Try to make a same type definition for mutually eval add expr

SimpleEval.hs

module SimpleEval where

import Prelude hiding (odd, even)
import Data.Dynamic


data Expr = Val Int | Add Expr Expr 
data Cont = HALT | EVAL Expr Cont | ADD Int Cont 

eval :: Expr -> Int
eval e = comp_eval e HALT

comp_eval :: Expr -> Cont -> Int
comp_eval (Val n) c = exec c n
comp_eval (Add x y) c = comp_eval x (EVAL y c) 


exec :: Cont -> Int -> Int
exec HALT n = n 
exec (ADD n c) m = exec c (n+m)
exec (EVAL y c) n = comp_eval y (ADD n c) 


eval2 :: Expr -> Int
eval2 e = comp_eval2 e HALT 0


comp_eval2 :: Expr -> Cont -> Int -> Int
comp_eval2 (Val n) c m  = exec2 (Val (n+m)) c n
comp_eval2 (Add x y) c m = comp_eval2 x (EVAL y c) m 

exec2 :: Expr -> Cont -> Int -> Int
exec2 (Val f) HALT n = n 
exec2 (Val f) (ADD n c) m = exec2 (Val (f+m+n)) c (n+m)
exec2 (Val f) (EVAL y c) n = comp_eval2 y (ADD n c) (f)


--   eval       (Add (Add (Val 2) (Val 3)) (Val 4))
-- = comp_eval  (Add (Add (Val 2) (Val 3)) (Val 4)) HALT
-- = comp_eval  (Add (Val 2) (Val 3)) (EVAL (Val 4) HALT)
-- = comp_eval  (Val 2) (EVAL (Val 3) (EVAL (Val 4) HALT))
-- = exec       (EVAL (Val 3) (EVAL (Val 4) HALT)) 2
-- = comp_eval  (Val 3) (ADD 2 (EVAL (Val 4) HALT))
-- = exec       (ADD 2 (EVAL (Val 4) HALT)) 3
-- = exec       (EVAL (Val 4) HALT ) 5
-- = comp_eval  (Val 4) (ADD 5 HALT )
-- = exec       (ADD 5 HALT ) 4
-- = exec       HALT 9 =9

--   eval       (Add (Add (Val 2) (Val 3)) (Val 4))
-- = comp_eval  (Add (Add (Val 2) (Val 3)) (Val 4)) HALT 0
-- = comp_eval  (Add (Val 2) (Val 3)) (EVAL (Val 4) HALT 0) 0
-- = comp_eval  (Val 2) (EVAL (Val 3) (EVAL (Val 4) HALT 0) 0) 0
-- = exec       (Val 2) (EVAL (Val 3) (EVAL (Val 4) HALT 0) 0) 
-- = comp_eval  (Val 3) (ADD 2 (EVAL (Val 4) HALT 0) 0) 2
-- = exec       (Val 5) (ADD 2 (EVAL (Val 4) HALT 0)) 3
-- = exec       (Val 9) (EVAL (Val 4) HALT 0) 5
-- = comp_eval  (Val 4) (ADD 5 HALT ) 9
-- = exec       (Val 9) (ADD 5 HALT ) 4
-- = exec       (Val 9) HALT 9 =9



comp_eval3 :: Expr -> Cont -> Int 
comp_eval3 (Val n) c   = exec3 (Val n) c
comp_eval3 (Add x y) c  = comp_eval3 x (EVAL y c) 

exec3 :: Expr -> Cont -> Int 
exec3 (Val f) HALT  = f 
exec3 (Val f) (ADD n c) = exec3 (Val (f+n)) c 
exec3 (Val f) (EVAL y c)  = comp_eval3 y (ADD f c)




primes :: [Integer]
primes =  sieve [2..]
  where sieve (p:xs) = p : sieve [x | x <- xs, x `mod` p > 0]


even :: Int -> Bool
even 0 = True
even n = odd (n - 1)

odd :: Int -> Bool
odd 0 = False
odd n = even (n - 1)




fact self 0 = 1
fact self n = n * self (pred n)

fix2 f = 
    let wrap = toDyn
        unwrap x = fromDyn x undefined
        aux g = g (wrap g)
    in aux (\x -> f (unwrap x x))

test2 = fix2 fact (5::Int)

fix_poly:: [[a]->a] -> [a]
fix_poly fl = fix (\self -> map ($ self) fl)
  where fix f = f (fix f)
    
test1 = (map iseven [0..5], map isodd [0..5])
  where
  [iseven, isodd] = fix_poly [fe,fo]
  fe [e,o] n = n == 0 || o (n-1)
  fo [e,o] n = n /= 0 && e (n-1)




--   eval (Add (Add (Val 2) (Val 3)) (Val 4))
-- = eval (Add (Val 2) (Val 3)) + eval (Val 4)
-- = eval ((Val 2) +  eval (Val 3) ) + eval (Val 4)
-- = ( 2 +  eval (Val 3) ) + eval (Val 4)
-- = ( 2 + 3 ) + eval (Val 4)
-- = 5 + eval (Val 4)
-- = 5 + 4
-- = 9


-- eval' (Add x y) c = eval' x (EVAL y c)
-- exec (EVAL y c) n = eval' y (ADD n c)