Copyright	(c) Ross Paterson 2017
License	BSD-style (see the file LICENSE)
Maintainer	R.Paterson@city.ac.uk
Stability	experimental
Portability	portable
Safe Haskell	Safe
Language	Haskell2010

Control.Monad.Trans.Select

Contents

The Select monad
The SelectT monad transformer
Monad transformation

Description

Selection monad transformer, modelling search algorithms.

Martin Escardo and Paulo Oliva. "Selection functions, bar recursion and backward induction", Mathematical Structures in Computer Science 20:2 (2010), pp. 127-168. https://www.cs.bham.ac.uk/~mhe/papers/selection-escardo-oliva.pdf
Jules Hedges. "Monad transformers for backtracking search". In Proceedings of MSFP 2014. https://arxiv.org/abs/1406.2058

Synopsis

type Select r = SelectT r Identity
select :: ((a -> r) -> a) -> Select r a
runSelect :: Select r a -> (a -> r) -> a
mapSelect :: (a -> a) -> Select r a -> Select r a
newtype SelectT r (m :: Type -> Type) a = SelectT ((a -> m r) -> m a)
runSelectT :: SelectT r m a -> (a -> m r) -> m a
mapSelectT :: (m a -> m a) -> SelectT r m a -> SelectT r m a
selectToContT :: forall (m :: Type -> Type) r a. Monad m => SelectT r m a -> ContT r m a

The Select monad

type Select r = SelectT r Identity Source #

Selection monad.

select :: ((a -> r) -> a) -> Select r a Source #

Constructor for computations in the selection monad.

runSelect :: Select r a -> (a -> r) -> a Source #

Runs a Select computation with a function for evaluating answers to select a particular answer. (The inverse of select.)

mapSelect :: (a -> a) -> Select r a -> Select r a Source #

Apply a function to transform the result of a selection computation.

runSelect (mapSelect f m) = f . runSelect m

The SelectT monad transformer

newtype SelectT r (m :: Type -> Type) a Source #

Selection monad transformer.

SelectT is not a functor on the category of monads, and many operations cannot be lifted through it.

Constructors

SelectT ((a -> m r) -> m a)

Instances

Instances details

MonadTrans (SelectT r) Source #

Instance details

Defined in Control.Monad.Trans.Select

Methods

lift :: Monad m => m a -> SelectT r m a Source #

MonadIO m => MonadIO (SelectT r m) Source #

Instance details

Defined in Control.Monad.Trans.Select

Methods

liftIO :: IO a -> SelectT r m a Source #

(Functor m, MonadPlus m) => Alternative (SelectT r m) Source #

Instance details

Defined in Control.Monad.Trans.Select

Methods

empty :: SelectT r m a #

(<|>) :: SelectT r m a -> SelectT r m a -> SelectT r m a #

some :: SelectT r m a -> SelectT r m [a] #

many :: SelectT r m a -> SelectT r m [a] #

(Functor m, Monad m) => Applicative (SelectT r m) Source #

Instance details

Defined in Control.Monad.Trans.Select

Methods

pure :: a -> SelectT r m a #

(<*>) :: SelectT r m (a -> b) -> SelectT r m a -> SelectT r m b #

liftA2 :: (a -> b -> c) -> SelectT r m a -> SelectT r m b -> SelectT r m c #

(*>) :: SelectT r m a -> SelectT r m b -> SelectT r m b #

(<*) :: SelectT r m a -> SelectT r m b -> SelectT r m a #

Functor m => Functor (SelectT r m) Source #

Instance details

Defined in Control.Monad.Trans.Select

Methods

fmap :: (a -> b) -> SelectT r m a -> SelectT r m b #

(<$) :: a -> SelectT r m b -> SelectT r m a #

Monad m => Monad (SelectT r m) Source #

Instance details

Defined in Control.Monad.Trans.Select

Methods

(>>=) :: SelectT r m a -> (a -> SelectT r m b) -> SelectT r m b #

(>>) :: SelectT r m a -> SelectT r m b -> SelectT r m b #

return :: a -> SelectT r m a #

MonadPlus m => MonadPlus (SelectT r m) Source #

Instance details

Defined in Control.Monad.Trans.Select

Methods

mzero :: SelectT r m a #

mplus :: SelectT r m a -> SelectT r m a -> SelectT r m a #

MonadFail m => MonadFail (SelectT r m) Source #

Instance details

Defined in Control.Monad.Trans.Select

Methods

fail :: String -> SelectT r m a #

Generic (SelectT r m a) Source #

Instance details

Defined in Control.Monad.Trans.Select

Associated Types

type Rep (SelectT r m a)
Instance details Defined in Control.Monad.Trans.Select type Rep (SelectT r m a) = D1 ('MetaData "SelectT" "Control.Monad.Trans.Select" "transformers-0.6.1.1-2aba" 'True) (C1 ('MetaCons "SelectT" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 ((a -> m r) -> m a))))

Methods

from :: SelectT r m a -> Rep (SelectT r m a) x #

to :: Rep (SelectT r m a) x -> SelectT r m a #

type Rep (SelectT r m a) Source #

Instance details

Defined in Control.Monad.Trans.Select

type Rep (SelectT r m a) = D1 ('MetaData "SelectT" "Control.Monad.Trans.Select" "transformers-0.6.1.1-2aba" 'True) (C1 ('MetaCons "SelectT" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 ((a -> m r) -> m a))))

runSelectT :: SelectT r m a -> (a -> m r) -> m a Source #

Runs a SelectT computation with a function for evaluating answers to select a particular answer. (The inverse of select.)

mapSelectT :: (m a -> m a) -> SelectT r m a -> SelectT r m a Source #

Apply a function to transform the result of a selection computation. This has a more restricted type than the map operations for other monad transformers, because SelectT does not define a functor in the category of monads.

runSelectT (mapSelectT f m) = f . runSelectT m

Monad transformation

selectToContT :: forall (m :: Type -> Type) r a. Monad m => SelectT r m a -> ContT r m a Source #

Convert a selection computation to a continuation-passing computation.