The semigroup on numbers whose opearion is addition. Since addition also has a unit, namely 0, this actually defines a monoid.

A failure where all failures are collected in a vector.

Promotes a semigroup into an apply. If the semigroup is a a monoid then the result is an applicative.

A failure applicative where only the first failure is kept.

Wraps a value as a failure so that failure? can detect it.

Checks if the input represents a failure, that it, if it is a map of the form {:failure <report>}.

The semigroup whose operation picks the first argumet and ignores the second. There is no unit for this operation.

This is the trivial applicative where there is no actual lifting.

Changes the failure type for a validation function.

Wraps a mapping operation and a binary operation lifter as {:fmap fmap :binary-lift binary-lift}. We assume that the wrapped functions satisfy the ‘semimonoidal functor’ laws. If there is also a pure operation which injects a regular value into the context then we assume that the wrapped values form an ‘applicative functor’.

Wraps a binary associative operator as {:binary-op binary-op}. If in addition there is a unit then the result is the map {:binary-op binary-op :unit unit}. If there is a unit, the semigroup is indeed a monoid. A unit should not be encoded by a nil.

Constructs an applicative where failures are accumulated using the semigroup.

The semigroup on vectors whose operation is concatenation. Since concatenation has a unit, namely [], this is actually a monoid.