IsomorphismNondeterminism

Nondeterministically sequence fs, collecting the results using a Monoid.

Nondeterministically sequence fs, collecting the results using a commutative Monoid.

Flipped variant of ap.

Alias for map.

Add a unit to any Apply to form an Applicative.

The composition of Functor F and Bifunctor G, [x, y]F[G[x, y]], is a Bifunctor

Obtain results from both a and b, nondeterministically ordering their effects.

A commutative operation which chooses nondeterministically to obtain a value from either a or b. If a 'wins', a 'residual' context for b is returned; if b wins, a residual context for a is returned. The residual is useful for various instances like Future, which may race the two computations and require a residual to ensure the result of the 'losing' computation is not discarded.

This function can be defined in terms of chooseAny or vice versa. The default implementation calls chooseAny with a two-element list and uses the Functor for F to fix up types.

A commutative operation which chooses nondeterministically to obtain a value from any of the elements of as. In the language of posets, this constructs an antichain (a set of elements which are all incomparable) in the effect poset for this computation.

The composition of Functors F and G, [x]F[G[x]], is a Functor

The composition of Applys F and G, [x]F[G[x]], is a Apply

The composition of Applicatives F and G, [x]F[G[x]], is an Applicative

Combine fa and fb according to Apply[F] with a function that discards the A(s)

Combine fa and fb according to Apply[F] with a function that discards the B(s)

Filter l according to an applicative predicate.

Filter l according to an applicative predicate.

Filter map according to an applicative predicate. *

An Applicative for F in which effects happen in the opposite order.

Repeats an applicative action infinitely

Twin all As in fa.

Pair all As in fa with the result of function application.

Nondeterministically gather results from the given sequence of actions. This function is the nondeterministic analogue of sequence and should behave identically to sequence so long as there is no interaction between the effects being gathered. However, unlike sequence, which decides on a total order of effects, the effects in a gather are unordered with respect to each other.

Although the effects are unordered, we ensure the order of results matches the order of the input sequence. Also see gatherUnordered.

Nondeterministically gather results from the given sequence of actions to a list. Same as calling reduceUnordered with the List Monoid.

To preserve the order of the output list while allowing nondetermininstic ordering of effects, use gather.

The composition of Functor F and Contravariant G, [x]F[G[x]], is contravariant.

if lifted into a binding. Unlike lift3((t,c,a)=>if(t)c else a), this will only include context from the chosen of ifTrue and ifFalse, not the other.

Execute an action repeatedly until its result satisfies the given predicate and return that result, discarding all others.

Execute an action repeatedly until its result fails to satisfy the given predicate and return that result, discarding all others.

Sequence the inner F of FFA after the outer F, forming a single F[A].

Lift f into F.

Apply a function to the results of a and b, nondeterminstically ordering their effects.

Lift apply(a), and apply the result to f.

Pair A with the result of function application.

Apply a function to 2 results, nondeterminstically ordering their effects, alias of mapBoth

Apply a function to 3 results, nondeterminstically ordering their effects

Apply a function to 4 results, nondeterminstically ordering their effects

Apply a function to 5 results, nondeterminstically ordering their effects

Apply a function to 6 results, nondeterminstically ordering their effects

A lawful implementation of this that is isomorphic up to the methods defined on Applicative allowing for optimised parallel implementations that would otherwise violate laws of more specific typeclasses (e.g. Monad).

Semigroups can be added within an Applicative

The product of Functors F and G, [x](F[x], G[x]]), is a Functor

The product of Applys F and G, [x](F[x], G[x]]), is a Apply

The product of Bind F and G, [x](F[x], G[x]]), is a Bind

The product of Applicatives F and G, [x](F[x], G[x]]), is an Applicative

The product of Monad F and G, [x](F[x], G[x]]), is a Monad

Nondeterministically gather results from the given sequence of actions. The result will be arbitrarily reordered, depending on the order results come back in a sequence of calls to chooseAny.

Performs the action n times, returning the list of results.

Performs the action n times, returning nothing.

Inject a to the left of Bs in f.

Inject b to the right of As in f.

Unfold seed to the right and combine effects left-to-right, using the given Reducer to combine values. Implementations may override this method to not unfold more than is necessary to determine the result.

Returns the given argument if cond is false, otherwise, unit lifted into F.

Execute an action repeatedly until the Boolean condition returns true. The condition is evaluated after the loop body. Collects results into an arbitrary MonadPlus value, such as a List.

Execute an action repeatedly until the Boolean condition returns true. The condition is evaluated after the loop body. Discards results.

Empty fa of meaningful pure values, preserving its structure.

Returns the given argument if cond is true, otherwise, unit lifted into F.

Execute an action repeatedly as long as the given Boolean expression returns true. The condition is evaluated before the loop body. Collects the results into an arbitrary MonadPlus value, such as a List.

Execute an action repeatedly as long as the given Boolean expression returns true. The condition is evaluated before the loop body. Discards results.

Functors are covariant by nature, so we can treat an F[A] as an F[B] if A is a subtype of B.

Converts ma to a value of type F[B] using the provided bijection.

Converts ma to a value of type F[B] using the provided isomorphism.