marginally.hs

-- Off-side rule.
infixr 9 .;
infixl 7 * , `div` , `mod`;
infixl 6 + , -;
infixr 5 ++;
infixl 4 <*> , <$> , <* , *>;
infix 4 == , /= , <=;
infixl 3 && , <|>;
infixl 2 ||;
infixl 1 >> , >>=;
infixr 0 $;

ffi "putchar" putChar :: Int -> IO Int;
ffi "getchar" getChar :: IO Int;
ffi "getargcount" getArgCount :: IO Int;
ffi "getargchar" getArgChar :: Int -> Int -> IO Char;

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
};
class Monad m where
{ return :: a -> m a
; (>>=) :: m a -> (a -> m b) -> m b
};
(<$>) = fmap;
liftA2 f x y = f <$> x <*> y;
(>>) f g = f >>= \_ -> g;
class Eq a where { (==) :: a -> a -> Bool };
instance Eq Int where { (==) = intEq };
instance Eq Char where { (==) = charEq };
($) f x = f x;
id x = x;
const x y = x;
flip f x y = f y x;
(&) x f = f x;
class Ord a where { (<=) :: a -> a -> Bool };
instance Ord Int where { (<=) = intLE };
instance Ord Char where { (<=) = charLE };
data Ordering = LT | GT | EQ;
compare x y = if x <= y then if y <= x then EQ else LT else 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 (x, y) f = f x y;
fst (x, y) = x;
snd (x, y) = y;
uncurry f (x, y) = f x y;
first f (x, y) = (f x, y);
second f (x, y) = (x, f y);
not a = if a then False else True;
x /= y = not $ x == y;
(.) f g x = f (g x);
(||) f g = if f then True else g;
(&&) f g = if f then g else 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
    }
  }};
take n xs = if n == 0 then [] else flst xs [] \h t -> h:take (n - 1) t;
maybe n j m = case m of { Nothing -> n; Just x -> j x };
instance Functor Maybe where { fmap f = maybe Nothing (Just . f) };
instance Applicative Maybe where { pure = Just ; mf <*> mx = maybe Nothing (\f -> maybe Nothing (Just . f) mx) mf };
instance Monad Maybe where { return = Just ; mf >>= mg = maybe Nothing mg mf };
foldr c n l = flst l n (\h t -> c h(foldr c n t));
length = foldr (\_ n -> n + 1) 0;
mapM f = foldr (\a rest -> liftA2 (:) (f a) rest) (pure []);
mapM_ f = foldr ((>>) . f) (pure ());
foldM f z0 xs = foldr (\x k z -> f z x >>= k) pure xs z0;
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;
getContents = getChar >>= \n -> if 0 <= n then (chr n:) <$> getContents else pure [];
interact f = getContents >>= putStr . f;
error s = unsafePerformIO $ putStr s >> putChar (ord '\n') >> exitSuccess;
undefined = error "undefined";
foldr1 c l@(h:t) = maybe undefined id $ foldr (\x m -> Just $ maybe x (c x) m) Nothing l;
foldl f a bs = foldr (\b g x -> g (f x b)) (\x -> x) bs a;
foldl1 f (h:t) = foldl f h t;
elem k xs = foldr (\x t -> x == k || t) False xs;
find f xs = foldr (\x t -> if f x then Just x else t) Nothing xs;
(++) = flip (foldr (:));
concat = foldr (++) [];
map = flip (foldr . ((:) .)) [];
instance Functor [] where { fmap = map };
concatMap = (concat .) . map;
lookup s = foldr (\(k, v) t -> if s == k then Just v else t) Nothing;
all f = foldr (&&) True . map f;
any f = foldr (||) False . map f;
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;
zip = zipWith (,);
data State s a = State (s -> (a, s));
runState (State f) = f;
instance Functor (State s) where { fmap f = \(State h) -> State (first f . h) };
instance Applicative (State s) where
{ pure a = State (a,)
; (State f) <*> (State x) = State \s -> fpair (f s) \g s' -> first g $ x s'
};
instance Monad (State s) where
{ return a = State (a,)
; (State h) >>= f = State $ uncurry (runState . f) . h
};
evalState m s = fst $ runState m s;
get = State \s -> (s, s);
put n = State \s -> ((), n);
either l r e = case e of { Left x -> l x; Right x -> r x };
instance Functor (Either a) where { fmap f e = case e of
  { Left x -> Left x
  ; Right x -> Right $ f x
  }
};
instance Applicative (Either a) where { pure = Right ; ef <*> ex = case ef of
  { Left s -> Left s
  ; Right f -> case ex of
    { Left s -> Left s
    ; Right x -> Right $ f x
    }
  }
};
instance Monad (Either a) where { return = Right ; ex >>= f = case ex of
  { Left s -> Left s
  ; Right x -> f x
  }
};
class Alternative f where { empty :: f a ; (<|>) :: f a -> f a -> f a };
asum = foldr (<|>) empty;
(*>) = 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 [];
between x y p = x *> (p <* y);

-- 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 (Bin _ rk rkx rl rr) = node rk rkx (node k x l rl) rr;
doubleL k x l (Bin _ rk rkx (Bin _ rlk rlkx rll rlr) rr) =
  node rlk rlkx (node k x l rll) (node rk rkx rlr rr);
singleR k x (Bin _ lk lkx ll lr) r = node lk lkx ll (node k x lr r);
doubleR k x (Bin _ lk lkx ll (Bin _ lrk lrkx lrl lrr)) r =
  node lrk lrkx (node lk lkx ll lrl) (node k x lrr r);
balance k x l r = (if size l + size r <= 1
  then node
  else if 5 * size l + 3 <= 2 * size r
    then case r of
      { Tip -> node
      ; Bin sz _ _ rl rr -> if 2 * size rl + 1 <= 3 * size rr
        then singleL
        else doubleL
      }
    else if 5 * size r + 3 <= 2 * size l
      then case l of
        { Tip -> node
        ; Bin sz _ _ ll lr -> if 2 * size lr + 1 <= 3 * size ll
          then singleR
          else doubleR
        }
      else 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
    }
  };
insertWith f kx x t = case t of
  { Tip -> singleton kx x
  ; Bin sy ky y l r -> case compare kx ky of
    { LT -> balance ky y (insertWith f kx x l) r
    ; GT -> balance ky y l (insertWith f kx x r)
    ; EQ -> Bin sy kx (f x y) 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 = foldl (\t (k, x) -> insert k x t) 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) [];

-- Syntax tree.

data Type = TC String | TV String | TAp Type Type;
arr a b = TAp (TAp (TC "->") a) b;
data Extra = Basic String | ForeignFun Int | Const Int | ChrCon Char | StrCon String;
data Pat = PatLit Extra | PatVar String (Maybe Pat) | PatCon String [Pat];
data Ast = E Extra | V String | A Ast Ast | L String Ast | Pa [([Pat], Ast)] | Ca Ast [(Pat, Ast)] | Proof Pred;
data Constr = Constr String [Type];
data Pred = Pred String Type;
data Qual = Qual [Pred] Type;
noQual = Qual [];

data Neat = Neat
  -- | Instance environment.
  (Map String [(String, Qual)])
  -- | Instance definitions.
  [(String, (Qual, [(String, Ast)]))]
  -- | Top-level definitions
  [(String, Ast)]
  -- | Typed ASTs, ready for compilation, including ADTs and methods,
  -- e.g. (==), (Eq a => a -> a -> Bool, select-==)
  [(String, (Qual, Ast))]
  -- | Data constructor table.
  (Map String [Constr])
  -- | FFI declarations.
  [(String, Type)]
  -- | Exports.
  [(String, String)]
  ;

ro = E . Basic;
conOf (Constr s _) = s;
specialCase (h:_) = '|':conOf h;
mkCase t cs = (specialCase cs,
  ( noQual $ arr t $ foldr arr (TV "case") $ map (\(Constr _ ts) -> foldr arr (TV "case") ts) cs
  , ro "I"));
mkStrs = snd . foldl (\(s, l) u -> ('@':s, s:l)) ("@", []);
scottEncode _ ":" _ = ro "CONS";
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;

showInt' n = if 0 == n then id else (showInt' $ n`div`10) . ((:) (chr $ 48+n`mod`10));
showInt n = if 0 == n then ('0':) else showInt' n;

mkFFIHelper n t acc = case t of
  { TC s -> acc
  ; TAp (TC "IO") _ -> acc
  ; TAp (TAp (TC "->") x) y -> L (showInt n "") $ mkFFIHelper (n + 1) y $ A (V $ showInt n "") acc
  };

updateDcs cs dcs = foldr (\(Constr s _) m -> insert s cs m) dcs cs;
addAdt t cs (Neat ienv defs fs typed dcs ffis exs) =
  Neat ienv defs fs (mkAdtDefs t cs ++ typed) (updateDcs cs dcs) ffis exs;

addClass classId v ms (Neat ienv idefs fs typed dcs ffis exs) = let
  { vars = zipWith (\_ n -> showInt n "") ms $ upFrom 0
  } in Neat ienv idefs fs (zipWith (\var (s, t) ->
    (s, (Qual [Pred classId v] t,
      L "@" $ A (V "@") $ foldr L (V var) vars))) vars ms ++ typed) dcs ffis exs;
dictName cl (Qual _ t) = '{':cl ++ (' ':showType t "") ++ "}";
addInst cl q ds (Neat ienv idefs fs typed dcs ffis exs) = let { name = dictName cl q } in
  Neat (insertWith (++) cl [(name, q)] ienv) ((name, (q, ds)):idefs) fs typed dcs ffis exs;
addFFI foreignname ourname t (Neat ienv idefs fs typed dcs ffis exs) =
  Neat ienv idefs fs ((ourname, (Qual [] t, mkFFIHelper 0 t $ E $ ForeignFun $ length ffis)) : typed) dcs ((foreignname, t):ffis) exs;
addDefs ds (Neat ienv idefs fs typed dcs ffis exs) = Neat ienv idefs (ds ++ fs) typed dcs ffis exs;
addExport e f (Neat ienv idefs fs typed dcs ffis exs) = Neat ienv idefs fs typed dcs ffis ((e, f):exs);

-- Lexer.
lex (Lexer f) inp = f inp;
data LexState = LexState String (Int, Int);
data Lexer a = Lexer (LexState -> Either String (a, LexState));
instance Functor Lexer where { fmap f (Lexer x) = Lexer $ fmap (first f) . x };
instance Applicative Lexer where
{ pure x = Lexer \inp -> Right (x, inp)
; f <*> x = Lexer \inp -> case lex f inp of
  { Left e -> Left e
  ; Right (fun, t) -> case lex x t of
    { Left e -> Left e
    ; Right (arg, u) -> Right (fun arg, u)
    }
  }
};
instance Monad Lexer where
{ return = pure
; x >>= f = Lexer \inp -> case lex x inp of
  { Left e -> Left e
  ; Right (a, t) -> lex (f a) t
  }
};
instance Alternative Lexer where
{ empty = Lexer \_ -> Left ""
; (<|>) x y = Lexer \inp -> either (const $ lex y inp) Right $ lex x inp
};

advanceRC x (r, c)
  | n `elem` [10, 11, 12, 13] = (r + 1, 1)
  | n == 9 = (r, (c + 8)`mod`8)
  | True = (r, c + 1)
  where { n = ord x }
  ;
pos = Lexer \inp@(LexState _ rc) -> Right (rc, inp);
sat f = Lexer \(LexState inp rc) -> flst inp (Left "EOF") \h t ->
  if f h then Right (h, LexState t $ advanceRC h rc) else Left "unsat";
char c = sat (c ==);

data Token = Reserved String
  | VarId String | VarSym String | ConId String | ConSym String
  | Lit Extra;

hexValue d
  | d <= '9' = ord d - ord '0'
  | d <= 'F' = 10 + ord d - ord 'A'
  | d <= 'f' = 10 + ord d - ord 'a';
isSpace c = elem (ord c) [32, 9, 10, 11, 12, 13, 160];
isNewline c = ord c `elem` [10, 11, 12, 13];
isSymbol = (`elem` "!#$%&*+./<=>?@\\^|-~:");
dashes = char '-' *> some (char '-');
comment = dashes *> (sat isNewline <|> sat (not . isSymbol) *> many (sat $ not . isNewline) *> sat isNewline);
small = sat \x -> ((x <= 'z') && ('a' <= x)) || (x == '_');
large = sat \x -> (x <= 'Z') && ('A' <= x);
hexit = sat \x -> (x <= '9') && ('0' <= x)
  || (x <= 'F') && ('A' <= x)
  || (x <= 'f') && ('a' <= x);
digit = sat \x -> (x <= '9') && ('0' <= x);
decimal = foldl (\n d -> 10*n + ord d - ord '0') 0 <$> some digit;
hexadecimal = foldl (\n d -> 16*n + hexValue d) 0 <$> some hexit;

escape = char '\\' *> (sat (`elem` "'\"\\") <|> char 'n' *> pure '\n');
tokOne delim = escape <|> sat (delim /=);

tokChar = between (char '\'') (char '\'') (tokOne '\'');
tokStr = between (char '"') (char '"') $ many (tokOne '"');
integer = char '0' *> (char 'x' <|> char 'X') *> hexadecimal <|> decimal;
literal = Lit . Const <$> integer <|> Lit . ChrCon <$> tokChar <|> Lit . StrCon <$> tokStr;
varId = fmap ck $ liftA2 (:) small $ many (small <|> large <|> digit <|> char '\'') where
  { ck s = (if elem s
    ["ffi", "export", "case", "class", "data", "default", "deriving", "do", "else", "foreign", "if", "import", "in", "infix", "infixl", "infixr", "instance", "let", "module", "newtype", "of", "then", "type", "where", "_"]
    then Reserved else VarId) s };
varSym = fmap ck $ (:) <$> sat (\c -> isSymbol c && c /= ':') <*> many (sat isSymbol) where
  { ck s = (if elem s ["..", "=", "\\", "|", "<-", "->", "@", "~", "=>"] then Reserved else VarSym) s };

conId = fmap ConId $ liftA2 (:) large $ many (small <|> large <|> digit <|> char '\'');
conSym = fmap ck $ liftA2 (:) (char ':') $ many $ sat isSymbol where
  { ck s = (if elem s [":", "::"] then Reserved else ConSym) s };
special = Reserved . (:"") <$> asum (char <$> "(),;[]`{}");

rawBody = (char '|' *> char ']' *> pure []) <|> (:) <$> sat (const True) <*> rawBody;
rawQQ = char '[' *> char 'r' *> char '|' *> (Lit . StrCon <$> rawBody);
lexeme = rawQQ <|> varId <|> varSym <|> conId <|> conSym
  <|> special <|> literal;

whitespace = many (sat isSpace <|> comment);
lexemes = whitespace *> many (lexeme <* whitespace);

getPos = Lexer \st@(LexState _ rc) -> Right (rc, st);
posLexemes = whitespace *> many (liftA2 (,) getPos lexeme <* whitespace);

-- Layout.
data Landin = Curly Int | Angle Int | PL ((Int, Int), Token);
beginLayout xs = case xs of
  { [] -> [Curly 0]
  ; ((r', _), Reserved "{"):_ -> margin r' xs
  ; ((r', c'), _):_ -> Curly c' : margin r' xs
  };

landin ls@(((r, _), Reserved "{"):_) = margin r ls;
landin ls@(((r, c), _):_) = Curly c : margin r ls;
landin [] = [];

margin r ls@(((r', c), _):_) | r /= r' = Angle c : embrace ls;
margin r ls = embrace ls;

embrace ls@(x@(_, Reserved w):rest) | elem w ["let", "where", "do", "of"] =
  PL x : beginLayout rest;
embrace ls@(x@(_, Reserved "\\"):y@(_, Reserved "case"):rest) =
  PL x : PL y : beginLayout rest;
embrace (x@((r,_),_):xt) = PL x : margin r xt;
embrace [] = [];

data Ell = Ell [Landin] [Int];
insPos x ts ms = Right (x, Ell ts ms);
ins w = insPos ((0, 0), Reserved w);

ell (Ell toks cols) = case toks of
  { t:ts -> case t of
    { Angle n -> case cols of
      { m:ms | m == n -> ins ";" ts (m:ms)
             | n + 1 <= m -> ins "}" (Angle n:ts) ms
      ; _ -> ell $ Ell ts cols
      }
    ; Curly n -> case cols of
      { m:ms | m + 1 <= n -> ins "{" ts (n:m:ms)
      ; [] | 1 <= n -> ins "{" ts [n]
      ; _ -> ell $ Ell (PL ((0,0),Reserved "{"): PL ((0,0),Reserved "}"):Angle n:ts) cols
      }
    ; PL x -> case snd x of
      { Reserved "}" -> case cols of
        { 0:ms -> ins "}" ts ms
        ; _ -> Left "unmatched }"
        }
      ; Reserved "{" -> insPos x ts (0:cols)
      ; _ -> insPos x ts cols
      }
    }
  ; [] -> case cols of
    { [] -> Left "EOF"
    ; m:ms | m /= 0 -> ins "}" [] ms
    ; _ -> Left "missing }"
    }
  };

parseErrorRule (Ell toks cols) = case cols of
  { m:ms | m /= 0 -> Right $ Ell toks ms
  ; _ -> Left "missing }"
  };

-- Parser.
data ParseState = ParseState Ell (Map String (Int, Assoc));
data Parser a = Parser (ParseState -> Either String (a, ParseState));
getPrecs = Parser \st@(ParseState _ precs) -> Right (precs, st);
putPrecs precs = Parser \(ParseState s _) -> Right ((), ParseState s precs);
parse (Parser f) inp = f inp;
instance Applicative Parser where
{ pure x = Parser \inp -> Right (x, inp)
; x <*> y = Parser \inp -> case parse x inp of
  { Left e -> Left e
  ; Right (fun, t) -> case parse y t of
    { Left e -> Left e
    ; Right (arg, u) -> Right (fun arg, u)
    }
  }
};
instance Monad Parser where
{ return = pure
; (>>=) x f = Parser \inp -> case parse x inp of
  { Left e -> Left e
  ; Right (a, t) -> parse (f a) t
  }
};
instance Functor Parser where { fmap f x = pure f <*> x };
instance Alternative Parser where
{ empty = Parser \_ -> Left ""
; x <|> y = Parser \inp -> either (const $ parse y inp) Right $ parse x inp
};

want f = Parser \(ParseState inp precs) -> case ell inp of
  { Right ((_, x), inp') -> (, ParseState inp' precs) <$> f x
  ; Left e -> Left e
  };

braceYourself = Parser \(ParseState inp precs) -> case ell inp of
  { Right ((_, Reserved "}"), inp') -> Right ((), ParseState inp' precs)
  ; _ -> case parseErrorRule inp of
    { Left e -> Left e
    ; Right inp' -> Right ((), ParseState inp' precs)
    }
  };

res w = want \case
  { Reserved s | s == w -> Right s
  ; _ -> Left $ "want \"" ++ w ++ "\""
  };
wantInt = want \case
  { Lit (Const i) -> Right i
  ; _ -> Left "want integer"
  };
wantString = want \case
  { Lit (StrCon s) -> Right s
  ; _ -> Left "want string"
  };
wantConId = want \case
  { ConId s -> Right s
  ; _ -> Left "want conid"
  };
wantVarId = want \case
  { VarId s -> Right s
  ; _ -> Left "want varid"
  };
wantLit = want \case
  { Lit x -> Right x
  ; _ -> Left "want literal"
  };

paren = between (res "(") (res ")");
braceSep f = between (res "{") braceYourself $ foldr ($) [] <$> sepBy ((:) <$> f <|> pure id) (res ";");

patVars = \case
  { PatLit _ -> []
  ; PatVar s m -> s : maybe [] patVars m
  ; PatCon _ args -> concat $ patVars <$> args
  };

union xs ys = foldr (\y acc -> (if elem y acc then id else (y:)) acc) xs ys;
fv bound = \case
  { V s | not (elem s bound) -> [s]
  ; A x y -> fv bound x `union` fv bound y
  ; L s t -> fv (s:bound) t
  ; _ -> []
  };

fvPro bound expr = case expr of
  { V s | not (elem s bound) -> [s]
  ; A x y -> fvPro bound x `union` fvPro bound y
  ; L s t -> fvPro (s:bound) t
  ; Pa vsts -> foldr union [] $ map (\(vs, t) -> fvPro (concatMap patVars vs ++ bound) t) vsts
  ; Ca x as -> fvPro bound x `union` fvPro bound (Pa $ first (:[]) <$> as)
  ; _ -> []
  };

overFree s f t = case t of
  { E _ -> t
  ; V s' -> if s == s' then f t else t
  ; A x y -> A (overFree s f x) (overFree s f y)
  ; L s' t' -> if s == s' then t else L s' $ overFree s f t'
  };

overFreePro s f t = case t of
  { E _ -> t
  ; V s' -> if s == s' then f t else t
  ; A x y -> A (overFreePro s f x) (overFreePro s f y)
  ; L s' t' -> if s == s' then t else L s' $ overFreePro s f t'
  ; Pa vsts -> Pa $ map (\(vs, t) -> (vs, if any (elem s . patVars) vs then t else overFreePro s f t)) vsts
  ; Ca x as -> Ca (overFreePro s f x) $ (\(p, t) -> (p, if elem s $ patVars p then t else overFreePro s f t)) <$> as
  };

beta s t x = overFree s (const t) x;

maybeFix s x = if elem s $ fvPro [] x then A (ro "Y") (L s x) else x;

nonemptyTails [] = [];
nonemptyTails xs@(x:xt) = xs : nonemptyTails xt;

addLets ls x = let
  { vs = fst <$> ls
  ; ios = foldr (\(s, dsts) (ins, outs) ->
    (foldr (\dst -> insertWith union dst [s]) ins dsts, insertWith union s dsts outs))
    (Tip, Tip) $ map (\(s, t) -> (s, intersect (fvPro [] t) vs)) ls
  ; components = scc (\k -> maybe [] id $ mlookup k $ fst ios) (\k -> maybe [] id $ mlookup k $ snd ios) vs
  ; triangle names expr = let
    { tnames = nonemptyTails names
    ; suball t = foldr (\(x:xt) t -> overFreePro x (const $ foldl (\acc s -> A acc (V s)) (V x) xt) t) t tnames
    ; insLams vs t = foldr L t vs
    } in foldr (\(x:xt) t -> A (L x t) $ maybeFix x $ insLams xt $ suball $ maybe undefined id $ lookup x ls) (suball expr) tnames
  } in foldr triangle x components;

data Assoc = NAssoc | LAssoc | RAssoc;
instance Eq Assoc where
{ NAssoc == NAssoc = True
; LAssoc == LAssoc = True
; RAssoc == RAssoc = True
; _ == _ = False
};
precOf s precTab = maybe 9 fst $ mlookup s precTab;
assocOf s precTab = maybe LAssoc snd $ mlookup s precTab;

parseErr s = Parser $ const $ Left s;

opFold precTab f x xs = case xs of
  { [] -> pure x
  ; (op, y):xt -> case find (\(op', _) -> assocOf op precTab /= assocOf op' precTab) xt of
    { Nothing -> case assocOf op precTab of
      { NAssoc -> case xt of
        { [] -> pure $ f op x y
        ; y:yt -> parseErr "NAssoc repeat"
        }
      ; LAssoc -> pure $ foldl (\a (op, y) -> f op a y) x xs
      ; RAssoc -> pure $ foldr (\(op, y) b -> \e -> f op e (b y)) id xs $ x
      }
    ; Just y -> parseErr "Assoc clash"
    }
  };

qconop = want f <|> between (res "`") (res "`") (want g) where
  { f (ConSym s) = Right s
  ; f (Reserved ":") = Right ":"
  ; f _ = Left ""
  ; g (ConId s) = Right s
  ; g _ = Left "want qconop"
  };

wantVarSym = want \case
  { VarSym s -> Right s
  ; _ -> Left "want VarSym"
  };

wantqconsym = want \case
  { ConSym s -> Right s
  ; Reserved ":" -> Right ":"
  ; _ -> Left "want qconsym"
  };

op = wantqconsym <|> want f <|> between (res "`") (res "`") (want g) where
  { f (VarSym s) = Right s
  ; f _ = Left ""
  ; g (VarId s) = Right s
  ; g (ConId s) = Right s
  ; g _ = Left "want op"
  };

con = wantConId <|> paren wantqconsym;
var = wantVarId <|> paren wantVarSym;

tycon = want \case
  { ConId s -> Right $ if s == "String" then TAp (TC "[]") (TC "Char") else TC s
  ; _ -> Left "want type constructor"
  };

aType =
  res "(" *>
    (   res ")" *> pure (TC "()")
    <|> ((&) <$> _type <*> ((res "," *> ((\a b -> TAp (TAp (TC ",") b) a) <$> _type)) <|> pure id)
    ) <* res ")")
  <|> tycon
  <|> TV <$> wantVarId
  <|> (res "[" *> (res "]" *> pure (TC "[]") <|> TAp (TC "[]") <$> (_type <* res "]")));
bType = foldl1 TAp <$> some aType;
_type = foldr1 arr <$> sepBy bType (res "->");

fixityList a = wantInt >>= \n -> sepBy op (res ",") >>= \os ->
  getPrecs >>= \precs -> putPrecs (foldr (\o m -> insert o (n, a) m) precs os) >>
  pure id;

fixityDecl w a = res w *> fixityList a;
fixity = fixityDecl "infix" NAssoc <|> fixityDecl "infixl" LAssoc <|> fixityDecl "infixr" RAssoc;

genDecl = (,) <$> var <*> (res "::" *> _type);

classDecl = res "class" *> (addClass <$> wantConId <*> (TV <$> wantVarId) <*> (res "where" *> braceSep genDecl));

simpleClass = Pred <$> wantConId <*> _type;
scontext = (:[]) <$> simpleClass <|> paren (sepBy simpleClass $ res ",");

instDecl = res "instance" *>
  ((\ps cl ty defs -> addInst cl (Qual ps ty) defs) <$>
  (scontext <* res "=>" <|> pure [])
    <*> wantConId <*> _type <*> (res "where" *> braceDef));

letin = addLets <$> between (res "let") (res "in") braceDef <*> expr;
ifthenelse = (\a b c -> A (A (A (V "if") a) b) c) <$>
  (res "if" *> expr) <*> (res "then" *> expr) <*> (res "else" *> expr);
listify = foldr (\h t -> A (A (V ":") h) t) (V "[]");

alts = braceSep $ (,) <$> pat <*> guards "->";
cas = Ca <$> between (res "case") (res "of") expr <*> alts;
lamCase = res "case" *> (L "\\case" . Ca (V "\\case") <$> alts);
lam = res "\\" *> (lamCase <|> liftA2 onePat (some apat) (res "->" *> expr));

flipPairize y x = A (A (V ",") x) y;
thenComma = res "," *> ((flipPairize <$> expr) <|> pure (A (V ",")));
parenExpr = (&) <$> expr <*> (((\v a -> A (V v) a) <$> op) <|> thenComma <|> pure id);
rightSect = ((\v a -> L "@" $ A (A (V v) $ V "@") a) <$> (op <|> res ",")) <*> expr;
section = res "(" *> (parenExpr <* res ")" <|> rightSect <* res ")" <|> res ")" *> pure (V "()"));

maybePureUnit = maybe (V "pure" `A` V "()") id;
stmt = (\p x -> Just . A (V ">>=" `A` x) . onePat [p] . maybePureUnit) <$> pat <*> (res "<-" *> expr)
  <|> (\x -> Just . maybe x (\y -> (V ">>=" `A` x) `A` (L "_" y))) <$> expr
  <|> (\ds -> Just . addLets ds . maybePureUnit) <$> (res "let" *> braceDef);
doblock = res "do" *> (maybePureUnit . foldr ($) Nothing <$> braceSep stmt);

atom = ifthenelse <|> doblock <|> letin <|> listify <$> sqList expr <|> section
  <|> cas <|> lam <|> (paren (res ",") *> pure (V ","))
  <|> fmap V (con <|> var) <|> E <$> wantLit;

aexp = foldl1 A <$> some atom;

withPrec precTab n p = p >>= \s ->
  if n == precOf s precTab then pure s else Parser $ const $ Left "";

exprP n = if n <= 9
  then getPrecs >>= \precTab
    -> exprP (succ n) >>= \a
    -> many ((,) <$> withPrec precTab n op <*> exprP (succ n)) >>= \as
    -> opFold precTab (\op x y -> A (A (V op) x) y) a as
  else aexp;
expr = exprP 0;

sqList r = between (res "[") (res "]") $ sepBy r (res ",");

gcon = wantConId <|> paren (wantqconsym <|> res ",") <|> ((++) <$> res "[" <*> (res "]"));

apat = PatVar <$> var <*> (res "@" *> (Just <$> apat) <|> pure Nothing)
  <|> flip PatVar Nothing <$> (res "_" *> pure "_")
  <|> flip PatCon [] <$> gcon
  <|> PatLit <$> wantLit
  <|> foldr (\h t -> PatCon ":" [h, t]) (PatCon "[]" []) <$> sqList pat
  <|> paren ((&) <$> pat <*> ((res "," *> ((\y x -> PatCon "," [x, y]) <$> pat)) <|> pure id))
  ;

binPat f x y = PatCon f [x, y];
patP n = if n <= 9
  then getPrecs >>= \precTab
    -> patP (succ n) >>= \a
    -> many ((,) <$> withPrec precTab n qconop <*> patP (succ n)) >>= \as
    -> opFold precTab binPat a as
  else PatCon <$> gcon <*> many apat <|> apat
  ;
pat = patP 0;

maybeWhere p = (&) <$> p <*> (res "where" *> (addLets <$> braceDef) <|> pure id);

guards s = maybeWhere $ res s *> expr <|> foldr ($) (V "pjoin#") <$> some ((\x y -> case x of
  { V "True" -> \_ -> y
  ; _ -> A (A (A (V "if") x) y)
  }) <$> (res "|" *> expr) <*> (res s *> expr));

onePat vs x = Pa [(vs, x)];
opDef x f y rhs = [(f, onePat [x, y] rhs)];
leftyPat p expr = case patVars p of
  { [] -> []
  ; (h:t) -> let { gen = '@':h } in
    (gen, expr):map (\v -> (v, Ca (V gen) [(p, V v)])) (patVars p)
  };
def = liftA2 (\l r -> [(l, r)]) var (liftA2 onePat (many apat) $ guards "=")
  <|> (pat >>= \x -> opDef x <$> wantVarSym <*> pat <*> guards "=" <|> leftyPat x <$> guards "=");
coalesce ds = flst ds [] \h@(s, x) t -> flst t [h] \(s', x') t' -> let
  { f (Pa vsts) (Pa vsts') = Pa $ vsts ++ vsts'
  ; f _ _ = error "bad multidef"
  } in if s == s' then coalesce $ (s, f x x'):t' else h:coalesce t
  ;
defSemi = coalesce . concat <$> sepBy1 def (some $ res ";");
braceDef = concat <$> braceSep defSemi;

simpleType c vs = foldl TAp (TC c) (map TV vs);
conop = want f <|> between (res "`") (res "`") (want g) where
  { f (ConSym s) = Right s
  ; f _ = Left ""
  ; g (ConId s) = Right s
  ; g _ = Left "want qconop"
  };
constr = (\x c y -> Constr c [x, y]) <$> aType <*> conop <*> aType
  <|> Constr <$> wantConId <*> many aType;
adt = addAdt <$> between (res "data") (res "=") (simpleType <$> wantConId <*> many wantVarId) <*> sepBy constr (res "|");

topdecls = braceSep
  (   adt
  <|> classDecl
  <|> instDecl
  <|> res "ffi" *> (addFFI <$> wantString <*> var <*> (res "::" *> _type))
  <|> res "export" *> (addExport <$> wantString <*> var)
  <|> addDefs <$> defSemi
  <|> fixity
  );

offside xs = Ell (landin xs) [];
program s = case lex posLexemes $ LexState s (1, 1) of
  { Left e -> Left e
  ; Right (xs, LexState [] _) -> parse topdecls $ ParseState (offside xs) $ insert ":" (5, RAssoc) Tip;
  ; Right (_, st) -> Left "unlexable"
  };
-- Primitives.

primAdts =
  [ addAdt (TC "()") [Constr "()" []]
  , addAdt (TC "Bool") [Constr "True" [], Constr "False" []]
  , 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"]]];

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 "EQ"))
    , ("intLE", (arr (TC "Int") (arr (TC "Int") (TC "Bool")), bin "LE"))
    , ("charEq", (arr (TC "Char") (arr (TC "Char") (TC "Bool")), bin "EQ"))
    , ("charLE", (arr (TC "Char") (arr (TC "Char") (TC "Bool")), bin "LE"))
    , ("if", (arr (TC "Bool") $ arr (TV "a") $ arr (TV "a") (TV "a"), ro "I"))
    , ("chr", (arr (TC "Int") (TC "Char"), ro "I"))
    , ("ord", (arr (TC "Char") (TC "Int"), ro "I"))
    , ("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")), A (A (ro "B") (ro "C")) (ro "T")))
    , ("newIORef", (arr (TV "a") (TAp (TC "IO") (TAp (TC "IORef") (TV "a"))),
      A (A (ro "B") (ro "C")) (A (A (ro "B") (ro "T")) (ro "REF"))))
    , ("readIORef", (arr (TAp (TC "IORef") (TV "a")) (TAp (TC "IO") (TV "a")),
      A (ro "T") (ro "READREF")))
    , ("writeIORef", (arr (TAp (TC "IORef") (TV "a")) (arr (TV "a") (TAp (TC "IO") (TC "()"))),
      A (A (ro "R") (ro "WRITEREF")) (ro "B")))
    , ("exitSuccess", (TAp (TC "IO") (TV "a"), ro "END"))
    , ("unsafePerformIO", (arr (TAp (TC "IO") (TV "a")) (TV "a"), A (A (ro "C") (A (ro "T") (ro "END"))) (ro "K")))
    , ("fail#", (TV "a", A (V "unsafePerformIO") (V "exitSuccess")))
    ] ++ map (\(s, v) -> (s, (iii, bin v)))
      [ ("+", "ADD")
      , ("-", "SUB")
      , ("*", "MUL")
      , ("div", "DIV")
      , ("mod", "MOD")
      , ("intAdd", "ADD")
      , ("intSub", "SUB")
      , ("intMul", "MUL")
      , ("intDiv", "DIV")
      , ("intMod", "MOD")
      ];

-- Conversion to De Bruijn indices.

data LC = Ze | Su LC | Pass Extra | PassVar String | La LC | App LC LC;

debruijn n e = case e of
  { E x -> Pass x
  ; V v -> maybe (PassVar v) id $
    foldr (\h found -> if h == v then Just Ze else Su <$> found) Nothing n
  ; A x y -> App (debruijn n x) (debruijn n y)
  ; L s t -> La (debruijn (s:n) t)
  };

-- Kiselyov bracket abstraction.

data IntTree = Lf Extra | LfVar String | Nd IntTree IntTree;
data Sem = Defer | Closed IntTree | Need Sem | Weak Sem;

lf = Lf . Basic;

ldef 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 $ (Closed (Nd (lf "S") (lf "I"))) ## e
  ; Weak e -> Need $ (Closed (lf "T")) ## e
  };

lclo d y = case y of
  { Defer -> Need $ Closed d
  ; Closed dd -> Closed $ Nd d dd
  ; Need e -> Need $ (Closed (Nd (lf "B") d)) ## e
  ; Weak e -> Weak $ (Closed d) ## e
  };

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

lwea e y = case y of
  { Defer -> Need e
  ; Closed d -> Weak $ e ## Closed d
  ; Need ee -> Need $ (Closed (lf "B")) ## e ## ee
  ; Weak ee -> Weak $ e ## ee
  };

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

babs t = case t of
  { Ze -> Defer
  ; Su x -> Weak (babs x)
  ; Pass x -> Closed (Lf x)
  ; PassVar s -> Closed (LfVar s)
  ; La t -> case babs t of
    { Defer -> Closed (lf "I")
    ; Closed d -> Closed (Nd (lf "K") d)
    ; Need e -> e
    ; Weak e -> Closed (lf "K") ## e
    }
  ; App x y -> babs x ## babs y
  };

nolam x = (\(Closed d) -> d) $ babs $ debruijn [] x;

optim t = let
  { go (Lf (Basic "I")) q = q
  ; go p q@(Lf (Basic c)) = case c of
    { "I" -> case p of
      { Lf (Basic "C") -> lf "T"
      ; Lf (Basic "B") -> lf "I"
      ; Nd p1 p2 -> case p1 of
        { Lf (Basic "B") -> p2
        ; Lf (Basic "R") -> Nd (lf "T") p2
        ; _ -> Nd (Nd p1 p2) q
        }
      ; _ -> Nd p q
      }
    ; "T" -> case p of
      { Nd (Lf (Basic "B")) (Lf (Basic "C")) -> lf "V"
      ; _ -> Nd p q
      }
    ; _ -> Nd p q
    }
  ; go p q = Nd p q
  } in case t of
  { Nd x y -> go (optim x) (optim y)
  ; _ -> t
  };

freeCount v expr = case expr of
  { E _ -> 0
  ; V s -> if s == v then 1 else 0
  ; A x y -> freeCount v x + freeCount v y
  ; L w t -> if v == w then 0 else freeCount v t
  };

app01 s x = let { n = freeCount s x } in case n of
  { 0 -> const x
  ; 1 -> flip (beta s) x
  ; _ -> A $ L s x
  };
optiApp t = case t of
  { A (L s x) y -> app01 s (optiApp x) (optiApp y)
  ; A x y -> A (optiApp x) (optiApp y)
  ; L s x -> L s (optiApp x)
  ; _ -> t
  };

-- Type checking.

apply sub t = case t of
  { TC v -> t
  ; TV v -> maybe t id $ lookup v sub
  ; 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 -> Right [(s, t)]
  ; TV v -> Right $ if v == s then [] else [(s, t)]
  ; TAp a b -> if occurs s t then Left "occurs check" else Right [(s, t)]
  };

mgu t u = case t of
  { TC a -> case u of
    { TC b -> if a == b then Right [] else Left "TC-TC clash"
    ; TV b -> varBind b t
    ; TAp a b -> Left "TC-TAp clash"
    }
  ; TV a -> varBind a u
  ; TAp a b -> case u of
    { TC b -> Left "TAp-TC clash"
    ; TV b -> varBind b t
    ; TAp c d -> mgu a c >>= unify b d
    }
  };

unify a b s = (@@ s) <$> mgu (apply s a) (apply s b);

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) \(t1, n1) tab1 ->
    fpair (instantiate' y n1 tab1) \(t2, n2) tab2 ->
    ((TAp t1 t2, n2), tab2)
  };

instantiatePred (Pred s t) ((out, n), tab) = first (first ((:out) . Pred s)) (instantiate' t n tab);

instantiate (Qual ps t) n =
  fpair (foldr instantiatePred (([], n), []) ps) \(ps1, n1) tab ->
  first (Qual ps1) (fst (instantiate' t n1 tab));

proofApply sub a = case a of
  { Proof (Pred cl ty) -> Proof (Pred cl $ apply sub ty)
  ; A x y -> A (proofApply sub x) (proofApply sub y)
  ; L s t -> L s $ proofApply sub t
  ; _ -> a
  };

typeAstSub sub (t, a) = (apply sub t, proofApply sub a);

infer typed loc ast csn = fpair csn \cs n ->
  let
    { va = TV (showInt n "")
    ; insta ty = fpair (instantiate ty n) \(Qual preds ty) n1 -> ((ty, foldl A ast (map Proof preds)), (cs, n1))
    }
  in case ast of
  { E x -> Right $ case x of
    { Basic "Y" -> insta $ noQual $ arr (arr (TV "a") (TV "a")) (TV "a")
    ; Const _ -> ((TC "Int", ast), csn)
    ; ChrCon _ -> ((TC "Char", ast), csn)
    ; StrCon _ -> ((TAp (TC "[]") (TC "Char"), ast), csn)
    }
  ; V s -> maybe
    (maybe (error $ "depGraph bug! " ++ s) (Right . insta) $ mlookup s typed)
    (\t -> Right ((t, ast), csn))
    $ lookup s loc
  ; A x y -> infer typed loc x (cs, n + 1) >>=
    \((tx, ax), csn1) -> infer typed loc y csn1 >>=
    \((ty, ay), (cs2, n2)) -> unify tx (arr ty va) cs2 >>=
    \cs -> Right ((va, A ax ay), (cs, n2))
  ; L s x -> first (\(t, a) -> (arr va t, L s a)) <$> infer typed ((s, va):loc) x (cs, n + 1)
  };

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

instance Eq Pred where { (Pred s a) == (Pred t b) = s == t && a == b };

filter f = foldr (\x xs -> if f x then x:xs else xs) [];
intersect xs ys = filter (\x -> maybe False (\_ -> True) $ find (x ==) ys) xs;

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

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

par f = ('(':) . f . (')':);
showType t = case t of
  { TC s -> (s++)
  ; TV s -> (s++)
  ; TAp (TAp (TC "->") a) b -> par $ showType a . (" -> "++) . showType b
  ; TAp a b -> par $ showType a . (' ':) . showType b
  };
showPred (Pred s t) = (s++) . (' ':) . showType t . (" => "++);

findInst ienv qn p@(Pred cl ty) insts = case insts of
  { [] -> fpair qn \q n -> let { v = '*':showInt n "" } in Right (((p, v):q, n + 1), V v)
  ; (name, Qual ps h):is -> case match h ty of
    { Nothing -> findInst ienv qn p is
    ; Just subs -> foldM (\(qn1, t) (Pred cl1 ty1) -> second (A t)
      <$> findProof ienv (Pred cl1 $ apply subs ty1) qn1) (qn, V name) ps
  }};

findProof ienv pred psn@(ps, n) = case lookup pred ps of
  { Nothing -> case pred of { Pred s t -> case mlookup s ienv of
    { Nothing -> Left $ "no instances: " ++ s
    ; Just insts -> findInst ienv psn pred insts
    }}
  ; Just s -> Right (psn, V s)
  };

prove' ienv psn a = case a of
  { Proof pred -> findProof ienv pred psn
  ; A x y -> prove' ienv psn x >>= \(psn1, x1) ->
    second (A x1) <$> prove' ienv psn1 y
  ; L s t -> second (L s) <$> prove' ienv psn t
  ; _ -> Right (psn, a)
  };

dictVars ps n = flst ps ([], n) \p pt -> first ((p, '*':showInt n ""):) (dictVars pt $ n + 1);

-- The 4th argument: e.g. Qual [Eq a] "[a]" for Eq a => Eq [a].
inferMethod ienv dcs typed (Qual psi ti) (s, expr) =
  infer typed [] (patternCompile dcs expr) ([], 0) >>=
  \(ta, (sub, n)) -> fpair (typeAstSub sub ta) \tx ax -> case mlookup s typed of
    { Nothing -> Left $ "no such method: " ++ s
    -- e.g. qc = Eq a => a -> a -> Bool
    -- We instantiate: Eq a1 => a1 -> a1 -> Bool.
    ; Just qc -> fpair (instantiate qc n) \(Qual [Pred _ headT] tc) n1 ->
      -- We mix the predicates `psi` with the type of `headT`, applying a
      -- substitution such as (a1, [a]) so the variable names match.
      -- e.g. Eq a => [a] -> [a] -> Bool
      -- Then instantiate and match.
      case match headT ti of { Just subc ->
        fpair (instantiate (Qual psi $ apply subc tc) n1) \(Qual ps2 t2) n2 ->
          case match tx t2 of
            { Nothing -> Left "class/instance type conflict"
            ; Just subx -> snd <$> prove' ienv (dictVars ps2 0) (proofApply subx ax)
          }}};

inferInst ienv dcs typed (name, (q@(Qual ps t), ds)) = let { dvs = map snd $ fst $ dictVars ps 0 } in
  (name,) . flip (foldr L) dvs . L "@" . foldl A (V "@") <$> mapM (inferMethod ienv dcs typed q) ds;

singleOut s cs = \scrutinee x ->
  foldl A (A (V $ specialCase cs) scrutinee) $ map (\(Constr s' ts) ->
    if s == s' then x else foldr L (V "pjoin#") $ map (const "_") ts) cs;

patEq lit b x y = A (A (A (V "if") (A (A (V "==") (E lit)) b)) x) y;

unpat dcs as t = case as of
  { [] -> pure t
  ; a:at -> get >>= \n -> put (n + 1) >> let { freshv = showInt n "#" } in L freshv <$> let
    { go p x = case p of
      { PatLit lit -> unpat dcs at $ patEq lit (V freshv) x $ V "pjoin#"
      ; PatVar s m -> maybe (unpat dcs at) (\p1 x1 -> go p1 x1) m $ beta s (V freshv) x
      ; PatCon con args -> case mlookup con dcs of
        { Nothing -> error "bad data constructor"
        ; Just cons -> unpat dcs args x >>= \y -> unpat dcs at $ singleOut con cons (V freshv) y
        }
      }
    } in go a t
  };

unpatTop dcs als x = case als of
  { [] -> pure x
  ; (a, l):alt -> let
    { go p t = case p of
      { PatLit lit -> unpatTop dcs alt $ patEq lit (V l) t $ V "pjoin#"
      ; PatVar s m -> maybe (unpatTop dcs alt) go m $ beta s (V l) t
      ; PatCon con args -> case mlookup con dcs of
        { Nothing -> error "bad data constructor"
        ; Just cons -> unpat dcs args t >>= \y -> unpatTop dcs alt $ singleOut con cons (V l) y
        }
      }
    } in go a x
  };

rewritePats' dcs asxs ls = case asxs of
  { [] -> pure $ V "fail#"
  ; (as, t):asxt -> unpatTop dcs (zip as ls) t >>=
    \y -> A (L "pjoin#" y) <$> rewritePats' dcs asxt ls
  };

rewritePats dcs vsxs@((vs0, _):_) = get >>= \n -> let
  { ls = map (flip showInt "#") $ take (length vs0) $ upFrom n }
  in put (n + length ls) >> flip (foldr L) ls <$> rewritePats' dcs vsxs ls;

classifyAlt v x = case v of
  { PatLit lit -> Left $ patEq lit (V "of") x
  ; PatVar s m -> maybe (Left . A . L "pjoin#") classifyAlt m $ A (L s x) $ V "of"
  ; PatCon s ps -> Right (insertWith (flip (.)) s ((ps, x):))
  };

genCase dcs tab = if size tab == 0 then id else A . L "cjoin#" $ let
  { firstC = flst (toAscList tab) undefined (\h _ -> fst h)
  ; cs = maybe (error $ "bad constructor: " ++ firstC) id $ mlookup firstC dcs
  } in foldl A (A (V $ specialCase cs) (V "of"))
    $ map (\(Constr s ts) -> case mlookup s tab of
      { Nothing -> foldr L (V "cjoin#") $ const "_" <$> ts
      ; Just f -> Pa $ f [(const (PatVar "_" Nothing) <$> ts, V "cjoin#")]
      }) cs;

updateCaseSt dcs (acc, tab) alt = case alt of
  { Left f -> (acc . genCase dcs tab . f, Tip)
  ; Right upd -> (acc, upd tab)
  };

rewriteCase dcs as = fpair (foldl (updateCaseSt dcs) (id, Tip) $ uncurry classifyAlt <$> as) \acc tab ->
  acc . genCase dcs tab $ V "fail#";

secondM f (a, b) = (a,) <$> f b;
patternCompile dcs t = let {
  go t = case t of
    { E _ -> pure t
    ; V _ -> pure t
    ; A x y -> liftA2 A (go x) (go y)
    ; L s x -> L s <$> go x
    ; Pa vsxs -> mapM (secondM go) vsxs >>= rewritePats dcs
    ; Ca x as -> liftA2 A (L "of" . rewriteCase dcs <$> mapM (secondM go) as >>= go) (go x)
    }
  } in optiApp $ evalState (go t) 0;

depGraph typed dcs (s, ast) (vs, es) = let
  { t = patternCompile dcs ast }
  in (insert s t vs, foldr (\k ios@(ins, outs) -> case lookup k typed of
    { Nothing -> (insertWith union k [s] ins, insertWith union s [k] outs)
    ; Just _ -> ios
    }) es $ fv [] t);

depthFirstSearch = (foldl .) \relation st@(visited, sequence) vertex ->
  if vertex `elem` visited then st else second (vertex:)
    $ depthFirstSearch relation (vertex:visited, sequence) (relation vertex);

spanningSearch   = (foldl .) \relation st@(visited, setSequence) vertex ->
  if vertex `elem` visited then st else second ((:setSequence) . (vertex:))
    $ depthFirstSearch relation (vertex:visited, []) (relation vertex);

scc ins outs = let
  { depthFirst = snd . depthFirstSearch outs ([], [])
  ; spanning   = snd . spanningSearch   ins  ([], [])
  } in spanning . depthFirst;

inferno tycl typed defmap syms = let
  { loc = zip syms $ TV . (' ':) <$> syms
  } in foldM (\(acc, (subs, n)) s ->
      maybe (Left $ "missing: " ++ s) Right (mlookup s defmap) >>=
      \expr -> infer typed loc expr (subs, n) >>=
      \((t, a), (ms, n1)) -> unify (TV (' ':s)) t ms >>=
      \cs -> Right ((s, (t, a)):acc, (cs, n1))
    ) ([], ([], 0)) syms >>=
    \(stas, (soln, _)) -> mapM id $ (\(s, ta) -> prove tycl s $ typeAstSub soln ta) <$> stas;

prove ienv s (t, a) = flip fmap (prove' ienv ([], 0) a) \((ps, _), x) ->
  let { applyDicts expr = foldl A expr $ map (V . snd) ps }
  in (s, (Qual (map fst ps) t, foldr L (overFree s applyDicts x) $ map snd ps));
inferDefs' ienv defmap (typeTab, lambF) syms = let
  { add stas = foldr (\(s, (q, cs)) (tt, f) -> (insert s q tt, f . ((s, cs):))) (typeTab, lambF) stas
  } in add <$> inferno ienv typeTab defmap syms
  ;
inferDefs ienv defs dcs typed = let
  { typeTab = foldr (\(k, (q, _)) -> insert k q) Tip typed
  ; lambs = second snd <$> typed
  ; (defmap, graph) = foldr (depGraph typed dcs) (Tip, (Tip, Tip)) defs
  ; ins k = maybe [] id $ mlookup k $ fst graph
  ; outs k = maybe [] id $ mlookup k $ snd graph
  } in foldM (inferDefs' ienv defmap) (typeTab, (lambs++)) $ scc ins outs $ map fst $ toAscList defmap
  ;

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

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

cTypeName (TC "()") = "void";
cTypeName (TC "Int") = "int";
cTypeName (TC "Char") = "int";

ffiDeclare (name, t) = let { tys = argList t } in concat
  [cTypeName $ last tys, " ", name, "(", intercalate "," $ cTypeName <$> init tys, ");\n"];

ffiArgs n t = case t of
  { TC s -> ("", ((True, s), n))
  ; TAp (TC "IO") (TC u) -> ("", ((False, u), n))
  ; TAp (TAp (TC "->") x) y -> first (((if 3 <= n then ", " else "") ++ "num(" ++ showInt n ")") ++) $ ffiArgs (n + 1) y
  };

ffiDefine n ffis = case ffis of
  { [] -> id
  ; (name, t):xt -> fpair (ffiArgs 2 t) \args ((isPure, ret), count) -> let
    { lazyn = ("lazy2(" ++) . showInt (if isPure then count - 1 else count + 1) . (", " ++)
    ; aa tgt = "app(arg(" ++ showInt (count + 1) "), " ++ tgt ++ "), arg(" ++ showInt count ")"
    ; longDistanceCall = name ++ "(" ++ args ++ ")"
    } in
    ("case " ++) . showInt n . (": " ++) . if ret == "()"
      then (longDistanceCall ++) . (';':) . lazyn . (((if isPure then "_I, _K" else aa "_K") ++ "); break;") ++) . ffiDefine (n - 1) xt
      else lazyn . (((if isPure then "_NUM, " ++ longDistanceCall else aa $ "app(_NUM, " ++ longDistanceCall ++ ")") ++ "); break;") ++) . ffiDefine (n - 1) xt
  };

untangle s = case program s of
  { Left e -> Left $ "parse error: " ++ e
  ; Right (prog, ParseState s _) -> case s of
    { Ell [] [] -> case foldr ($) (Neat Tip [] [] prims Tip [] []) $ primAdts ++ prog of
      { Neat ienv idefs defs typed dcs ffis exs
        -> inferDefs ienv defs dcs typed >>= \(qas, lambF)
        -> mapM (inferInst ienv dcs qas) idefs >>= \lambs
        -> pure ((qas, lambF lambs), (ffis, exs))
      }
    ; _ -> Left $ "parse error: " ++ case ell s of
      { Left e -> e
      ; Right (((r, c), _), _) -> ("row "++) . showInt r . (" col "++) . showInt c $ ""
      }
    }
  };

optiComb' (subs, combs) (s, lamb) = let
  { gosub t = case t of
    { LfVar v -> maybe t id $ lookup v subs
    ; Nd a b -> Nd (gosub a) (gosub b)
    ; _ -> t
    }
  ; c = optim $ gosub $ nolam $ optiApp lamb
  ; combs' = combs . ((s, c):)
  } in case c of
  { Lf (Basic _) -> ((s, c):subs, combs')
  ; LfVar v -> if v == s then (subs, combs . ((s, Nd (lf "Y") (lf "I")):)) else ((s, gosub c):subs, combs')
  ; _ -> (subs, combs')
  };
optiComb lambs = ($[]) . snd $ foldl optiComb' ([], id) lambs;

-- Code generation.
genMain n = "int main(int argc,char**argv){env_argc=argc;env_argv=argv;rts_init();rts_reduce(" ++ showInt n ");return 0;}\n";

compile s = case untangle s of
  { Left err -> err
  ; Right ((_, lambs), (ffis, exs)) -> fpair (hashcons $ optiComb lambs) \tab mem ->
      ("typedef unsigned u;\n"++)
    . ("enum{_UNDEFINED=0,"++)
    . foldr (.) id (map (\(s, _) -> ('_':) . (s++) . (',':)) comdefs)
    . ("};\n"++)
    . ("static const u prog[]={" ++)
    . foldr (.) id (map (\n -> showInt n . (',':)) mem)
    . ("};\nstatic const u prog_size="++) . showInt (length mem) . (";\n"++)
    . ("static u root[]={" ++)
    . foldr (\(x, y) f -> maybe undefined showInt (mlookup y tab) . (", " ++) . f) id exs
    . ("0};\n" ++)
    . (preamble++)
    . (concatMap ffiDeclare ffis ++)
    . ("static void foreign(u n) {\n  switch(n) {\n" ++)
    . ffiDefine (length ffis - 1) ffis
    . ("\n  }\n}\n" ++)
    . runFun
    . (foldr (.) id $ zipWith (\p n -> (("EXPORT(f" ++ showInt n ", \"" ++ fst p ++ "\", " ++ showInt n ")\n") ++)) exs (upFrom 0))
    $ maybe "" genMain (mlookup "main" tab)
  };

showVar s@(h:_) = (if elem h ":!#$%&*+./<=>?@\\^|-~" then par else id) (s++);

showExtra = \case
  { Basic s -> (s++)
  ; ForeignFun n -> ("FFI_"++) . showInt n
  ; Const i -> showInt i
  ; ChrCon c -> ('\'':) . (c:) . ('\'':)
  ; StrCon s -> ('"':) . (s++) . ('"':)
  };
showPat = \case
  { PatLit e -> showExtra e
  ; PatVar s mp -> (s++) . maybe id ((('@':) .) . showPat) mp
  ; PatCon s ps -> (s++) . ("TODO"++)
  };
showAst prec t = case t of
  { E e -> showExtra e
  ; V s -> showVar s
  ; A x y -> (if prec then par else id) (showAst False x . (' ':) . showAst True y)
  ; L s t -> par $ ('\\':) . (s++) . (" -> "++) . showAst prec t
  ; Pa vsts -> ('\\':) . par (foldr (.) id $ intersperse (';':) $ map (\(vs, t) -> foldr (.) id (intersperse (' ':) $ map (par . showPat) vs) . (" -> "++) . showAst False t) vsts)
  ; Ca x as -> ("case "++) . showAst False x . ("of {"++) . foldr (.) id (intersperse (',':) $ map (\(p, a) -> showPat p . (" -> "++) . showAst False a) as)
  };

showTree prec t = case t of
  { LfVar s -> showVar s
  ; Lf extra -> showExtra extra
  ; Nd x y -> (if prec then par else id) (showTree False x . (' ':) . showTree True y)
  };
disasm (s, t) = (s++) . (" = "++) . showTree False t . (";\n"++);

dumpCombs s = case untangle s of
  { Left err -> err
  ; Right ((_, lambs), _) -> foldr ($) [] $ map disasm $ optiComb lambs
  };

dumpLambs s = case untangle s of
  { Left err -> err
  ; Right ((_, lambs), _) -> foldr ($) [] $
    (\(s, t) -> (s++) . (" = "++) . showAst False t . ('\n':)) <$> lambs
  };

showQual (Qual ps t) = foldr (.) id (map showPred ps) . showType t;

dumpTypes s = case untangle s of
  { Left err -> err
  ; Right ((typed, _), _) -> ($ "") $ foldr (.) id $
    map (\(s, q) -> (s++) . (" :: "++) . showQual q . ('\n':)) $ toAscList typed
  };

data NdKey = NdKey (Either String Int) (Either String Int);
instance Eq (Either String Int) where
{ (Left a) == (Left b) = a == b
; (Right a) == (Right b) = a == b
; _ == _ = False
};
instance Ord (Either String Int) where
{ x <= y = case x of
  { Left a -> case y of
    { Left b -> a <= b
    ; Right _ -> True
    }
  ; Right a -> case y of
    { Left _ -> False
    ; Right b -> a <= b
    }
  }
};
instance Eq NdKey where
{ (NdKey a1 b1) == (NdKey a2 b2) = a1 == a2 && b1 == b2
};
instance Ord NdKey where
{ (NdKey a1 b1) <= (NdKey a2 b2) = a1 <= a2 && (a1 /= a2 || b1 <= b2)
};

memget k@(NdKey a b) = get >>= \(tab, (hp, f)) -> case mlookup k tab of
  { Nothing -> put (insert k hp tab, (hp + 2, f . (a:) . (b:))) >> pure hp
  ; Just v -> pure v
  };

enc t = case t of
  { Lf n -> case n of
    { Basic c -> pure $ Right $ comEnum c
    ; ForeignFun n -> Right <$> memget (NdKey (Right $ comEnum "F") (Right n))
    ; Const c -> Right <$> memget (NdKey (Right $ comEnum "NUM") (Right c))
    ; ChrCon c -> enc $ Lf $ Const $ ord c
    ; StrCon s -> enc $ foldr (\h t -> Nd (Nd (lf "CONS") (Lf $ ChrCon h)) t) (lf "K") s
    }
  ; LfVar s -> pure $ Left s
  ; Nd x y -> enc x >>= \hx -> enc y >>= \hy -> Right <$> memget (NdKey hx hy)
  };

asm combs = foldM
  (\symtab (s, t) -> either (const symtab) (flip (insert s) symtab) <$> enc t)
  Tip combs;

hashcons combs = fpair (runState (asm combs) (Tip, (128, id)))
  \symtab (_, (_, f)) -> (symtab,) $ either (maybe undefined id . (`mlookup` symtab)) id <$> f [];

getArg' k n = getArgChar n k >>= \c -> if ord c == 0 then pure [] else (c:) <$> getArg' (k + 1) n;
getArgs = getArgCount >>= \n -> mapM (getArg' 0) (take (n - 1) $ upFrom 1);

-- Main VM loop.
comdefsrc = [r|
F x = "foreign(arg(1));"
Y x = x "sp[1]"
Q x y z = z(y x)
S x y z = x z(y z)
B x y z = x (y z)
C x y z = x z y
R x y z = y z x
V x y z = z x y
T x y = y x
K x y = "_I" x
I x = "sp[1] = arg(1); sp++;"
CONS x y z w = w x y
NUM x y = y "sp[1]"
ADD x y = "_NUM" "num(1) + num(2)"
SUB x y = "_NUM" "num(1) - num(2)"
MUL x y = "_NUM" "num(1) * num(2)"
DIV x y = "_NUM" "num(1) / num(2)"
MOD x y = "_NUM" "num(1) % num(2)"
EQ x y = "num(1) == num(2) ? lazy2(2, _I, _K) : lazy2(2, _K, _I);"
LE x y = "num(1) <= num(2) ? lazy2(2, _I, _K) : lazy2(2, _K, _I);"
REF x y = y "sp[1]"
READREF x y z = z "num(1)" y
WRITEREF x y z w = w "((mem[arg(2) + 1] = arg(1)), _K)" z
END = "return;"
|];

comb = (,) <$> wantConId <*> ((,) <$> many wantVarId <*> (res "=" *> combExpr));
combExpr = foldl1 A <$> some
  (V <$> wantVarId <|> E . StrCon <$> wantString <|> paren combExpr);

comdefs = case lex posLexemes $ LexState comdefsrc (1, 1) of
  { Left e -> error e
  ; Right (xs, _) -> case parse (braceSep comb) $ ParseState (offside xs) Tip of
    { Left e -> error e
    ; Right (cs, _) -> cs
    }
  };

comEnum s = maybe (error s) id $ lookup s $ zip (fst <$> comdefs) (upFrom 1);
comName i = maybe undefined id $ lookup i $ zip (upFrom 1) (fst <$> comdefs);

preamble = [r|#define EXPORT(f, sym, n) void f() asm(sym) __attribute__((visibility("default"))); void f(){rts_reduce(root[n]);}
void *malloc(unsigned long);
enum { FORWARD = 127, REDUCING = 126 };
enum { TOP = 1<<24 };
static u *mem, *altmem, *sp, *spTop, hp;
static inline u isAddr(u n) { return n>=128; }
static u evac(u n) {
  if (!isAddr(n)) return 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 *r = root; *r; r++) *r = evac(*r);
  *sp = evac(*spTop);
  while (di < hp) {
    u x = altmem[di] = evac(altmem[di]);
    di++;
    if (x != _F && x != _NUM) 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; return (hp += 2) - 2; }
static inline u arg(u n) { return mem[sp [n] + 1]; }
static inline int num(u n) { return mem[arg(n) + 1]; }
static inline void lazy2(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 int env_argc;
int getargcount() { return env_argc; }
static char **env_argv;
int getargchar(int n, int k) { return env_argv[n][k]; }
|];

runFun = ([r|static void run() {
  for(;;) {
    if (mem + hp > sp - 8) gc();
    u x = *sp;
    if (isAddr(x)) *--sp = mem[x]; else switch(x) {
|]++)
  . foldr (.) id (genComb <$> comdefs)
  . ([r|
    }
  }
}

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;
}

void rts_reduce(u n) {
  *(sp = spTop) = app(app(n, _UNDEFINED), _END);
  run();
}
|]++)
  ;

genArg m a = case a of
  { V s -> ("arg("++) . (maybe undefined showInt $ lookup s m) . (')':)
  ; E (StrCon s) -> (s++)
  ; A x y -> ("app("++) . genArg m x . (',':) . genArg m y . (')':)
  };
genArgs m as = foldl1 (.) $ map (\a -> (","++) . genArg m a) as;
genComb (s, (args, body)) = let
  { argc = ('(':) . showInt (length args)
  ; m = zip args $ upFrom 1
  } in ("case _"++) . (s++) . (':':) . (case body of
  { A (A x y) z -> ("lazy3"++) . argc . genArgs m [x, y, z] . (");"++)
  ; A x y -> ("lazy2"++) . argc . genArgs m [x, y] . (");"++)
  ; E (StrCon s) -> (s++)
  }) . ("break;\n"++)
  ;

main = getArgs >>= \case
  { "comb":_ -> interact dumpCombs
  ; "lamb":_ -> interact dumpLambs
  ; "type":_ -> interact dumpTypes
  ; _ -> interact compile
  };