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Merged
garyb merged 2 commits into from
Jun 30, 2017
Merged

Add Parity #27

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743afad
Add `Parity`
garyb Jun 30, 2017
117f84e
Add `Show` and `Bounded` instances for `Parity`
garyb Jun 30, 2017
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27 changes: 26 additions & 1 deletion src/Data/Int.purs
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Original file line number Diff line number Diff line change
Expand Up @@ -14,6 +14,8 @@ module Data.Int
, base36
, fromStringAs
, toStringAs
, Parity(..)
, parity
, even
, odd
, pow
Expand Down Expand Up @@ -77,6 +79,29 @@ foreign import toNumber :: Int -> Number
fromString :: String -> Maybe Int
fromString = fromStringAs (Radix 10)

-- | A type for describing whether an integer is even or odd.
data Parity = Even | Odd

derive instance eqParity :: Eq Parity
derive instance ordParity :: Ord Parity
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@hdgarrood hdgarrood Jun 30, 2017

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Maybe Show too?

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@garyb garyb Jun 30, 2017

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Good thinking. I added Bounded also.

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@paf31 paf31 Jun 30, 2017

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Also CommutativeRing.

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@hdgarrood hdgarrood Jun 30, 2017

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It's a field, isn't it, if we're going to give it numeric instances? If we treat Parity as Z/2Z with Even = [0] and Odd = [1]?

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@paf31 paf31 Jun 30, 2017

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I'm thinking of this as being an approximation to integers, not Z/2Z. Dividing an even integer by another even integer could be even or odd.

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@hdgarrood hdgarrood Jul 1, 2017

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Although I think sometimes "ring" is defined such that multiplication need only be a semigroup, not necessarily a monoid; in that case you might be able to find two such rings with two elements.

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@paf31 paf31 Jul 1, 2017

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Yeah your logic seems sound to me. I was going from this:

https://en.wikipedia.org/wiki/Finite_ring

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@hdgarrood hdgarrood Jul 1, 2017

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Does that suggest that we should give Boolean a Field instance?

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@paf31 paf31 Jul 1, 2017

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I don't think we should. Just because it has two elements doesn't mean we should think of it as Z/2 in my opinion. I would rather have a separate type.

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@hdgarrood hdgarrood Jul 1, 2017

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Makes sense, although we can make it into a field without thinking of it as Z/2Z - just by thinking of addition as xor and multiplication as &&. But yeah in the absence of any concrete use case I'm inclined to leave it how it is too.


instance showParity :: Show Parity where
show Even = "Even"
show Odd = "Odd"

instance boundedParity :: Bounded Parity where
bottom = Even
top = Odd

-- | Returns whether an `Int` is `Even` or `Odd`.
-- |
-- | ``` purescript
-- | parity 0 == Even
-- | parity 1 == Odd
-- | ```
parity :: Int -> Parity
parity n = if even n then Even else Odd

-- | Returns whether an `Int` is an even number.
-- |
-- | ``` purescript
Expand All @@ -90,7 +115,7 @@ even x = x .&. 1 == 0
-- |
-- | ``` purescript
-- | odd 0 == false
-- | odd 1 == false
-- | odd 1 == true
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@hdgarrood hdgarrood Jun 30, 2017

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😱

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@garyb garyb Jun 30, 2017

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Haha yeah! 😆

-- | ```
odd :: Int -> Boolean
odd x = x .&. 1 /= 0
Expand Down