1{-# OPTIONS -fglasgow-exts #-} 2 3module Bits (tests) where 4 5{- 6 7This test exercices some oldies of generic programming, namely 8encoding terms as bit streams and decoding these bit streams in turn 9to obtain terms again. (This sort of function might actually be useful 10for serialisation and sending companies and other terms over the 11internet.) 12 13Here is how it works. 14 15A constuctor is encoded as a bit stream. To this end, we encode the 16index of the constructor as a binary number of a fixed length taking 17into account the maximum index for the type at hand. (Similarly, we 18could view the list of constructors as a binary tree, and then encode 19a constructor as the path to the constructor in this tree.) If there 20is just a single constructor, as for newtypes, for example, then the 21computed bit stream is empty. 22 23Otherwise we just recurse into subterms. 24 25Well, we need to handle basic datatypes in a special way. We observe 26such basic datatypes by testing the maximum index to be 0 for the 27datatype at hand. An efficient encoding should be tuned per basic 28datatype. The following solution is generic, but it wastes space. 29That is, we turn the basic value into a string relying on the general 30Data API. This string can now be encoded by first converting it into a 31list of bit streams at the term level, which can then be easily 32encoded as a single bit stream (because lists and bits can be 33encoded). 34 35-} 36 37import Test.HUnit 38 39import Data.Generics 40import Data.Char 41import Data.Maybe 42import Control.Applicative (Alternative(..), Applicative(..)) 43import Control.Monad 44import CompanyDatatypes 45 46 47 48----------------------------------------------------------------------------- 49 50 51 52-- | We need bits and bit streams. 53data Bit = Zero | One deriving (Show, Eq, Typeable, Data) 54type Bin = [Bit] 55 56 57 58----------------------------------------------------------------------------- 59 60 61 62-- Compute length of bit stream for a natural 63lengthNat :: Int -> Int 64lengthNat x = ceiling (logBase 2 (fromIntegral (x + 1))) 65 66 67-- Encode a natural as a bit stream 68varNat2bin :: Int -> Bin 69varNat2bin 0 = [] 70varNat2bin x = 71 ( ( if even x then Zero else One ) 72 : varNat2bin (x `div` 2) 73 ) 74 75 76-- Encode a natural as a bit stream of fixed length 77fixedNat2bin :: Int -> Int -> Bin 78fixedNat2bin 0 0 = [] 79fixedNat2bin p x | p>0 = 80 ( ( if even x then Zero else One ) 81 : fixedNat2bin (p - 1) (x `div` 2) 82 ) 83 84 85-- Decode a natural 86bin2nat :: Bin -> Int 87bin2nat [] = 0 88bin2nat (Zero : bs) = 2 * (bin2nat bs) 89bin2nat (One : bs) = 2 * (bin2nat bs) + 1 90 91 92 93----------------------------------------------------------------------------- 94 95 96 97-- | Generically map terms to bit streams 98showBin :: Data t => t -> Bin 99 100showBin t 101 = if isAlgType myDataType 102 then con2bin ++ concat (gmapQ showBin t) 103 else showBin base 104 105 where 106 107 -- The datatype for introspection 108 myDataType = dataTypeOf t 109 110 -- Obtain the maximum index for the type at hand 111 max :: Int 112 max = maxConstrIndex myDataType 113 114 -- Obtain the index for the constructor at hand 115 idx :: Int 116 idx = constrIndex (toConstr t) 117 118 -- Map basic values to strings, then to lists of bit streams 119 base = map (varNat2bin . ord) (showConstr (toConstr t)) 120 121 -- Map constructors to bit streams of fixed length 122 con2bin = fixedNat2bin (lengthNat (max - 1)) (idx - 1) 123 124 125----------------------------------------------------------------------------- 126 127 128 129-- | A monad on bit streams 130data ReadB a = ReadB (Bin -> (Maybe a, Bin)) 131unReadB (ReadB f) = f 132 133instance Functor ReadB where 134 fmap = liftM 135 136instance Applicative ReadB where 137 pure = return 138 (<*>) = ap 139 140instance Alternative ReadB where 141 (<|>) = mplus 142 empty = mzero 143 144-- It's a monad. 145instance Monad ReadB where 146 return a = ReadB (\bs -> (Just a, bs)) 147 (ReadB c) >>= f = ReadB (\bs -> case c bs of 148 (Just a, bs') -> unReadB (f a) bs' 149 (Nothing, bs') -> (Nothing, bs') 150 ) 151 152 153-- It's a bit monad with 0 and +. 154instance MonadPlus ReadB where 155 mzero = ReadB (\bs -> (Nothing, bs)) 156 (ReadB f) `mplus` (ReadB g) = ReadB (\bs -> case f bs of 157 (Just a, bs') -> (Just a, bs') 158 (Nothing, _) -> g bs 159 ) 160 161 162-- Read a few bits 163readB :: Int -> ReadB Bin 164readB x = ReadB (\bs -> if length bs >= x 165 then (Just (take x bs), drop x bs) 166 else (Nothing, bs) 167 ) 168 169 170 171----------------------------------------------------------------------------- 172 173 174 175-- | Generically map bit streams to terms 176readBin :: Data t => ReadB t 177readBin = result 178 where 179 180 -- The worker, which we also use as type argument 181 result = if isAlgType myDataType 182 183 then do bin <- readB (lengthNat (max - 1)) 184 fromConstrM readBin (bin2con bin) 185 186 else do str <- readBin 187 con <- str2con (map (chr . bin2nat) str) 188 return (fromConstr con) 189 190 -- Determine result type 191 myDataType = dataTypeOf (getArg result) 192 where 193 getArg :: ReadB a -> a 194 getArg = undefined 195 196 -- Obtain the maximum index for the type at hand 197 max :: Int 198 max = maxConstrIndex myDataType 199 200 -- Convert a bit stream into a constructor 201 bin2con :: Bin -> Constr 202 bin2con bin = indexConstr myDataType ((bin2nat bin) + 1) 203 204 -- Convert string to constructor; could fail 205 str2con :: String -> ReadB Constr 206 str2con = maybe mzero return 207 . readConstr myDataType 208 209 210 211----------------------------------------------------------------------------- 212 213 214 215tests = ( showBin True 216 , ( showBin [True] 217 , ( showBin (1::Int) 218 , ( showBin "1" 219 , ( showBin genCom 220 , ( geq genCom genCom' 221 )))))) ~=? output 222 where 223 genCom' = fromJust (fst (unReadB readBin (showBin genCom))) :: Company 224 225output = 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226