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Reformat Spec using code blocks

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Also removed some unnecessary parens revealed by the clearer structure.
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Steven Dee 2013-10-26 15:38:08 -04:00
parent ae205692cb
commit 757f5a406a
2 changed files with 75 additions and 104 deletions
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2
Language/Nock5K.hs
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@ -1,4 +1,4 @@
module Language.Nock5K (Noun(Atom, (:-)), nock, noun, repl) where
module Language.Nock5K (Noun(Atom, (:-)), Nock, nock, noun, repl) where
import Language.Nock5K.Parse
import Language.Nock5K.Repl

177
Language/Nock5K/Spec.lhs
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@ -1,154 +1,125 @@
> module Language.Nock5K.Spec where
> import Control.Monad.Instances
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)
> type Comp = Either String
\begin{code}
module Language.Nock5K.Spec where
import Control.Monad.Instances
data Noun = Atom Integer | Noun :- Noun deriving (Eq)
-- | Either a computed result or an error message.
-- E.g. 'Comp' 'Noun' is either a 'Noun' or an error.
type Comp = Either String
\end{code}
2 Reductions
nock(a) *a
> nock :: Noun -> Comp Noun
> nock = tar
[a b c] [a [b c]]
> infixr 1 :-
\begin{code}
nock :: Noun -> Comp Noun
nock = tar
infixr 1 :-
\end{code}
?[a b] 0
> wut (a :- b) = return $ Atom 0
?a 1
> wut a = return $ Atom 1
+[a b] +[a b]
> lus (a :- b) = Left "+[a b]"
+a 1 + a
> lus (Atom a) = return $ Atom (1 + a)
=[a a] 0
> tis (a :- a') | a == a' = return $ Atom 0
=[a b] 1
> tis (a :- b) = return $ Atom 1
=a =a
> tis a = Left "=a"
\begin{code}
wut, lus, tis :: Noun -> Comp Noun
wut (a :- b) = return $ Atom 0
wut a = return $ Atom 1
lus (a :- b) = Left "+[a b]"
lus (Atom a) = return $ Atom (1 + a)
tis (a :- a') | a == a' = return $ Atom 0
tis (a :- b) = return $ Atom 1
tis a = Left "=a"
\end{code}
/[1 a] a
> fas (Atom 1 :- a) = return a
/[2 a b] a
> fas (Atom 2 :- a :- b) = return a
/[3 a b] b
> fas (Atom 3 :- a :- b) = return b
/[(a + a) b] /[2 /[a b]]
> fas (Atom a :- b) | a > 2 && a `mod` 2 == 0 = do
> x <- fas $ Atom (a `div` 2) :- b
> fas $ Atom 2 :- x
/[(a + a + 1) b] /[3 /[a b]]
> fas (Atom a :- b) | a > 3 && a `mod` 2 == 1 = do
> x <- fas $ Atom (a `div` 2) :- b
> fas $ Atom 3 :- x
/a /a
> fas a = Left "/a"
\begin{code}
fas :: Noun -> Comp Noun
fas (Atom 1 :- a) = return a
fas (Atom 2 :- a :- b) = return a
fas (Atom 3 :- a :- b) = return b
fas (Atom a :- b) | a > 2 && a `mod` 2 == 0 = do
x <- fas $ Atom (a `div` 2) :- b
fas $ Atom 2 :- x
fas (Atom a :- b) | a > 3 && a `mod` 2 == 1 = do
x <- fas $ Atom (a `div` 2) :- b
fas $ Atom 3 :- x
fas a = Left "/a"
\end{code}
*[a [b c] d] [*[a b c] *[a d]]
> tar (a :- (b :- c) :- d) = do
> x <- tar (a :- b :- c)
> y <- tar (a :- d)
> return $ x :- y
\begin{code}
tar :: Noun -> Comp Noun
tar (a :- (b :- c) :- d) = do
x <- tar (a :- b :- c)
y <- tar (a :- d)
return $ x :- y
\end{code}
*[a 0 b] /[b a]
> tar (a :- (Atom 0 :- b)) = fas $ b :- a
*[a 1 b] b
> tar (a :- (Atom 1 :- b)) = return b
*[a 2 b c] *[*[a b] *[a c]]
> tar (a :- Atom 2 :- b :- c) = do
> x <- tar (a :- b)
> y <- tar (a :- c)
> tar $ x :- y
*[a 3 b] ?*[a b]
> tar (a :- Atom 3 :- b) = tar (a :- b) >>= wut
*[a 4 b] +*[a b]
> tar (a :- Atom 4 :- b) = tar (a :- b) >>= lus
*[a 5 b] =*[a b]
> tar (a :- Atom 5 :- b) = tar (a :- b) >>= tis
\begin{code}
tar (a :- Atom 0 :- b) = fas $ b :- a
tar (a :- Atom 1 :- b) = return b
tar (a :- Atom 2 :- b :- c) = do x <- tar (a :- b)
y <- tar (a :- c)
tar $ x :- y
tar (a :- Atom 3 :- b) = tar (a :- b) >>= wut
tar (a :- Atom 4 :- b) = tar (a :- b) >>= lus
tar (a :- Atom 5 :- b) = tar (a :- b) >>= tis
\end{code}
*[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
\begin{code}
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)
tar (a :- Atom 7 :- b :- c) = tar (a :- Atom 2 :- b :- Atom 1 :- c)
tar (a :- Atom 8 :- b :- c) = tar (a :- Atom 7 :-
((Atom 7 :- (Atom 0 :- Atom 1) :- b) :-
Atom 0 :- Atom 1) :- c)
tar (a :- Atom 9 :- b :- c) = tar (a :- Atom 7 :- c :- Atom 2 :-
(Atom 0 :- Atom 1) :- Atom 0 :- b)
tar (a :- Atom 10 :- (b :- c) :- d) = tar (a :- Atom 8 :- c :- Atom 7 :-
(Atom 0 :- Atom 3) :- d)
tar (a :- Atom 10 :- b :- c) = tar (a :- c)
\end{code}
*a *a
> tar a = Left "*a"
\begin{code}
tar a = Left "*a"
\end{code}