From 9189e7c8e4cec68d169be4b5b67f9df56bba13cc Mon Sep 17 00:00:00 2001
From: Gary Burgess <gary.burgess@gmail.com>
Date: Sat, 2 Apr 2016 14:08:39 +0100
Subject: [PATCH] Updates for PureScript 0.8

---
 .gitignore         |   5 +-
 .travis.yml        |  16 ++-
 README.md          |   6 +-
 bower.json         |   9 +-
 docs/Data/Enum.md  | 151 ---------------------
 package.json       |   8 +-
 src/Data/Enum.purs | 318 ++++++++++++++++++++++-----------------------
 7 files changed, 182 insertions(+), 331 deletions(-)
 delete mode 100644 docs/Data/Enum.md

diff --git a/.gitignore b/.gitignore
index e2f8a69..307f9c0 100644
--- a/.gitignore
+++ b/.gitignore
@@ -1,5 +1,6 @@
-.psci
+/.*
+!/.gitignore
+!/.travis.yml
 /bower_components/
 /node_modules/
 /output/
-/tmp/
diff --git a/.travis.yml b/.travis.yml
index 791313a..36183ef 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -1,7 +1,7 @@
 language: node_js
-sudo: false
-node_js:
-  - 0.10
+sudo: required
+dist: trusty
+node_js: 5
 env:
   - PATH=$HOME/purescript:$PATH
 install:
@@ -9,6 +9,16 @@ install:
   - wget -O $HOME/purescript.tar.gz https://github.com/purescript/purescript/releases/download/$TAG/linux64.tar.gz
   - tar -xvf $HOME/purescript.tar.gz -C $HOME/
   - chmod a+x $HOME/purescript
+  - npm install -g bower
   - npm install
+  - bower install
 script:
   - npm run build
+after_success:
+- >-
+  test $TRAVIS_TAG &&
+  psc-publish > .pursuit.json &&
+  curl -X POST http://pursuit.purescript.org/packages \
+    -d @.pursuit.json \
+    -H 'Accept: application/json' \
+    -H "Authorization: token ${GITHUB_TOKEN}"
diff --git a/README.md b/README.md
index 50d438e..329185a 100644
--- a/README.md
+++ b/README.md
@@ -4,7 +4,7 @@
 [![Build Status](https://travis-ci.org/purescript/purescript-enums.svg?branch=master)](https://travis-ci.org/purescript/purescript-enums)
 [![Dependency Status](https://www.versioneye.com/user/projects/55848c63363861001d000330/badge.svg?style=flat)](https://www.versioneye.com/user/projects/55848c63363861001d000330)
 
-Operations for small ordered sum types.
+Operations for sequentially ordered types.
 
 ## Installation
 
@@ -12,6 +12,6 @@ Operations for small ordered sum types.
 bower install purescript-enums
 ```
 
-## Module documentation
+## Documentation
 
-- [Data.Enum](docs/Data/Enum.md)
+Module documentation is [published on Pursuit](http://pursuit.purescript.org/packages/purescript-enums).
diff --git a/bower.json b/bower.json
index 6b5567e..6fda6c7 100644
--- a/bower.json
+++ b/bower.json
@@ -2,9 +2,6 @@
   "name": "purescript-enums",
   "homepage": "https://github.com/purescript/purescript-enums",
   "description": "Operations for sequentially ordered types",
-  "keywords": [
-    "purescript"
-  ],
   "license": "MIT",
   "repository": {
     "type": "git",
@@ -21,8 +18,8 @@
     "package.json"
   ],
   "dependencies": {
-    "purescript-either": "^0.2.0",
-    "purescript-strings": "^0.7.0",
-    "purescript-unfoldable": "^0.4.0"
+    "purescript-either": "^1.0.0-rc.1",
+    "purescript-strings": "^1.0.0-rc.1",
+    "purescript-unfoldable": "^1.0.0-rc.1"
   }
 }
diff --git a/docs/Data/Enum.md b/docs/Data/Enum.md
deleted file mode 100644
index cec3add..0000000
--- a/docs/Data/Enum.md
+++ /dev/null
@@ -1,151 +0,0 @@
-## Module Data.Enum
-
-#### `Cardinality`
-
-``` purescript
-newtype Cardinality a
-  = Cardinality Int
-```
-
-#### `runCardinality`
-
-``` purescript
-runCardinality :: forall a. Cardinality a -> Int
-```
-
-#### `Enum`
-
-``` purescript
-class Enum a where
-  succ :: a -> Maybe a
-  pred :: a -> Maybe a
-  toEnum :: Int -> Maybe a
-  fromEnum :: a -> Int
-```
-
-Type class for enumerations. This should not be considered a part of a
-numeric hierarchy, ala Haskell. Rather, this is a type class for small,
-ordered sum types with the ability to easily compute successor and
-predecessor elements. e.g. `DayOfWeek`, etc.
-
-Laws:
-
-- ```e1 `compare` e2 == fromEnum e1 `compare` fromEnum e2```
-- ```pred >=> succ >=> pred = pred```
-- ```succ >=> pred >=> succ = succ```
-- ```toEnum (fromEnum a) = Just a```
-
-##### Instances
-``` purescript
-instance enumUnit :: Enum Unit
-instance enumChar :: Enum Char
-instance enumMaybe :: (Finite a) => Enum (Maybe a)
-instance enumBoolean :: Enum Boolean
-instance enumTuple :: (Finite a, Finite b) => Enum (Tuple a b)
-instance enumEither :: (Finite a, Finite b) => Enum (Either a b)
-```
-
-#### `defaultSucc`
-
-``` purescript
-defaultSucc :: forall a. (Int -> Maybe a) -> (a -> Int) -> a -> Maybe a
-```
-
-```defaultSucc toEnum fromEnum = succ```
-
-#### `defaultPred`
-
-``` purescript
-defaultPred :: forall a. (Int -> Maybe a) -> (a -> Int) -> a -> Maybe a
-```
-
-```defaultPred toEnum fromEnum = pred```
-
-#### `defaultToEnum`
-
-``` purescript
-defaultToEnum :: forall a. (a -> Maybe a) -> a -> Int -> Maybe a
-```
-
-Runs in `O(n)` where `n` is `fromEnum a`
-
-```defaultToEnum succ bottom = toEnum```
-
-#### `defaultFromEnum`
-
-``` purescript
-defaultFromEnum :: forall a. (a -> Maybe a) -> a -> Int
-```
-
-Runs in `O(n)` where `n` is `fromEnum a`
-
-```defaultFromEnum pred = fromEnum```
-
-#### `enumFromTo`
-
-``` purescript
-enumFromTo :: forall a. (Enum a) => a -> a -> Array a
-```
-
-Property: ```fromEnum a = a', fromEnum b = b' => forall e', a' <= e' <= b': Exists e: toEnum e' = Just e```
-
-Following from the propery of `intFromTo`, we are sure all elements in `intFromTo (fromEnum a) (fromEnum b)` are `Just`s.
-
-#### `enumFromThenTo`
-
-``` purescript
-enumFromThenTo :: forall a. (Enum a) => a -> a -> a -> Array a
-```
-
-`[a,b..c]`
-
-Correctness for using `fromJust` is the same as for `enumFromTo`.
-
-#### `intFromTo`
-
-``` purescript
-intFromTo :: Int -> Int -> Array Int
-```
-
-Property: ```forall e in intFromTo a b: a <= e <= b```
-
-#### `intStepFromTo`
-
-``` purescript
-intStepFromTo :: Int -> Int -> Int -> Array Int
-```
-
-Property: ```forall e in intStepFromTo step a b: a <= e <= b```
-
-#### `Finite`
-
-``` purescript
-class (Bounded a, Enum a) <= Finite a where
-  cardinality :: Cardinality a
-```
-
-Type class for finite enumerations. This should not be considered a part of
-a numeric hierarchy, ala Haskell. Rather, this is a type class for small,
-ordered sum types with statically-determined cardinality and the ability
-to easily compute successor and predecessor elements. e.g. `DayOfWeek`, etc.
-
-Laws:
-
-- ```succ bottom >>= succ >>= succ ... succ [cardinality - 1 times] == top```
-- ```pred top    >>= pred >>= pred ... pred [cardinality - 1 times] == bottom```
-- ```forall a > bottom: pred a >>= succ == Just a```
-- ```forall a < top:  succ a >>= pred == Just a```
-- ```forall a > bottom: fromEnum <$> pred a = Just (fromEnum a - 1)```
-- ```forall a < top:  fromEnum <$> succ a = Just (fromEnum a + 1)```
-
-##### Instances
-``` purescript
-instance finiteUnit :: Finite Unit
-instance finiteChar :: Finite Char
-instance finiteMaybe :: (Finite a) => Finite (Maybe a)
-instance finiteBoolean :: Finite Boolean
-instance finiteTuple :: (Finite a, Finite b) => Finite (Tuple a b)
-instance finiteEither :: (Finite a, Finite b) => Finite (Either a b)
-```
-
-
diff --git a/package.json b/package.json
index 509a91f..f7e0e40 100644
--- a/package.json
+++ b/package.json
@@ -1,11 +1,11 @@
 {
   "private": true,
   "scripts": {
-    "postinstall": "pulp dep install",
-    "build": "pulp build && rimraf docs && pulp docs"
+    "clean": "rimraf output && rimraf .pulp-cache",
+    "build": "pulp build"
   },
   "devDependencies": {
-    "pulp": "^4.0.2",
-    "rimraf": "^2.4.1"
+    "pulp": "^8.1.0",
+    "rimraf": "^2.5.0"
   }
 }
diff --git a/src/Data/Enum.purs b/src/Data/Enum.purs
index 5593275..cf18a30 100644
--- a/src/Data/Enum.purs
+++ b/src/Data/Enum.purs
@@ -1,58 +1,97 @@
 module Data.Enum
-  ( Enum
-  , BoundedEnum
-  , Cardinality(..)
-  , cardinality
-  , fromEnum
-  , pred
-  , runCardinality
-  , succ
-  , toEnum
+  ( class Enum, succ, pred
   , defaultSucc
   , defaultPred
-  , defaultCardinality
-  , defaultToEnum
-  , defaultFromEnum
   , enumFromTo
   , enumFromThenTo
   , upFrom
   , downFrom
+  , Cardinality(..), runCardinality
+  , class BoundedEnum, cardinality, toEnum, fromEnum
+  , defaultCardinality
+  , defaultToEnum
+  , defaultFromEnum
   ) where
 
 import Prelude
+
 import Data.Char (fromCharCode, toCharCode)
-import Data.Either
-import Data.Maybe
-import Data.Maybe.Unsafe
-import Data.Tuple
-import Data.Unfoldable
+import Data.Either (Either(..))
+import Data.Maybe (Maybe(..), maybe, fromJust)
+import Data.Tuple (Tuple(..))
+import Data.Unfoldable (class Unfoldable, unfoldr)
+
+import Partial.Unsafe (unsafePartial)
 
 newtype Cardinality a = Cardinality Int
 
 runCardinality :: forall a. Cardinality a -> Int
 runCardinality (Cardinality a) = a
 
--- | Type class for enumerations. This should not be considered a part of a
--- | numeric hierarchy, ala Haskell. Rather, this is a type class for small,
--- | ordered sum types with the ability to easily compute successor and
--- | predecessor elements. e.g. `DayOfWeek`, etc.
+-- | Type class for enumerations.
 -- |
 -- | Laws:
--- |
--- | - ```pred >=> succ >=> pred = pred```
--- | - ```succ >=> pred >=> succ = succ```
-
-class (Ord a) <= Enum a where
+-- | - `succ a > pred a`
+-- | - `pred a < succ a`
+-- | - `pred >=> succ >=> pred = pred`
+-- | - `succ >=> pred >=> succ = succ`
+class Ord a <= Enum a where
   succ :: a -> Maybe a
   pred :: a -> Maybe a
 
+instance enumBoolean :: Enum Boolean where
+  succ false = Just true
+  succ _ = Nothing
+  pred true = Just false
+  pred _= Nothing
+
+instance enumInt :: Enum Int where
+  succ n = if n < top then Just (n + 1) else Nothing
+  pred n = if n > bottom then Just (n - 1) else Nothing
+
+instance enumChar :: Enum Char where
+  succ = defaultSucc charToEnum toCharCode
+  pred = defaultPred charToEnum toCharCode
+
+charToEnum :: Int -> Maybe Char
+charToEnum n | n >= bottom && n <= top = Just $ fromCharCode n
+charToEnum _ = Nothing
+
+instance enumUnit :: Enum Unit where
+  succ = const Nothing
+  pred = const Nothing
+
+instance enumOrdering :: Enum Ordering where
+  succ LT = Just EQ
+  succ EQ = Just GT
+  succ GT = Nothing
+  pred LT = Nothing
+  pred EQ = Just LT
+  pred GT = Just EQ
+
+instance enumMaybe :: BoundedEnum a => Enum (Maybe a) where
+  succ Nothing = Just $ Just bottom
+  succ (Just a) = Just <$> succ a
+  pred Nothing = Nothing
+  pred (Just a) = Just $ pred a
+
+instance enumEither :: (BoundedEnum a, BoundedEnum b) => Enum (Either a b) where
+  succ (Left a) = maybe (Just $ Right bottom) (Just <<< Left) (succ a)
+  succ (Right b) = maybe (Nothing) (Just <<< Right) (succ b)
+  pred (Left a) = maybe (Nothing) (Just <<< Left) (pred a)
+  pred (Right b) = maybe (Just $ Left top) (Just <<< Right) (pred b)
+
+instance enumTuple :: (Enum a, BoundedEnum b) => Enum (Tuple a b) where
+  succ (Tuple a b) = maybe (flip Tuple bottom <$> succ a) (Just <<< Tuple a) (succ b)
+  pred (Tuple a b) = maybe (flip Tuple top <$> pred a) (Just <<< Tuple a) (pred b)
+
 -- | ```defaultSucc toEnum fromEnum = succ```
-defaultSucc :: forall a. (Int -> Maybe a) -> (a -> Int) -> (a -> Maybe a)
-defaultSucc toEnum' fromEnum' a = toEnum' (fromEnum' a + one)
+defaultSucc :: forall a. (Int -> Maybe a) -> (a -> Int) -> a -> Maybe a
+defaultSucc toEnum' fromEnum' a = toEnum' (fromEnum' a + 1)
 
 -- | ```defaultPred toEnum fromEnum = pred```
-defaultPred :: forall a. (Int -> Maybe a) -> (a -> Int) -> (a -> Maybe a)
-defaultPred toEnum' fromEnum' a = toEnum' (fromEnum' a - one)
+defaultPred :: forall a. (Int -> Maybe a) -> (a -> Int) -> a -> Maybe a
+defaultPred toEnum' fromEnum' a = toEnum' (fromEnum' a - 1)
 
 -- | Property: ```fromEnum a = a', fromEnum b = b' => forall e', a' <= e' <= b': Exists e: toEnum e' = Just e```
 -- |
@@ -62,13 +101,12 @@ enumFromTo :: forall a u. (Enum a, Unfoldable u) => a -> a -> u a
 enumFromTo from to = unfoldr (\x -> succ x >>= \x' -> if x <= to then pure $ Tuple x x' else Nothing) from
 
 -- | `[a,b..c]`
--- |
--- | Correctness for using `fromJust` is the same as for `enumFromTo`.
-enumFromThenTo :: forall a. (BoundedEnum a) => a -> a -> a -> Array a
-enumFromThenTo a b c = (toEnum >>> fromJust) <$> intStepFromTo (b' - a') a' c'
-  where a' = fromEnum a
-        b' = fromEnum b
-        c' = fromEnum c
+enumFromThenTo :: forall a. BoundedEnum a => a -> a -> a -> Array a
+enumFromThenTo = unsafePartial \a b c ->
+  let a' = fromEnum a
+      b' = fromEnum b
+      c' = fromEnum c
+  in (toEnum >>> fromJust) <$> intStepFromTo (b' - a') a' c'
 
 -- | Property: ```forall e in intStepFromTo step a b: a <= e <= b```
 intStepFromTo :: Int -> Int -> Int -> Array Int
@@ -79,6 +117,7 @@ intStepFromTo step from to =
             else Nothing                    -- End of the collection.
           ) from
 
+diag :: forall a. a -> Tuple a a
 diag a = Tuple a a
 
 upFrom :: forall a u. (Enum a, Unfoldable u) => a -> u a
@@ -87,10 +126,12 @@ upFrom = unfoldr (map diag <<< succ)
 downFrom :: forall a u. (Enum a, Unfoldable u) => a -> u a
 downFrom = unfoldr (map diag <<< pred)
 
--- | Type class for finite enumerations. This should not be considered a part of
--- | a numeric hierarchy, ala Haskell. Rather, this is a type class for small,
--- | ordered sum types with statically-determined cardinality and the ability
--- | to easily compute successor and predecessor elements. e.g. `DayOfWeek`, etc.
+-- | Type class for finite enumerations.
+-- |
+-- | This should not be considered a part of a numeric hierarchy, as in Haskell.
+-- | Rather, this is a type class for small, ordered sum types with
+-- | statically-determined cardinality and the ability to easily compute
+-- | successor and predecessor elements, e.g. `DayOfWeek`.
 -- |
 -- | Laws:
 -- |
@@ -102,39 +143,28 @@ downFrom = unfoldr (map diag <<< pred)
 -- | - ```forall a < top:  fromEnum <$> succ a = Just (fromEnum a + 1)```
 -- | - ```e1 `compare` e2 == fromEnum e1 `compare` fromEnum e2```
 -- | - ```toEnum (fromEnum a) = Just a```
-
 class (Bounded a, Enum a) <= BoundedEnum a where
   cardinality :: Cardinality a
   toEnum :: Int -> Maybe a
   fromEnum :: a -> Int
 
--- | Runs in `O(n)` where `n` is `fromEnum top`
--- |
--- | ```defaultCardinality = cardinality```
-defaultCardinality :: forall a. (Bounded a, Enum a) => Cardinality a
-defaultCardinality = Cardinality $ defaultCardinality' one (bottom :: a) where
-  defaultCardinality' i = maybe i (defaultCardinality' $ i + one) <<< succ
-
-  -- | Runs in `O(n)` where `n` is `fromEnum a`
-  -- |
-  -- | ```defaultToEnum succ bottom = toEnum```
--- TODO do we need to pass in bottom? It's a superclass if yes then we should pass it in for defaultCardinality too
-defaultToEnum :: forall a. (a -> Maybe a) -> a -> (Int -> Maybe a)
-defaultToEnum succ' bottom' n | n < zero = Nothing
-                              | n == zero = Just bottom'
-                              | otherwise = defaultToEnum succ' bottom' (n - one) >>= succ'
-
-  -- | Runs in `O(n)` where `n` is `fromEnum a`
-  -- |
-  -- | ```defaultFromEnum pred = fromEnum```
-defaultFromEnum :: forall a. (a -> Maybe a) -> (a -> Int)
-defaultFromEnum pred' e = maybe zero (\prd -> defaultFromEnum pred' prd + one) (pred' e)
+instance boundedEnumBoolean :: BoundedEnum Boolean where
+  cardinality = Cardinality 2
+  toEnum 0 = Just false
+  toEnum 1 = Just true
+  toEnum _ = Nothing
+  fromEnum false = 0
+  fromEnum true = 1
 
--- | ## Instances
+instance boundedEnumInt :: BoundedEnum Int where
+  cardinality = Cardinality (top - bottom)
+  toEnum = Just
+  fromEnum = id
 
-instance enumUnit :: Enum Unit where
-  succ = const Nothing
-  pred = const Nothing
+instance boundedEnumChar :: BoundedEnum Char where
+  cardinality = Cardinality (toCharCode top - toCharCode bottom)
+  toEnum = charToEnum
+  fromEnum = toCharCode
 
 instance boundedEnumUnit :: BoundedEnum Unit where
   cardinality = Cardinality 1
@@ -142,104 +172,68 @@ instance boundedEnumUnit :: BoundedEnum Unit where
   toEnum _ = Nothing
   fromEnum = const 0
 
-instance enumChar :: Enum Char where
-  succ = defaultSucc charToEnum charFromEnum
-  pred = defaultPred charToEnum charFromEnum
-
--- | To avoid a compiler bug - can't pass self-class functions, workaround: need to make a concrete function.
-charToEnum :: Int -> Maybe Char
-charToEnum n | n >= 0 && n <= 65535 = Just $ fromCharCode n
-charToEnum _ = Nothing
-
-charFromEnum :: Char -> Int
-charFromEnum = toCharCode
-
-instance boundedEnumChar :: BoundedEnum Char where
-  cardinality = Cardinality 65536
-  toEnum = charToEnum
-  fromEnum = charFromEnum
-
--- TODO JB BoundedEnum is too restrictive on a, all we need is bottom
-instance enumMaybe :: (BoundedEnum a) => Enum (Maybe a) where
-  succ Nothing = Just $ Just bottom
-  succ (Just a) = Just <$> succ a
-  pred Nothing = Nothing
-  pred (Just a) = Just $ pred a
-
-instance boundedEnumMaybe :: (BoundedEnum a) => BoundedEnum (Maybe a) where
-  cardinality = maybeCardinality cardinality
-  toEnum = maybeToEnum cardinality
-  fromEnum Nothing = zero
-  fromEnum (Just e) = fromEnum e + one
-
-maybeToEnum :: forall a. (BoundedEnum a) => Cardinality a -> Int -> Maybe (Maybe a)
-maybeToEnum carda n | n <= runCardinality (maybeCardinality carda) =
-  if n == zero
-  then Just $ Nothing
-  else Just $ toEnum (n - one)
-maybeToEnum _    _ = Nothing
-
-maybeCardinality :: forall a. (BoundedEnum a) => Cardinality a -> Cardinality (Maybe a)
-maybeCardinality c = Cardinality $ one + (runCardinality c)
-
-instance enumBoolean :: Enum Boolean where
-  succ = booleanSucc
-  pred = booleanPred
-
-instance boundedEnumBoolean :: BoundedEnum Boolean where
-  cardinality = Cardinality 2
-  toEnum = defaultToEnum booleanSucc bottom
-  fromEnum = defaultFromEnum booleanPred
-
-booleanSucc :: Boolean -> Maybe Boolean
-booleanSucc false = Just true
-booleanSucc _     = Nothing
-
-booleanPred :: Boolean -> Maybe Boolean
-booleanPred true  = Just false
-booleanPred _     = Nothing
+instance boundedEnumOrdering :: BoundedEnum Ordering where
+  cardinality = Cardinality 3
+  toEnum 0 = Just LT
+  toEnum 1 = Just EQ
+  toEnum 2 = Just GT
+  toEnum _ = Nothing
+  fromEnum LT = 0
+  fromEnum EQ = 1
+  fromEnum GT = 2
+
+instance boundedEnumMaybe :: BoundedEnum a => BoundedEnum (Maybe a) where
+  cardinality = Cardinality $ runCardinality (cardinality :: Cardinality a) + 1
+  toEnum = to cardinality
+    where
+    to :: Cardinality a -> Int -> Maybe (Maybe a)
+    to _ 0 = Nothing
+    to (Cardinality ca) n | n <= ca = Just $ toEnum (n - 1)
+    to _ _ = Nothing
+  fromEnum Nothing = 0
+  fromEnum (Just e) = fromEnum e + 1
 
-instance enumTuple :: (Enum a, BoundedEnum b) => Enum (Tuple a b) where
-  succ (Tuple a b) = maybe (flip Tuple bottom <$> succ a) (Just <<< Tuple a) (succ b)
-  pred (Tuple a b) = maybe (flip Tuple top <$> pred a) (Just <<< Tuple a) (pred b)
+instance boundedEnumEither :: (BoundedEnum a, BoundedEnum b) => BoundedEnum (Either a b) where
+  cardinality =
+    Cardinality
+      $ runCardinality (cardinality :: Cardinality a)
+      + runCardinality (cardinality :: Cardinality b)
+  toEnum = to cardinality cardinality
+    where
+    to :: Cardinality a -> Cardinality (Either a b) -> Int -> Maybe (Either a b)
+    to (Cardinality ca) (Cardinality cab) n
+      | n >= 0 && n < ca = Left <$> toEnum n
+      | n >= ca && n < cab = Right <$> toEnum (n - ca)
+      | otherwise = Nothing
+  fromEnum (Left a) = fromEnum a
+  fromEnum (Right b) = fromEnum b + runCardinality (cardinality :: Cardinality a)
 
 instance boundedEnumTuple :: (BoundedEnum a, BoundedEnum b) => BoundedEnum (Tuple a b) where
-  cardinality = tupleCardinality cardinality cardinality
-  toEnum = tupleToEnum cardinality
-  fromEnum = tupleFromEnum cardinality
+  cardinality =
+    Cardinality
+      $ runCardinality (cardinality :: Cardinality a)
+      * runCardinality (cardinality :: Cardinality b)
+  toEnum = to cardinality
+    where
+    to :: Cardinality b -> Int -> Maybe (Tuple a b)
+    to (Cardinality cb) n = Tuple <$> toEnum (n / cb) <*> toEnum (n `mod` cb)
+  fromEnum = from cardinality
+    where
+    from :: Cardinality b -> Tuple a b -> Int
+    from (Cardinality cb) (Tuple a b) = fromEnum a * cb + fromEnum b
 
--- | All of these are as a workaround for `ScopedTypeVariables`. (not yet supported in Purescript)
-tupleToEnum :: forall a b. (BoundedEnum a, BoundedEnum b) => Cardinality b -> Int -> Maybe (Tuple a b)
-tupleToEnum cardb n = Tuple <$> (toEnum (n / (runCardinality cardb))) <*> (toEnum (n `mod` (runCardinality cardb)))
-
-tupleFromEnum :: forall a b. (BoundedEnum a, BoundedEnum b) => Cardinality b -> Tuple a b -> Int
-tupleFromEnum cardb (Tuple a b) = (fromEnum a) * runCardinality cardb + fromEnum b
-
-tupleCardinality :: forall a b. (Enum a, Enum b) => Cardinality a -> Cardinality b -> Cardinality (Tuple a b)
-tupleCardinality l r = Cardinality $ (runCardinality l) * (runCardinality r)
+-- | Runs in `O(n)` where `n` is `fromEnum top`
+defaultCardinality :: forall a. (Bounded a, Enum a) => Cardinality a
+defaultCardinality = Cardinality $ defaultCardinality' 1 (bottom :: a) where
+  defaultCardinality' i = maybe i (defaultCardinality' $ i + 1) <<< succ
 
-instance enumEither :: (BoundedEnum a, BoundedEnum b) => Enum (Either a b) where
-  succ (Left a) = maybe (Just $ Right bottom) (Just <<< Left) (succ a)
-  succ (Right b) = maybe (Nothing) (Just <<< Right) (succ b)
-  pred (Left a) = maybe (Nothing) (Just <<< Left) (pred a)
-  pred (Right b) = maybe (Just $ Left top) (Just <<< Right) (pred b)
+  -- | Runs in `O(n)` where `n` is `fromEnum a`
+defaultToEnum :: forall a. (Bounded a, Enum a) => Int -> Maybe a
+defaultToEnum n
+  | n < 0 = Nothing
+  | n == 0 = Just bottom
+  | otherwise = defaultToEnum (n - 1) >>= succ
 
-instance boundedEnumEither :: (BoundedEnum a, BoundedEnum b) => BoundedEnum (Either a b) where
-  cardinality = eitherCardinality cardinality cardinality
-  toEnum = eitherToEnum cardinality cardinality
-  fromEnum = eitherFromEnum cardinality
-
-eitherToEnum :: forall a b. (BoundedEnum a, BoundedEnum b) => Cardinality a -> Cardinality b -> Int -> Maybe (Either a b)
-eitherToEnum carda cardb n =
-      if n >= zero && n < runCardinality carda
-      then Left <$> toEnum n
-      else if n >= (runCardinality carda) && n < runCardinality (eitherCardinality carda cardb)
-           then Right <$> toEnum (n - runCardinality carda)
-           else Nothing
-
-eitherFromEnum :: forall a b. (BoundedEnum a, BoundedEnum b) => Cardinality a -> (Either a b -> Int)
-eitherFromEnum carda (Left a) = fromEnum a
-eitherFromEnum carda (Right b) = fromEnum b + runCardinality carda
-
-eitherCardinality :: forall a b. (BoundedEnum a, BoundedEnum b) => Cardinality a -> Cardinality b -> Cardinality (Either a b)
-eitherCardinality l r = Cardinality $ (runCardinality l) + (runCardinality r)
+  -- | Runs in `O(n)` where `n` is `fromEnum a`
+defaultFromEnum :: forall a. Enum a => a -> Int
+defaultFromEnum = maybe 0 (\prd -> defaultFromEnum prd + 1) <<< pred