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# bit-stream

Lazy, infinite, compact stream of Bool with O(1) indexing.

 LTS Haskell 13.30: 0.1.0.2 Stackage Nightly 2019-01-07: 0.1.0.2 Latest on Hackage: 0.1.0.2

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#### Module documentation for 0.1.0.2

Depends on 4 packages(full list with versions):
Used by 1 package in lts-11.22(full list with versions):

# bit-stream

Lazy, infinite, compact stream of Bool with O(1) indexing. Most useful for memoization of predicates.

## Example 1

Consider following predicate:

isOdd :: Word -> Bool
isOdd 0 = False
isOdd n = not (isOdd (n - 1))

Its computation is expensive, so we’d like to memoize its values into BitStream using tabulate and access this stream via index instead of recalculation of isOdd:

isOddBS :: BitStream
isOddBS = tabulate isOdd

isOdd' :: Word -> Bool
isOdd' = index isOddBS

We can do even better by replacing part of recursive calls to isOdd by indexing memoized values. Write isOddF such that isOdd = fix isOddF:

isOddF :: (Word -> Bool) -> Word -> Bool
isOddF _ 0 = False
isOddF f n = not (f (n - 1))

and use tabulateFix:

isOddBS :: BitStream
isOddBS = tabulateFix isOddF

isOdd' :: Word -> Bool
isOdd' = index isOddBS

## Example 2

Define a predicate, which checks whether its argument is a prime number by trial division.

isPrime :: Word -> Bool
isPrime n
| n < 2     = False
| n < 4     = True
| even n    = False
| otherwise = and [ n `rem` d /= 0 | d <- [3, 5 .. ceiling (sqrt (fromIntegral n))], isPrime d]

Convert it to unfixed form:

isPrimeF :: (Word -> Bool) -> Word -> Bool
isPrimeF f n
| n < 2     = False
| n < 4     = True
| even n    = False
| otherwise = and [ n `rem` d /= 0 | d <- [3, 5 .. ceiling (sqrt (fromIntegral n))], f d]

Create its memoized version for faster evaluation:

isPrimeBS :: BitStream
isPrimeBS = tabulateFix isPrimeF

isPrime' :: Word -> Bool
isPrime' = index isPrimeBS