Control.Monad.Levels

This library provides an implementation of the MonadPlus type class that enumerates the levels of the search space and allows to implement breadth-first search.

The implementation is inspired by Mike Spivey and Silvija Seres: cf. Chapter 9 of the book 'The Fun of Programming'.

Warning: Levels is only a monad when the results of the enumeration functions are interpreted as a multiset, i.e., a valid transformation according to the monad laws may change the order of the results.

Documentation

data Levels a

Non-Deterministic computations of type Levels a can be searched level-wise.

Instances

Monad Levels

MonadPlus Levels

levels :: Levels a -> [[a]]

The function levels yields the results of a non-deterministic computation grouped in levels.

breadthFirstSearch :: Levels a -> [a]

The function breadthFirstSearch enumerates the results of a non-deterministic computation in breadth-first order.

data DepthBound a

The type DepthBound represents computations with a bounded depth. It's monad instances implements iterative deepening.

Instances

Monad DepthBound

MonadPlus DepthBound

iterLevels :: DepthBound a -> Levels a

The function iterLevels computes the levels of a depth bound computation using iterative deepening.

iterativeDeepening :: DepthBound a -> [a]

The function iterativeDeepening enumerates the results of a non-deterministic computations using iterative deepening.

diagonals :: [[a]] -> [[a]]

The function diagonals enumarates the entries of a matrix diagonally. The matrix may contain an infinite number of infinite rows.