Safe Haskell | Safe |
---|---|

Language | Haskell2010 |

## Synopsis

- iterWhile :: (b -> Bool) -> (a -> (b, a)) -> a -> [(b, a)]
- repeatWhile :: (a -> (Bool, a)) -> a -> a
- repeatWhileM :: Monad m => (a -> m (Bool, a)) -> a -> m a
- trampolineWhile :: (a -> (Bool, a)) -> a -> a
- trampolineWhileM :: Monad m => (a -> m (Bool, a)) -> a -> m a
- trampoline :: (a -> Either b a) -> a -> b
- trampolineM :: Monad m => (a -> m (Either b a)) -> a -> m b
- iterateUntil :: (a -> a -> Bool) -> (a -> a) -> a -> a
- iterateUntilM :: Monad m => (a -> a -> Bool) -> (a -> m a) -> a -> m a
- iterate' :: Integral i => i -> (a -> a) -> a -> a
- applyWhen :: Bool -> (a -> a) -> a -> a
- applyUnless :: Bool -> (a -> a) -> a -> a
- applyWhenM :: Monad m => m Bool -> (m a -> m a) -> m a -> m a
- applyUnlessM :: Monad m => m Bool -> (m a -> m a) -> m a -> m a

# Documentation

iterWhile :: (b -> Bool) -> (a -> (b, a)) -> a -> [(b, a)] Source #

Repeat a state transition `f :: a -> (b, a)`

with output `b`

while condition `cond`

on the output is true.
Return all intermediate results and the final result
where `cond`

is `False`

.

Postconditions (when it terminates):
`fst (last (iterWhile cond f a)) == False`

.
`all fst (init (interWhile cond f a))`

.

repeatWhile :: (a -> (Bool, a)) -> a -> a Source #

Repeat something while a condition on some state is true. Return the last state (including the changes of the last transition, even if the condition became false then).

repeatWhileM :: Monad m => (a -> m (Bool, a)) -> a -> m a Source #

Monadic version of `repeatWhile`

.

trampolineWhile :: (a -> (Bool, a)) -> a -> a Source #

A version of the trampoline function.

The usual function iterates `f :: a -> Maybe a`

as long
as `Just{}`

is returned, and returns the last value of `a`

upon `Nothing`

.

`usualTrampoline f = trampolineWhile $ a -> maybe (False,a) (True,) (f a)`

.

`trampolineWhile`

is very similar to `repeatWhile`

, only that
it discards the state on which the condition went `False`

,
and returns the last state on which the condition was `True`

.

trampolineWhileM :: Monad m => (a -> m (Bool, a)) -> a -> m a Source #

Monadic version of `trampolineWhile`

.

trampoline :: (a -> Either b a) -> a -> b Source #

More general trampoline, which allows some final computation
from iteration state `a`

into result type `b`

.

trampolineM :: Monad m => (a -> m (Either b a)) -> a -> m b Source #

Monadic version of `trampoline`

.

iterateUntil :: (a -> a -> Bool) -> (a -> a) -> a -> a Source #

Iteration to fixed-point.

`iterateUntil r f a0`

iterates endofunction `f`

, starting with `a0`

,
until `r`

relates its result to its input, i.e., `f a `

.`r`

a

This is the generic pattern behind saturation algorithms.

If `f`

is monotone with regard to `r`

,
meaning `a `

implies `r`

b`f a `

,
and `r`

f b`f`

-chains starting with `a0`

are finite
then iteration is guaranteed to terminate.

A typical instance will work on sets, and `r`

could be set inclusion,
and `a0`

the empty set, and `f`

the step function of a saturation algorithm.

iterateUntilM :: Monad m => (a -> a -> Bool) -> (a -> m a) -> a -> m a Source #

Monadic version of `iterateUntil`

.

iterate' :: Integral i => i -> (a -> a) -> a -> a Source #

applies `iterate'`

n f x`f`

to `x`

`n`

times and returns the
result.

The applications are calculated strictly.

# Iteration over Booleans.

applyUnless :: Bool -> (a -> a) -> a -> a Source #

`applyUnless b f a`

applies `f`

to `a`

unless `b`

.

applyWhenM :: Monad m => m Bool -> (m a -> m a) -> m a -> m a Source #

Monadic version of `applyWhen`

applyUnlessM :: Monad m => m Bool -> (m a -> m a) -> m a -> m a Source #

Monadic version of `applyUnless`