Related papers: Decomposing Probabilistic Lambda-calculi
We investigate the possibility of a semantic account of the execution time (i.e. the number of beta-steps leading to the normal form, if any) for the shuffling calculus, an extension of Plotkin's call-by-value lambda-calculus. For this…
Computing the probability of a formula given the probabilities or weights associated with other formulas is a natural extension of logical inference to the probabilistic setting. Surprisingly, this problem has received little attention in…
Safety is a syntactic condition of higher-order grammars that constrains occurrences of variables in the production rules according to their type-theoretic order. In this paper, we introduce the safe lambda calculus, which is obtained by…
We investigate the possibility of a semantic account of the execution time (i.e. the number of \beta_v-steps leading to the normal form, if any) for the shuffling calculus, an extension of Plotkin's call-by-value {\lambda}-calculus. For…
We show that lambda calculus is a computation model which can step by step simulate any sequential deterministic algorithm for any computable function over integers or words or any datatype. More formally, given an algorithm above a family…
We introduce the structural resource lambda-calculus, a new formalism in which strongly normalizing terms of the lambda-calculus can naturally be represented, and at the same time any type derivation can be internally rewritten to its…
A famous result by Milner is that the lambda-calculus can be simulated inside the pi-calculus. This simulation, however, holds only modulo strong bisimilarity on processes, i.e. there is a slight mismatch between beta-reduction and how it…
Probabilistic programming languages have recently gained a lot of attention, in particular due to their applications in domains such as machine learning and differential privacy. To establish invariants of interest, many such languages…
Filinski constructed a symmetric lambda-calculus consisting of expressions and continuations which are symmetric, and functions which have duality. In his calculus, functions can be encoded to expressions and continuations using primitive…
Recently, Miller and Wu introduced the positive $\lambda$-calculus, a call-by-value $\lambda$-calculus with sharing obtained by assigning proof terms to the positively polarized focused proofs for minimal intuitionistic logic. The positive…
It is commonly agreed that the success of future proof assistants will rely on their ability to incorporate computations within deduction in order to mimic the mathematician when replacing the proof of a proposition P by the proof of an…
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 present an abstract machine that implements a full-reducing (a.k.a. strong) call-by-value strategy for pure $\lambda$-calculus. It is derived using Danvy et al.'s functional correspondence from Cr\'egut's KN by: (1) deconstructing KN to…
The elegant theory of the call-by-value lambda-calculus relies on weak evaluation and closed terms, that are natural hypotheses in the study of programming languages. To model proof assistants, however, strong evaluation and open terms are…
The resource calculus is an extension of the lambda-calculus allowing to model resource consumption. It is intrinsically non-deterministic and has two general notions of reduction - one parallel, preserving all the possible results as a…
We study the two Girard's translations of intuitionistic implication into linear logic by exploiting the bang calculus, a paradigmatic functional language with an explicit box-operator that allows both call-by-name and call-by-value…
This paper concerns the explicit treatment of substitutions in the lambda calculus. One of its contributions is the simplification and rationalization of the suspension calculus that embodies such a treatment. The earlier version of this…
Driven by the interest of reasoning about probabilistic programming languages, we set out to study a notion of unicity of normal forms for them. To provide a tractable proof method for it, we define a property of distribution confluence…
We develop the operational semantics of an untyped probabilistic lambda-calculus with continuous distributions, as a foundation for universal probabilistic programming languages such as Church, Anglican, and Venture. Our first contribution…
We define sound and adequate denotational and operational semantics for the stochastic lambda calculus. These two semantic approaches build on previous work that used similar techniques to reason about higher-order probabilistic programs,…