916 papers · page 3 of 46
Abstract We present PolyChor $\lambda$ , a language for higher-order functional choreographic programming —an emerging paradigm for concurrent programming. In choreographic programming, programmers write the desired cooperative behaviour of a system of processes and then compile …
Abstract We study a fundamental efficiency benefit afforded by delimited control, showing that for certain higher-order functions, a language with advanced control features offers an asymptotic improvement in runtime over a language without them. Specifically, we consider the gen…
Although Abstracting Gradual Typing provides a systematic approach to design gradual languages, the original framework has limitations: first, it accepts design choices that lead to type inconsistencies sneaking through evaluation.Second, when a type inconsistency is identified a…
Abstract Gradual typing provides a model for when a legacy language with less precise types interacts with a newer language with more precise types. Casts mediate between types of different precision, allocating blame when a value fails to conform to a type. The blame theorem ass…
Abstract Invertibility is a fundamental concept in computer science, with various manifestations in software development (serializer/deserializer, parser/printer, redo/undo, compressor/decompressor, and so on). Full invertibility necessarily requires bijectivity, but the direct a…
Abstract The Knuth–Morris–Pratt (KMP) algorithm for string search is notoriously difficult to understand. Lost in a sea of index arithmetic, most explanations of KMP obscure its essence. This paper constructs KMP incrementally, using pictures to illustrate each step. The end resu…
Abstract Some top-down problem specifications, if executed, may compute sub-problems repeatedly. Instead, we may want a bottom-up algorithm that stores solutions of sub-problems in a table to be reused. How the table can be represented and efficiently maintained, however, can be …
Functional Programming for the Masses" Second Edition, by
Abstract We present an arrow calculus with operations and handlers and its operational and denotational semantics. The calculus is an extension of Lindley, Wadler and Yallop’s arrow calculus. The denotational semantics is given using a strong (pro)monad $\mathcal{A}$ in the bicat…
Abstract The naive combination of polymorphic effects and polymorphic type assignment has been well known to break type safety. In the literature, there are two kinds of approaches to this problem: one is to restrict how effects are triggered and the other is to restrict how they…
ContextCombinator libraries have been well studied in countless papers.Indeed, as Peyton Jones, Eber, and Seward wrote in 2000, At this point, any red-blooded functional programmer should start to foam at the mouth, yelling "build a combinator library."(Peyton Jones et al., 2000)
Abstract Gradual typing integrates static and dynamic typing by introducing a dynamic type and a consistency relation. A problem of gradual type systems is that dynamic types can easily hide erroneous data flows since consistency relations are not transitive. Therefore, a more ri…
Abstract Some effects are considered to be higher level than others. High-level effects provide expressive and succinct abstraction of programming concepts, while low-level effects allow more fine-grained control over program execution and resources. Yet, often it is desirable to…
Abstract The semantics of gradually typed languages is typically given indirectly via an elaboration into a cast calculus. This contrasts with more conventional formulations of programming language semantics, where the semantics of a language is given directly using, for instance…
Abstract In the cons-free programming paradigm, we eschew constructors and program using only destructors. Cons-free programs in a simple first-order language with string data capture exactly P, the class of polynomial-time relations. By varying the underlying language and consid…
Abstract Contemporary proof assistants such as Coq require that recursive functions be terminating and corecursive functions be productive to maintain logical consistency of their type theories, and some ensure these properties using syntactic checks. However, being syntactic, th…
Abstract The equivalence of folding left and right over Peano numbers and lists makes it possible to minimalistically inter-derive (1) structurally recursive functions in direct style, (2) structurally tail-recursive functions that use an accumulator, and (3) structurally tail-re…
Abstract Recursion is a mature, well-understood topic in the theory and practice of programming. Yet its dual, corecursion is underappreciated and still seen as exotic. We aim to put them both on equal footing by giving a foundation for primitive corecursion based on computation,…
The other day, I was assembling lecture material for a course on Agda. Pursuing an application-driven approach, I was looking for correctness proofs of popular algorithms. One of my all-time favourites is Huffman data compression (Huffman, 1952). Even though it is probably safe t…