# C Below

Let’s descend from the realm of pure functions and step into the real world.

## Effectively

We add the IO monad and support FFI. The VM passes around a combinator ? that represents the real world. Reducing this combinator is a bug; it should always be an argument to other combinators.

A value x of type IO a should behave as follows:

x w c --> c y w

where y is some value of type a. In normal operation, w is the real-world token ?, and the continuation c should expect two arguments but never reduce the second one.

pure y = \w c -> c y w
x >>= f = \w c -> x w f c

Hence we can use the V and C combinators for pure and (>>=).

We add a crude syntax for FFI, with crude code for generating the requisite C wrappers. An F combinator invokes these foreign functions.

Threading the unused token ? protects us from lazily updating the result of a call to an impure function. Can we get rid of it? If we simply drop the token, we wind up with the continuation monad:

pure :: a -> (a -> r) -> r
pure y = \c -> c y
(>>=) :: ((a -> r) -> r) -> (a -> (b -> r) -> r) -> (b -> r) -> r
x >>= f = \c -> x f c

This time pure and (>>=) are the T and I combinators. With this scheme, we must skip lazy updates for every IO function. Generated wrappers for FFI imports in the IO monad should create an ephemeral node to push on top of the stack, rather than reduce in place.

This ought to work, except that it breaks an invariant that our runtime depends on, namely, the stack always holds part of the spine starting from the root. In particular, the garbage collector only evacuates the bottom of the stack and relies on the invariant to re-expand the spine. Ephemeral cells would require our GC to carefully evacuate the whole stack.

It’s unclear if these changes are worth the effort, especially since Haskell code tends to avoid the IO monad as much as possible.

-- Effects with IO monad.
infixr 9 .;
infixl 7 *;
infixl 6 + , -;
infixr 5 ++;
infixl 4 <*> , <$> , <* , *>; infix 4 == , <=; infixl 3 && , <|>; infixl 2 ||; infixr 0$;
class Eq a where { (==) :: a -> a -> Bool };
instance Eq Int where { (==) = intEq };
undefined = undefined;
($) f x = f x; id x = x; flip f x y = f y x; (&) x f = f x; data Bool = True | False; class Ord a where { (<=) :: a -> a -> Bool }; instance Ord Int where { (<=) = intLE }; data Ordering = LT | GT | EQ; compare x y = case x <= y of { True -> case y <= x of { True -> EQ ; False -> LT } ; False -> GT }; instance Ord a => Ord [a] where { (<=) xs ys = case xs of { [] -> True ; (:) x xt -> case ys of { [] -> False ; (:) y yt -> case compare x y of { LT -> True ; GT -> False ; EQ -> xt <= yt } } } }; data Maybe a = Nothing | Just a; fpair p = \f -> case p of { (,) x y -> f x y }; fst p = case p of { (,) x y -> x }; snd p = case p of { (,) x y -> y }; first f p = fpair p \x y -> (f x, y); second f p = fpair p \x y -> (x, f y); ife a b c = case a of { True -> b ; False -> c }; not a = case a of { True -> False; False -> True }; (.) f g x = f (g x); (||) f g = ife f True g; (&&) f g = ife f g False; flst xs n c = case xs of { [] -> n; (:) h t -> c h t }; instance Eq a => Eq [a] where { (==) xs ys = case xs of { [] -> case ys of { [] -> True ; (:) _ _ -> False } ; (:) x xt -> case ys of { [] -> False ; (:) y yt -> x == y && xt == yt } }}; maybe n j m = case m of { Nothing -> n; Just x -> j x }; foldr c n l = flst l n (\h t -> c h(foldr c n t)); foldr1 c l = maybe undefined id (flst l undefined (\h t -> foldr (\x m -> Just (case m of { Nothing -> x ; Just y -> c x y })) Nothing l)); foldl f a bs = foldr (\b g x -> g (f x b)) (\x -> x) bs a; foldl1 f bs = flst bs undefined (\h t -> foldl f h t); elem k xs = foldr (\x t -> ife (x == k) True t) False xs; find f xs = foldr (\x t -> ife (f x) (Just x) t) Nothing xs; (++) = flip (foldr (:)); concat = foldr (++) []; wrap c = c:[]; map = flip (foldr . ((:) .)) []; concatMap = (concat .) . map; fmaybe m n j = case m of { Nothing -> n; Just x -> j x }; lookup s = foldr (\h t -> fpair h (\k v -> ife (s == k) (Just v) t)) Nothing; -- Map. data Map k a = Tip | Bin Int k a (Map k a) (Map k a); size m = case m of { Tip -> 0 ; Bin sz _ _ _ _ -> sz }; node k x l r = Bin (succ$ size l + size r) k x l r;
singleton k x = Bin 1 k x Tip Tip;
singleL k x l r = case r of
{ Tip -> undefined
; Bin _ rk rkx rl rr -> node rk rkx (node k x l rl) rr
};
singleR k x l r = case l of
{ Tip -> undefined
; Bin _ lk lkx ll lr -> node lk lkx ll (node k x lr r)
};
doubleL k x l r = case r of
{ Tip -> undefined
; Bin _ rk rkx rl rr -> case rl of
{ Tip -> undefined
; Bin _ rlk rlkx rll rlr -> node rlk rlkx (node k x l rll) (node rk rkx rlr rr)
}
};
doubleR k x l r = case l of
{ Tip -> undefined
; Bin _ lk lkx ll lr -> case lr of
{ Tip -> undefined
; Bin _ lrk lrkx lrl lrr -> node lrk lrkx (node lk lkx ll lrl) (node k x lrr r)
}
};
balance k x l r = case size l + size r <= 1 of
{ True -> node
; False -> case 5 * size l + 3 <= 2 * size r of
{ True -> case r of
{ Tip -> node
; Bin sz _ _ rl rr -> case 3 * size rr <= 2 * size rl of
{ True -> doubleL
; False -> singleL
}
}
; False -> case 5 * size r + 3 <= 2 * size l of
{ True -> case l of
{ Tip -> node
; Bin sz _ _ ll lr -> case 3 * size ll <= 2 * size lr of
{ True -> doubleR
; False -> singleR
}
}
; False -> node
}
}
} k x l r;
insert kx x t = case t of
{ Tip -> singleton kx x
; Bin sz ky y l r -> case compare kx ky of
{ LT -> balance ky y (insert kx x l) r
; GT -> balance ky y l (insert kx x r)
; EQ -> Bin sz kx x l r
}
};
mlookup kx t = case t of
{ Tip -> Nothing
; Bin _ ky y l r -> case compare kx ky of
{ LT -> mlookup kx l
; GT -> mlookup kx r
; EQ -> Just y
}
};
fromList = let
{ ins t kx = case kx of { (,) k x -> insert k x t }
} in foldl ins Tip;

foldrWithKey f = let
{ go z t = case t of
{ Tip -> z
; Bin _ kx x l r -> go (f kx x (go z r)) l
}
} in go;

toAscList = foldrWithKey (\k x xs -> (k,x):xs) [];

-- Parsing.

data Type = TC String | TV String | TAp Type Type;
data Extra = Basic Int | Const Int | StrCon String | Proof Pred;
data Ast = E Extra | V String | A Ast Ast | L String Ast;
ro = E . Basic . ord;

pure x = \inp -> Just (x, inp);
sat' f = \h t -> ife (f h) (pure h t) Nothing;
sat f inp = flst inp Nothing (sat' f);
bind f m = case m of
{ Nothing -> Nothing
; Just x -> fpair x f
};
ap x y = \inp -> bind (\a t -> bind (\b u -> pure (a b) u) (y t)) (x inp);
(<*>) = ap;
fmap f x = ap (pure f) x;
(<$>) = fmap; (>>=) x y = \inp -> bind (\a t -> y a t) (x inp); (<|>) x y = \inp -> case x inp of { Nothing -> y inp ; Just x -> Just x }; liftA2 f x y = ap (fmap f x) y; (*>) = liftA2 \x y -> y; (<*) = liftA2 \x y -> x; many p = liftA2 (:) p (many p) <|> pure []; some p = liftA2 (:) p (many p); sepBy1 p sep = liftA2 (:) p (many (sep *> p)); sepBy p sep = sepBy1 p sep <|> pure []; char c = sat \x -> x == c; between x y p = x *> (p <* y); com = char '-' *> between (char '-') (char '\n') (many (sat \c -> not (c == '\n'))); sp = many ((wrap <$> (sat (\c -> (c == ' ') || (c == '\n')))) <|> com);
spc f = f <* sp;
spch = spc . char;
wantWith pred f inp = bind (sat' pred) (f inp);
want f s inp = wantWith (s ==) f inp;

paren = between (spch '(') (spch ')');
small = sat \x -> ((x <= 'z') && ('a' <= x)) || (x == '_');
large = sat \x -> (x <= 'Z') && ('A' <= x);
digit = sat \x -> (x <= '9') && ('0' <= x);
varLex = liftA2 (:) small (many (small <|> large <|> digit <|> char '\''));
conId = spc (liftA2 (:) large (many (small <|> large <|> digit <|> char '\'')));
keyword s = spc (want varLex s);
varId = spc (wantWith (\s -> not $s == "of" || s == "where") varLex); opLex = some (sat (\c -> elem c ":!#$%&*+./<=>?@\\^|-~"));
op = spc opLex <|> between (spch '') (spch '') varId;
var = varId <|> paren (spc opLex);

listify = foldr (\h t -> A (A (V ":") h) t) (V "[]");
escChar = char '\\' *> ((sat (\c -> elem c "'\"\\")) <|> ((\c -> '\n') <$> char 'n')); litOne delim = escChar <|> sat \c -> not (c == delim); litInt = E . Const . foldl (\n d -> 10*n + ord d - ord '0') 0 <$> spc (some digit);
litStr = between (char '"') (spch '"') $many (litOne '"'); litChar = E . Const . ord <$> between (char '\'') (spch '\'') (litOne '\'');
lit = E . StrCon <$> litStr <|> litChar <|> litInt; sqLst r = between (spch '[') (spch ']')$ listify <$> sepBy r (spch ','); alt r = (,) <$> (conId <|> (wrap <$> paren (spch ':' <|> spch ',')) <|> ((:) <$> spch '[' <*> (wrap <$> spch ']'))) <*> (flip (foldr L) <$> many varId <*> (want op "->" *> r));
braceSep f = between (spch '{') (spch '}') (sepBy f (spch ';'));
alts r = braceSep (alt r);
cas' x as = foldl A (V (concatMap (('|':) . fst) as)) (x:map snd as);
cas r = cas' <$> between (keyword "case") (keyword "of") r <*> alts r; lamCase r = keyword "case" *> (L "of" . cas' (V "of") <$> alts r);
lam r = spch '\\' *> (lamCase r <|> liftA2 (flip (foldr L)) (some varId) (char '-' *> (spch '>' *> r)));

thenComma r = spch ',' *> (((\x y -> A (A (V ",") y) x) <$> r) <|> pure (A (V ","))); parenExpr r = (&) <$> r <*> (((\v a -> A (V v) a) <$> op) <|> thenComma r <|> pure id); rightSect r = ((\v a -> L "@"$ A (A (V v) $V "@") a) <$> (op <|> (wrap <$> spch ','))) <*> r; section r = spch '(' *> (parenExpr r <* spch ')' <|> rightSect r <* spch ')' <|> spch ')' *> pure (V "()")); isFree v expr = case expr of { E _ -> False ; V s -> s == v ; A x y -> isFree v x || isFree v y ; L w t -> not (v == w) && isFree v t }; maybeFix s x = ife (isFree s x) (A (ro 'Y') (L s x)) x; def r = liftA2 (,) var (liftA2 (flip (foldr L)) (many varId) (spch '=' *> r)); addLets ls x = foldr (\p t -> fpair p (\name def -> A (L name t)$ maybeFix name def)) x ls;
letin r = addLets <$> between (keyword "let") (keyword "in") (braceSep (def r)) <*> r; atom r = letin r <|> sqLst r <|> section r <|> cas r <|> lam r <|> (paren (spch ',') *> pure (V ",")) <|> fmap V (conId <|> var) <|> lit; aexp r = fmap (foldl1 A) (some (atom r)); fix f = f (fix f); data Assoc = NAssoc | LAssoc | RAssoc; eqAssoc x y = case x of { NAssoc -> case y of { NAssoc -> True ; LAssoc -> False ; RAssoc -> False } ; LAssoc -> case y of { NAssoc -> False ; LAssoc -> True ; RAssoc -> False } ; RAssoc -> case y of { NAssoc -> False ; LAssoc -> False ; RAssoc -> True } }; precOf s precTab = fmaybe (lookup s precTab) 9 fst; assocOf s precTab = fmaybe (lookup s precTab) LAssoc snd; opWithPrec precTab n = wantWith (\s -> n == precOf s precTab) op; opFold precTab e xs = case xs of { [] -> e ; (:) x xt -> case find (\y -> not (eqAssoc (assocOf (fst x) precTab) (assocOf (fst y) precTab))) xt of { Nothing -> case assocOf (fst x) precTab of { NAssoc -> case xt of { [] -> fpair x (\op y -> A (A (V op) e) y) ; (:) y yt -> undefined } ; LAssoc -> foldl (\a b -> fpair b (\op y -> A (A (V op) a) y)) e xs ; RAssoc -> (foldr (\a b -> fpair a (\op y -> \e -> A (A (V op) e) (b y))) id xs) e } ; Just y -> undefined } }; expr precTab = fix \r n -> ife (n <= 9) (liftA2 (opFold precTab) (r (succ n)) (many (liftA2 (\a b -> (a,b)) (opWithPrec precTab n) (r (succ n))))) (aexp (r 0)); data Constr = Constr String [Type]; data Pred = Pred String Type; data Qual = Qual [Pred] Type; data Top = Adt Type [Constr] | Def (Maybe String) (String, Ast) | Class String Type [(String, Type)] | Inst String Qual [(String, Ast)] | FFI String String Type; arr a b = TAp (TAp (TC "->") a) b; bType r = foldl1 TAp <$> some r;
_type r = foldr1 arr <$> sepBy (bType r) (spc (want opLex "->")); typeConst = (\s -> ife (s == "String") (TAp (TC "[]") (TC "Int")) (TC s)) <$> conId;
aType = spch '(' *> (spch ')' *> pure (TC "()") <|> ((&) <$> _type aType <*> ((spch ',' *> ((\a b -> TAp (TAp (TC ",") b) a) <$> _type aType)) <|> pure id)) <* spch ')') <|>
typeConst <|> (TV <$> varId) <|> (spch '[' *> (spch ']' *> pure (TC "[]") <|> TAp (TC "[]") <$> (_type aType <* spch ']')));

simpleType c vs = foldl TAp (TC c) (map TV vs);

adt = Adt <$> between (keyword "data") (spch '=') (simpleType <$> conId <*> many varId) <*> (sepBy (Constr <$> conId <*> many aType) (spch '|')); prec = (\c -> ord c - ord '0') <$> spc digit;
fixityList a n os = map (\o -> (o, (n, a))) os;
fixityDecl kw a = between (keyword kw) (spch ';') (fixityList a <$> prec <*> sepBy op (spch ',')); fixity = fixityDecl "infix" NAssoc <|> fixityDecl "infixl" LAssoc <|> fixityDecl "infixr" RAssoc; noQual = Qual []; genDecl = (,) <$> var <*> (char ':' *> spch ':' *> _type aType);
classDecl = keyword "class" *> (Class <$> conId <*> (TV <$> varId) <*> (keyword "where" *> braceSep genDecl));

inst = _type aType;
instDecl r = keyword "instance" *>
((\ps cl ty defs -> Inst cl (Qual ps ty) defs) <$> (((wrap .) . Pred <$> conId <*> (inst <* want op "=>")) <|> pure [])
<*> conId <*> inst <*> (keyword "where" *> braceSep (def r)));

ffiDecl = keyword "foreign" *> keyword "import" *> var *>
(FFI <$> litStr <*> var <*> (char ':' *> spch ':' *> _type aType)); eqn r = Def <$> (keyword "export" *> (Just <$> litStr) <|> pure Nothing) <*> def r; tops precTab = sepBy ( adt <|> classDecl <|> instDecl (expr precTab 0) <|> ffiDecl <|> eqn (expr precTab 0) ) (spch ';'); program' = sp *> (((":", (5, RAssoc)):) . concat <$> many fixity) >>= tops;

-- Primitives.

program = (
[ Adt (TAp (TC "[]") (TV "a")) [Constr "[]" [], Constr ":" [TV "a", TAp (TC "[]") (TV "a")]]
, Adt (TAp (TAp (TC ",") (TV "a")) (TV "b")) [Constr "," [TV "a", TV "b"]]] ++) <$> program'; prims = let { ii = arr (TC "Int") (TC "Int") ; iii = arr (TC "Int") ii ; bin s = A (ro 'Q') (ro s) } in map (second (first noQual))$
[ ("intEq", (arr (TC "Int") (arr (TC "Int") (TC "Bool")), bin '='))
, ("intLE", (arr (TC "Int") (arr (TC "Int") (TC "Bool")), bin 'L'))
, ("()", (TC "()", ro 'K'))
, ("chr", (ii, ro 'I'))
, ("ord", (ii, ro 'I'))
, ("succ", (ii, A (ro 'T') (A (E $Const$ 1) (ro '+'))))
, ("ioBind", (arr (TAp (TC "IO") (TV "a")) (arr (arr (TV "a") (TAp (TC "IO") (TV "b"))) (TAp (TC "IO") (TV "b"))), ro 'C'))
, ("ioPure", (arr (TV "a") (TAp (TC "IO") (TV "a")), ro 'V'))
, ("exitSuccess", (TAp (TC "IO") (TV "a"), ro '.'))
, ("unsafePerformIO", (arr (TAp (TC "IO") (TV "a")) (TV "a"), A (A (ro 'C') (A (ro 'T') (ro '?'))) (ro 'K')))
] ++ map (\s -> (wrap s, (iii, bin s))) "+-*/%";

ifz n = ife (0 == n);
showInt' n = ifz n id ((showInt' (n/10)) . ((:) (chr (48+(n%10)))));
showInt n s = ifz n ('0':) (showInt' n) s;

-- Conversion to De Bruijn indices.

data LC = Ze | Su LC | Pass Int | La LC | App LC LC;

debruijn m n e = case e of
{ E x -> case x of
{ Basic b -> Pass b
; Const c -> App (Pass $ord '#') (Pass c) ; StrCon s -> foldr (\h t -> App (App (Pass$ ord ':') (App (Pass $ord '#') (Pass$ ord h))) t) (Pass $ord 'K') s ; Proof _ -> undefined } ; V v -> maybe (fmaybe (mlookup v m) undefined Pass) id$
foldr (\h found -> ife (h == v) (Just Ze) (maybe Nothing (Just . Su) found)) Nothing n
; A x y -> App (debruijn m n x) (debruijn m n y)
; L s t -> La (debruijn m (s:n) t)
};

-- Kiselyov bracket abstraction.

data IntTree = Lf Int | Nd IntTree IntTree;
data Sem = Defer | Closed IntTree | Need Sem | Weak Sem;

lf = Lf . ord;

ldef = \r y -> case y of
{ Defer -> Need (Closed (Nd (Nd (lf 'S') (lf 'I')) (lf 'I')))
; Closed d -> Need (Closed (Nd (lf 'T') d))
; Need e -> Need (r (Closed (Nd (lf 'S') (lf 'I'))) e)
; Weak e -> Need (r (Closed (lf 'T')) e)
};

lclo = \r d y -> case y of
{ Defer -> Need (Closed d)
; Closed dd -> Closed (Nd d dd)
; Need e -> Need (r (Closed (Nd (lf 'B') d)) e)
; Weak e -> Weak (r (Closed d) e)
};

lnee = \r e y -> case y of
{ Defer -> Need (r (r (Closed (lf 'S')) e) (Closed (lf 'I')))
; Closed d -> Need (r (Closed (Nd (lf 'R') d)) e)
; Need ee -> Need (r (r (Closed (lf 'S')) e) ee)
; Weak ee -> Need (r (r (Closed (lf 'C')) e) ee)
};

lwea = \r e y -> case y of
{ Defer -> Need e
; Closed d -> Weak (r e (Closed d))
; Need ee -> Need (r (r (Closed (lf 'B')) e) ee)
; Weak ee -> Weak (r e ee)
};

babsa x y = case x of
{ Defer -> ldef babsa y
; Closed d -> lclo babsa d y
; Need e -> lnee babsa e y
; Weak e -> lwea babsa e y
};

babs t = case t of
{ Ze -> Defer
; Su x -> Weak (babs x)
; Pass n -> Closed (Lf n)
; La t -> case babs t of
{ Defer -> Closed (lf 'I')
; Closed d -> Closed (Nd (lf 'K') d)
; Need e -> e
; Weak e -> babsa (Closed (lf 'K')) e
}
; App x y -> babsa (babs x) (babs y)
};

nolam m x = case babs $debruijn m [] x of { Defer -> undefined ; Closed d -> d ; Need e -> undefined ; Weak e -> undefined }; enc mem t = case t of { Lf n -> (n, mem) ; Nd x y -> fpair (enc mem x) \p mem' -> fpair (enc mem' y) \q mem'' -> ife (p == ord 'I') (q, mem'')$
ife (q == ord 'I') (
ife (p == ord 'C') (ord 'T', mem) $ife (p == ord 'B') (ord 'I', mem)$
fpair mem'' \hp bs -> (hp, (hp + 2, bs . (p:) . (q:)))
) $fpair mem'' \hp bs -> (hp, (hp + 2, bs . (p:) . (q:))) }; asm qas = foldl (\tabmem def -> fpair def \s qt -> fpair tabmem \tab mem -> fpair (enc mem$ nolam tab $snd qt) \p m' -> (insert s p tab, m')) (Tip, (128, id)) qas; -- Type checking. apply sub t = case t of { TC v -> t ; TV v -> fmaybe (lookup v sub) t id ; TAp a b -> TAp (apply sub a) (apply sub b) }; (@@) s1 s2 = map (second (apply s1)) s2 ++ s1; occurs s t = case t of { TC v -> False ; TV v -> s == v ; TAp a b -> occurs s a || occurs s b }; varBind s t = case t of { TC v -> Just [(s, t)] ; TV v -> ife (v == s) (Just []) (Just [(s, t)]) ; TAp a b -> ife (occurs s t) Nothing (Just [(s, t)]) }; charIsInt s = ife (s == "Char") "Int" s; mgu unify t u = case t of { TC a -> case u of { TC b -> ife (charIsInt a == charIsInt b) (Just []) Nothing ; TV b -> varBind b t ; TAp a b -> Nothing } ; TV a -> varBind a u ; TAp a b -> case u of { TC b -> Nothing ; TV b -> varBind b t ; TAp c d -> unify b d (mgu unify a c) } }; maybeMap f = maybe Nothing (Just . f); unify a b = maybe Nothing \s -> maybeMap (@@ s) (mgu unify (apply s a) (apply s b)); --instantiate' :: Type -> Int -> [(String, Type)] -> ((Type, Int), [(String, Type)]) instantiate' t n tab = case t of { TC s -> ((t, n), tab) ; TV s -> case lookup s tab of { Nothing -> let { va = TV (showInt n "") } in ((va, n + 1), (s, va):tab) ; Just v -> ((v, n), tab) } ; TAp x y -> fpair (instantiate' x n tab) \tn1 tab1 -> fpair tn1 \t1 n1 -> fpair (instantiate' y n1 tab1) \tn2 tab2 -> fpair tn2 \t2 n2 -> ((TAp t1 t2, n2), tab2) }; instantiatePred pred xyz = case pred of { Pred s t -> fpair xyz \xy tab -> fpair xy \out n -> first (first ((:out) . Pred s)) (instantiate' t n tab) }; --instantiate :: Qual -> Int -> (Qual, Int) instantiate qt n = case qt of { Qual ps t -> fpair (foldr instantiatePred (([], n), []) ps) \xy tab -> fpair xy \ps1 n1 -> first (Qual ps1) (fst (instantiate' t n1 tab)) }; --type SymTab = [(String, (Qual, Ast))]; --type Subst = [(String, Type)]; --infer :: SymTab -> Subst -> Ast -> (Maybe Subst, Int) -> ((Type, Ast), (Maybe Subst, Int)) infer typed loc ast csn = fpair csn \cs n -> let { va = TV (showInt n "") ; insta ty = fpair (instantiate ty n) \q n1 -> case q of { Qual preds ty -> ((ty, foldl A ast (map (E . Proof) preds)), (cs, n1)) } } in case ast of { E x -> case x of { Basic b -> ife (b == ord 'Y') (insta$ noQual $arr (arr (TV "a") (TV "a")) (TV "a")) undefined ; Const _ -> ((TC "Int", ast), csn) ; StrCon _ -> ((TAp (TC "[]") (TC "Int"), ast), csn) ; Proof _ -> undefined } ; V s -> fmaybe (lookup s loc) (fmaybe (lookup s typed) undefined$ insta . fst)
((, csn) . (, ast))
; A x y ->
fpair (infer typed loc x (cs, n + 1)) \tax csn1 -> fpair tax \tx ax ->
fpair (infer typed loc y csn1) \tay csn2 -> fpair tay \ty ay ->
((va, A ax ay), first (unify tx (arr ty va)) csn2)
; L s x -> first (\ta -> fpair ta \t a -> (arr va t, L s a)) (infer typed ((s, va):loc) x (cs, n + 1))
};

onType f pred = case pred of { Pred s t -> Pred s (f t) };

instance Eq Type where { (==) t u = case t of
{ TC s -> case u of
{ TC t -> t == s
; TV _ -> False
; TAp _ _ -> False
}
; TV s ->  case u of
{ TC _ -> False
; TV t -> t == s
; TAp _ _ -> False
}
; TAp a b -> case u of
{ TC _ -> False
; TV _ -> False
; TAp c d -> a == c && b == d
}
}};

instance Eq Pred where { (==) p q =
case p of { Pred s a -> case q of { Pred t b -> s == t && a == b }}};

predApply sub p = onType (apply sub) p;

all f = foldr (&&) True . map f;

filter f = foldr (\x xs ->ife (f x) (x:xs) xs) [];

intersect xs ys = filter (\x -> fmaybe (find (x ==) ys) False (\_ -> True)) xs;

merge s1 s2 = ife (all (\v -> apply s1 (TV v) == apply s2 (TV v))
$map fst s1 intersect map fst s2) (Just$ s1 ++ s2) Nothing;

match h t = case h of
{ TC a -> case t of
{ TC b -> ife (a == b) (Just []) Nothing
; TV b -> Nothing
; TAp a b -> Nothing
}
; TV a -> Just [(a, t)]
; TAp a b -> case t of
{ TC b -> Nothing
; TV b -> Nothing
; TAp c d -> case match a c of
{ Nothing -> Nothing
; Just ac -> case match b d of
{ Nothing -> Nothing
; Just bd -> merge ac bd
}
}
}
};

matchPred h p = case p of { Pred _ t -> match h t };

showType t = case t of
{ TC s -> s
; TV s -> s
; TAp a b -> concat ["(", showType a, " ", showType b, ")"]
};
showPred p = case p of { Pred s t -> s ++ (' ':showType t) ++ " => "};

findInst r qn p insts = case insts of
{ [] ->
fpair qn \q n -> let { v = '*':showInt n "" } in (((p, v):q, n + 1), V v)
; (:) i is -> case i of { Qual ps h -> case matchPred h p of
{ Nothing -> findInst r qn p is
; Just u -> foldl (\qnt p -> fpair qnt \qn1 t -> second (A t)
(r (predApply u p) qn1)) (qn, V (case p of { Pred s _ -> showPred $Pred s h})) ps }}}; findProof is pred psn = fpair psn \ps n -> case lookup pred ps of { Nothing -> case pred of { Pred s t -> case lookup s is of { Nothing -> undefined -- No instances! ; Just insts -> findInst (findProof is) psn pred insts }} ; Just s -> (psn, V s) }; prove' ienv sub psn a = case a of { E x -> case x of { Basic _ -> (psn, a) ; Const _ -> (psn, a) ; StrCon _ -> (psn, a) ; Proof raw -> findProof ienv (predApply sub raw) psn } ; V _ -> (psn, a) ; A x y -> let { p1 = prove' ienv sub psn x } in fpair p1 \psn1 x1 -> second (A x1) (prove' ienv sub psn1 y) ; L s t -> second (L s) (prove' ienv sub psn t) }; --prove :: [(String, [Qual])] -> (Type, Ast) -> Subst -> (Qual, Ast) prove ienv ta sub = fpair ta \t a -> fpair (prove' ienv sub ([], 0) a) \psn x -> fpair psn \ps _ -> (Qual (map fst ps) (apply sub t), foldr L x (map snd ps)); data Either a b = Left a | Right b; dictVars ps n = flst ps ([], n) \p pt -> first ((p, '*':showInt n ""):) (dictVars pt$ n + 1);

-- qi = Qual of instance, e.g. Eq t => [t] -> [t] -> Bool
inferMethod ienv typed qi def = fpair def \s expr ->
fpair (infer typed [] expr (Just [], 0)) \ta msn ->
case lookup s typed of
{ Nothing -> undefined -- No such method.
-- e.g. qac = Eq a => a -> a -> Bool, some AST (product of single method)
; Just qac -> fpair msn \ms n -> case ms of
{ Nothing -> undefined  -- Type check fails.
; Just sub -> fpair (instantiate (fst qac) n) \q1 n1 -> case q1 of { Qual psc tc -> case psc of
{ [] -> undefined  -- Unreachable.
; (:) headPred shouldBeNull -> case qi of { Qual psi ti ->
{ Nothing -> undefined
-- e.g. Eq t => [t] -> [t] -> Bool
-- instantiate and match it against type of ta
; Just subc ->
fpair (instantiate (Qual psi $apply subc tc) n1) \q2 n2 -> case q2 of { Qual ps2 t2 -> fpair ta \tx ax -> case match (apply sub tx) t2 of { Nothing -> undefined -- Class/instance type conflict. ; Just subx -> snd$ prove' ienv (subx @@ sub) (dictVars ps2 0) ax
}}}}}}}}};

inferInst ienv typed inst = fpair inst \cl qds -> fpair qds \q ds ->
case q of { Qual ps t -> let { s = showPred $Pred cl t } in (s, (,) (noQual$ TC "DICT") $maybeFix s$ foldr L (L "@" $foldl A (V "@") (map (inferMethod ienv typed q) ds)) (map snd$ fst $dictVars ps 0)) }; reverse = foldl (flip (:)) []; inferDefs ienv defs typed = flst defs (Right$ reverse typed) \edef rest -> case edef of
{ Left def -> fpair def \s expr -> fpair (infer typed [] (maybeFix s expr) (Just [], 0)) \ta msn ->
fpair msn \ms _ -> case maybeMap (prove ienv ta) ms of
{ Nothing -> Left ("bad type: " ++ s)
; Just qa -> inferDefs ienv rest ((s, qa):typed)
}
; Right inst -> inferDefs ienv rest (inferInst ienv typed inst:typed)
};

conOf con = case con of { Constr s _ -> s };
mkCase t cs = (concatMap (('|':) . conOf) cs,
( noQual $arr t$ foldr arr (TV "case") $map (\c -> case c of { Constr _ ts -> foldr arr (TV "case") ts}) cs , ro 'I')); mkStrs = snd . foldl (\p u -> fpair p (\s l -> ('@':s, s : l))) ("@", []); length = foldr (\_ n -> succ n) 0; scottEncode vs s ts = foldr L (foldl (\a b -> A a (V b)) (V s) ts) (ts ++ vs); scottConstr t cs c = case c of { Constr s ts -> (s, ( noQual$ foldr arr t ts
, scottEncode (map conOf cs) s $mkStrs ts)) }; mkAdtDefs t cs = mkCase t cs : map (scottConstr t cs) cs; data Neat = Neat -- | Instance environment. [(String, [Qual])] -- | Either top-level or instance definitions. [Either (String, Ast) (String, (Qual, [(String, Ast)]))] -- | Typed ASTs, ready for compilation, including ADTs and methods, -- e.g. (==), (Eq a => a -> a -> Bool, select-==) [(String, (Qual, Ast))] -- | FFI declarations. [(String, Type)] -- | Exports. [(String, String)] ; fneat neat f = case neat of { Neat a b c d e -> f a b c d e }; select f xs acc = flst xs (Nothing, acc) \x xt -> ife (f x) (Just x, xt ++ acc) (select f xt (x:acc)); addInstance s q is = fpair (select (\kv -> s == fst kv) is []) \m xs -> case m of { Nothing -> (s, [q]):xs ; Just sqs -> second (q:) sqs:xs }; mkSel ms s = L "*"$ A (V "*") $foldr L (V$ '*':s) $map (('*':) . fst) ms; mkFFIHelper n t acc = case t of { TC s -> acc ; TV s -> undefined ; TAp g y -> case g of { TC s -> ife (s == "IO") acc undefined ; TV s -> undefined ; TAp f x -> case f of { TC s -> ife (s == "->") (L (showInt n "")$ mkFFIHelper (n + 1) y $A (V$ showInt n "") acc) undefined
; TV s -> undefined
; TAp _ _ -> undefined
}
}
};

untangle = foldr (\top acc -> fneat acc \ienv fs typed ffis exs -> case top of
{ Adt t cs -> Neat ienv fs (mkAdtDefs t cs ++ typed) ffis exs
; Def e f -> Neat ienv (Left f : fs) typed ffis $case e of { Nothing -> id ; Just name -> ((name, fst f):) } exs ; Class classId v ms -> Neat ienv fs ( map (\st -> fpair st \s t -> (s, (Qual [Pred classId v] t, mkSel ms s))) ms ++ typed) ffis exs ; Inst cl q ds -> Neat (addInstance cl q ienv) (Right (cl, (q, ds)):fs) typed ffis exs ; FFI foreignname ourname t -> Neat ienv fs ( (ourname, (Qual [] t, mkFFIHelper 0 t$ A (ro 'F') (ro $chr$ length ffis))) : typed) ((foreignname, t):ffis) exs
}) (Neat [] [] prims [] []);

showQual q = case q of { Qual ps t -> concatMap showPred ps ++ showType t };

dumpTypes s = fmaybe (program s) "parse error" \progRest ->
fpair progRest \prog rest -> fneat (untangle prog) \ienv fs typed ffis exs -> case inferDefs ienv fs typed of
{ Left err -> err
; Right typed -> concatMap (\p -> fpair p \s qa -> s ++ " :: " ++ showQual (fst qa) ++ "\n") typed
};

last' x xt = flst xt x \y yt -> last' y yt;
last xs = flst xs undefined last';
init xs = flst xs undefined \x xt -> flst xt [] \_ _ -> x : init xt;
intercalate sep xs = flst xs [] \x xt -> x ++ concatMap (sep ++) xt;

argList t = case t of
{ TC s -> [TC s]
; TV s -> [TV s]
; TAp g y -> case g of
{ TC s -> case y of
{ TC u -> ife (s == "IO") [TC u] undefined
; TV _ -> undefined
; TAp _ _ -> undefined
}
; TV s -> undefined
; TAp f x -> case f of
{ TC s -> ife (s == "->") (x : argList y) undefined
; TV s -> undefined
; TAp _ _ -> undefined
}
}
};

cTypeName t = case t of
{ TC s -> ife (s == "()") "void" $ife (s == "Int") "int"$
ife (s == "Char") "char" undefined
; TV _ -> undefined
; TAp _ _ -> undefined
};

ffiDeclare namet = fpair namet \name t -> let { tys = argList t } in concat
[ cTypeName $last tys , " " , name , "(" , intercalate ","$ map cTypeName $init tys , ");\n" ]; ffiArgs n t = case t of { TC s -> ("", ((True, s), n)) ; TV s -> undefined ; TAp g y -> case g of { TC s -> case y of { TC u -> ife (s == "IO") ("", ((False, u), n)) undefined ; TV _ -> undefined ; TAp _ _ -> undefined } ; TV s -> undefined ; TAp f x -> case f of { TC s -> ife (s == "->") (first ((ife (3 <= n) ", " "" ++ "num(" ++ showInt n ")") ++)$ ffiArgs (n + 1) y) undefined
; TV s -> undefined
; TAp _ _ -> undefined
}
}
};

ffiDefine n ffis = case ffis of
{ [] -> id
; (:) x xt -> fpair x \name t -> fpair (ffiArgs 2 t) \args pRetCount -> fpair pRetCount \pRet count -> fpair pRet \isPure ret -> let
{ lazyn = ("lazy(" ++) . showInt (ife isPure (count - 1) (count + 1)) . (", " ++)
; cont tgt = ife isPure (("'I', "++) . tgt) $("app(arg("++) . showInt (count + 1) . ("), "++) . tgt . ("), arg("++) . showInt count . (")"++) ; longDistanceCall = (name++) . ("("++) . (args++) . ("); "++) . lazyn } in ("case " ++) . showInt n . (": " ++) . ife (ret == "()") (longDistanceCall . cont ("'K'"++) . ("); break;"++) . ffiDefine (n - 1) xt) (("{u r = "++) . longDistanceCall . cont ("app('#', r)" ++) . ("); break;}\n"++) . ffiDefine (n - 1) xt) }; upFrom n = n : upFrom (n + 1); zipWith f xs ys = flst xs []$ \x xt -> flst ys [] $\y yt -> f x y : zipWith f xt yt; compile s = fmaybe (program s) "parse error" \progRest -> fpair progRest \prog rest -> fneat (untangle prog) \ienv fs typed ffis exs -> case inferDefs ienv fs typed of { Left err -> err ; Right qas -> fpair (asm qas) \tab mem -> (concatMap ffiDeclare ffis ++) . ("static void foreign(u n) {\n switch(n) {\n" ++) . ffiDefine (length ffis - 1) ffis . ("\n }\n}\n" ++) . ("static const u prog[]={" ++) . foldr (.) id (map (\n -> showInt n . (',':))$ snd mem []) .
("};\nstatic const u prog_size=sizeof(prog)/sizeof(*prog);\n" ++) .
("static u root[]={" ++) .
foldr (\p f -> fpair p \x y -> maybe undefined showInt (mlookup y tab) . (", " ++) . f) id exs .
("};\n" ++) .
("static const u root_size=" ++) . showInt (length exs) . (";\n" ++) $flst exs ("int main(){rts_init();rts_reduce(" ++ maybe undefined showInt (mlookup (fst$ last qas) tab) ");return 0;}") $\_ _ -> concat$ zipWith (\p n -> "EXPORT(f" ++ showInt n ", \"" ++ fst p ++ "\", " ++ showInt n ")\n") exs (upFrom 0)
};

Rather than a bunch of numbers, our compiler generates C code that should be appended to the following C implementation of the VM:

void *malloc(unsigned long);
typedef unsigned u;

static const u prog[];
static const u prog_size;
static u root[];
static const u root_size;

enum { FORWARD = 27, REDUCING = 9 };

enum { TOP = 1<<24 };
u *mem, *altmem, *sp, *spTop, hp;

static inline u isAddr(u n) { return n>=128; }

static u evac(u n) {
u x = mem[n];
while (isAddr(x) && mem[x] == 'T') {
mem[n] = mem[n + 1];
mem[n + 1] = mem[x + 1];
x = mem[n];
}
if (isAddr(x) && mem[x] == 'K') {
mem[n + 1] = mem[x + 1];
x = mem[n] = 'I';
}
u y = mem[n + 1];
switch(x) {
case FORWARD: return y;
case REDUCING:
mem[n] = FORWARD;
mem[n + 1] = hp;
hp += 2;
return mem[n + 1];
case 'I':
mem[n] = REDUCING;
y = evac(y);
if (mem[n] == FORWARD) {
altmem[mem[n + 1]] = 'I';
altmem[mem[n + 1] + 1] = y;
} else {
mem[n] = FORWARD;
mem[n + 1] = y;
}
return mem[n + 1];
default: break;
}
u z = hp;
hp += 2;
mem[n] = FORWARD;
mem[n + 1] = z;
altmem[z] = x;
altmem[z + 1] = y;
return z;
}

static void gc() {
hp = 128;
u di = hp;
sp = altmem + TOP - 1;
for(u i = 0; i < root_size; i++) root[i] = evac(root[i]);
*sp = evac(*spTop);
while (di < hp) {
u x = altmem[di] = evac(altmem[di]);
di++;
if (x != 'F' && x != '#') altmem[di] = evac(altmem[di]);
di++;
}
spTop = sp;
u *tmp = mem;
mem = altmem;
altmem = tmp;
}

static inline u app(u f, u x) {
mem[hp] = f;
mem[hp + 1] = x;
hp += 2;
return hp - 2;
}

static inline u arg(u n) { return mem[sp [n] + 1]; }
static inline u num(u n) { return mem[arg(n) + 1]; }

static inline void lazy(u height, u f, u x) {
u *p = mem + sp[height];
*p = f;
*++p = x;
sp += height - 1;
*sp = f;
}

static void lazy3(u height,u x1,u x2,u x3){u*p=mem+sp[height];sp[height-1]=*p=app(x1,x2);*++p=x3;*(sp+=height-2)=x1;}

static inline u apparg(u i, u j) { return app(arg(i), arg(j)); }

static void foreign(u n);

static void run() {
for(;;) {
if (mem + hp > sp - 8) gc();
u x = *sp;
if (isAddr(x)) *--sp = mem[x]; else switch(x) {
case 'F': foreign(arg(1)); break;
case 'Y': lazy(1, arg(1), sp[1]); break;
case 'Q': lazy(3, arg(3), apparg(2, 1)); break;
case 'S': lazy3(3, arg(1), arg(3), apparg(2, 3)); break;
case 'B': lazy(3, arg(1), apparg(2, 3)); break;
case 'C': lazy3(3, arg(1), arg(3), arg(2)); break;
case 'R': lazy3(3, arg(2), arg(3), arg(1)); break;
case 'V': lazy3(3, arg(3), arg(1), arg(2)); break;
case 'I': sp[1] = arg(1); sp++; break;
case 'T': lazy(2, arg(2), arg(1)); break;
case 'K': lazy(2, 'I', arg(1)); break;
case ':': lazy3(4, arg(4), arg(1), arg(2)); break;
case '#': lazy(2, arg(2), sp[1]); break;
case '=': num(1) == num(2) ? lazy(2, 'I', 'K') : lazy(2, 'K', 'I'); break;
case 'L': num(1) <= num(2) ? lazy(2, 'I', 'K') : lazy(2, 'K', 'I'); break;
case '*': lazy(2, '#', num(1) * num(2)); break;
case '/': lazy(2, '#', num(1) / num(2)); break;
case '%': lazy(2, '#', num(1) % num(2)); break;
case '+': lazy(2, '#', num(1) + num(2)); break;
case '-': lazy(2, '#', num(1) - num(2)); break;
case '.': return;
case FORWARD: return;  // die("stray forwarding pointer");
default: return;  // printf("?%u\n", x); die("unknown combinator");
}
}
}

void rts_reduce(u n) {
*(sp = spTop) = app(app(n, '?'), '.');
run();
}

#if __has_attribute(export_name)
void rts_init() __attribute__((export_name("rts_init")));
#endif
void rts_init() {
mem = malloc(TOP * sizeof(u)); altmem = malloc(TOP * sizeof(u));
hp = 128;
for (u i = 0; i < prog_size; i++) mem[hp++] = prog[i];
spTop = mem + TOP - 1;
}

static int env_argc;
int getargcount() { return env_argc; }
static char **env_argv;
int getargchar(int n, int k) { return env_argv[n][k]; }

#define EXPORT(f, sym, n) void f() asm(sym) __attribute__((export_name(sym))); void f(){rts_reduce(root[n]);}

We employ a stop-the-world copying garbage collector. It turns out we should reduce projection functions (such as fst and snd) as we collect garbage. See:

We partially achieve this by reducing K I T nodes during garbage collection.

Eliminating applications of I during garbage collection makes up for not doing so during evaluation.

Our simple design means the only garbage collection root we need is the top of the stack.

## Lonely

We’ve made it to the real world. Our next compiler has a main function of type IO (), and calls getchar() and putchar() via FFI. Running effectively on this compiler produces C source. Appending this to rts.c and compiling yields a standalone compiler. This contrasts with our previous compilers, which require a program that understands ION assembly or a bunch of integers representing VM memory contents.

We also add support for if expressions and infix patterns in case expressions.

-- Standalone compiler.
infixr 9 .;
infixl 7 *;
infixl 6 + , -;
infixr 5 ++;
infixl 4 <*> , <$> , <* , *>; infix 4 == , <=; infixl 3 && , <|>; infixl 2 ||; infixl 1 >> , >>=; infixr 0$;

foreign import ccall "putchar" putChar :: Int -> IO Int;
foreign import ccall "getchar" getChar :: IO Int;

class Functor f where { fmap :: (a -> b) -> f a -> f b };
class Applicative f where
{ pure :: a -> f a
; (<*>) :: f (a -> b) -> f a -> f b
};
{ return :: a -> m a
; (>>=) :: m a -> (a -> m b) -> m b
};
(>>) f g = f >>= \_ -> g;
class Eq a where { (==) :: a -> a -> Bool };
instance Eq Int where { (==) = intEq };
($) f x = f x; id x = x; flip f x y = f y x; (&) x f = f x; data Bool = True | False; class Ord a where { (<=) :: a -> a -> Bool }; instance Ord Int where { (<=) = intLE }; data Ordering = LT | GT | EQ; compare x y = case x <= y of { True -> case y <= x of { True -> EQ ; False -> LT } ; False -> GT }; instance Ord a => Ord [a] where { (<=) xs ys = case xs of { [] -> True ; (:) x xt -> case ys of { [] -> False ; (:) y yt -> case compare x y of { LT -> True ; GT -> False ; EQ -> xt <= yt } } } }; data Maybe a = Nothing | Just a; data Either a b = Left a | Right b; fpair p = \f -> case p of { (,) x y -> f x y }; fst p = case p of { (,) x y -> x }; snd p = case p of { (,) x y -> y }; first f p = fpair p \x y -> (f x, y); second f p = fpair p \x y -> (x, f y); ife a b c = case a of { True -> b ; False -> c }; not a = case a of { True -> False; False -> True }; (.) f g x = f (g x); (||) f g = ife f True g; (&&) f g = ife f g False; flst xs n c = case xs of { [] -> n; (:) h t -> c h t }; instance Eq a => Eq [a] where { (==) xs ys = case xs of { [] -> case ys of { [] -> True ; (:) _ _ -> False } ; (:) x xt -> case ys of { [] -> False ; (:) y yt -> x == y && xt == yt } }}; maybe n j m = case m of { Nothing -> n; Just x -> j x }; foldr c n l = flst l n (\h t -> c h(foldr c n t)); mapM_ f = foldr ((>>) . f) (pure ()); instance Applicative IO where { pure = ioPure ; (<*>) f x = ioBind f \g -> ioBind x \y -> ioPure (g y) }; instance Monad IO where { return = ioPure ; (>>=) = ioBind }; instance Functor IO where { fmap f x = ioPure f <*> x }; putStr = mapM_$ putChar . ord;
error s = unsafePerformIO $putStr s >> putChar (ord '\n') >> exitSuccess; undefined = error "undefined"; foldr1 c l = maybe undefined id (flst l undefined (\h t -> foldr (\x m -> Just (case m of { Nothing -> x ; Just y -> c x y })) Nothing l)); foldl f a bs = foldr (\b g x -> g (f x b)) (\x -> x) bs a; foldl1 f bs = flst bs undefined (\h t -> foldl f h t); elem k xs = foldr (\x t -> x == k || t) False xs; find f xs = foldr (\x t -> ife (f x) (Just x) t) Nothing xs; (++) = flip (foldr (:)); concat = foldr (++) []; wrap c = c:[]; map = flip (foldr . ((:) .)) []; concatMap = (concat .) . map; fmaybe m n j = case m of { Nothing -> n; Just x -> j x }; lookup s = foldr (\h t -> fpair h (\k v -> ife (s == k) (Just v) t)) Nothing; -- Map. data Map k a = Tip | Bin Int k a (Map k a) (Map k a); size m = case m of { Tip -> 0 ; Bin sz _ _ _ _ -> sz }; node k x l r = Bin (1 + size l + size r) k x l r; singleton k x = Bin 1 k x Tip Tip; singleL k x l r = case r of { Tip -> undefined ; Bin _ rk rkx rl rr -> node rk rkx (node k x l rl) rr }; singleR k x l r = case l of { Tip -> undefined ; Bin _ lk lkx ll lr -> node lk lkx ll (node k x lr r) }; doubleL k x l r = case r of { Tip -> undefined ; Bin _ rk rkx rl rr -> case rl of { Tip -> undefined ; Bin _ rlk rlkx rll rlr -> node rlk rlkx (node k x l rll) (node rk rkx rlr rr) } }; doubleR k x l r = case l of { Tip -> undefined ; Bin _ lk lkx ll lr -> case lr of { Tip -> undefined ; Bin _ lrk lrkx lrl lrr -> node lrk lrkx (node lk lkx ll lrl) (node k x lrr r) } }; balance k x l r = case size l + size r <= 1 of { True -> node ; False -> case 5 * size l + 3 <= 2 * size r of { True -> case r of { Tip -> node ; Bin sz _ _ rl rr -> case 2 * size rl + 1 <= 3 * size rr of { True -> singleL ; False -> doubleL } } ; False -> case 5 * size r + 3 <= 2 * size l of { True -> case l of { Tip -> node ; Bin sz _ _ ll lr -> case 2 * size lr + 1 <= 3 * size ll of { True -> singleR ; False -> doubleR } } ; False -> node } } } k x l r; insert kx x t = case t of { Tip -> singleton kx x ; Bin sz ky y l r -> case compare kx ky of { LT -> balance ky y (insert kx x l) r ; GT -> balance ky y l (insert kx x r) ; EQ -> Bin sz kx x l r } }; mlookup kx t = case t of { Tip -> Nothing ; Bin _ ky y l r -> case compare kx ky of { LT -> mlookup kx l ; GT -> mlookup kx r ; EQ -> Just y } }; fromList = let { ins t kx = case kx of { (,) k x -> insert k x t } } in foldl ins Tip; foldrWithKey f = let { go z t = case t of { Tip -> z ; Bin _ kx x l r -> go (f kx x (go z r)) l } } in go; toAscList = foldrWithKey (\k x xs -> (k,x):xs) []; -- Parsing. data Type = TC String | TV String | TAp Type Type; arr a b = TAp (TAp (TC "->") a) b; data Extra = Basic Int | Const Int | StrCon String | Proof Pred; data Ast = E Extra | V String | A Ast Ast | L String Ast; ro = E . Basic . ord; data Parser a = Parser (String -> Maybe (a, String)); data Constr = Constr String [Type]; data Pred = Pred String Type; data Qual = Qual [Pred] Type; noQual = Qual []; data Neat = Neat -- | Instance environment. [(String, [Qual])] -- | Either top-level or instance definitions. -- e.g. -- Left ("id", L "x" (V "x")) -- Right ("Monad", (TC "IO" , [("return", ...), (">>=", ...)])) [Either (String, Ast) (String, (Qual, [(String, Ast)]))] -- | Typed ASTs, ready for compilation, including ADTs and methods, -- e.g. (==), (Eq a => a -> a -> Bool, select-==) [(String, (Qual, Ast))] -- | FFI declarations. [(String, Type)] -- | Exports. [(String, String)] ; parse p inp = case p of { Parser f -> f inp }; fneat neat f = case neat of { Neat a b c d e -> f a b c d e }; conOf con = case con of { Constr s _ -> s }; mkCase t cs = (concatMap (('|':) . conOf) cs, ( noQual$ arr t $foldr arr (TV "case")$ map (\c -> case c of { Constr _ ts -> foldr arr (TV "case") ts}) cs
, ro 'I'));
mkStrs = snd . foldl (\p u -> fpair p (\s l -> ('@':s, s : l))) ("@", []);
length = foldr (\_ n -> n + 1) 0;
scottEncode vs s ts = foldr L (foldl (\a b -> A a (V b)) (V s) ts) (ts ++ vs);
scottConstr t cs c = case c of { Constr s ts -> (s,
( noQual $foldr arr t ts , scottEncode (map conOf cs) s$ mkStrs ts)) };
mkAdtDefs t cs = mkCase t cs : map (scottConstr t cs) cs;

select f xs acc = flst xs (Nothing, acc) \x xt -> ife (f x) (Just x, xt ++ acc) (select f xt (x:acc));

addInstance s q is = fpair (select (\kv -> s == fst kv) is []) \m xs -> case m of
{ Nothing -> (s, [q]):xs
; Just sqs -> second (q:) sqs:xs
};

mkSel ms s = L "*" $A (V "*")$ foldr L (V $'*':s)$ map (('*':) . fst) ms;

ifz n = ife (0 == n);
showInt' n = ifz n id ((showInt' (n/10)) . ((:) (chr (48+(n%10)))));
showInt n s = ifz n ('0':) (showInt' n) s;

mkFFIHelper n t acc = case t of
{ TC s -> acc
; TV s -> undefined
; TAp g y -> case g of
{ TC s -> ife (s == "IO") acc undefined
; TV s -> undefined
; TAp f x -> case f of
{ TC s -> ife (s == "->") (L (showInt n "") $mkFFIHelper (n + 1) y$ A (V $showInt n "") acc) undefined ; TV s -> undefined ; TAp _ _ -> undefined } } }; addAdt t cs acc = fneat acc \ienv fs typed ffis exs -> Neat ienv fs (mkAdtDefs t cs ++ typed) ffis exs; addClass classId v ms acc = fneat acc \ienv fs typed ffis exs -> Neat ienv fs ( map (\st -> fpair st \s t -> (s, (Qual [Pred classId v] t, mkSel ms s))) ms ++ typed) ffis exs; addInst cl q ds acc = fneat acc \ienv fs typed ffis exs -> Neat (addInstance cl q ienv) (Right (cl, (q, ds)):fs) typed ffis exs; addFFI foreignname ourname t acc = fneat acc \ienv fs typed ffis exs -> Neat ienv fs ( (ourname, (Qual [] t, mkFFIHelper 0 t$ A (ro 'F') (ro $chr$ length ffis))) : typed) ((foreignname, t):ffis) exs;
addDef f acc = fneat acc \ienv fs typed ffis exs -> Neat ienv (Left f : fs) typed ffis exs;
addExport e f acc = fneat acc \ienv fs typed ffis exs -> Neat ienv fs typed ffis ((e, f):exs);

instance Applicative Parser where
{ pure x = Parser \inp -> Just (x, inp)
; (<*>) x y = Parser \inp -> case parse x inp of
{ Nothing -> Nothing
; Just funt -> fpair funt \fun t -> case parse y t of
{ Nothing -> Nothing
; Just argu -> fpair argu \arg u -> Just (fun arg, u)
}
}
};
{ return = pure
; (>>=) x f = Parser \inp -> case parse x inp of
{ Nothing -> Nothing
; Just at -> fpair at \a t -> parse (f a) t
}
};

sat' f = \h t -> ife (f h) (Just (h, t)) Nothing;
sat f = Parser \inp -> flst inp Nothing (sat' f);

instance Functor Parser where { fmap f x = pure f <*> x };
(<|>) x y = Parser \inp -> case parse x inp of
{ Nothing -> parse y inp
; Just at -> Just at
};
(<$>) = fmap; liftA2 f x y = f <$> x <*> y;
(*>) = liftA2 \x y -> y;
(<*) = liftA2 \x y -> x;
many p = liftA2 (:) p (many p) <|> pure [];
some p = liftA2 (:) p (many p);
sepBy1 p sep = liftA2 (:) p (many (sep *> p));
sepBy p sep = sepBy1 p sep <|> pure [];

char c = sat \x -> x == c;
between x y p = x *> (p <* y);
com = char '-' *> between (char '-') (char '\n') (many (sat \c -> not (c == '\n')));
sp = many ((wrap <$> (sat (\c -> (c == ' ') || (c == '\n')))) <|> com); spc f = f <* sp; spch = spc . char; wantWith pred f = Parser \inp -> case parse f inp of { Nothing -> Nothing ; Just at -> ife (pred$ fst at) (Just at) Nothing
};

want f s = wantWith (s ==) f;

paren = between (spch '(') (spch ')');
small = sat \x -> ((x <= 'z') && ('a' <= x)) || (x == '_');
large = sat \x -> (x <= 'Z') && ('A' <= x);
digit = sat \x -> (x <= '9') && ('0' <= x);
symbo = sat \c -> elem c "!#$%&*+./<=>?@\\^|-~"; varLex = liftA2 (:) small (many (small <|> large <|> digit <|> char '\'')); conId = spc (liftA2 (:) large (many (small <|> large <|> digit <|> char '\''))); keyword s = spc$ want varLex s;
varId = spc $wantWith (\s -> not$ elem s ["of", "where", "if", "then", "else"]) varLex;
opTail = many $char ':' <|> symbo; conSym = spc$ liftA2 (:) (char ':') opTail;
varSym = spc $liftA2 (:) symbo opTail; con = conId <|> paren conSym; var = varId <|> paren varSym; op = varSym <|> conSym <|> between (spch '') (spch '') (conId <|> varId); conop = conSym <|> between (spch '') (spch '') conId; listify = foldr (\h t -> A (A (V ":") h) t) (V "[]"); escChar = char '\\' *> ((sat (\c -> elem c "'\"\\")) <|> ((\c -> '\n') <$> char 'n'));
litOne delim = escChar <|> sat \c -> not (c == delim);
litInt = E . Const . foldl (\n d -> 10*n + ord d - ord '0') 0 <$> spc (some digit); litStr = between (char '"') (spch '"')$ many (litOne '"');
litChar = E . Const . ord <$> between (char '\'') (spch '\'') (litOne '\''); lit = E . StrCon <$> litStr <|> litChar <|> litInt;
sqLst r = between (spch '[') (spch ']') $listify <$> sepBy r (spch ',');

gcon = conId <|> paren (conSym <|> (wrap <$> spch ',')) <|> ((:) <$> spch '[' <*> (wrap <$> spch ']')); pat = (,) <$> gcon <*> many varId <|> (\x c y -> (c, [x, y])) <$> varId <*> conop <*> varId; lamAlt conArgs expr = fpair conArgs \con args -> (con, foldr L expr args); alt r = lamAlt <$> pat <*> (want varSym "->" *> r);

braceSep f = between (spch '{') (spch '}') (sepBy f (spch ';'));
alts r = braceSep (alt r);
cas' x as = foldl A (V (concatMap (('|':) . fst) as)) (x:map snd as);
cas r = cas' <$> between (keyword "case") (keyword "of") r <*> alts r; lamCase r = keyword "case" *> (L "of" . cas' (V "of") <$> alts r);
lam r = spch '\\' *> (lamCase r <|> liftA2 (flip (foldr L)) (some varId) (char '-' *> (spch '>' *> r)));

thenComma r = spch ',' *> (((\x y -> A (A (V ",") y) x) <$> r) <|> pure (A (V ","))); parenExpr r = (&) <$> r <*> (((\v a -> A (V v) a) <$> op) <|> thenComma r <|> pure id); rightSect r = ((\v a -> L "@"$ A (A (V v) $V "@") a) <$> (op <|> (wrap <$> spch ','))) <*> r; section r = spch '(' *> (parenExpr r <* spch ')' <|> rightSect r <* spch ')' <|> spch ')' *> pure (V "()")); isFree v expr = case expr of { E _ -> False ; V s -> s == v ; A x y -> isFree v x || isFree v y ; L w t -> not (v == w) && isFree v t }; maybeFix s x = ife (isFree s x) (A (ro 'Y') (L s x)) x; opDef x f y rhs = (f, L x$ L y rhs);
def r =
opDef <$> varId <*> varSym <*> varId <*> (spch '=' *> r) <|> liftA2 (,) var (liftA2 (flip (foldr L)) (many varId) (spch '=' *> r)); addLets ls x = foldr (\p t -> fpair p (\name def -> A (L name t)$ maybeFix name def)) x ls;
letin r = addLets <$> between (keyword "let") (keyword "in") (braceSep (def r)) <*> r; ifthenelse r = (\a b c -> A (A (A (V "if") a) b) c) <$>
(keyword "if" *> r) <*> (keyword "then" *> r) <*> (keyword "else" *> r);
atom r = ifthenelse r <|> letin r <|> sqLst r <|> section r <|> cas r <|> lam r <|> (paren (spch ',') *> pure (V ",")) <|> fmap V (con <|> var) <|> lit;
aexp r = fmap (foldl1 A) (some (atom r));
fix f = f (fix f);

data Assoc = NAssoc | LAssoc | RAssoc;
eqAssoc x y = case x of
{ NAssoc -> case y of { NAssoc -> True  ; LAssoc -> False ; RAssoc -> False }
; LAssoc -> case y of { NAssoc -> False ; LAssoc -> True  ; RAssoc -> False }
; RAssoc -> case y of { NAssoc -> False ; LAssoc -> False ; RAssoc -> True }
};
precOf s precTab = fmaybe (lookup s precTab) 9 fst;
assocOf s precTab = fmaybe (lookup s precTab) LAssoc snd;
opWithPrec precTab n = wantWith (\s -> n == precOf s precTab) op;
opFold precTab e xs = case xs of
{ [] -> e
; (:) x xt -> case find (\y -> not (eqAssoc (assocOf (fst x) precTab) (assocOf (fst y) precTab))) xt of
{ Nothing -> case assocOf (fst x) precTab of
{ NAssoc -> case xt of
{ [] -> fpair x (\op y -> A (A (V op) e) y)
; (:) y yt -> undefined
}
; LAssoc -> foldl (\a b -> fpair b (\op y -> A (A (V op) a) y)) e xs
; RAssoc -> (foldr (\a b -> fpair a (\op y -> \e -> A (A (V op) e) (b y))) id xs) e
}
; Just y -> undefined
}
};
expr precTab = fix \r n -> ife (n <= 9) (liftA2 (opFold precTab) (r (succ n)) (many (liftA2 (\a b -> (a,b)) (opWithPrec precTab n) (r (succ n))))) (aexp (r 0));

bType r = foldl1 TAp <$> some r; _type r = foldr1 arr <$> sepBy (bType r) (spc (want varSym "->"));
typeConst = (\s -> ife (s == "String") (TAp (TC "[]") (TC "Int")) (TC s)) <$> conId; aType = spch '(' *> (spch ')' *> pure (TC "()") <|> ((&) <$> _type aType <*> ((spch ',' *> ((\a b -> TAp (TAp (TC ",") b) a) <$> _type aType)) <|> pure id)) <* spch ')') <|> typeConst <|> (TV <$> varId) <|>
(spch '[' *> (spch ']' *> pure (TC "[]") <|> TAp (TC "[]") <$> (_type aType <* spch ']'))); simpleType c vs = foldl TAp (TC c) (map TV vs); -- Can we reduce backtracking here? constr = (\x c y -> Constr c [x, y]) <$> aType <*> conSym <*> aType
<|> Constr <$> conId <*> many aType; adt = addAdt <$> between (keyword "data") (spch '=') (simpleType <$> conId <*> many varId) <*> sepBy constr (spch '|'); prec = (\c -> ord c - ord '0') <$> spc digit;
fixityList a n os = map (\o -> (o, (n, a))) os;
fixityDecl kw a = between (keyword kw) (spch ';') (fixityList a <$> prec <*> sepBy op (spch ',')); fixity = fixityDecl "infix" NAssoc <|> fixityDecl "infixl" LAssoc <|> fixityDecl "infixr" RAssoc; genDecl = (,) <$> var <*> (char ':' *> spch ':' *> _type aType);
classDecl = keyword "class" *> (addClass <$> conId <*> (TV <$> varId) <*> (keyword "where" *> braceSep genDecl));

inst = _type aType;
instDecl r = keyword "instance" *>
((\ps cl ty defs -> addInst cl (Qual ps ty) defs) <$> (((wrap .) . Pred <$> conId <*> (inst <* want varSym "=>")) <|> pure [])
<*> conId <*> inst <*> (keyword "where" *> braceSep (def r)));

tops precTab = sepBy
<|> classDecl
<|> instDecl (expr precTab 0)
<|> keyword "foreign" *>
( keyword "import" *> var *>
(addFFI <$> litStr <*> var <*> (char ':' *> spch ':' *> _type aType)) <|> keyword "export" *> var *> (addExport <$> litStr <*> var)
)
<|> addDef <$> def (expr precTab 0) ) (spch ';'); program' = sp *> (((":", (5, RAssoc)):) . concat <$> many fixity) >>= tops;

-- Primitives.

program = parse $( [ addAdt (TAp (TC "[]") (TV "a")) [Constr "[]" [], Constr ":" [TV "a", TAp (TC "[]") (TV "a")]] , addAdt (TAp (TAp (TC ",") (TV "a")) (TV "b")) [Constr "," [TV "a", TV "b"]]] ++) <$> program';

prims = let
{ ii = arr (TC "Int") (TC "Int")
; iii = arr (TC "Int") ii
; bin s = A (A (ro 'B') (ro 'T')) (A (ro 'T') (ro s)) } in map (second (first noQual)) $[ ("intEq", (arr (TC "Int") (arr (TC "Int") (TC "Bool")), bin '=')) , ("intLE", (arr (TC "Int") (arr (TC "Int") (TC "Bool")), bin 'L')) , ("if", (arr (TC "Bool")$ arr (TV "a") $arr (TV "a") (TV "a"), ro 'I')) , ("()", (TC "()", ro 'K')) , ("chr", (ii, ro 'I')) , ("ord", (ii, ro 'I')) , ("succ", (ii, A (ro 'T') (A (E$ Const $1) (ro '+')))) , ("ioBind", (arr (TAp (TC "IO") (TV "a")) (arr (arr (TV "a") (TAp (TC "IO") (TV "b"))) (TAp (TC "IO") (TV "b"))), ro 'C')) , ("ioPure", (arr (TV "a") (TAp (TC "IO") (TV "a")), ro 'V')) , ("exitSuccess", (TAp (TC "IO") (TV "a"), ro '.')) , ("unsafePerformIO", (arr (TAp (TC "IO") (TV "a")) (TV "a"), A (A (ro 'C') (A (ro 'T') (ro '?'))) (ro 'K'))) ] ++ map (\s -> (wrap s, (iii, bin s))) "+-*/%"; -- Conversion to De Bruijn indices. data LC = Ze | Su LC | Pass Int | La LC | App LC LC; debruijn m n e = case e of { E x -> case x of { Basic b -> Pass b ; Const c -> App (Pass$ ord '#') (Pass c)
; StrCon s -> foldr (\h t -> App (App (Pass $ord ':') (App (Pass$ ord '#') (Pass $ord h))) t) (Pass$ ord 'K') s
; Proof _ -> undefined
}
; V v -> maybe (fmaybe (mlookup v m) undefined Pass) id $foldr (\h found -> ife (h == v) (Just Ze) (maybe Nothing (Just . Su) found)) Nothing n ; A x y -> App (debruijn m n x) (debruijn m n y) ; L s t -> La (debruijn m (s:n) t) }; -- Kiselyov bracket abstraction. data IntTree = Lf Int | Nd IntTree IntTree; data Sem = Defer | Closed IntTree | Need Sem | Weak Sem; lf = Lf . ord; ldef = \r y -> case y of { Defer -> Need (Closed (Nd (Nd (lf 'S') (lf 'I')) (lf 'I'))) ; Closed d -> Need (Closed (Nd (lf 'T') d)) ; Need e -> Need (r (Closed (Nd (lf 'S') (lf 'I'))) e) ; Weak e -> Need (r (Closed (lf 'T')) e) }; lclo = \r d y -> case y of { Defer -> Need (Closed d) ; Closed dd -> Closed (Nd d dd) ; Need e -> Need (r (Closed (Nd (lf 'B') d)) e) ; Weak e -> Weak (r (Closed d) e) }; lnee = \r e y -> case y of { Defer -> Need (r (r (Closed (lf 'S')) e) (Closed (lf 'I'))) ; Closed d -> Need (r (Closed (Nd (lf 'R') d)) e) ; Need ee -> Need (r (r (Closed (lf 'S')) e) ee) ; Weak ee -> Need (r (r (Closed (lf 'C')) e) ee) }; lwea = \r e y -> case y of { Defer -> Need e ; Closed d -> Weak (r e (Closed d)) ; Need ee -> Need (r (r (Closed (lf 'B')) e) ee) ; Weak ee -> Weak (r e ee) }; babsa x y = case x of { Defer -> ldef babsa y ; Closed d -> lclo babsa d y ; Need e -> lnee babsa e y ; Weak e -> lwea babsa e y }; babs t = case t of { Ze -> Defer ; Su x -> Weak (babs x) ; Pass n -> Closed (Lf n) ; La t -> case babs t of { Defer -> Closed (lf 'I') ; Closed d -> Closed (Nd (lf 'K') d) ; Need e -> e ; Weak e -> babsa (Closed (lf 'K')) e } ; App x y -> babsa (babs x) (babs y) }; nolam m x = case babs$ debruijn m [] x of
{ Defer -> undefined
; Closed d -> d
; Need e -> undefined
; Weak e -> undefined
};

isLeaf t c = case t of { Lf n -> n == ord c ; Nd _ _ -> False };

optim t = case t of
{ Lf n -> t
; Nd x y -> let { p = optim x; q = optim y } in
ife (isLeaf p 'I') q $ife (isLeaf q 'I') ( ife (isLeaf p 'C') (Lf$ ord 'T') $ife (isLeaf p 'B') (Lf$ ord 'I') $Nd p q )$ Nd p q
};

enc mem t = case optim t of
{ Lf n -> (n, mem)
; Nd x y -> fpair mem \hp bs -> let
{ pm qm = enc (hp + 2, bs . (fst (pm qm):) . (fst qm:)) x
; qm = enc (snd $pm qm) y } in (hp, snd qm) }; asm qas = foldl (\tabmem def -> fpair def \s qt -> fpair tabmem \tab mem -> fpair (enc mem$ nolam (insert s (fst mem) tab) $snd qt) \p m' -> let -- Definitions like "t = t;" must be handled with care. { m'' = fpair m' \hp bs -> ife (p == hp) (hp + 2, bs . (ord 'I':) . (p:)) m' } in (insert s p tab, m'')) (Tip, (128, id)) qas; -- Type checking. apply sub t = case t of { TC v -> t ; TV v -> fmaybe (lookup v sub) t id ; TAp a b -> TAp (apply sub a) (apply sub b) }; (@@) s1 s2 = map (second (apply s1)) s2 ++ s1; occurs s t = case t of { TC v -> False ; TV v -> s == v ; TAp a b -> occurs s a || occurs s b }; varBind s t = case t of { TC v -> Just [(s, t)] ; TV v -> ife (v == s) (Just []) (Just [(s, t)]) ; TAp a b -> ife (occurs s t) Nothing (Just [(s, t)]) }; charIsInt s = ife (s == "Char") "Int" s; mgu unify t u = case t of { TC a -> case u of { TC b -> ife (charIsInt a == charIsInt b) (Just []) Nothing ; TV b -> varBind b t ; TAp a b -> Nothing } ; TV a -> varBind a u ; TAp a b -> case u of { TC b -> Nothing ; TV b -> varBind b t ; TAp c d -> unify b d (mgu unify a c) } }; instance Functor Maybe where { fmap f = maybe Nothing (Just . f) }; unify a b = maybe Nothing \s -> (@@ s) <$> (mgu unify (apply s a) (apply s b));

--instantiate' :: Type -> Int -> [(String, Type)] -> ((Type, Int), [(String, Type)])
instantiate' t n tab = case t of
{ TC s -> ((t, n), tab)
; TV s -> case lookup s tab of
{ Nothing -> let { va = TV (showInt n "") } in ((va, n + 1), (s, va):tab)
; Just v -> ((v, n), tab)
}
; TAp x y ->
fpair (instantiate' x n tab) \tn1 tab1 ->
fpair tn1 \t1 n1 -> fpair (instantiate' y n1 tab1) \tn2 tab2 ->
fpair tn2 \t2 n2 -> ((TAp t1 t2, n2), tab2)
};

instantiatePred pred xyz = case pred of { Pred s t -> fpair xyz \xy tab -> fpair xy \out n -> first (first ((:out) . Pred s)) (instantiate' t n tab) };

--instantiate :: Qual -> Int -> (Qual, Int)
instantiate qt n = case qt of { Qual ps t ->
fpair (foldr instantiatePred (([], n), []) ps) \xy tab -> fpair xy \ps1 n1 ->
first (Qual ps1) (fst (instantiate' t n1 tab))
};

--type SymTab = [(String, (Qual, Ast))];
--type Subst = [(String, Type)];

--infer :: SymTab -> Subst -> Ast -> (Maybe Subst, Int) -> ((Type, Ast), (Maybe Subst, Int))
infer typed loc ast csn = fpair csn \cs n ->
let
{ va = TV (showInt n "")
; insta ty = fpair (instantiate ty n) \q n1 -> case q of { Qual preds ty -> ((ty, foldl A ast (map (E . Proof) preds)), (cs, n1)) }
}
in case ast of
{ E x -> case x of
{ Basic b -> ife (b == ord 'Y')
(insta $noQual$ arr (arr (TV "a") (TV "a")) (TV "a"))
undefined
; Const c -> ((TC "Int", ast), csn)
; StrCon _ -> ((TAp (TC "[]") (TC "Int"), ast), csn)
; Proof _ -> undefined
}
; V s -> fmaybe (lookup s loc)
(fmaybe (lookup s typed) (error $"bad symbol: " ++ s)$ insta . fst)
((, csn) . (, ast))
; A x y ->
fpair (infer typed loc x (cs, n + 1)) \tax csn1 -> fpair tax \tx ax ->
fpair (infer typed loc y csn1) \tay csn2 -> fpair tay \ty ay ->
((va, A ax ay), first (unify tx (arr ty va)) csn2)
; L s x -> first (\ta -> fpair ta \t a -> (arr va t, L s a)) (infer typed ((s, va):loc) x (cs, n + 1))
};

onType f pred = case pred of { Pred s t -> Pred s (f t) };

instance Eq Type where { (==) t u = case t of
{ TC s -> case u of
{ TC t -> t == s
; TV _ -> False
; TAp _ _ -> False
}
; TV s ->  case u of
{ TC _ -> False
; TV t -> t == s
; TAp _ _ -> False
}
; TAp a b -> case u of
{ TC _ -> False
; TV _ -> False
; TAp c d -> a == c && b == d
}
}};

instance Eq Pred where { (==) p q =
case p of { Pred s a -> case q of { Pred t b -> s == t && a == b }}};

predApply sub p = onType (apply sub) p;

all f = foldr (&&) True . map f;

filter f = foldr (\x xs ->ife (f x) (x:xs) xs) [];

intersect xs ys = filter (\x -> fmaybe (find (x ==) ys) False (\_ -> True)) xs;

merge s1 s2 = ife (all (\v -> apply s1 (TV v) == apply s2 (TV v))
$map fst s1 intersect map fst s2) (Just$ s1 ++ s2) Nothing;

match h t = case h of
{ TC a -> case t of
{ TC b -> ife (a == b) (Just []) Nothing
; TV b -> Nothing
; TAp a b -> Nothing
}
; TV a -> Just [(a, t)]
; TAp a b -> case t of
{ TC b -> Nothing
; TV b -> Nothing
; TAp c d -> case match a c of
{ Nothing -> Nothing
; Just ac -> case match b d of
{ Nothing -> Nothing
; Just bd -> merge ac bd
}
}
}
};

matchPred h p = case p of { Pred _ t -> match h t };

showType t = case t of
{ TC s -> s
; TV s -> s
; TAp a b -> concat ["(", showType a, " ", showType b, ")"]
};
showPred p = case p of { Pred s t -> s ++ (' ':showType t) ++ " => "};

findInst r qn p insts = case insts of
{ [] ->
fpair qn \q n -> let { v = '*':showInt n "" } in (((p, v):q, n + 1), V v)
; (:) i is -> case i of { Qual ps h -> case matchPred h p of
{ Nothing -> findInst r qn p is
; Just u -> foldl (\qnt p -> fpair qnt \qn1 t -> second (A t)
(r (predApply u p) qn1)) (qn, V (case p of { Pred s _ -> showPred $Pred s h})) ps }}}; findProof is pred psn = fpair psn \ps n -> case lookup pred ps of { Nothing -> case pred of { Pred s t -> case lookup s is of { Nothing -> error "no instances" ; Just insts -> findInst (findProof is) psn pred insts }} ; Just s -> (psn, V s) }; prove' ienv sub psn a = case a of { E x -> case x of { Basic _ -> (psn, a) ; Const _ -> (psn, a) ; StrCon _ -> (psn, a) ; Proof raw -> findProof ienv (predApply sub raw) psn } ; V _ -> (psn, a) ; A x y -> let { p1 = prove' ienv sub psn x } in fpair p1 \psn1 x1 -> second (A x1) (prove' ienv sub psn1 y) ; L s t -> second (L s) (prove' ienv sub psn t) }; overFree s f t = case t of { E _ -> t ; V s' -> ife (s == s') (f t) t ; A x y -> A (overFree s f x) (overFree s f y) ; L s' t' -> ife (s == s') t$ L s' $overFree s f t' }; --prove :: [(String, [Qual])] -> String -> (Type, Ast) -> Subst -> (Qual, Ast) prove ienv s ta sub = fpair ta \t a -> fpair (prove' ienv sub ([], 0) a) \psn x -> fpair psn \ps _ -> let { applyDicts expr = foldl A expr$ map (V . snd) ps }
in (Qual (map fst ps) (apply sub t), foldr L (overFree s applyDicts x) $map snd ps); dictVars ps n = flst ps ([], n) \p pt -> first ((p, '*':showInt n ""):) (dictVars pt$ n + 1);

-- qi = Qual of instance, e.g. Eq t => [t] -> [t] -> Bool
inferMethod ienv typed qi def = fpair def \s expr ->
fpair (infer typed [] expr (Just [], 0)) \ta msn ->
case lookup s typed of
{ Nothing -> error $"no such method: " ++ s -- e.g. qac = Eq a => a -> a -> Bool, some AST (product of single method) ; Just qac -> fpair msn \ms n -> case ms of { Nothing -> error "method: type mismatch" ; Just sub -> fpair (instantiate (fst qac) n) \q1 n1 -> case q1 of { Qual psc tc -> case psc of { [] -> undefined -- Unreachable. ; (:) headPred shouldBeNull -> case qi of { Qual psi ti -> case headPred of { Pred _ headT -> case match headT ti of { Nothing -> undefined -- e.g. Eq t => [t] -> [t] -> Bool -- instantiate and match it against type of ta ; Just subc -> fpair (instantiate (Qual psi$ apply subc tc) n1) \q2 n2 ->
case q2 of { Qual ps2 t2 -> fpair ta \tx ax ->
case match (apply sub tx) t2 of
{ Nothing -> error "class/instance type conflict"
; Just subx -> snd $prove' ienv (subx @@ sub) (dictVars ps2 0) ax }}}}}}}}}; inferInst ienv typed inst = fpair inst \cl qds -> fpair qds \q ds -> case q of { Qual ps t -> let { s = showPred$ Pred cl t } in
(s, (,) (noQual $TC "DICT")$ foldr L (L "@" $foldl A (V "@") (map (inferMethod ienv typed q) ds)) (map snd$ fst $dictVars ps 0)) }; reverse = foldl (flip (:)) []; inferDefs ienv defs typed = flst defs (Right$ reverse typed) \edef rest -> case edef of
{ Left def -> fpair def \s expr ->
fpair (infer typed [(s, TV "self!")] expr (Just [], 0)) \ta msn ->
fpair msn \ms _ -> case prove ienv s ta <$> (unify (TV "self!") (fst ta) ms) of { Nothing -> Left ("bad type: " ++ s) ; Just qa -> inferDefs ienv rest ((s, qa):typed) } ; Right inst -> inferDefs ienv rest (inferInst ienv typed inst:typed) }; showQual q = case q of { Qual ps t -> concatMap showPred ps ++ showType t }; untangle = foldr ($) $Neat [] [] prims [] []; dumpTypes s = fmaybe (program s) "parse error" \progRest -> fpair progRest \prog rest -> fneat (untangle prog) \ienv fs typed ffis exs -> case inferDefs ienv fs typed of { Left err -> err ; Right typed -> concatMap (\p -> fpair p \s qa -> s ++ " :: " ++ showQual (fst qa) ++ "\n") typed }; last' x xt = flst xt x \y yt -> last' y yt; last xs = flst xs undefined last'; init xs = flst xs undefined \x xt -> flst xt [] \_ _ -> x : init xt; intercalate sep xs = flst xs [] \x xt -> x ++ concatMap (sep ++) xt; argList t = case t of { TC s -> [TC s] ; TV s -> [TV s] ; TAp g y -> case g of { TC s -> case y of { TC u -> ife (s == "IO") [TC u] undefined ; TV _ -> undefined ; TAp _ _ -> undefined } ; TV s -> undefined ; TAp f x -> case f of { TC s -> ife (s == "->") (x : argList y) undefined ; TV s -> undefined ; TAp _ _ -> undefined } } }; cTypeName t = case t of { TC s -> ife (s == "()") "void"$
ife (s == "Int") "int" $ife (s == "Char") "char"$ error $"bad type constant: " ++ s ; TV _ -> undefined ; TAp _ _ -> undefined }; ffiDeclare namet = fpair namet \name t -> let { tys = argList t } in concat [ cTypeName$ last tys
, " "
, name
, "("
, intercalate "," $map cTypeName$ init tys
, ");\n"
];

ffiArgs n t = case t of
{ TC s -> ("", ((True, s), n))
; TV s -> undefined
; TAp g y -> case g of
{ TC s -> case y of
{ TC u -> ife (s == "IO") ("", ((False, u), n)) undefined
; TV _ -> undefined
; TAp _ _ -> undefined
}
; TV s -> undefined
; TAp f x -> case f of
{ TC s -> ife (s == "->") (first ((ife (3 <= n) ", " "" ++ "num(" ++ showInt n ")") ++) $ffiArgs (n + 1) y) undefined ; TV s -> undefined ; TAp _ _ -> undefined } } }; ffiDefine n ffis = case ffis of { [] -> id ; (:) x xt -> fpair x \name t -> fpair (ffiArgs 2 t) \args pRetCount -> fpair pRetCount \pRet count -> fpair pRet \isPure ret -> let { lazyn = ("lazy(" ++) . showInt (ife isPure (count - 1) (count + 1)) . (", " ++) ; cont tgt = ife isPure (("'I', "++) . tgt)$ ("app(arg("++) . showInt (count + 1) . ("), "++) . tgt . ("), arg("++) . showInt count . (")"++)
; longDistanceCall = (name++) . ("("++) . (args++) . ("); "++) . lazyn
} in ("case " ++) . showInt n . (": " ++) . ife (ret == "()")
(longDistanceCall . cont ("'K'"++) . ("); break;"++) . ffiDefine (n - 1) xt)
(("{u r = "++) . longDistanceCall . cont ("app('#', r)" ++) . ("); break;}\n"++) . ffiDefine (n - 1) xt)
};

getContents = getChar >>= \n -> ife (n <= 255) ((chr n:) <$> getContents) (pure []); upFrom n = n : upFrom (n + 1); zipWith f xs ys = flst xs []$ \x xt -> flst ys [] $\y yt -> f x y : zipWith f xt yt; compile s = fmaybe (program s) "parse error" \progRest -> fpair progRest \prog rest -> fneat (untangle prog) \ienv fs typed ffis exs -> case inferDefs ienv fs typed of { Left err -> err ; Right qas -> fpair (asm qas) \tab mem -> (concatMap ffiDeclare ffis ++) . ("static void foreign(u n) {\n switch(n) {\n" ++) . ffiDefine (length ffis - 1) ffis . ("\n }\n}\n" ++) . ("static const u prog[]={" ++) . foldr (.) id (map (\n -> showInt n . (',':))$ snd mem []) .
("};\nstatic const u prog_size=sizeof(prog)/sizeof(*prog);\n" ++) .
("static u root[]={" ++) .
foldr (\p f -> fpair p \x y -> maybe undefined showInt (mlookup y tab) . (", " ++) . f) id exs .
("};\n" ++) .
("static const u root_size=" ++) . showInt (length exs) . (";\n" ++) $flst exs ("int main(){rts_init();rts_reduce(" ++ maybe undefined showInt (mlookup (fst$ last qas) tab) ");return 0;}") $\_ _ -> concat$ zipWith (\p n -> "EXPORT(f" ++ showInt n ", \"" ++ fst p ++ "\", " ++ showInt n ")\n") exs (upFrom 0)
};

main = getContents >>= putStr . compile;

Ben Lynn blynn@cs.stanford.edu 💡