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1. enumFromThen' :: Expr -> Expr -> Expr

   express	Data.Express.Fixtures

   enumFromThen lifted over Exprs

   > enumFromThen' zero ten
   enumFromThen 0 10 :: [Int]
   

2. enumFromThenTo' :: Expr -> Expr -> Expr -> Expr

   express	Data.Express.Fixtures

   enumFromThenTo lifted over Exprs.

   > enumFromThenTo' zero two ten
   enumFromThenTo 0 2 10 :: [Int]
   

3. enumFromTo' :: Expr -> Expr -> Expr

   express	Data.Express.Fixtures

   enumFromTo lifted over Exprs

   > enumFromTo' zero four
   enumFromTo 0 4 :: [Int]
   

4. signum' :: Expr -> Expr

   express	Data.Express.Fixtures

   signum over the Int type lifted over the Expr type.

   > signum' xx'
   signum x' :: Int
   

   > evl (signum' minusTwo) :: Int
   -1
   

5. signumE :: Expr

   express	Data.Express.Fixtures

   signum over the Int type encoded as an Expr.

   > signumE
   signum :: Int -> Int
   

6. reflectToNum :: forall (n :: Nat) m proxy . (SNatI n, Num m) => proxy n -> m

   fin	Data.Type.Nat

   As reflect but with any Num.

7. class Enum a

   foundation	Foundation

   Class Enum defines operations on sequentially ordered types. The enumFrom... methods are used in Haskell's translation of arithmetic sequences. Instances of Enum may be derived for any enumeration type (types whose constructors have no fields). The nullary constructors are assumed to be numbered left-to-right by fromEnum from 0 through n-1. See Chapter 10 of the Haskell Report for more details. For any type that is an instance of class Bounded as well as Enum, the following should hold:

   • The calls succ maxBound and pred minBound should result in a runtime error.
   • fromEnum and toEnum should give a runtime error if the result value is not representable in the result type. For example, toEnum 7 :: Bool is an error.
   • enumFrom and enumFromThen should be defined with an implicit bound, thus:

   enumFrom     x   = enumFromTo     x maxBound
   enumFromThen x y = enumFromThenTo x y bound
   where
   bound | fromEnum y >= fromEnum x = maxBound
   | otherwise                = minBound
   

8. enumFrom :: Enum a => a -> [a]

   foundation	Foundation

   Used in Haskell's translation of [n..] with [n..] = enumFrom n, a possible implementation being enumFrom n = n : enumFrom (succ n).

   Examples

   • enumFrom 4 :: [Integer] = [4,5,6,7,...]

   • enumFrom 6 :: [Int] = [6,7,8,9,...,maxBound ::
     Int]

9. enumFromThen :: Enum a => a -> a -> [a]

   foundation	Foundation

   Used in Haskell's translation of [n,n'..] with [n,n'..] = enumFromThen n n', a possible implementation being enumFromThen n n' = n : n' : worker (f x) (f x n'), worker s v = v : worker s (s v), x = fromEnum n' - fromEnum n and

   f n y
   | n > 0 = f (n - 1) (succ y)
   | n < 0 = f (n + 1) (pred y)
   | otherwise = y
   
   

   Examples

   • enumFromThen 4 6 :: [Integer] = [4,6,8,10...]

   • enumFromThen 6 2 :: [Int] = [6,2,-2,-6,...,minBound ::
     Int]

10. enumFromThenTo :: Enum a => a -> a -> a -> [a]

    foundation	Foundation

    Used in Haskell's translation of [n,n'..m] with [n,n'..m] = enumFromThenTo n n' m, a possible implementation being enumFromThenTo n n' m = worker (f x) (c x) n m, x = fromEnum n' - fromEnum n, c x = bool (>=) ((x 0)

    f n y
    | n > 0 = f (n - 1) (succ y)
    | n < 0 = f (n + 1) (pred y)
    | otherwise = y
    
    

    and

    worker s c v m
    | c v m = v : worker s c (s v) m
    | otherwise = []
    
    

    Examples

    • enumFromThenTo 4 2 -6 :: [Integer] =
      [4,2,0,-2,-4,-6]

    • enumFromThenTo 6 8 2 :: [Int] = []

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