% Basic Types for Lazy Non-Deterministic Data % Sebastian Fischer (sebf@informatik.uni-kiel.de) This module defines the basic types to represent lazy non-deterministic data.
> {-# LANGUAGE
>       PatternGuards,
>       FlexibleInstances
>   #-}
>
> module Data.LazyNondet.Types (
>
>   ID(..), NormalForm(..), HeadNormalForm(..), Untyped, Nondet(..),
>
>   mkHNF, freeVar, delayed
>
> ) where
>
> import Data.Data
>
> import Control.Monad.Update
>
> import Data.Supply
>
> newtype ID = ID (Supply Int)
>
> data NormalForm = NormalForm Constr [NormalForm] | Var Int
The normal form of data is represented by the type `NormalForm` which defines a tree of constructors and logic variables. The type `Constr` is a representation of constructors defined in the `Data.Generics` package. With generic programming we can convert between Haskell data types and the `NormalForm` type.
> data HeadNormalForm cs m
>   = Cons DataType ConIndex [Untyped cs m]
>   | FreeVar ID (Untyped cs m)
>   | Delayed (cs -> Bool) (cs -> Untyped cs m)
>
> type Untyped cs m = m (HeadNormalForm cs m)
Data in lazy functional-logic programs is evaluated on demand. The evaluation of arguments of a constructor may lead to different non-deterministic results. Hence, we use a monad around every constructor in the head-normal form of a value.
> newtype Nondet cs m a = Typed { untyped :: Untyped cs m }
Untyped non-deterministic data can be phantom typed in order to define logic variables by overloading. The phantom type must be the Haskell data type that should be used for conversion into primitive data.
> mkHNF :: Constr -> [Untyped cs m] -> HeadNormalForm cs m
> mkHNF c = Cons (constrType c) (constrIndex c)
In head-normal forms we split the constructor representation into a representation of the data type and the index of the constructor, to enable pattern matching on the index. Free (logic) variables are represented by `FreeVar u x` where `u` is a uniqe identifier and `x` represents the result of narrowing the variable according to the constraint store passed to the operation that creates the variable.
> freeVar :: Monad m => ID -> Nondet cs m a -> Nondet cs m a
> freeVar u = Typed . return . FreeVar u . untyped
The function `freeVar` is used to put a name around a narrowed free variable.
> delayed :: Monad m => (cs -> Bool) -> (cs -> Nondet cs m a) -> Nondet cs m a
> delayed p resume = Typed . return . Delayed p $ (untyped . resume)
With `delayed` computations can be delayed to be reexecuted with the current constraint store whenever they are demanded. This is useful to avoid unessary branching when narrowing logic variables. Use with care: `delayed` intentionally destroys sharing! The first parameter is a predicate on constraint stores that specifies whether the result of pattern matching the constructed delayed value should be delayed again. `Show` Instances ----------------
> instance Show (HeadNormalForm cs [])
>  where
>   show (FreeVar (ID u) _) = '_':show (supplyValue u)
>   show (Delayed _ _) = "<delayed>"
>   show (Cons typ idx args) 
>     | null args = show con
>     | otherwise = unwords (('(':show con):map show args++[")"])
>    where con = indexConstr typ idx
>
> instance Show (Nondet cs [] a)
>  where
>   show = show . untyped
>
> instance Show (Nondet cs (UpdateT cs []) a)
>  where
>   show = show . untyped
>
> instance Show (HeadNormalForm cs (UpdateT cs []))
>  where
>   show (FreeVar (ID u) _)  = '_':show (supplyValue u)
>   show (Delayed _ _)         = "<delayed>"
>   show (Cons typ idx [])   = show (indexConstr typ idx)
>   show (Cons typ idx args) =
>     "("++show (indexConstr typ idx)++" "++unwords (map show args)++")" 
To simplify debugging, we provide `Show` instances for head-normal forms and non-deterministic values.
> instance Show NormalForm
>  where
>   showsPrec _ (Var u) = ('_':) . shows u
>   showsPrec _ (NormalForm cons []) = shows cons
>   showsPrec n x@(NormalForm cons args)
>     | Just xs <- fromList x = shows xs
>     | n == 0 = shows cons . (' ':) . foldr1 (\y z -> y.(' ':).z)
>                 (map (showsPrec 1) args)
>     | otherwise = ('(':) . shows x . (')':)
>
> fromList :: NormalForm -> Maybe [NormalForm]
> fromList (NormalForm cons args)
>   | show cons == "[]" = Just []
>   | show cons == "(:)", [x,l] <- args, Just xs <- fromList l = Just (x:xs)
> fromList _ = Nothing
For normal forms we provide a custum `Show` instance because we want to use it to print partial values in the evaluator.