natural

Safe natural number, positive integer, and non-zero integer types with lens integration.

Types

Each type has corresponding newtype wrappers for alternative semigroups:

Optics

The library uses lens for type-safe conversions:

-- Prisms for safe construction from integral types
(5 :: Integer) ^? _Natural   -- Just (Natural 5)
(-1 :: Integer) ^? _Natural  -- Nothing

(3 :: Integer) ^? _Positive  -- Just (Positive 3)
(0 :: Integer) ^? _Positive  -- Nothing

(7 :: Integer) ^? _NotZero   -- Just (NotZero True (Positive 7))
(0 :: Integer) ^? _NotZero   -- Nothing

-- Structural prisms
Natural 5 ^? successor       -- Just (Natural 4)
Natural 0 ^? successor       -- Nothing

Positive 3 ^? successor1     -- Just (Positive 2)
Positive 1 ^? successor1     -- Nothing

-- Isos between related types
Natural 4 ^. successorW      -- Positive 5
Natural 3 ^. naturalPositive -- Just (Positive 3)
Natural 3 ^. list            -- [(), (), ()]

Type classes

Each type has Has* (lens) and As* (prism) classes with instances for standard integral types (Int, Integer, Word, Const, Identity):

class HasNatural a where
  natural :: Lens' a Natural

class AsNatural a where
  _Natural :: Prism' a Natural

NotZero

A non-zero integer represented as a sign (Bool: True = positive) and a magnitude (Positive):

data NotZero = NotZero Bool Positive

positiveNotZero (Positive 5)  -- NotZero True (Positive 5)
negativeNotZero (Positive 3)  -- NotZero False (Positive 3)
notZeroInteger (NotZero False (Positive 3))  -- -3

-- Multiplication is always total
multiplyNZ (NotZero False (Positive 3)) (NotZero False (Positive 4))
  -- NotZero True (Positive 12)

-- Addition can produce zero
plusNZ (NotZero True (Positive 3)) (NotZero False (Positive 3))
  -- Nothing

Building

cabal build
cabal test doctest
cabal bench