Documentation

Note that using a CoalgebraM “directly” is partial (e.g., with anaM). However, ana . Compose can accept a CoalgebraM and produce something like an effectful stream.

Coinductive (potentially-infinite) structures that guarantee _productivity_ rather than termination.

There are a number of distributive laws, including sequenceA, distribute, and sequenceL. Yaya also provides others for specific recursion schemes.

A fixed-point operator for inductive / finite data structures.

NB: This is only guaranteed to be finite when f a is strict in a (having strict functors won't prevent Nu from being lazy). Using -XStrictData can help with this a lot.

A fixed-point operator for coinductive / potentially-infinite data structures.

This type class is lawless on its own, but there exist types that can’t implement the corresponding embed operation. Laws are induced by implementing either Steppable (which extends this) or Corecursive (which doesn’t).

Inductive structures that can be reasoned about in the way we usually do – with pattern matching.

Structures you can walk through step-by-step.

Converts an Algebra to one that annotates the tree with the result for each node.

Converts a Coalgebra to one that annotates the tree with the seed that generated each node.

By analogy with liftA2 (which also relies on Day, at least conceptually).

A less-constrained distribute for Identity.

This is just a more obvious name for composing lowerEnvT with your algebra directly.

Makes it possible to provide a GAlgebra to cata.

Makes it possible to provide a GAlgebraM to cataM.

Makes it possible to provide a GCoalgebra to ana.

Makes it possible to provide a GCoalgebraM to anaM.

Algebras over Day convolution are convenient for binary operations, but aren’t directly handleable by cata.

An implementation of == for any Recursive instance. Note that this is actually more general than Ord’s compare, as it can compare between different fixed-point representations of the same functor.

NB: Use recursiveCompare' if you need to use a custom comparator for f.

Since: 0.6.1.0

Like recursiveCompare, but allows you to provide a custom comparator for f.

Since: 0.6.1.0

An implementation of == for any Recursive instance. Note that this is actually more general than Eq’s ==, as it can compare between different fixed-point representations of the same functor.

NB: Use recursiveEq' if you need to use a custom comparator for f.

Like recursiveEq, but allows you to provide a custom comparator for f.

Since: 0.6.1.0

An implementation of showsPrec for any Recursive instance.

Like recursiveShowsPrec, but allows you to provide a custom display function for f.

Since: 0.6.1.0

A less-constrained sequenceA for Identity.

An implementation of readPrec for any Steppable instance.

NB: Use steppableReadPrec' if you need to use a custom parsing function for f.

NB: This only requires Steppable, but the inverse operation is recursiveShowsPrec, which requires Recursive instead.

Since: 0.6.1.0

Like steppableReadPrec, but allows you to provide a custom display function for f.

Since: 0.6.1.0

It is somewhat common to have a natural transformation that looks like η :: forall a. f a -> Free g a. This maps naturally to a GCoalgebra (to pass to apo) with η . project, but the desired Algebra is more likely to be cata unFree . η than embed . η. See yaya-streams for some examples of this.

Combines two AlgebraMs with different carriers into a single tupled AlgebraM.

Combines two Algebras with different carriers into a single tupled Algebra.