Kazuyuki Asada

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Hughes' <i>arrows</i> were shown, by Jacobs et al., to be roughly monads in the bicategory <b>Prof</b> of profunctors (distributors, modules). However in their work as well as others', the categorical nature of the <b>first</b> operator was not pursued and its formulation remained rather ad hoc. In this paper, we identify <b>first</b> with <i>strength</i>(More)
Structural recursion, in the form of, for example, folds on lists and catamorphisms on algebraic data structures including trees, plays an important role in functional programming, by providing a systematic way for constructing and manipulating functional programs. It is, however, a challenge to define structural recursions for graph data structures, the(More)
We introduce a lambda calculus &#955;<sup><i>T</i></sup><sub>FG</sub> for transformations of <i>finite</i> graphs by generalizing and extending an existing calculus UnCAL. Whereas UnCAL can treat only unordered graphs, &#955;<sup><i>T</i></sup><sub>FG</sub> can treat a variety of graph models: directed edge-labeled graphs whose branch styles are represented(More)
The notion of arrow by Hughes is an axiomatization of the algebraic structure possessed by structured computations in general. We claim that an arrow also serves as a basic component calculus for composing state-based systems as components—in fact, it is a categorified version of arrow that does so. In this paper, following the second author’s previous work(More)
Much progress has been made recently on fully automated verification of higher-order functional programs, based on refinement types and higher-order model checking. Most of those verification techniques are, however, based on <i>first-order</i> refinement types, hence unable to verify certain properties of functions (such as the equality of two recursive(More)
This paper introduces a variant of the resource calculus, the rigid resource calculus, in which a permutation of elements in a bag is distinct from but isomorphic to the original bag. It is designed so that the Taylor expansion within it coincides with the interpretation by generalised species of Fiore et al., which generalises both Joyal's combinatorial(More)
Overview We give: 1. the λ c 2 η-calculus (and λ c 2-calculus): a second-order polymorphic call-by-value calculus with extensional universal types 2. • λ c 2 η-models: categorical semantics for λ c 2 η-calculus • monadic λ c 2 η-models: categorical semantics for λ c 2 η-calculus with the focus on monadic metalanguages like Haskell 3. relevant parametric(More)