RATH

Relation-Algebraic Tools for Haskell

The RATH project strives to provide Haskell libraries for relation-algebraic treatment of relations and related structures, and for explorations in the meta-theory of relation algebras and related abstractions.

• The first release of the RATH-1 framework, produced in collaboration with Gunther Schmidt, was geared mainly towards computer-aided exploration of finite (non-standard) relation algebras, and relation-algebraic computation in these structures.
• Finite maps as provided by Data.Map in Haskell do not give rise to a category: On infinite types, like Integer, there is no identity, which would have to be a total map of type Map Integer Integer.

  An appropriate mathematical generalisation of categories are semigroupoids; I am currently working on a library of semigroupoid interfaces to relational datatypes in Haskell, see [Kahl-2006a_Semigroupoids].