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|
--------------------------------
-- The Game of Life --
--------------------------------
generations x = 30
data L a = N | C1 a (L a)
data Tuple2 a b = T2 a b
data Tuple3 a b c = T3 a b c
main = putStr (listChar_string
(append1 (C1 '\FF' N)
(life1 (generations ()) (start ()))))
listChar_string :: L Char -> String
listChar_string N = []
listChar_string (C1 x xs) = x : listChar_string xs
start :: a -> L (L Int)
start x = (C1 N
(C1 N
(C1 N
(C1 N
(C1 N
(C1 N
(C1 N
(C1 N
(C1 N
(C1 N
(C1 N
(C1 N
(C1 N
(C1 N
(C1
(C1 0
(C1 0
(C1 0
(C1 1
(C1 1
(C1 1
(C1 1
(C1 1
(C1 0
(C1 1
(C1 1
(C1 1
(C1 1
(C1 1
(C1 0
(C1 1
(C1 1
(C1 1
(C1 1
(C1 1
(C1 0
(C1 1
(C1 1
(C1 1
(C1 1
(C1 1
(C1 0 N))))))))))))))))))))))))))) N)))))))))))))))
-- Calculating the next generation
gen1 :: Int -> L (L Int) -> L (L Int)
gen1 n board = map1 row1 (shift1 (copy1 n 0) board)
row1 :: Tuple3 (L Int) (L Int) (L Int) -> L Int
row1 (T3 last this next)
= zipWith31 elt1 (shift2 0 last)
(shift2 0 this)
(shift2 0 next)
elt1 :: Tuple3 Int Int Int
-> (Tuple3 Int Int Int)
-> (Tuple3 Int Int Int) -> Int
elt1 (T3 a b c) (T3 d e f) (T3 g h i)
= if (not (eq tot 2))
&& (not (eq tot 3))
then 0
else if (eq tot 3) then 1 else e
where tot = a `plus` b `plus` c `plus` d
`plus` f `plus` g `plus` h `plus` i
eq :: Int -> Int -> Bool
eq x y = x == y
plus :: Int -> Int -> Int
plus x y = x + y
shiftr1 :: L Int -> L (L Int) -> L (L Int)
shiftr1 x xs = append2 (C1 x N) (init1 xs)
shiftl1 :: L Int -> L (L Int) -> L (L Int)
shiftl1 x xs = append2 (tail1 xs) (C1 x N)
shift1 :: L Int -> L (L Int)
-> L (Tuple3 (L Int) (L Int) (L Int))
shift1 x xs = zip31 (shiftr1 x xs) xs (shiftl1 x xs)
shiftr2 :: Int -> L Int -> L Int
shiftr2 x xs = append3 (C1 x N) (init2 xs)
shiftl2 :: Int -> L Int -> L Int
shiftl2 x xs = append3 (tail2 xs) (C1 x N)
shift2 :: Int -> L Int -> L (Tuple3 Int Int Int)
shift2 x xs = zip32 (shiftr2 x xs) xs (shiftl2 x xs)
-- copy
copy1 :: Int -> Int -> L Int
copy1 0 x = N
copy1 n x = C1 x (copy1 (n-1) x)
copy2 :: Int -> L Int -> L (L Int)
copy2 0 x = N
copy2 n x = C1 x (copy2 (n-1) x)
copy3 :: Int -> Char -> L Char
copy3 0 x = N
copy3 n x = C1 x (copy3 (n-1) x)
-- Displaying one generation
disp1 :: (Tuple2 (L Char) (L (L Int))) -> L Char
disp1 (T2 gen xss)
= append1 gen
(append1 (C1 '\n' (C1 '\n' N))
(foldr_1 (glue1 (C1 '\n' N)) N
(map4 (compose2 concat1 (map2 star1)) xss)))
star1 :: Int -> L Char
star1 i = case i of
0 -> C1 ' ' (C1 ' ' N)
1 -> C1 ' ' (C1 'o' N)
glue1 :: L Char -> L Char -> L Char -> L Char
glue1 s xs ys = append1 xs (append1 s ys)
-- Generating and displaying a sequence of generations
life1 :: Int -> L (L Int) -> L Char
life1 n xss
= foldr_1 (glue1 (copy3 (n+2) '\VT')) N
(map5 disp1
(zip1_ (map6 (string_ListChar.show) (ints 0))
gens))
where
gens = take3 (740::Int) (iterate1 (gen1 n) (initial1 n xss))
ints :: Int -> L Int
ints x = C1 x (ints (x+1))
string_ListChar :: String -> L Char
string_ListChar [] = N
string_ListChar (x:xs) = C1 x (string_ListChar xs)
initial1 :: Int -> L (L Int) -> L (L Int)
initial1 n xss = take1 n (append2 (map3 (compose1 (take2 n)
(`append3` (copy1 n 0))) xss)
(copy2 n (copy1 n 0)))
iterate1 :: (L (L Int) -> L (L Int))
-> L (L Int) -> L (L (L Int))
iterate1 f x = C1 x (iterate1 f (f x))
-- versions of built in functions
-- take
take1 :: Int -> L (L Int) -> L (L Int)
take1 0 _ = N
take1 _ N = N
--should be:take1 (n+1) (C1 x xs) = C1 x (take1 n xs)
take1 n (C1 x xs) | n < 0 = error "Main.take1"
| otherwise = C1 x (take1 (n-1) xs)
take2 :: Int -> L Int -> L Int
take2 0 _ = N
take2 _ N = N
--should be:take2 (n+1) (C1 x xs) = C1 x (take2 n xs)
take2 n (C1 x xs) | n < 0 = error "Main.take2"
| otherwise = C1 x (take2 (n-1) xs)
take3 :: Int -> L (L (L Int))
-> L (L (L Int))
take3 0 _ = N
take3 _ N = N
take3 n (C1 x xs) = C1 x (take3 (n-1) xs)
-- init
init1 :: L (L Int) -> L (L Int)
init1 (C1 x N) = N
init1 (C1 x xs) = C1 x (init1 xs)
init1 N = error "init1 got a bad list"
init2 :: L Int -> L Int
init2 (C1 x N) = N
init2 (C1 x xs) = C1 x (init2 xs)
init2 N = error "init1 got a bad list"
-- tail
tail1 :: L (L Int) -> L (L Int)
tail1 (C1 _ xs) = xs
tail1 N = error "tail1 got a bad list"
tail2 :: L Int -> L Int
tail2 (C1 _ xs) = xs
tail2 N = error "tail2 got a bad list"
-- maps
map1 :: (Tuple3 (L Int) (L Int) (L Int) -> L Int) ->
L (Tuple3 (L Int) (L Int) (L Int))
-> L (L Int)
map1 f N = N
map1 f (C1 x xs) = C1 (f x) (map1 f xs)
map2 :: (Int -> L Char) -> L Int -> L (L Char)
map2 f N = N
map2 f (C1 x xs) = C1 (f x) (map2 f xs)
map3 :: (L Int -> L Int) -> L (L Int) -> L (L Int)
map3 f N = N
map3 f (C1 x xs) = C1 (f x) (map3 f xs)
map4 :: (L Int -> L Char)
-> L (L Int) -> L (L Char)
map4 f N = N
map4 f (C1 x xs) = C1 (f x) (map4 f xs)
map5 :: (Tuple2 (L Char) (L (L Int)) -> L Char)
-> L (Tuple2 (L Char) (L (L Int)))
-> L (L Char)
map5 f N = N
map5 f (C1 x xs) = C1 (f x) (map5 f xs)
map6 :: (Int -> L Char) -> L Int -> L (L Char)
map6 f N = N
map6 f (C1 x xs) = C1 (f x) (map6 f xs)
-- compose
compose2 :: (L (L Char) -> L Char)
-> (L Int -> L (L Char))
-> L Int -> L Char
compose2 f g xs = f (g xs)
compose1 :: (L Int -> L Int)
-> (L Int -> L Int) -> L Int -> L Int
compose1 f g xs = f (g xs)
-- concat
concat1 :: L (L Char) -> L Char
concat1 = foldr_1 append1 N
-- foldr
foldr_1 :: (L Char -> L Char -> L Char)
-> L Char -> L (L Char) -> L Char
foldr_1 f a N = a
foldr_1 f a (C1 x xs) = f x (foldr_1 f a xs)
-- appends
append1 :: L Char -> L Char -> L Char
append1 N ys = ys
append1 (C1 x xs) ys = C1 x (append1 xs ys)
append2 :: L (L Int) -> L (L Int) -> L (L Int)
append2 N ys = ys
append2 (C1 x xs) ys = C1 x (append2 xs ys)
append3 :: L Int -> L Int -> L Int
append3 N ys = ys
append3 (C1 x xs) ys = C1 x (append3 xs ys)
-- zips
pzip f (C1 x1 xs) (C1 y1 ys)
= C1 (f x1 y1) (pzip f xs ys)
pzip f _ _ = N
zip1_ :: L (L Char)
-> L (L (L Int))
-> L (Tuple2 (L Char) (L (L Int)))
zip1_ = pzip T2
zip2_ :: L (L Int)
-> L (L Int)
-> L (Tuple2 (L Int) (L Int))
zip2_ = pzip T2
zip3d :: L Int -> (Tuple2 (L Int) (L Int))
-> (Tuple3 (L Int) (L Int) (L Int))
zip3d x (T2 y z) = T3 x y z
zip3_ :: L (L Int)
-> L (Tuple2 (L Int) (L Int))
-> L (Tuple3 (L Int) (L Int) (L Int))
zip3_ = pzip zip3d
zip4_ :: L Int
-> L Int
-> L (Tuple2 Int Int)
zip4_ = pzip T2
zip5d :: Int -> (Tuple2 Int Int) -> (Tuple3 Int Int Int)
zip5d x (T2 y z) = T3 x y z
zip5_ :: L Int
-> L (Tuple2 Int Int)
-> L (Tuple3 Int Int Int)
zip5_ = pzip zip5d
zip6_ :: L (Tuple3 Int Int Int)
-> L (Tuple3 Int Int Int)
-> L (Tuple2 (Tuple3 Int Int Int)
(Tuple3 Int Int Int))
zip6_ = pzip T2
zip31 :: L (L Int) -> L (L Int)
-> L (L Int)
-> L (Tuple3 (L Int) (L Int) (L Int))
zip31 as bs cs
= zip3_ as (zip2_ bs cs)
zip32 :: L Int -> L Int -> L Int
-> L (Tuple3 Int Int Int)
zip32 as bs cs
= zip5_ as (zip4_ bs cs)
-- zipWith
zipWith21 :: ((Tuple3 Int Int Int)
-> (Tuple2 (Tuple3 Int Int Int)
(Tuple3 Int Int Int)) -> Int)
-> L (Tuple3 Int Int Int)
-> L (Tuple2 (Tuple3 Int Int Int)
(Tuple3 Int Int Int))
-> L Int
zipWith21 = pzip
zipWith31 :: ((Tuple3 Int Int Int)
-> (Tuple3 Int Int Int)
-> (Tuple3 Int Int Int) -> Int)
-> L (Tuple3 Int Int Int)
-> L (Tuple3 Int Int Int)
-> L (Tuple3 Int Int Int) -> L Int
zipWith31 z as bs cs
= zipWith21 z' as (zip6_ bs cs)
where z' a (T2 b c) = z a b c
|
