GHC.Enum

fromEnum just truncates its argument, beware of all sorts of overflows.

List generators have extremely peculiar behavior, mandated by Haskell Report 2010:

>>> [0..1.5][0.0,1.0,2.0]

fromEnum just truncates its argument, beware of all sorts of overflows.

List generators have extremely peculiar behavior, mandated by Haskell Report 2010:

>>> [0..1.5 :: Float][0.0,1.0,2.0]

This is needed only as a superclass of Integral.

maps Q1..Q4 to 1..4

"Circular", so for example [Tuesday ..] gives an endless sequence. Also: fromEnum gives [1 .. 7] for [Monday .. Sunday], and toEnum performs mod 7 to give a cycle of days.

Swaps succ and pred of the underlying type.

Recall that, for numeric types, succ and pred typically add and subtract 1, respectively. This is not true in the case of Fixed, whose successor and predecessor functions intuitively return the "next" and "previous" values in the enumeration. The results of these functions thus depend on the resolution of the Fixed value. For example, when enumerating values of resolution 10^-3 of type Milli = Fixed E3,

>>> succ (0.000 :: Milli)0.001

and likewise

>>> pred (0.000 :: Milli)-0.001

In other words, succ and pred increment and decrement a fixed-precision value by the least amount such that the value's resolution is unchanged. For example, 10^-12 is the smallest (positive) amount that can be added to a value of type Pico = Fixed E12 without changing its resolution, and so

>>> succ (0.000000000000 :: Pico)0.000000000001

and similarly

>>> pred (0.000000000000 :: Pico)-0.000000000001

This is worth bearing in mind when defining Fixed arithmetic sequences. In particular, you may be forgiven for thinking the sequence

  [1..10] :: [Pico]

evaluates to [1, 2, 3, 4, 5, 6, 7, 8, 9, 10] :: [Pico].

However, this is not true. On the contrary, similarly to the above implementations of succ and pred, enumFromTo :: Pico -> Pico -> [Pico] has a "step size" of 10^-12. Hence, the list [1..10] :: [Pico] has the form

  [1.000000000000, 1.00000000001, 1.00000000002, ..., 10.000000000000]

and contains 9 * 10^12 + 1 values.

Swaps minBound and maxBound of the underlying type.