binary

------------------------------------------------------------------------
-- Operators. Lists.
------------------------------------------------------------------------

or f g x y = f x (g x y);
and f g x y = @C f y (g x y);
lstEq = @Y \r xs ys a b -> xs (ys a (\u u -> b)) (\x xt -> ys b (\y yt -> x(y(@=)) (r xt yt a b) b));
pair x y f = f x y;
Just x f g = g x;
Nothing f g = f;
foldr = @Y \r c n l -> l n (\h t -> c h(r c n t));
foldl = \f a bs -> foldr (\b g x -> g (f x b)) @I bs a;
foldlOne = \f bs -> bs @? (\h t -> foldl f h t);
elem k xs = \a b -> foldr (\x t -> (x(k(@=))) a t) b xs;
append = @C (foldr @:);

pure x inp = Just (pair x inp);
bind f m = m @K (\x -> x f);
ap x y = \inp -> bind (\a t -> bind (\b u -> pure (a b) u) (y t)) (x inp);
fmap f x = ap (pure f) x;
alt x y = \inp -> (x inp) (y inp) Just;
liftaa f x y = ap (fmap f x) y;
many = @Y \r p -> alt (liftaa @: p (r p)) (pure @K);
some p = liftaa @: p (many p);
liftKI = liftaa (@K @I);
liftK = liftaa @K;
between x y p = liftKI x (liftK p y);
sat f inp = inp @K (\h t -> f h (pure h t) @K);
char c = sat (\x -> x(c(@=)));

R s   = \a b c d -> a s;
V v   = \a b c d -> b v;
A x y = \a b c d -> c x y;
L x y = \a b c d -> d x y;
raw s = R (append s);

com = between (liftKI (char '-') (char '-')) (char '\n') (many (sat (\c -> @C (c('\n' @=)))));
sp = many (alt (char ' ') (alt (char '\n') com));
spc f = liftK f sp;
spch = @B spc char;
paren = between (spch '(') (spch ')');
letter = sat (\x -> or
  (and ('z'(x(@L))) (x('a'(@L))))
  (and ('Z'(x(@L))) (x('A'(@L))))
  );
digit = sat (\x -> and ('9'(x @L)) (x('0' @L)));
varId = spc (liftaa @: letter (many (alt letter digit)));
varSym = spc (some (sat (@C elem ":!#$%&*+./<=>?@\\^|-~")));
op = alt varSym (between (spch '`') (spch '`') varId);
var = alt varId (paren varSym);
pre = liftKI (char '@') (fmap (@:) (spc (sat (@K @K))));
lam r = liftKI (spch '\\') (liftaa (@C (foldr L)) (some var) (liftKI (char '-') (liftKI (spch '>') r)));
listify = fmap (foldr (\h t -> A (A (R (@:':')) h) t) (R (@:'K')));
escchar = liftKI (char '\\') (alt (sat (\c -> or (c('"'(@=))) (or (c('\\'(@=))) (c('\''(@=)))))) (fmap (@K '\n') (char 'n')));
litOne delim = fmap (\c -> R (@B (@:'#') (@:c))) (alt escchar (sat (\c -> @C (delim(c @=)))));
litStr = listify (between (char '"') (spch '"') (many (litOne '"')));
litChar = between (char '\'') (spch '\'') (litOne '\'');
lit = alt litStr litChar;
sepByOne p sep = liftaa (@:) p (many (liftKI sep p));
sepBy p sep = alt (sepByOne p sep) (pure @K);
sqLst r = listify (between (spch '[') (spch ']') (sepBy r (spch ',')));
atom r = alt (paren r) (alt (fmap V var) (alt (fmap R pre) (alt (lam r) (alt lit (sqLst r)))));
aexp r = fmap (foldlOne A) (some (atom r));
expr = @Y \r -> liftaa (foldl @T) (aexp r) (many (liftaa (\f b a -> A (A (V f) a) b) op (aexp r)));
def = liftaa pair var (liftaa (@C (foldr L)) (many var) (liftKI (spch '=') expr));
program = liftKI sp (some (liftK def (spch ';')));

Ze   = \    a b c d e -> a;
Su   = \x   a b c d e -> b x;
Pass = \x   a b c d e -> c x;
La   = \x   a b c d e -> d x;
App  = \x y a b c d e -> e x y;

debruijn = @Y \r n e -> e
  (\s -> Pass (R s))
  (\v -> foldr (\h m -> lstEq h v Ze (Su m)) (Pass (V v)) n)
  (\x y -> App (r n x) (r n y))
  (\s t -> La (r (@: s n) t))
  ;

Defer = \a b c d -> a;
Closed = \t a b c d -> b t;
Need = \x a b c d -> c x;
Weak = \x a b c d -> d x;

ldef = \r y -> y
  (Need (Closed (raw "``SII")))
  (\d -> Need (Closed (A (raw "T") d)))
  (\e -> Need (r (Closed (raw "`SI")) e))
  (\e -> Need (r (Closed (raw "T")) e))
  ;

lclo = \r d y -> y
  (Need (Closed d))
  (\dd -> Closed (A d dd))
  (\e -> Need (r (Closed (A (raw "B") d)) e))
  (\e -> Weak (r (Closed d) e))
  ;

lnee = \r e y -> y
  (Need (r (r (Closed (raw "S")) e) (Closed (raw "I"))))
  (\d -> Need (r (Closed (A (raw "R") d)) e))
  (\ee -> Need (r (r (Closed (raw "S")) e) ee))
  (\ee -> Need (r (r (Closed (raw "C")) e) ee))
  ;

lwea = \r e y -> y
  (Need e)
  (\d -> Weak (r e (Closed d)))
  (\ee -> Need (r (r (Closed (raw "B")) e) ee))
  (\ee -> Weak (r e ee))
  ;

babsa = @Y \r x y -> x
  (ldef r y)
  (\d -> lclo r d y)
  (\e -> lnee r e y)
  (\e -> lwea r e y)
  ;

babs = @Y \r t -> t
  Defer
  (@B Weak r)
  Closed
  (\t -> r t
    (Closed (raw "I"))
    (\d -> Closed (A (raw "K") d))
    @I
    (babsa (Closed (raw "K"))))
  (\x y -> babsa (r x) (r y))
  ;

nolam x = babs (debruijn @K x) @? @I @? @?;
insPrim = @B (@: (pair ":" (raw ":"))) (@B (@: (pair "<=" (raw "``BT`TL"))) (@: (pair "==" (raw "``BT`T="))));
rank ds v = foldr (\d t -> lstEq v (d @K) (\n -> @B (@:'@') (@:n)) (@B t \n -> '0'('1'@-)(n @+))) @? ds ' ';
shows f = @Y \r t -> t @I f (\x y -> @B (@B (@:'`') (r x)) (r y)) @?;
dump tab = foldr (\h t -> shows (rank tab) (nolam (h (@K @I))) (@:';'t)) "" tab;
main s = program s "?" (@B (@B dump insPrim) (@T @K));