{-# OPTIONS -fglasgow-exts #-} module Bits (tests) where {- This test exercices some oldies of generic programming, namely encoding terms as bit streams and decoding these bit streams in turn to obtain terms again. (This sort of function might actually be useful for serialisation and sending companies and other terms over the internet.) Here is how it works. A constuctor is encoded as a bit stream. To this end, we encode the index of the constructor as a binary number of a fixed length taking into account the maximum index for the type at hand. (Similarly, we could view the list of constructors as a binary tree, and then encode a constructor as the path to the constructor in this tree.) If there is just a single constructor, as for newtypes, for example, then the computed bit stream is empty. Otherwise we just recurse into subterms. Well, we need to handle basic datatypes in a special way. We observe such basic datatypes by testing the maximum index to be 0 for the datatype at hand. An efficient encoding should be tuned per basic datatype. The following solution is generic, but it wastes space. That is, we turn the basic value into a string relying on the general Data API. This string can now be encoded by first converting it into a list of bit streams at the term level, which can then be easily encoded as a single bit stream (because lists and bits can be encoded). -} import Test.HUnit import Data.Generics import Data.Char import Data.Maybe import Control.Monad import CompanyDatatypes ----------------------------------------------------------------------------- -- | We need bits and bit streams. data Bit = Zero | One deriving (Show, Eq, Typeable, Data) type Bin = [Bit] ----------------------------------------------------------------------------- -- Compute length of bit stream for a natural lengthNat :: Int -> Int lengthNat x = ceiling (logBase 2 (fromIntegral (x + 1))) -- Encode a natural as a bit stream varNat2bin :: Int -> Bin varNat2bin 0 = [] varNat2bin x = ( ( if even x then Zero else One ) : varNat2bin (x `div` 2) ) -- Encode a natural as a bit stream of fixed length fixedNat2bin :: Int -> Int -> Bin fixedNat2bin 0 0 = [] fixedNat2bin p x | p>0 = ( ( if even x then Zero else One ) : fixedNat2bin (p - 1) (x `div` 2) ) -- Decode a natural bin2nat :: Bin -> Int bin2nat [] = 0 bin2nat (Zero : bs) = 2 * (bin2nat bs) bin2nat (One : bs) = 2 * (bin2nat bs) + 1 ----------------------------------------------------------------------------- -- | Generically map terms to bit streams showBin :: Data t => t -> Bin showBin t = if isAlgType myDataType then con2bin ++ concat (gmapQ showBin t) else showBin base where -- The datatype for introspection myDataType = dataTypeOf t -- Obtain the maximum index for the type at hand max :: Int max = maxConstrIndex myDataType -- Obtain the index for the constructor at hand idx :: Int idx = constrIndex (toConstr t) -- Map basic values to strings, then to lists of bit streams base = map (varNat2bin . ord) (showConstr (toConstr t)) -- Map constructors to bit streams of fixed length con2bin = fixedNat2bin (lengthNat (max - 1)) (idx - 1) ----------------------------------------------------------------------------- -- | A monad on bit streams data ReadB a = ReadB (Bin -> (Maybe a, Bin)) unReadB (ReadB f) = f -- It's a monad. instance Monad ReadB where return a = ReadB (\bs -> (Just a, bs)) (ReadB c) >>= f = ReadB (\bs -> case c bs of (Just a, bs') -> unReadB (f a) bs' (Nothing, bs') -> (Nothing, bs') ) -- It's a bit monad with 0 and +. instance MonadPlus ReadB where mzero = ReadB (\bs -> (Nothing, bs)) (ReadB f) `mplus` (ReadB g) = ReadB (\bs -> case f bs of (Just a, bs') -> (Just a, bs') (Nothing, _) -> g bs ) -- Read a few bits readB :: Int -> ReadB Bin readB x = ReadB (\bs -> if length bs >= x then (Just (take x bs), drop x bs) else (Nothing, bs) ) ----------------------------------------------------------------------------- -- | Generically map bit streams to terms readBin :: Data t => ReadB t readBin = result where -- The worker, which we also use as type argument result = if isAlgType myDataType then do bin <- readB (lengthNat (max - 1)) fromConstrM readBin (bin2con bin) else do str <- readBin con <- str2con (map (chr . bin2nat) str) return (fromConstr con) -- Determine result type myDataType = dataTypeOf (getArg result) where getArg :: ReadB a -> a getArg = undefined -- Obtain the maximum index for the type at hand max :: Int max = maxConstrIndex myDataType -- Convert a bit stream into a constructor bin2con :: Bin -> Constr bin2con bin = indexConstr myDataType ((bin2nat bin) + 1) -- Convert string to constructor; could fail str2con :: String -> ReadB Constr str2con = maybe mzero return . readConstr myDataType ----------------------------------------------------------------------------- tests = ( showBin True , ( showBin [True] , ( showBin (1::Int) , ( showBin "1" , ( showBin genCom , ( geq genCom genCom' )))))) ~=? output where genCom' = fromJust (fst (unReadB readBin (showBin genCom))) :: Company output = 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