. -package:between

Right to left function composition.

(f . g) x = f (g x)

f . id = f = id . f

Examples

>>> map ((*2) . length) [[], [0, 1, 2], [0]]
[0,6,2]

>>> foldr (.) id [(+1), (*3), (^3)] 2
25

>>> let (...) = (.).(.) in ((*2)...(+)) 5 10
30

Morphism composition. Implementations should satisfy the law:

• Associativity f . (g . h) = (f . g) . h

This means that the way morphisms are grouped is irrelevant, so it is unambiguous to write a composition of morphisms as f . g . h, without parentheses.

Function composition.

morphism composition

morphism composition

Function composition.

Bijection composition

morphism composition

Bitwise "and"

Infix version of shiftL.

Infix version of shiftR.

Infix version of xor.

Bitwise "or"

Conjunction: p1 .&&. p2 passes if both p1 and p2 pass.

Nondeterministic choice: p1 .&. p2 picks randomly one of p1 and p2 to test. If you test the property 100 times it makes 100 random choices.

Disjunction: p1 .||. p2 passes unless p1 and p2 simultaneously fail.

Helper for use in combination with .:? to provide default values for optional JSON object fields. This combinator is most useful if the key and value can be absent from an object without affecting its validity and we know a default value to assign in that case. If the key and value are mandatory, use .: instead. Example usage:

v1 <- o .:? "opt_field_with_dfl" .!= "default_val"
v2 <- o .:  "mandatory_field"
v3 <- o .:? "opt_field2"

Retrieve the value associated with the given key of an Object. The result is empty if the key is not present or the value cannot be converted to the desired type. This accessor is appropriate if the key and value must be present in an object for it to be valid. If the key and value are optional, use .:? instead.

Retrieve the value associated with the given key of an Object. The result is Nothing if the key is not present or empty if the value cannot be converted to the desired type. This differs from .:? by attempting to parse Null the same as any other JSON value, instead of interpreting it as Nothing.

Retrieve the value associated with the given key of an Object. If the key is not present and the omittedField is Just x for some x, the result will be that x. This differs from .:?= by attempting to parse Null the same as any other JSON value, instead of using omittedField when it's Just.

Retrieve the value associated with the given key of an Object. The result is Nothing if the key is not present or if its value is Null, or empty if the value cannot be converted to the desired type. This accessor is most useful if the key and value can be absent from an object without affecting its validity. If the key and value are mandatory, use .: instead.

Retrieve the value associated with the given key of an Object. If the key is not present or the field is null and the omittedField is Just x for some x, the result will be that x.