The arrow calculus
نویسندگان
چکیده
We introduce the arrow calculus, a metalanguage for manipulating Hughes’s arrows with close relations both to Moggi’s metalanguage for monads and to Paterson’s arrow notation. Arrows are classically defined by extending lambda calculus with three constructs satisfying nine (somewhat idiosyncratic) laws; in contrast, the arrow calculus adds four constructs satisfying five laws (which fit two well-known patterns). The five laws were previously known to be sound; we show that they are also complete, and hence that the five laws may replace the nine.
منابع مشابه
The Arrow Calculus (Functional Pearl)
We introduce the arrow calculus, a metalanguage for manipulating Hughes’s arrows with close relations both toMoggi’s metalanguage for monads and to Paterson’s arrow notation.
متن کاملA Rewriting Calculus for Graphs: Applications to Biology and Autonomous Systems. (Un calcul de réécriture de graphes : applications à la biologie et aux systèmes autonomes)
ions A first-order abstraction in the ρpg-calculus consists of two object port graphs for the leftand the right-hand sides, and an arrow node embedding the correspondence between the two sides. The arrow node has two particular ports, a handler port p0 and a black hole port bh. Some restrictions must be imposed on the connectivity of these two types of ports. A handler port can be connected onl...
متن کاملCategorifying Computations into Components via Arrows as Profunctors
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 with Heunen, Jacobs and Sokolova, we ...
متن کاملThe Mathematical Morpho-Logical View on Reasoning about Space
Qualitative reasoning about mereotopological relations has been extensively investigated, while more recently geometrical and spatio-temporal reasoning are gaining increasing attention. We propose to consider mathematical morphologic operators as the inspiration for a new language and inference mechanism to reason about space. Interestingly, the proposed morpho-logic captures not only tradition...
متن کاملCraig Interpolation in the Presence of Unreliable Connectives
Arrow and turnstile interpolations are investigated in UCL (introduced in [32]), a logic that is a complete extension of classical propositional logic for reasoning about connectives that only behave as expected with a given probability. Arrow interpolation is shown to hold in general and turnstile interpolation is established under some provisos. Mathematics Subject Classification (2010). 03B4...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- J. Funct. Program.
دوره 20 شماره
صفحات -
تاریخ انتشار 2010