% 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 CFLP.Data.Types ( > > Context(..), ID(..), label, > > ConsLabel(..), NormalForm(..), HeadNormalForm(..), Untyped, Nondet(..), > > freeVar, delayed, joinNondet > > ) where > > import Data.Supply > > import Control.Monad > > import CFLP.Control.Monad.Update > > newtype Context cs = Context cs > > newtype ID = ID (Supply Int) > > label :: ID -> Int > label (ID us) = supplyValue us The normal form of data is represented by the type `NormalForm` which defines a tree of constructors and logic variables or functions. > data NormalForm > = Data ConsLabel [NormalForm] > | Var Int > | Fun (NormalForm -> NormalForm) > > data ConsLabel = ConsLabel { index :: Int, name :: String } > > instance Show ConsLabel > where > showsPrec _ = (++) . name 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. > data HeadNormalForm cs m > = Cons ConsLabel [Untyped cs m] > | FreeVar ID (Untyped cs m) > | Delayed (Context cs -> m Bool) (Context cs -> Untyped cs m) > | Lambda (Untyped cs m -> Context cs -> ID -> Untyped cs m) > > type Untyped cs m = m (HeadNormalForm 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. > newtype Nondet cs m a = Typed { untyped :: Untyped cs m } 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. The function `freeVar` is used to put a name around a narrowed free variable. > freeVar :: Monad m => ID -> Nondet cs m a -> Nondet cs m a > freeVar u = Typed . return . FreeVar u . untyped 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! > delayed :: Monad m => (Context cs -> m Bool) -> (Context cs -> Nondet cs m a) > -> Nondet cs m a > delayed p resume = Typed . return . Delayed p $ (untyped . resume) The first parameter is a predicate on constraint stores that specifies whether the result of pattern matching the constructed delayed value is narrowed w.r.t. the current evaluation context. If it is not, pattern matching on it will be delayed again. The function `joinNondet` transforms a monadic action that yields a non-deterministic value into a single non-deterministic value by lifting the monad inside the newtype constructor. > joinNondet :: Monad m => m (Nondet c m a) -> Nondet c m a > joinNondet = Typed . join . liftM untyped `Show` Instances ---------------- > instance Show (HeadNormalForm cs []) > where > show (FreeVar (ID u) _) = '_':show (supplyValue u) > show (Delayed _ _) = "<delayed>" > show (Lambda _) = "<function>" > show (Cons label args) > | null args = show label > | otherwise = unwords (('(':show label):map show args++[")"]) > > 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 (Lambda _) = "<function>" > show (Cons label []) = show label > show (Cons label args) = > "("++show label++" "++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 _ (Fun _) = ("<function>"++) > showsPrec _ (Data label []) = shows label > showsPrec n x@(Data label args) > | Just xs <- fromList x = shows xs > | n == 0 = shows label . (' ':) . foldr1 (\y z -> y.(' ':).z) > (map (showsPrec 1) args) > | otherwise = ('(':) . shows x . (')':) > > fromList :: NormalForm -> Maybe [NormalForm] > fromList (Data label args) > | show label == "[]" = Just [] > | show label == "(:)", [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.