> module Language.Nock5K.Spec where
1 Structures A noun is an atom or a cell. An atom is any natural number. A cell is an ordered pair of nouns. 
> data Noun = Atom Integer | Noun :- Noun deriving (Eq)
2 Reductions nock(a) *a 
> nock :: Noun -> Noun
> nock = tar
[a b c] [a [b c]] 
> infixr 1 :-
?[a b] 0 
> wut (a :- b) = Atom 0
?a 1 
> wut a = Atom 1
+[a b] +[a b] 
> lus (a :- b) = error "+[a b]"
+a 1 + a 
> lus (Atom a) = Atom (1 + a)
=[a a] 0 
> tis (a :- a') | a == a' = Atom 0
=[a b] 1 
> tis (a :- b) = Atom 1
=a =a 
> tis a = error "=a"
/[1 a] a 
> fas (Atom 1 :- a) = a
/[2 a b] a 
> fas (Atom 2 :- a :- b) = a
/[3 a b] b 
> fas (Atom 3 :- a :- b) = b
/[(a + a) b] /[2 /[a b]] 
> fas (Atom a :- b) | a > 2 && a `mod` 2 == 0 =
>   fas $ Atom 2 :- fas (Atom (a `div` 2) :- b)
/[(a + a + 1) b] /[3 /[a b]] 
> fas (Atom a :- b) | a > 3 && a `mod` 2 == 1 =
>   fas $ Atom 3 :- fas (Atom (a `div` 2) :- b)
/a /a 
> fas a = error "/a"
*[a [b c] d] [*[a b c] *[a d]] 
> tar (a :- (b :- c) :- d) = tar (a :- b :- c) :- tar (a :- d)
*[a 0 b] /[b a] 
> tar (a :- (Atom 0 :- b)) = fas $ b :- a
*[a 1 b] b 
> tar (a :- (Atom 1 :- b)) = b
*[a 2 b c] *[*[a b] *[a c]] 
> tar (a :- Atom 2 :- b :- c) = tar $ tar (a :- b) :- tar (a :- c)
*[a 3 b] ?*[a b] 
> tar (a :- Atom 3 :- b) = (wut.tar) (a :- b)
*[a 4 b] +*[a b] 
> tar (a :- Atom 4 :- b) = (lus.tar) (a :- b)
*[a 5 b] =*[a b] 
> tar (a :- Atom 5 :- b) = (tis.tar) (a :- b)
*[a 6 b c d] *[a 2 [0 1] 2 [1 c d] [1 0] 2 [1 2 3] [1 0] 4 4 b] 
> tar (a :- Atom 6 :- b :- c :- d) =
>   tar (a :- Atom 2 :- (Atom 0 :- Atom 1) :- Atom 2 :- (Atom 1 :- c :- d) :-
>        (Atom 1 :- Atom 0) :- Atom 2 :- (Atom 1 :- Atom 2 :- Atom 3) :-
>        (Atom 1 :- Atom 0) :- Atom 4 :- Atom 4 :- b)
*[a 7 b c] *[a 2 b 1 c] 
> tar (a :- Atom 7 :- b :- c) = tar $ a :- Atom 2 :- b :- Atom 1 :- c
*[a 8 b c] *[a 7 [[7 [0 1] b] 0 1] c] 
> tar (a :- Atom 8 :- b :- c) =
>   tar (a :- Atom 7 :- ((Atom 7 :- (Atom 0 :- Atom 1) :- b) :-
>         Atom 0 :- Atom 1) :- c)
*[a 9 b c] *[a 7 c 2 [0 1] 0 b] 
> tar (a :- Atom 9 :- b :- c) =
>   tar (a :- Atom 7 :- c :- Atom 2 :- (Atom 0 :- Atom 1) :- Atom 0 :- b)
*[a 10 [b c] d] *[a 8 c 7 [0 3] d] 
> tar (a :- Atom 10 :- (b :- c) :- d) =
>   tar (a :- Atom 8 :- c :- Atom 7 :- (Atom 0 :- Atom 3) :- d)
*[a 10 b c] *[a c] 
> tar (a :- Atom 10 :- b :- c) = tar $ a :- c
*a *a 
> tar a = error "*a"