Add preliminary Haddock docs

number.cabal

@@ -1,6 +1,6 @@
 name:                number
 version:             0.1.0.0
-synopsis:            A datatype for real numbers
+synopsis:            A library for real numbers
 description:
 
   Data.Number is an attempt to give an almost complete

src/Data/Number.hs

@@ -1,8 +1,15 @@
+-- | A library for real number arithmetics
 module Data.Number
-( module Data.Number.Types
-, module Data.Number.Functions
-, module Data.Number.Instances
-, Nat(..)
+( -- * Classes
+  Continued(..), Number
+, Nat(..), Whole(..)
+  -- * Functions
+, fromList, toList
+, fromNumber, toNumber
+  -- * Constants
+, σ, φ, π, e
+  -- * Internals
+, operator, cut
 ) where
 
 import Data.Number.Types

src/Data/Number/Functions.hs

@@ -1,3 +1,4 @@
+-- | Common functions and constants
 module Data.Number.Functions where
 
 import Data.Number.Types
@@ -8,10 +9,13 @@ import Data.Number.Peano
 
 -- Various --
 
+-- | Get the precision of a 'Number' (i.e. length)
 precision :: Number -> Nat
 precision E       = Z
 precision (_:|xs) = S (precision xs)
 
+-- | Alternative show function that pretty prints a 'Number'
+-- also doing conversions from Peano numbers
 show' :: Number -> String
 show' E           = "0"
 show' (x:|E)      = show (toInteger x)
@@ -21,10 +25,12 @@ show' (M (x:|xs)) = '-' : show (toInteger x) ++ " - 1/(" ++ show' xs ++ ")"
 
 -- Conversion --
 
+-- | Create a 'Number' from a list of naturals
 fromList :: [Nat] -> Number
 fromList []     = E
 fromList (x:xs) = x :| fromList xs
 
+-- | Convert a 'Number' to a list of naturals (losing the sign)
 toList :: Number -> [Nat]
 toList E = []
 toList (x:|xs) = x : toList xs
@@ -32,16 +38,28 @@ toList (x:|xs) = x : toList xs
 
 -- constants --
 
-φ :: Number
-φ = 1 :| φ
-
+-- | The infinite continued fraction whose terms are naturals numbers
+--
+-- \[0, 1, 2, 3, 4,...\] = 0.6977746...
 σ :: Number
 σ = σ' 0 where
   σ' n = n :| σ' (succ n)
 
+-- | The golden ratio
+--
+-- φ = (1 + √5)/2 = 1.6180339...
+φ :: Number
+φ = 1 :| φ
+
+-- | Pi: the ratio of a circle's circumference to its diameter
+--
+--  π = 3.1415926...
 π :: Number
 π = toNumber pi
 
+-- | Euler's number: the base of the natural logarithm
+--
+-- e = 2.7182818...
 e :: Number
 e = fmap a σ where 
   a n | p == 0    = 2*q

src/Data/Number/Instances.hs

@@ -1,3 +1,4 @@
+-- | Class instances for the continued fraction datatype
 {-# LANGUAGE TypeSynonymInstances, FlexibleInstances #-}
 
 module Data.Number.Instances where
@@ -5,21 +6,27 @@ module Data.Number.Instances where
 import Data.Number.Types
 import Data.Number.Internal
 
+-- | transform a number applying a function ('Nat' -> 'Nat') to each
+-- number preserving the sign.
 instance Functor Continued where
   fmap _ E       = E
   fmap f (M x)   = M (fmap f x)
   fmap f (x:|xs) = f x :| fmap f xs 
 
+-- | Basic Foldable instance implemented exactly as a list.
 instance Foldable Continued where
   foldr f z E       = z
   foldr f z (M x)   = foldr f z x
   foldr f z (x:|xs) = f x (foldr f z xs)
 
+-- | Same as above.
 instance Traversable Continued where
   traverse _ E       = pure E
   traverse f (M x)   = traverse f x
   traverse f (x:|xs) = (:|) <$> f x <*> traverse f xs 
 
+-- | The sign is given by the first number of the fraction.
+-- Other number are always considered positive.
 instance Num Number where
   (+) = operator (0, 1,  1, 0, 1, 0, 0, 0)
   (-) = operator (0, 1, -1, 0, 1, 0, 0, 0)
@@ -37,9 +44,11 @@ instance Num Number where
   signum (M _) = -1
   signum _     = 1
 
+-- | Allows conversion to a rational
 instance Real Number where
   toRational = fromNumber
 
+-- | Allows division between 'Number's and conversion from a rational
 instance Fractional Number where
   (/) = operator (0, 1, 0, 0, 0, 0, 1, 0)
   fromRational = toNumber
@@ -47,12 +56,14 @@ instance Fractional Number where
 
 -- Helpers --
 
+-- | Convert a 'Number' into a 'RealFrac' number
 fromNumber :: RealFrac a => Number -> a
 fromNumber E         = 0
 fromNumber (M x)     = negate (fromNumber x)
 fromNumber (x :| E)  = fromIntegral x
 fromNumber (x :| xs) = fromIntegral x + 1 / (fromNumber xs)
 
+-- | Convert a 'RealFrac' number into a 'Number'
 toNumber :: (Show a, RealFrac a) => a -> Number
 toNumber 0  = E
 toNumber x0

src/Data/Number/Internal.hs

@@ -1,3 +1,4 @@
+-- | Data.Number internals
 module Data.Number.Internal
 ( operator
 , cut
@@ -11,9 +12,17 @@ import Data.Number.Peano
 import Data.Ratio
 
 
+-- | Operator Matrix
 type Matrix = (Whole, Whole, Whole, Whole, Whole, Whole, Whole, Whole)
 
-
+-- | Continued fraction operator (implements Gosper's arithmetics)
+--
+-- Given two 'Number' @x@, @y@ and the operator matrix
+-- @\<a, b, c, d, e, f, g, h\>@
+-- calculates @z = (a + bx + cy + dxy) / (e + fx + gy + hxy)@
+--
+-- See <http://perl.plover.com/yak/cftalk/INFO/gosper.txt> for a complete
+-- explanation.
 operator :: Matrix -> Number -> Number -> Number
 operator c x y =
   case operator' c x y False of
@@ -43,6 +52,7 @@ operator' (a,b,c,d,e,f,g,h) x y end
       | otherwise           = abs (b%f - a%e) > abs (c%g - a%e)
 
 
+-- | Truncate a 'Number' to a given length @n@
 cut :: Nat -> Number -> Number
 cut _ E          = E
 cut n (M x)      = M (cut n x)
@@ -50,10 +60,14 @@ cut n _ | n <= 0 = E
 cut n (x :| xs)  = x :| cut (n-1) xs
 
 
+-- | Split a Number into a 'Whole' (the most significant of the fraction)
+-- and the rest of the Number. Equivalent to @(floor x, x - floor x)@
+-- for a floating point.
 split :: Number -> (Whole, Number)
 split x = (first x, rest x)
 
 
+-- | Extract the first natural of the fraction as a 'Whole' number
 first :: Number -> Whole
 first E          = 0
 first (M E)      = 0
@@ -61,6 +75,8 @@ first (M (x:|_)) = Whole x Neg
 first (x:|_)     = Whole x Pos
 
 
+-- | Extract the "tail" of a 'Number' as a new 'Number'
+-- Equivalent to @(x - floor x)@ for a floating point.
 rest :: Number -> Number
 rest E       = E
 rest (M E)   = E

src/Data/Number/Types.hs

@@ -1,9 +1,20 @@
+-- | Definition of the continued fraction type
 module Data.Number.Types where
 
 import Data.Number.Peano
 
-infixr 5 :|
-data Continued a =  M (Continued a) | a :| (Continued a) | E
+infixr 5 :| 
+-- | ==Continued fraction type
+-- represents a simple continued fraction of the form:
+-- @[a0, a1, a2,...] = a0 + 1\/(a1 + 1\/(a2 + 1\/...))@
+--
+-- == /Cons/ operator
+-- @n :| x @ equivalent to @n@ + 1/@x@
+data Continued a =
+  M (Continued a)      -- ^Negative number
+  | a :| (Continued a) -- ^Positive number
+  | E                  -- ^Zero
   deriving (Eq, Ord, Show, Read)
 
-type Number = Continued Nat
+-- | Real numbers datatype (a continued fraction of naturals)
+type Number = Continued Nat