peano: Peano numbers

Lazy unary natural numbers.

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Versions [RSS]	0.1.0.0, 0.1.0.1, 0.1.0.2, 0.1.0.3
Change log	CHANGELOG.md
Dependencies	base (>=4.9 && <5) [details]
Tested with	ghc ==9.14.1, ghc ==9.12.2, ghc ==9.10.2, ghc ==9.8.4, ghc ==9.6.7, ghc ==9.4.8, ghc ==9.2.8, ghc ==9.0.2, ghc ==8.10.7, ghc ==8.8.4, ghc ==8.6.5, ghc ==8.4.4, ghc ==8.2.2, ghc ==8.0.2
License	BSD-3-Clause
Author	M Farkas-Dyck, Andreas Abel
Maintainer	Andreas Abel
Category	Data, Math
Source repo	head: git clone https://github.com/andreasabel/peano.hs
Uploaded	by AndreasAbel at 2025-09-02T06:32:45Z
Distributions	Arch:0.1.0.3, Fedora:0.1.0.2, LTSHaskell:0.1.0.3, NixOS:0.1.0.2, Stackage:0.1.0.3
Reverse Dependencies	11 direct, 14 indirect [details]
Downloads	4945 total (9 in the last 30 days)
Rating	(no votes yet) [estimated by Bayesian average]
Your Rating	λ λ λ
Status	Docs available [build log] Last success reported on 2025-09-02 [all 1 reports]

This package provides natural numbers in unary notation

data Peano
  = Zero
  | Succ Peano

implementing Num, Ord etc.

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