We study the logical semantics of an untyped λ-calculus equipped with operators representing read and write operations from and to a global store. Such a logic consists of an intersection type ...assignment system, which we derive from the denotational semantics of the calculus, based on the monadic approach to model computational λ-calculi.
The system is obtained by constructing a filter model in the category of ω-algebraic lattices, such that the typing rules can be recovered out of the term interpretation. By construction, the so-obtained type system satisfies the “type-semantics” property and completeness.
•State monad.•Imperative λ-calculus.•Intersection types assignment system.
We introduce interaction nets for a fragment of the differential lambda-calculus and exhibit in this framework a new symmetry between the
of course and the
why not modalities of linear logic, which ...is completely similar to the symmetry between the
tensor and
par connectives of linear logic. We use algebraic intuitions for introducing these nets and their reduction rules, and then we develop two correctness criteria (weak typability and acyclicity) and show that they guarantee strong normalization. Finally, we outline the correspondence between this interaction nets formalism and the resource lambda-calculus.
This paper considers the applicative computing technology (ACT), within the framework of which the semantic analysis of a number of natural language constructs is performed. The necessary elements of ...grammatical analysis are involved. Much first-order logical means is used, and predicate variables are necessarily used for analysis. At the same time, the advantages of higher-order systems, which include ACT, are extracted. The fact is that the semantics of a natural language is characterized by a multi-tiered nesting of grammatical structures, which conflicts with first-order logical systems.
Online algorithms and lambda calculus 28, In fact, few statisticians would disagree with the visualization of compilers, which embodies the key principles of complexity theory. Gab, our new ...application for superpages, is the solution to all of these problems.
An Understanding of IPv6 using Muck
International journal of recent technology and engineering,
9/2019, Volume:
8, Issue:
2S8
Journal Article
Open access
The cyber informatics solution to lambda calculus is defined not only by the emulation of 802.11 mesh networks, but also by the extensive need for expert systems. Following quite a while of natural ...examination into IPv4, we demonstrate the copying of superpages, which epitomizes the affirmed standards of algorithms. So as to understand this mission, we present an investigation of Byzantine adaptation to non-critical failure (Muck), which we use to demonstrate that the little-known decentralized algorithm for the improvement of voice-over-IP by White et al. 1 keeps running in O(N2) time.
Automatic differentiation in PCF Mazza, Damiano; Pagani, Michele
Proceedings of ACM on programming languages,
01/2021, Volume:
5, Issue:
POPL
Journal Article
Peer reviewed
Open access
We study the correctness of automatic differentiation (AD) in the context of a higher-order, Turing-complete language (PCF with real numbers), both in forward and reverse mode. Our main result is ...that, under mild hypotheses on the primitive functions included in the language, AD is almost everywhere correct, that is, it computes the derivative or gradient of the program under consideration except for a set of Lebesgue measure zero. Stated otherwise, there are inputs on which AD is incorrect, but the probability of randomly choosing one such input is zero. Our result is in fact more precise, in that the set of failure points admits a more explicit description: for example, in case the primitive functions are just constants, addition and multiplication, the set of points where AD fails is contained in a countable union of zero sets of polynomials.
We solve the inhabitation problem for a language called λ!, a subsuming paradigm (inspired by call-by-push-value) being able to encode, among others, call-by-name and call-by-value strategies of ...functional programming. The type specification uses a non-idempotent intersection type system, which is able to capture quantitative properties about the dynamics of programs. As an application, we show how our general methodology can be used to derive inhabitation algorithms for different lambda-calculi that are encodable into λ!.
The given paper considers a problem of generating words of a context-dependent language. It reviews the application of the problem to the unit testing of functions, examines in detail the use of ...generators in property-based testing. The context-dependent language of λ-calculus with a simple type system Λ→ is considered, and the problem is refined up to generating λ-terms with the given type within the given context. The article proposes a generation method that was implemented using the combinators of the fast-check library, which provides property-based testing in JavaScript.
We investigate encodings for modular arithmetic in the lambda-calculus. There are two approaches: adapting well-known numeral systems, and building a new one. This paper focuses on providing original ...techniques to encode modular arithmetic directly. We present a modular arithmetic numeral system complete with multiplication and an implementation of the Chinese remainder theorem, all without recursion i.e., without using fixed-point operators.
•Modular arithmetic has a simple implementation in the lambda-calculus.•The Chinese remainder theorem reduces computational complexity.•The Chinese remainder theorem has a simple implementation using pairs.
We investigate an unsuspected connection between logical connectives with non-harmonious deduction rules, such as Prior's tonk, and quantum computing. We argue that these connectives model the ...information-erasure, the non-reversibility, and the non-determinism that occur, among other places, in quantum measurement. We introduce an intuitionistic propositional logic with a non-harmonious logical connective sup and two interstitial rules, and show that the proof language of this logic forms the core of a quantum programming language.
•Introducing a propositional logic with non-harmonious rules and the ⊙ (read “sup”) connective.•The proof language of this logic forms core of a quantum programming language.•Non-harmonious rules of ⊙ model quantum properties of measurement: info-erasure, non-reversibility, non-determinism.
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