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fp-ts-numerics

Enum.Internal overview

Added in v1.0.0

Table of contents

utils

Enum (interface)

Typeclass for types which can be enumerated

Adapted from https://github.com/purescript/purescript-enums/blob/mast./Enum.purs

Laws:

  1. Successor: all (a < _) (next a)
  2. Predecessor: all (_ < a) (prev a)
  3. next retracts prev: prev >=> next >=> prev = prev
  4. prev retracts next: next >=> prev >=> next = next
  5. Non-skipping next: b <= a || any (_ <= b) (next a)
  6. Non-skipping prev: a <= b || any (b <= _) (prev a)

The retraction laws can intuitively be understood as saying that next is the opposite of prev; if you apply next and then prev to something, you should end up with what you started with (although of course this doesn’t apply if you tried to next the last value in an enumeration and therefore got none out).

The non-skipping laws can intuitively be understood as saying that next shouldn’t skip over any elements of your type. For example, without the non-skipping laws, it would be permissible to write an Enum<Int> instance where next(x) = some(x+2), and similarly prev(x) = some(x-2).

Signature

export interface Enum<A> extends Ord<A> {
  readonly next: (a: A) => Option<A>
  readonly prev: (a: A) => Option<A>
}

Added in v1.0.0