Related papers: An Abstract Machine for Strong Call by Value
Cody & Waite argument reduction technique works perfectly for reasonably large arguments but as the input grows there are no bit left to approximate the constant with enough accuracy. Under mild assumptions, we show that the result computed…
The Functional Machine Calculus (FMC, Heijltjes 2022) extends the lambda-calculus with the computational effects of global mutable store, input/output, and probabilistic choice while maintaining confluent reduction and simply-typed strong…
We show that call-by-need is observationally equivalent to weak-head needed reduction. The proof of this result uses a semantical argument based on a (non-idempotent) intersection type system called $\mathcal{V}$. Interestingly, system…
The call-by-value lambda calculus can be endowed with permutation rules, arising from linear logic proof-nets, having the advantage of unblocking some redexes that otherwise get stuck during the reduction. We show that such an extension…
We present a technique to study normalizing strategies when termination is asymptotic, that is, it appears as a limit, as opposite to reaching a normal form in a finite number of steps. Asymptotic termination occurs in several settings,…
Under the extension of Curry-Howard's correspondence to classical logic, Gentzen's NK and LK systems can be seen as syntax-directed systems of simple types respectively for Parigot's Lambda Mu Calculus and Curien-Herbelin's Lambda Bar Mu Mu…
Recent analysis of classical algorithms resulted in their axiomatization as transition systems satisfying some simple postulates, and in the formulation of the Abstract State Machine Theorem, which assures us that any classical algorithm…
An abstract machine is a theoretical model designed to perform a rigorous study of computation. Such a model usually consists of configurations, instructions, programs, inputs and outputs for the machine. In this paper we formalize these…
Many different systems with explicit substitutions have been proposed to implement a large class of higher-order languages. Motivations and challenges that guided the development of such calculi in functional frameworks are surveyed in the…
We consider the probabilistic applicative bisimilarity (PAB), a coinductive relation comparing the applicative behaviour of probabilistic untyped lambda terms according to a specific operational semantics. This notion has been studied with…
Calculational abstract interpretation, long advocated by Cousot, is a technique for deriving correct-by-construction abstract interpreters from the formal semantics of programming languages. This paper addresses the problem of deriving…
We prove the Stability Property for the call-by-value $\lambda$-calculus (CbV in the following). This result states necessary conditions under which the contexts of the CbV $\lambda$-calculus commute with intersections of approximants. This…
In this paper we introduce a typed, concurrent $\lambda$-calculus with references featuring explicit substitutions for variables and references. Alongside usual safety properties, we recover strong normalization. The proof is based on a…
Higher-order representations of objects such as programs, proofs, formulas and types have become important to many symbolic computation tasks. Systems that support such representations usually depend on the implementation of an intensional…
The intuitionistic fragment of the call-by-name version of Curien and Herbelin's \lambda\_mu\_{\~mu}-calculus is isolated and proved strongly normalising by means of an embedding into the simply-typed lambda-calculus. Our embedding is a…
Long-form numerical reasoning in financial analysis aims to generate a reasoning program to calculate the correct answer for a given question. Previous work followed a retriever-generator framework, where the retriever selects key facts…
We consider the non-deterministic extension of the call-by-value lambda calculus, which corresponds to the additive fragment of the linear-algebraic lambda-calculus. We define a fine-grained type system, capturing the right linearity…
Approximation semantics capture the observable behaviour of {\lambda}-terms, with B\"ohm Trees and Taylor Expansion standing as two central paradigms. Although conceptually different, these notions are related via the Commutation Theorem,…
We define the syntax and reduction relation of a recursively typed lambda calculus with a parallel case-function (a parallel conditional). The reduction is shown to be confluent. We interpret the recursive types as information systems in a…
We adapt Fiore, Plotkin, and Turi's treatment of abstract syntax with binding, substitution, and holes to account for languages with second-class sorts. These situations include programming calculi such as the Call-by-Value lambda-calculus…