successors-0.1.0.3: An applicative functor to manage successors
Copyright© Joachim Breitner 2017
LicenseMIT
Maintainermail@joachim-breitner.de
Safe HaskellSafe-Inferred
LanguageHaskell2010

Control.Applicative.Successors

Description

A value of type Succs a represents a step in a graph with nodes of type a, or in other words, a node plus the list of its successors.

The Applicative instance for Succs a is such that the node represented by a <*> b is the application of the node of a applied to the node of b, and (more importantly) the successors modeled by a <*> b are the node of a applied to the succesors of b in addition to the succesors of a applied to the node of b. This way, at most one step is taken.

>>> (++) <$> Succs "0" ["1","2"] <*> Succs "A" ["B","C"]
Succs "0A" ["1A","2A","0B", "0C"]
>>> skip x = Succs [x] [[]]
>>> getSuccs $ (concat <$> traverse skip "Hello")
["ello","Hllo","Helo","Helo","Hell"]

This applicative functor can be useful to define shrink functions for QuickCheck, using the helper

shrinkSuccs x = Succs x (shrink x)

as explained in a StackExchange answer.

Synopsis

Documentation

data Succs a Source #

Constructors

Succs a [a] 

Instances

Instances details
Monad Succs Source # 
Instance details

Defined in Control.Applicative.Successors

Methods

(>>=) :: Succs a -> (a -> Succs b) -> Succs b #

(>>) :: Succs a -> Succs b -> Succs b #

return :: a -> Succs a #

Functor Succs Source # 
Instance details

Defined in Control.Applicative.Successors

Methods

fmap :: (a -> b) -> Succs a -> Succs b #

(<$) :: a -> Succs b -> Succs a #

Applicative Succs Source # 
Instance details

Defined in Control.Applicative.Successors

Methods

pure :: a -> Succs a #

(<*>) :: Succs (a -> b) -> Succs a -> Succs b #

liftA2 :: (a -> b -> c) -> Succs a -> Succs b -> Succs c #

(*>) :: Succs a -> Succs b -> Succs b #

(<*) :: Succs a -> Succs b -> Succs a #

Eq a => Eq (Succs a) Source # 
Instance details

Defined in Control.Applicative.Successors

Methods

(==) :: Succs a -> Succs a -> Bool #

(/=) :: Succs a -> Succs a -> Bool #

Show a => Show (Succs a) Source # 
Instance details

Defined in Control.Applicative.Successors

Methods

showsPrec :: Int -> Succs a -> ShowS #

show :: Succs a -> String #

showList :: [Succs a] -> ShowS #

getCurrent :: Succs t -> t Source #

Returns the represented node

Properties:

getCurrent (pure x)  == x
getCurrent (f <*> x) == (getCurrent f) (getCurrent x)
getCurrent (x >>= k) == getCurrent (k (getCurrent x))

getSuccs :: Succs t -> [t] Source #

Returns the represented successors

getSuccs (pure x)  == []
getSuccs (f <*> x) == map ($ getCurrent x) (getSuccs f) ++ map (getCurrent f) (getSuccs x)
getSuccs (x >>= k) == map (getCurrent . k) (getSuccs x) ++ getSuccs k (getCurrent x)