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An algebra is a set of values, a set of operators that it is closed under and some laws it must obey. Each Fantasy Land algebra is a separate specification. An algebra may have dependencies on other algebras which must be implemented.

fantasy-land functional specification algebraic monad applicative functor monoid semigroup chain applyAbstractions and constructions from math (Category theory, Abstract algebra) implementations in Scala, minimal description, links to good explanations, links to implementations in other FP languages: Haskell, Idris, Purescript, non FP too: Java, C++ and to formalizations in proof assistants: Coq (UniMath, HoTT book), Cubical Agda.

category-theory monads comonads functor applicative-functors contravariant-functors free-monads free-applicative kan-extensions coyoneda yoneda arrows profunctors semigroup monoid day-convolution abstract-algebraAljebra provides toy implementations of the algebraic structures defined in the Fantasy Land specification, mostly borrowed from Haskell libraries. The following objects each implement a constructor allowing you to lift values into these base objects. Many of the other instances in this library are built on top of these base objects. As such, they implement a similar constructor pattern.

algebraic semigroup monoid functor applicative monadThe current version of libsemigroups is 0.6.3. libsemigroups is a C++ library for semigroups and monoids using C++11; it is partly based on Algorithms for computing finite semigroups, Expository Slides, and Semigroupe 2.01 by Jean-Eric Pin. libsemigroups uses catch for its unit tests.

computer-algebra semigroup monoid congruence enumerationThis was once provided by the semigroups package, but is now in the Haskell standard library as of base 4.9.0.0 in 2016. The partial semigroup associativity axiom is a natural adaptation of the semigroup associativity axiom, with a slight modification to accommodate the situations wherein x <> y = ⊥. First we'll express the axiom in terms of Semigroup and ⊥, and then we'll rephrase it in terms of PartialSemigroup.

haskell haskell-library algebraic-structures semigroup partial-semigroupSee How to start using co-log? for simple example of the co-log library usage.

haskell logging contravariant comonad semigroup dependent-typesFantasy Options uses nodeunit for all the tests and because of this there is currently an existing adapter in the library to help with integration between nodeunit and Fantasy Check. This assumes that you have istanbul installed correctly.

fantasyland tuples semigroup
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