Deprecated

In favour of

bit-stream

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

https://github.com/Bodigrim/bit-stream#readme

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

See all snapshots bit-stream appears in

BSD-3-Clause licensed by Bodigrim
Maintained by [email protected]
This version can be pinned in stack with:bit-stream-0.1.0.2@sha256:ff350f6b6bc6810c70defed9bbab90d33651ebbf96d1e1545329118729dca4e8,2069

Module documentation for 0.1.0.2

Used by 1 package in nightly-2018-04-04(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