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 = ([One],([One,One,Zero],([One,One,One,One,Zero,One,Zero,One,Zero,One,One,One,One,Zero,Zero],([One,One,One,One,One,One,One,One,One,Zero,One,Zero,One,One,Zero,One,One,One,One,Zero,One,Zero,One,Zero,One,One,One,One,Zero,One,One,One,One,One,One,One,One,Zero,One,Zero,One,One,Zero,Zero,Zero],([One,One,One,One,One,One,One,One,One,One,Zero,One,Zero,One,One,Zero,One,One,Zero,One,One,One,Zero,One,Zero,One,One,One,Zero,One,One,Zero,One,One,One,One,One,One,One,One,Zero,One,Zero,One,One,Zero,Zero,One,One,One,One,One,One,One,One,One,Zero,One,Zero,One,One,Zero,One,One,One,One,Zero,One,One,One,Zero,One,Zero,One,One,One,One,Zero,One,One,One,One,One,One,One,One,Zero,One,Zero,One,One,Zero,Zero,One,One,One,One,One,One,One,One,One,Zero,One,Zero,One,One,Zero,One,One,One,One,One,One,Zero,One,Zero,One,One,One,One,One,One,Zero,One,One,One,One,One,One,One,One,Zero,One,Zero,One,One,Zero,Zero,One,One,One,One,One,One,One,One,One,Zero,One,Zero,One,One,Zero,One,One,One,One,Zero,One,One,One,Zero,One,Zero,One,One,One,One,Zero,One,One,One,One,One,One,One,One,Zero,One,Zero,One,One,Zero,Zero,One,One,One,One,One,One,One,One,One,Zero,One,Zero,One,One,Zero,One,One,One,One,Zero,One,Zero,One,Zero,One,Zero,One,One,One,One,Zero,One,One,One,One,One,One,One,One,Zero,One,Zero,One,One,Zero,Zero,One,One,One,One,One,One,One,One,One,Zero,One,Zero,One,One,Zero,One,One,Zero,One,One,One,Zero,One,Zero,One,One,One,One,One,One,Zero,One,One,One,One,One,One,One,One,Zero,One,Zero,One,One,Zero,Zero,One,One,One,One,One,One,One,One,One,Zero,One,Zero,One,One,Zero,One,One,One,One,One,One,Zero,One,Zero,One,Zero,One,One,One,One,Zero,One,One,One,One,One,One,One,One,Zero,One,Zero,One,One,Zero,Zero,One,One,One,One,One,One,One,One,One,Zero,One,Zero,One,One,Zero,One,One,Zero,One,Zero,One,Zero,One,One,One,Zero,One,One,One,One,Zero,One,One,One,One,One,One,One,One,Zero,One,Zero,One,One,Zero,Zero,Zero,One,One,One,One,One,One,One,One,One,Zero,One,Zero,One,One,Zero,One,One,Zero,One,Zero,One,One,One,One,One,Zero,One,Zero,One,One,Zero,One,One,One,One,One,One,One,One,Zero,One,Zero,One,One,Zero,Zero,One,One,One,One,One,One,One,One,One,Zero,One,Zero,One,One,Zero,One,One,One,One,Zero,One,Zero,One,Zero,One,Zero,One,One,One,One,Zero,One,One,One,One,One,One,One,One,Zero,One,Zero,One,One,Zero,Zero,One,One,One,One,One,One,One,One,One,Zero,One,Zero,One,One,Zero,One,One,One,One,Zero,One,One,One,Zero,One,Zero,One,One,One,One,Zero,One,One,One,One,One,One,One,One,Zero,One,Zero,One,One,Zero,Zero,One,One,One,One,One,One,One,One,One,Zero,One,Zero,One,One,Zero,One,One,One,One,Zero,One,One,One,One,One,Zero,One,One,One,One,Zero,One,One,One,One,One,One,One,One,Zero,One,Zero,One,One,Zero,Zero,One,One,One,One,One,One,One,One,One,Zero,One,Zero,One,One,Zero,One,One,One,One,Zero,One,One,One,One,One,Zero,One,One,One,One,Zero,One,One,One,One,One,One,One,One,Zero,One,Zero,One,One,Zero,Zero,One,One,One,One,One,One,One,One,One,Zero,One,Zero,One,One,Zero,One,One,One,One,Zero,One,One,One,Zero,One,Zero,One,One,One,One,Zero,One,One,One,One,One,One,One,One,Zero,One,Zero,One,One,Zero,Zero,One,One,One,One,One,One,One,One,One,Zero,One,Zero,One,One,Zero,One,One,Zero,One,Zero,One,One,One,One,One,Zero,One,One,One,One,Zero,One,One,One,One,One,One,One,One,Zero,One,Zero,One,One,Zero,Zero,Zero,One,One,One,One,One,One,One,One,One,Zero,One,Zero,One,One,Zero,One,One,One,One,Zero,One,Zero,One,Zero,One,Zero,One,Zero,One,One,Zero,One,One,One,One,One,One,One,One,Zero,One,Zero,One,One,Zero,Zero,One,One,One,One,One,One,One,One,One,Zero,One,Zero,One,One,Zero,One,One,One,One,Zero,One,One,One,One,One,Zero,One,One,One,One,Zero,One,One,One,One,One,One,One,One,Zero,One,Zero,One,One,Zero,Zero,One,One,One,One,One,One,One,One,One,Zero,One,Zero,One,One,Zero,One,One,One,One,One,One,Zero,One,Zero,One,One,One,One,One,One,Zero,One,One,One,One,One,One,One,One,Zero,One,Zero,One,One,Zero,Zero,One,One,One,One,One,One,One,One,One,Zero,One,Zero,One,One,Zero,One,One,Zero,One,Zero,One,One,One,Zero,One,One,One,One,One,One,Zero,One,One,One,One,One,One,One,One,Zero,One,Zero,One,One,Zero,Zero,One,One,One,One,One,One,One,One,One,Zero,One,Zero,One,One,Zero,One,One,One,One,Zero,One,One,One,Zero,One,Zero,One,One,One,One,Zero,One,One,One,One,One,One,One,One,Zero,One,Zero,One,One,Zero,Zero,One,One,One,One,One,One,One,One,One,Zero,One,Zero,One,One,Zero,One,One,Zero,One,One,One,Zero,One,Zero,One,One,One,One,One,One,Zero,One,One,One,One,One,One,One,One,Zero,One,Zero,One,One,Zero,Zero,One,One,One,One,One,One,One,One,One,Zero,One,Zero,One,One,Zero,One,One,Zero,One,Zero,One,One,One,Zero,One,Zero,One,One,One,One,Zero,One,One,One,One,One,One,One,One,Zero,One,Zero,One,One,Zero,Zero,One,One,One,One,One,One,One,One,One,Zero,One,Zero,One,One,Zero,One,One,One,One,Zero,One,Zero,One,Zero,One,Zero,One,One,One,One,Zero,One,One,One,One,One,One,One,One,Zero,One,Zero,One,One,Zero,Zero,One,One,One,One,One,One,One,One,One,Zero,One,Zero,One,One,Zero,One,One,One,One,Zero,One,One,One,One,One,Zero,One,One,One,One,Zero,One,One,One,One,One,One,One,One,Zero,One,Zero,One,One,Zero,Zero,Zero,One,One,Ze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226