Eq package:numhask

The Eq class defines equality (==) and inequality (/=). All the basic datatypes exported by the Prelude are instances of Eq, and Eq may be derived for any datatype whose constituents are also instances of Eq. The Haskell Report defines no laws for Eq. However, instances are encouraged to follow these properties:

• Reflexivity x == x = True
• Symmetry x == y = y == x
• Transitivity if x == y && y == z = True, then x == z = True
• Extensionality if x == y = True and f is a function whose return type is an instance of Eq, then f x == f y = True
• Negation x /= y = not (x == y)

Minimal complete definition: either == or /=.

Approximate equality

>>> aboutEqual zero (epsilon :: Double)
True

The partial ordering induced by the join-semilattice structure

The partial ordering induced by the meet-semilattice structure

The value of seq a b is bottom if a is bottom, and otherwise equal to b. In other words, it evaluates the first argument a to weak head normal form (WHNF). seq is usually introduced to improve performance by avoiding unneeded laziness. A note on evaluation order: the expression seq a b does not guarantee that a will be evaluated before b. The only guarantee given by seq is that the both a and b will be evaluated before seq returns a value. In particular, this means that b may be evaluated before a. If you need to guarantee a specific order of evaluation, you must use the function pseq from the "parallel" package.

Evaluate each monadic action in the structure from left to right, and collect the results. For a version that ignores the results see sequence_.

Examples

Basic usage: The first two examples are instances where the input and and output of sequence are isomorphic.

>>> sequence $ Right [1,2,3,4]
[Right 1,Right 2,Right 3,Right 4]

>>> sequence $ [Right 1,Right 2,Right 3,Right 4]
Right [1,2,3,4]

The following examples demonstrate short circuit behavior for sequence.

>>> sequence $ Left [1,2,3,4]
Left [1,2,3,4]

>>> sequence $ [Left 0, Right 1,Right 2,Right 3,Right 4]
Left 0

Evaluate each action in the structure from left to right, and collect the results. For a version that ignores the results see sequenceA_.

Examples

Basic usage: For the first two examples we show sequenceA fully evaluating a a structure and collecting the results.

>>> sequenceA [Just 1, Just 2, Just 3]
Just [1,2,3]

>>> sequenceA [Right 1, Right 2, Right 3]
Right [1,2,3]

The next two example show Nothing and Just will short circuit the resulting structure if present in the input. For more context, check the Traversable instances for Either and Maybe.

>>> sequenceA [Just 1, Just 2, Just 3, Nothing]
Nothing

>>> sequenceA [Right 1, Right 2, Right 3, Left 4]
Left 4

Evaluate each action in the structure from left to right, and ignore the results. For a version that doesn't ignore the results see sequenceA. sequenceA_ is just like sequence_, but generalised to Applicative actions.

Examples

Basic usage:

>>> sequenceA_ [print "Hello", print "world", print "!"]
"Hello"
"world"
"!"

Evaluate each monadic action in the structure from left to right, and ignore the results. For a version that doesn't ignore the results see sequence. sequence_ is just like sequenceA_, but specialised to monadic actions.