Related papers: Lazy Evaluation and Delimited Control
Programming languages are expected to support programmer's effort to structure program code. The ML module system, object systems and mixins are good examples of language constructs promoting modular programming. Among the three, mixins can…
The lambda calculus is a widely accepted computational model of higher-order functional pro- grams, yet there is not any direct and universally accepted cost model for it. As a consequence, the computational difficulty of reducing lambda…
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…
Lazy evaluation is a powerful tool that enables better compositionality and potentially better performance in functional programming, but it is challenging to analyze its computation cost. Existing works either require manually annotating…
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,…
In this paper we invite the reader to a journey through three lambda calculi with resource control: the lambda calculus, the sequent lambda calculus, and the lambda calculus with explicit substitution. All three calculi enable explicit…
This paper presents the Functional Machine Calculus (FMC) as a simple model of higher-order computation with "reader/writer" effects: higher-order mutable store, input/output, and probabilistic and non-deterministic computation. The FMC…
We propose a call-by-value lambda calculus extended with a new construct inspired by abductive inference and motivated by the programming idioms of machine learning. Although syntactically simple the abductive construct has a complex and…
Whether the number of beta-steps in the lambda-calculus can be taken as a reasonable time cost model (that is, polynomially related to the one of Turing machines) is a delicate problem, which depends on the notion of evaluation strategy.…
We extend the {\lambda}-calculus with constructs suitable for relational and functional-logic programming: non-deterministic choice, fresh variable introduction, and unification of expressions. In order to be able to unify…
Convertibility checking - determining whether two lambda-terms are equal up to reductions - is a crucial component of proof assistants and dependently-typed languages. Practical implementations often use heuristics to quickly conclude that…
A cornerstone of the theory of lambda-calculus is that intersection types characterise termination properties. They are a flexible tool that can be adapted to various notions of termination, and that also induces adequate denotational…
In compositional model-theoretic semantics, researchers assemble truth-conditions or other kinds of denotations using the lambda calculus. It was previously observed that the lambda terms and/or the denotations studied tend to follow the…
We define a new cost model for the call-by-value lambda-calculus satisfying the invariance thesis. That is, under the proposed cost model, Turing machines and the call-by-value lambda-calculus can simulate each other within a polynomial…
We give a categorical semantics for a call-by-value linear lambda calculus. Such a lambda calculus was used by Selinger and Valiron as the backbone of a functional programming language for quantum computation. One feature of this lambda…
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…
This paper explores two topics at once: the use of denotational semantics to bound the evaluation length of functional programs, and the semantics of strong (that is, possibly under abstractions) call-by-value evaluation. About the first,…
Debugging lazy functional programs poses serious challenges. In support of the "stop, examine, and resume" debugging style of imperative languages, some debugging tools abandon lazy evaluation. Other debuggers preserve laziness but present…
We formally verify an abstract machine for a call-by-value lambda-calculus with de Bruijn terms, simple substitution, and small-step semantics. We follow a stepwise refinement approach starting with a naive stack machine with substitution.…
We examine the relationship between the algebraic lambda-calculus, a fragment of the differential lambda-calculus and the linear-algebraic lambda-calculus, a candidate lambda-calculus for quantum computation. Both calculi are algebraic:…