Control.Monad.Trans.Select

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

The Select monad

type Select r = SelectT r Identity

Selection monad.

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

Constructor for computations in the selection monad.

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

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

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 a

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

MonadTrans (SelectT r)

Defined in Control.Monad.Trans.Select

Methods

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

Monad m => Monad (SelectT r m)

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

Functor m => Functor (SelectT r m)

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

MonadFail m => MonadFail (SelectT r m)

Defined in Control.Monad.Trans.Select

Methods

fail :: String -> SelectT r m a

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

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

MonadIO m => MonadIO (SelectT r m)

Defined in Control.Monad.Trans.Select

Methods

liftIO :: IO a -> SelectT r m a

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

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]

MonadPlus m => MonadPlus (SelectT r m)

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

Generic (SelectT r m a)

Defined in Control.Monad.Trans.Select

Associated Types

type Rep (SelectT r m a) :: Type -> Type

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)

Defined in Control.Monad.Trans.Select

type Rep (SelectT r m a) = D1 ('MetaData "SelectT" "Control.Monad.Trans.Select" "transformers-0.6.0.2-3vZqekptSPoIT7uEdKk0Uz" '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

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

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 :: Monad m => SelectT r m a -> ContT r m a

Convert a selection computation to a continuation-passing computation.