let ZERO  = \f x -> x
let ONE   = \f x -> f x
let TWO   = \f x -> f (f x)
let THREE = \f x -> f (f (f x))
let FOUR  = \f x -> f (f (f (f x)))
let FIVE  = \f x -> f (f (f (f (f x))))
let SIX  = \f x -> f (f (f (f (f (f x)))))
let TEN = \f x -> f ( f ( f ( f ( f ( f ( f ( f ( f ( f x)))))))))

let TRUE  = \x y -> x
let FALSE = \x y -> y
let ITE   = \b x y -> b x y
let AND   = \b1 b2 -> ITE b1 b2 FALSE
let OR    = \b1 b2 -> ITE b1 TRUE b2

--------------------------------------------------------------------------------
-- Numbers
--------------------------------------------------------------------------------

let INCR  = \n f x -> f (n f x)

--------------------------------------------------------------------------------
-- Pairs
--------------------------------------------------------------------------------

let PAIR  = \x y b -> b x y
let FST   = \p     -> p TRUE
let SND   = \p     -> p FALSE

--------------------------------------------------------------------------------
-- do not modify text BEFORE this line
--------------------------------------------------------------------------------

let SKIP1 = \j k -> (\b -> b TRUE ((AND TRUE (k(TRUE))) (j(k(FALSE))) (k(FALSE))))     -- (a)
let DECR  =  \n -> (n (SKIP1 INCR) (PAIR FALSE ZERO)) FALSE -- (b)
let SUB   = \m n -> (n DECR) m       -- (c)
let ISZ   =  \n -> n(\a -> FALSE) TRUE      -- (d)
let EQL   = \n m -> AND (ISZ (SUB m n)) (ISZ (SUB n m))     -- (e)

let SUC   = \n f x -> f (n f x)
let ADD   = \n m -> n SUC m
let MUL   = \n m -> n (ADD m) ZERO
let REPEAT = \n m -> n (PAIR m) FALSE
let EMPTY = \p -> p (\x y z -> FALSE) TRUE
let FIX = \stp -> (\x -> stp (x x)) (\x -> stp (x x))
let LEN = FIX (\rec n -> (EMPTY n) ZERO (INCR (rec (SND n))))
let STEP = \rec n -> ITE (ISZ n) ZERO (ADD n (rec (DECR n)))
let SUM = FIX STEP
let DIV = FIX (\rec n m -> ITE (EQL n m) ONE (ITE (ISZ (SUB n m) ) ZERO (INCR (rec (SUB n m) m))))
let MOD = FIX (\rec n m -> ITE (EQL n m) ZERO (ITE (ISZ (SUB n m) ) n (rec (SUB n m) m)))
let INSERT = \n m -> (PAIR n m)
let RECAPPEND = FIX (\rec n m -> ITE (EMPTY n) m (INSERT (FST n) (rec (SND n) m)))
let PAIR1 = \n -> SND n
let PAIR2 = \n -> FST n
let BEEP = \n m -> (EMPTY n) m (INSERT (FST n) m)

eval repeat :
  BEEP (FALSE) (PAIR TWO FALSE)
  =*> (PAIR TWO FALSE)