Peano numbers.

Lazy unary natural numbers.

peano - Lazy unary natural numbers

This package provides natural numbers in unary notation

data Peano
  = Zero
  | Succ Peano

implementing Num, Ord etc.

Purpose

One application is to check whether the length of a (potentially long) list is greater than a (small) number.

E.g., without optimization (-O 0),

genericLength (replicate (10 ^ 6) True) >= (5 :: Peano)

outperforms the same test for 5 :: Int by a factor of 10⁵, see benchmark:

  length
    Peano: OK
      450  ns ±  45 ns
    Int:   OK
      136  ms ± 4.1 ms