coe a b w x = DFun Fcoe (TType :~> TType :~> CW (CstrT TType (Var 1) (Var 0)) :~> Var 2 :~> Var 2) [a,b,w,x]
pattern ParEval t a b = DFun FparEval (TType :~> Var 0 :~> Var 1 :~> Var 2) [t, a, b]
pattern T2 a b = DFun F'T2 (TConstraint :~> TConstraint :~> TConstraint) [a, b]
pattern CW a = DFun F'CW (TConstraint :~> TType) [a]
pattern CSplit a b c <- UFun F'Split [a, b, c]
pattern HLit a <- (hnf -> ELit a)
where HLit = ELit
pattern HInt a = HLit (LInt a)
pattern HFloat a = HLit (LFloat a)
pattern HChar a = HLit (LChar a)
pattern HString a = HLit (LString a)
pattern EBool a <- (getEBool -> Just a)
where EBool = \case
False -> tCon FFalse 0 TBool []
True -> tCon FTrue 1 TBool []
getEBool (hnf -> ConN FFalse _) = Just False
getEBool (hnf -> ConN FTrue _) = Just True
getEBool _ = Nothing
pattern ENat n <- (fromNatE -> Just n)
where ENat 0 = tCon FZero 0 TNat []
ENat n | n > 0 = tCon FSucc 1 (TNat :~> TNat) [ENat (n-1)]
fromNatE :: Exp -> Maybe Int
fromNatE (hnf -> ConN FZero _) = Just 0
fromNatE (hnf -> ConN FSucc (n:_)) = succ <$> fromNatE n
fromNatE _ = Nothing
mkOrdering x = case x of
LT -> tCon FLT 0 TOrdering []
EQ -> tCon FEQ 1 TOrdering []
GT -> tCon FGT 2 TOrdering []
conTypeName :: ConName -> TyConName
conTypeName (ConName _ _ t) = case snd $ getParams t of TyCon n _ -> n
mkFun_ md (FunName _ _ (DeltaDef ar f) _) as _ | length as == ar = f md $ reverse as
mkFun_ md f xs y = Neut $ Fun_ md f xs $ hnf y
mkFun :: FunName -> [Exp] -> Exp -> Exp
mkFun f xs e = mkFun_ (foldMap getFreeVars xs) f xs e
pattern ReducedN y <- Fun _ _ (RHS y)
pattern Reduced y <- Neut (ReducedN y)
{-
-- TODO: too much hnf call
reduce (Neut (ReducedN y)) = Just $ hnf y
reduce (SubstLet x) = Just $ hnf x
reduce _ = Nothing
-}
hnf (Reduced y) = hnf y -- TODO: review hnf call here
hnf a = a
outputType = tTyCon0 F'Output $ error "cs 9"
-- TODO: remove
boolType = TBool
-- TODO: remove
trueExp = EBool True
-------------------------------------------------------------------------------- low-level toolbox
class Subst b a where
subst_ :: Int -> FreeVars -> b -> a -> a
--subst :: Subst b a => Int -> FreeVars -> b -> a -> a
subst i x a = subst_ i (getFreeVars x) x a
instance Subst Exp ExpType where
subst_ i dx x (ET a b) = ET (subst_ i dx x a) (subst_ i dx x b)
instance Subst ExpType SExp2 where
subst_ j _ x = mapS (\_ _ -> error "subst: TODO") (const . SGlobal) f2 0
where
f2 sn i k = case compare i (k + j) of
GT -> SVar sn $ i - 1
LT -> SVar sn i
EQ -> STyped $ up k x
down :: (PShow a, Subst Exp a, HasFreeVars a{-usedVar-}) => Int -> a -> Maybe a
down t x | usedVar t x = Nothing
| otherwise = Just $ subst_ t mempty (error $ "impossible: down" ++ ppShow (t,x, getFreeVars x) :: Exp) x
instance Eq Exp where
Neut a == Neut a' = a == a' -- try to compare by structure before reduction
Reduced a == a' = a == a'
a == Reduced a' = a == a'
Lam a == Lam a' = a == a'
Pi a b c == Pi a' b' c' = (a, b, c) == (a', b', c')
Con a n b == Con a' n' b' = (a, n, b) == (a', n', b')
TyCon a b == TyCon a' b' = (a, b) == (a', b')
TType_ f == TType_ f' = f == f'
ELit l == ELit l' = l == l'
RHS a == RHS a' = a == a'
_ == _ = False
instance Eq Neutral where
Fun f a _ == Fun f' a' _ = (f, a) == (f', a') -- try to compare by structure before reduction
ReducedN a == a' = a == Neut a'
a == ReducedN a' = Neut a == a'
CaseFun_ a b c == CaseFun_ a' b' c' = (a, b, c) == (a', b', c')
TyCaseFun_ a b c == TyCaseFun_ a' b' c' = (a, b, c) == (a', b', c')
App_ a b == App_ a' b' = (a, b) == (a', b')
Var_ a == Var_ a' = a == a'
_ == _ = False
instance Subst Exp Exp where
subst_ i0 dx x = f i0
where
f i (Neut n) = substNeut n
where
substNeut e | dbGE i e = Neut e
substNeut e = case e of
Var_ k -> case compare k i of GT -> Var $ k - 1; LT -> Var k; EQ -> up (i - i0) x
CaseFun__ fs s as n -> evalCaseFun (adjustDB i fs) s (f i <$> as) (substNeut n)
TyCaseFun__ fs s as n -> evalTyCaseFun_ (adjustDB i fs) s (f i <$> as) (substNeut n)
App__ fs a b -> app__ (adjustDB i fs) (substNeut a) (f i b)
Fun_ md fn xs v -> mkFun_ (adjustDB i md) fn (f i <$> xs) $ f i v
f i e | dbGE i e = e
f i e = case e of
Lam_ md b -> Lam_ (adjustDB i md) (f (i+1) b)
Con_ md s n as -> Con_ (adjustDB i md) s n $ f i <$> as
Pi_ md h a b -> Pi_ (adjustDB i md) h (f i a) (f (i+1) b)
TyCon_ md s as -> TyCon_ (adjustDB i md) s $ f i <$> as
Let_ md a b -> Let_ (adjustDB i md) (subst_ i dx x a) (f (i+1) b)
RHS a -> RHS $ hnf $ f i a
x -> x
adjustDB i md = if usedVar i md then delVar i md <> shiftFreeVars (i-i0) dx else delVar i md
instance Rearrange Exp where
rearrange i g = f i where
f i e | dbGE i e = e
f i e = case e of
Lam_ md b -> Lam_ (rearrangeFreeVars g i md) (f (i+1) b)
Pi_ md h a b -> Pi_ (rearrangeFreeVars g i md) h (f i a) (f (i+1) b)
Con_ md s pn as -> Con_ (rearrangeFreeVars g i md) s pn $ map (f i) as
TyCon_ md s as -> TyCon_ (rearrangeFreeVars g i md) s $ map (f i) as
Neut x -> Neut $ rearrange i g x
Let x y -> Let (rearrange i g x) (rearrange (i+1) g y)
RHS x -> RHS $ rearrange i g x
instance Rearrange Neutral where
rearrange i g = f i where
f i e | dbGE i e = e
f i e = case e of
Var_ k -> Var_ $ if k >= i then rearrangeFun g (k-i) + i else k
CaseFun__ md s as ne -> CaseFun__ (rearrangeFreeVars g i md) s (rearrange i g <$> as) (rearrange i g ne)
TyCaseFun__ md s as ne -> TyCaseFun__ (rearrangeFreeVars g i md) s (rearrange i g <$> as) (rearrange i g ne)
App__ md a b -> App__ (rearrangeFreeVars g i md) (rearrange i g a) (rearrange i g b)
Fun_ md fn x y -> Fun_ (rearrangeFreeVars g i md) fn (rearrange i g <$> x) $ rearrange i g y
instance HasFreeVars Exp where
getFreeVars = \case
Lam_ c _ -> c
Pi_ c _ _ _ -> c
Con_ c _ _ _ -> c
TyCon_ c _ _ -> c
Let_ c _ _ -> c
TType_ _ -> mempty
ELit{} -> mempty
Neut x -> getFreeVars x
RHS x -> getFreeVars x
instance HasFreeVars Neutral where
getFreeVars = \case
Var_ k -> freeVar k
CaseFun__ c _ _ _ -> c
TyCaseFun__ c _ _ _ -> c
App__ c a b -> c
Fun_ c _ _ _ -> c
varType' :: Int -> [Exp] -> Exp
varType' i vs = vs !! i
-------------------------------------------------------------------------------- pretty print
instance PShow Exp where
pShow = mkDoc (False, False)
instance PShow Neutral where
pShow = mkDoc (False, False)
class MkDoc a where
mkDoc :: (Bool {-print reduced-}, Bool{-print function bodies-}) -> a -> Doc
instance MkDoc ExpType where
mkDoc pr (ET e TType) = mkDoc pr e
mkDoc pr (ET e t) = DAnn (mkDoc pr e) (mkDoc pr t)
instance MkDoc Exp where
mkDoc pr@(reduce, body) = \case
Lam b -> shLam_ (usedVar 0 b) (BLam Visible) Nothing (mkDoc pr b)
Pi h TType b -> shLam_ (usedVar 0 b) (BPi h) Nothing (mkDoc pr b)
Pi h a b -> shLam (usedVar 0 b) (BPi h) (mkDoc pr a) (mkDoc pr b)
ENat n -> pShow n
Con s@(ConName _ i _) _ xs | body -> text $ "<<" ++ showNth i ++ " constructor of " ++ show (conTypeName s) ++ ">>"
ConN FHCons [_, _, x, xs] -> foldl DApp (text "HCons") (mkDoc pr <$> [x, xs])
Con s _ xs -> foldl DApp (pShow s) (mkDoc pr <$> xs)
TyCon s@(TyConName _ i _ cs _) xs | body
-> text $ "<<type constructor with " ++ show i ++ " indices; constructors: " ++ intercalate ", " (show . fst <$> cs) ++ ">>"
TyConN s xs -> foldl DApp (pShow s) (mkDoc pr <$> xs)
TType -> text "Type"
ELit l -> pShow l
Neut x -> mkDoc pr x
Let a b -> shLet_ (pShow a) (pShow b)
RHS x -> text "_rhs" `DApp` mkDoc pr x
showNth n = show n ++ f (n `div` 10 `mod` 10) (n `mod` 10)
where
f 1 _ = "th"
f _ 1 = "st"
f _ 2 = "nd"
f _ 3 = "rd"
f _ _ = "th"
pattern FFix f <- Fun (FunName (FTag FprimFix) _ _ _) [f, _] _
getFixLam (Lam (Neut (Fun s@(FunName _ loc _ _) xs _)))
| loc > 0
, (h, v) <- splitAt loc $ reverse xs
, Neut (Var_ 0) <- last h
= Just (s, v)
getFixLam _ = Nothing
instance MkDoc Neutral where
mkDoc pr@(reduce, body) = \case
CstrT' t a b -> shCstr (mkDoc pr a) (mkDoc pr (ET b t))
Fun (FunName _ _ (ExpDef d) _) xs _ | body -> mkDoc (reduce, False) (foldl app_ d $ reverse xs)
FFix (getFixLam -> Just (s, xs)) | not body -> foldl DApp (pShow s) $ mkDoc pr <$> xs
FFix f {- | body -} -> foldl DApp "primFix" [{-pShow t -}"_", mkDoc pr f]
Fun (FunName _ _ (DeltaDef n _) _) _ _ | body -> text $ "<<delta function with arity " ++ show n ++ ">>"
Fun (FunName _ _ NoDef _) _ _ | body -> "<<builtin>>"
ReducedN a | reduce -> mkDoc pr a
Fun s@(FunName _ loc _ _) xs _ -> foldl DApp ({-foldl DHApp (-}pShow s{-) h-}) v
where (_h, v) = splitAt loc $ mkDoc pr <$> reverse xs
Var_ k -> shVar k
App_ a b -> mkDoc pr a `DApp` mkDoc pr b
CaseFun_ s@(CaseFunName _ _ p) xs n | body -> text $ "<<case function of a type with " ++ show p ++ " parameters>>"
CaseFun_ s xs n -> foldl DApp (pShow s) (map (mkDoc pr) $ xs ++ [Neut n])
TyCaseFun_ _ _ _ | body -> text "<<type case function>>"
TyCaseFun_ s [m, t, f] n -> foldl DApp (pShow s) (mkDoc pr <$> [m, t, Neut n, f])
TyCaseFun_ s _ n -> error $ "mkDoc TyCaseFun"
_ -> "()"
-------------------------------------------------------------------------------- reduction
{- todo: generate
DFun n@(FunName "natElim" _) [a, z, s, Succ x] -> let -- todo: replace let with better abstraction
sx = s `app_` x
in sx `app_` eval (DFun n [a, z, s, x])
MT "natElim" [_, z, s, Zero] -> z
DFun na@(FunName "finElim" _) [m, z, s, n, ConN "FSucc" [i, x]] -> let six = s `app_` i `app_` x-- todo: replace let with better abstraction
in six `app_` eval (DFun na [m, z, s, i, x])
MT "finElim" [m, z, s, n, ConN "FZero" [i]] -> z `app_` i
-}
pattern FunName' a t <- FunName a _ _ t
where FunName' a t = mkFunDef a t
mkFunDef a@(show -> "primFix") t = fn
where
fn = FunName a 0 (DeltaDef (length $ fst $ getParams t) fx) t
fx s xs = Neut $ Fun_ s fn (reverse xs) $ case xs of
_: f: _ -> RHS x where x = f `app_` Neut (Fun_ s fn (reverse xs) $ RHS x)
_ -> delta
mkFunDef a t = fn
where
fn = FunName a 0 (maybe NoDef (DeltaDef (length $ fst $ getParams t) . const) $ getFunDef t a $ \xs -> Neut $ Fun fn (reverse xs) delta) t
getFunDef t s f = case show s of
"'EqCT" -> Just $ \case (t: a: b: _) -> cstr t a b
"'T2" -> Just $ \case (a: b: _) -> t2 a b
"'CW" -> Just $ \case (a: _) -> cw a
"t2C" -> Just $ \case (a: b: _) -> t2C a b
"coe" -> Just $ \case (a: b: t: d: _) -> evalCoe a b t d
"parEval" -> Just $ \case (t: a: b: _) -> parEval t a b
where
parEval _ x@RHS{} _ = x
parEval _ _ x@RHS{} = x
parEval t a b = ParEval t a b
"unsafeCoerce" -> Just $ \case xs@(_: _: x@(hnf -> NonNeut): _) -> x; xs -> f xs
"reflCstr" -> Just $ \case (a: _) -> TT
"hlistNilCase" -> Just $ \case (_: x: (hnf -> Con n@(ConName _ 0 _) _ _): _) -> x; xs -> f xs
"hlistConsCase" -> Just $ \case (_: _: _: x: (hnf -> Con n@(ConName _ 1 _) _ (_: _: a: b: _)): _) -> x `app_` a `app_` b; xs -> f xs
-- general compiler primitives
"primAddInt" -> Just $ \case (HInt i: HInt j: _) -> HInt (i + j); xs -> f xs
"primSubInt" -> Just $ \case (HInt i: HInt j: _) -> HInt (i - j); xs -> f xs
"primModInt" -> Just $ \case (HInt i: HInt j: _) -> HInt (i `mod` j); xs -> f xs
"primSqrtFloat" -> Just $ \case (HFloat i: _) -> HFloat $ sqrt i; xs -> f xs
"primRound" -> Just $ \case (HFloat i: _) -> HInt $ round i; xs -> f xs
"primIntToFloat" -> Just $ \case (HInt i: _) -> HFloat $ fromIntegral i; xs -> f xs
"primIntToNat" -> Just $ \case (HInt i: _) -> ENat $ fromIntegral i; xs -> f xs
"primCompareInt" -> Just $ \case (HInt x: HInt y: _) -> mkOrdering $ x `compare` y; xs -> f xs
"primCompareFloat" -> Just $ \case (HFloat x: HFloat y: _) -> mkOrdering $ x `compare` y; xs -> f xs
"primCompareChar" -> Just $ \case (HChar x: HChar y: _) -> mkOrdering $ x `compare` y; xs -> f xs
"primCompareString" -> Just $ \case (HString x: HString y: _) -> mkOrdering $ x `compare` y; xs -> f xs
-- LambdaCube 3D specific primitives
"PrimGreaterThan" -> Just $ \case (t: _: _: _: _: _: _: x: y: _) | Just r <- twoOpBool (>) t x y -> r; xs -> f xs
"PrimGreaterThanEqual"
-> Just $ \case (t: _: _: _: _: _: _: x: y: _) | Just r <- twoOpBool (>=) t x y -> r; xs -> f xs
"PrimLessThan" -> Just $ \case (t: _: _: _: _: _: _: x: y: _) | Just r <- twoOpBool (<) t x y -> r; xs -> f xs
"PrimLessThanEqual" -> Just $ \case (t: _: _: _: _: _: _: x: y: _) | Just r <- twoOpBool (<=) t x y -> r; xs -> f xs
"PrimEqualV" -> Just $ \case (t: _: _: _: _: _: _: x: y: _) | Just r <- twoOpBool (==) t x y -> r; xs -> f xs
"PrimNotEqualV" -> Just $ \case (t: _: _: _: _: _: _: x: y: _) | Just r <- twoOpBool (/=) t x y -> r; xs -> f xs
"PrimEqual" -> Just $ \case (t: _: _: x: y: _) | Just r <- twoOpBool (==) t x y -> r; xs -> f xs
"PrimNotEqual" -> Just $ \case (t: _: _: x: y: _) | Just r <- twoOpBool (/=) t x y -> r; xs -> f xs
"PrimSubS" -> Just $ \case (_: _: _: _: x: y: _) | Just r <- twoOp (-) x y -> r; xs -> f xs
"PrimSub" -> Just $ \case (_: _: x: y: _) | Just r <- twoOp (-) x y -> r; xs -> f xs
"PrimAddS" -> Just $ \case (_: _: _: _: x: y: _) | Just r <- twoOp (+) x y -> r; xs -> f xs
"PrimAdd" -> Just $ \case (_: _: x: y: _) | Just r <- twoOp (+) x y -> r; xs -> f xs
"PrimMulS" -> Just $ \case (_: _: _: _: x: y: _) | Just r <- twoOp (*) x y -> r; xs -> f xs
"PrimMul" -> Just $ \case (_: _: x: y: _) | Just r <- twoOp (*) x y -> r; xs -> f xs
"PrimDivS" -> Just $ \case (_: _: _: _: _: x: y: _) | Just r <- twoOp_ (/) div x y -> r; xs -> f xs
"PrimDiv" -> Just $ \case (_: _: _: _: _: x: y: _) | Just r <- twoOp_ (/) div x y -> r; xs -> f xs
"PrimModS" -> Just $ \case (_: _: _: _: _: x: y: _) | Just r <- twoOp_ modF mod x y -> r; xs -> f xs
"PrimMod" -> Just $ \case (_: _: _: _: _: x: y: _) | Just r <- twoOp_ modF mod x y -> r; xs -> f xs
"PrimNeg" -> Just $ \case (_: x: _) | Just r <- oneOp negate x -> r; xs -> f xs
"PrimAnd" -> Just $ \case (EBool x: EBool y: _) -> EBool (x && y); xs -> f xs
"PrimOr" -> Just $ \case (EBool x: EBool y: _) -> EBool (x || y); xs -> f xs
"PrimXor" -> Just $ \case (EBool x: EBool y: _) -> EBool (x /= y); xs -> f xs
"PrimNot" -> Just $ \case ((hnf -> TNat): _: _: EBool x: _) -> EBool $ not x; xs -> f xs
_ -> Nothing
where
twoOpBool :: (forall a . Ord a => a -> a -> Bool) -> Exp -> Exp -> Exp -> Maybe Exp
twoOpBool f t (HFloat x) (HFloat y) = Just $ EBool $ f x y
twoOpBool f t (HInt x) (HInt y) = Just $ EBool $ f x y
twoOpBool f t (HString x) (HString y) = Just $ EBool $ f x y
twoOpBool f t (HChar x) (HChar y) = Just $ EBool $ f x y
twoOpBool f t (ENat x) (ENat y) = Just $ EBool $ f x y
twoOpBool _ _ _ _ = Nothing
oneOp :: (forall a . Num a => a -> a) -> Exp -> Maybe Exp
oneOp f = oneOp_ f f
oneOp_ f _ (HFloat x) = Just $ HFloat $ f x
oneOp_ _ f (HInt x) = Just $ HInt $ f x
oneOp_ _ _ _ = Nothing
twoOp :: (forall a . Num a => a -> a -> a) -> Exp -> Exp -> Maybe Exp
twoOp f = twoOp_ f f
twoOp_ f _ (HFloat x) (HFloat y) = Just $ HFloat $ f x y
twoOp_ _ f (HInt x) (HInt y) = Just $ HInt $ f x y
twoOp_ _ _ _ _ = Nothing
modF x y = x - fromIntegral (floor (x / y)) * y
evalCaseFun _ a ps (Con n@(ConName _ i _) _ vs)
| i /= (-1) = foldl app_ (ps !!! (i + 1)) vs
| otherwise = error "evcf"
where
xs !!! i | i >= length xs = error $ "!!! " ++ ppShow a ++ " " ++ show i ++ " " ++ ppShow n ++ "\n" ++ ppShow ps
xs !!! i = xs !! i
evalCaseFun fs a b (Reduced c) = evalCaseFun fs a b c
evalCaseFun fs a b (Neut c) = Neut $ CaseFun__ fs a b c
evalCaseFun _ a b x = error $ "evalCaseFun: " ++ ppShow (a, x)
evalCaseFun' a b c = evalCaseFun (getFreeVars c <> foldMap getFreeVars b) a b c
evalTyCaseFun a b c = evalTyCaseFun_ (foldMap getFreeVars b <> getFreeVars c) a b c
evalTyCaseFun_ s a b (Reduced c) = evalTyCaseFun_ s a b c
evalTyCaseFun_ s a b (Neut c) = Neut $ TyCaseFun__ s a b c
evalTyCaseFun_ _ (TyCaseFunName (FTag F'Type) ty) (_: t: f: _) TType = t
evalTyCaseFun_ _ (TyCaseFunName n ty) (_: t: f: _) (TyCon (TyConName n' _ _ _ _) vs) | n == n' = foldl app_ t vs
--evalTyCaseFun (TyCaseFunName n ty) [_, t, f] (DFun (FunName n' _) vs) | n == n' = foldl app_ t vs -- hack
evalTyCaseFun_ _ (TyCaseFunName n ty) (_: t: f: _) _ = f
evalCoe a b (Reduced x) d = evalCoe a b x d
evalCoe a b TT d = d
evalCoe a b t d = Coe a b t d
cstr_ t a b = cw $ cstr t a b
cstr = f []
where
f z ty a a' = f_ z (hnf ty) (hnf a) (hnf a')
f_ _ _ a a' | a == a' = CUnit
f_ ns typ (RHS a) (RHS a') = f ns typ a a'
f_ ns typ (Con a n xs) (Con a' n' xs') | a == a' && n == n' && length xs == length xs' =
ff ns (foldl appTy (conType typ a) $ mkConPars n typ) $ zip xs xs'
f_ ns typ (TyCon a xs) (TyCon a' xs') | a == a' && length xs == length xs' =
ff ns (nType a) $ zip xs xs'
f_ (_: ns) typ{-down?-} (down 0 -> Just a) (down 0 -> Just a') = f ns typ a a'
f_ ns TType (Pi h a b) (Pi h' a' b') | h == h' = t2 (f ns TType a a') (f ((a, a'): ns) TType b b')
f_ [] TType (UFun F'VecScalar [a, b]) (UFun F'VecScalar [a', b']) = t2 (f [] TNat a a') (f [] TType b b')
f_ [] TType (UFun F'VecScalar [a, b]) (TVec a' b') = t2 (f [] TNat a a') (f [] TType b b')
f_ [] TType (UFun F'VecScalar [a, b]) t@NonNeut = t2 (f [] TNat a (ENat 1)) (f [] TType b t)
f_ [] TType (TVec a' b') (UFun F'VecScalar [a, b]) = t2 (f [] TNat a' a) (f [] TType b' b)
f_ [] TType t@NonNeut (UFun F'VecScalar [a, b]) = t2 (f [] TNat a (ENat 1)) (f [] TType b t)
f_ [] typ a@Neut{} a' = CstrT typ a a'
f_ [] typ a a'@Neut{} = CstrT typ a a'
f_ ns typ a a' = CEmpty $ simpleShow $ nest 2 ("can not unify" <$$> DTypeNamespace True (pShow a)) <$$> nest 2 ("with" <$$> DTypeNamespace True (pShow a'))
ff _ _ [] = CUnit
ff ns tt@(Pi v t _) ((t1, t2'): ts) = t2 (f ns t t1 t2') $ ff ns (appTy tt t1) ts
ff ns t zs = error $ "ff: " -- ++ show (a, n, length xs', length $ mkConPars n typ) ++ "\n" ++ ppShow (nType a) ++ "\n" ++ ppShow (foldl appTy (nType a) $ mkConPars n typ) ++ "\n" ++ ppShow (zip xs xs') ++ "\n" ++ ppShow zs ++ "\n" ++ ppShow t
pattern NonNeut <- (nonNeut -> True)
nonNeut Neut{} = False
nonNeut _ = True
t2C (hnf -> TT) (hnf -> TT) = TT
t2C a b = DFun Ft2C (Unit :~> Unit :~> Unit) [a, b]
cw (hnf -> CUnit) = Unit
cw (hnf -> CEmpty a) = Empty a
cw a = CW a
t2 (hnf -> CUnit) a = a
t2 a (hnf -> CUnit) = a
t2 (hnf -> CEmpty a) (hnf -> CEmpty b) = CEmpty (a <> b)
t2 (hnf -> CEmpty s) _ = CEmpty s
t2 _ (hnf -> CEmpty s) = CEmpty s
t2 a b = T2 a b
app_ :: Exp -> Exp -> Exp
app_ a b = app__ (getFreeVars a <> getFreeVars b) a b
app__ _ (Lam x) a = subst 0 a x
app__ _ (Con s n xs) a = if n < conParams s then Con s (n+1) xs else Con s n (xs ++ [a])
app__ _ (TyCon s xs) a = TyCon s (xs ++ [a])
app__ _ (SubstLet f) a = app_ f a
app__ s (Neut f) a = neutApp f a
where
neutApp (ReducedN x) a = app_ x a
neutApp (Fun_ db f xs (Lam e)) a = mkFun_ (db <> getFreeVars a) f (a: xs) (subst 0 a e)
neutApp f a = Neut $ App__ s f a
conType (snd . getParams . hnf -> TyCon (TyConName _ _ _ cs _) _) (ConName _ n t) = t --snd $ cs !! n
appTy (Pi _ a b) x = subst 0 x b
appTy t x = error $ "appTy: " ++ ppShow t
getParams :: Exp -> ([(Visibility, Exp)], Exp)
getParams (Pi h a b) = first ((h, a):) $ getParams b
getParams x = ([], x)
--------------------------------------------------------- evident types
class NType a where nType :: a -> Type
instance NType FunName where nType (FunName _ _ _ t) = t
instance NType TyConName where nType (TyConName _ _ t _ _) = t
instance NType CaseFunName where nType (CaseFunName _ t _) = t
instance NType TyCaseFunName where nType (TyCaseFunName _ t) = t
instance NType Lit where
nType = \case
LInt _ -> TInt
LFloat _ -> TFloat
LString _ -> TString
LChar _ -> TChar
|