12 research outputs found
A 2-categories companion
This paper is a rather informal guide to some of the basic theory of
2-categories and bicategories, including notions of limit and colimit,
2-dimensional universal algebra, formal category theory, and nerves of
bicategories. As is the way of these things, the choice of topics is somewhat
personal. No attempt is made at either rigour or completeness. Nor is it
completely introductory: you will not find a definition of bicategory; but then
nor will you really need one to read it. In keeping with the philosophy of
category theory, the morphisms between bicategories play more of a role than
the bicategories themselves.Comment: 73 pages; published in Towards Higher Categories, eds. John C. Baez
and J. Peter May, Springer, 200
Modules over monads and operational semantics
This paper is a contribution to the search for efficient and high-level
mathematical tools to specify and reason about (abstract) programming languages
or calculi. Generalising the reduction monads of Ahrens et al., we introduce
transition monads, thus covering new applications such as
lambda-bar-mu-calculus, pi-calculus, Positive GSOS specifications, differential
lambda-calculus, and the big-step, simply-typed, call-by-value lambda-calculus.
Moreover, we design a suitable notion of signature for transition monads
Categorical semantics and composition of tree transducers
In this thesis we see two new approaches to compose tree transducers and more general to fuse functional programs. The first abroach is based on initial algebras. We prove a new variant of the acid rain theorem for mutually recursive functions where the build function is substituted by a concrete functor. Moreover, we give a symmetric form (i.e. consumer and producer have the same syntactic form) of our new acid rain theorem where fusion is composition in a category and thus in particular associative. Applying this to compose top-down tree transducers yields the same result (on a syntactic level) as the classical top-down tree transducer composition. The second approach is based on free monads and monad transformers. In the same way as monoids are used in the theory of character string automata, we use monads in the theory of tree transducers. We generalize the notion of a tree transducer defining the monadic transducer, and we prove an according fusion theorem. Moreover, we prove that homomorphic monadic transducers are semantically equivalent. The latter makes it possible to compose syntactic classes of tree transducers (or particular functional programs) by simply composing endofunctors