Semantics of a Relational λ-Calculus (Extended Version)

09/23/2020
by   Pablo Barenbaum, et al.
0

We extend the λ-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 λ-expressions and still obtain a confluent theory, we depart from related approaches, such as λProlog, in that we do not attempt to solve higher-order unification. Instead, abstractions are decorated with a location, which intuitively may be understood as its memory address, and we impose a simple coherence invariant: abstractions in the same location must be equal. This allows us to formulate a confluent small-step operational semantics which only performs first-order unification and does not require strong evaluation (below lambdas). We study a simply typed version of the system. Moreover, a denotational semantics for the calculus is proposed and reduction is shown to be sound with respect to the denotational semantics.

READ FULL TEXT
POST COMMENT

Comments

There are no comments yet.

Authors

page 1

page 2

page 3

page 4

02/27/2018

Relational Reasoning for Markov Chains in a Probabilistic Guarded Lambda Calculus

We extend the simply-typed guarded λ-calculus with discrete probabilitie...
11/26/2020

Universal Semantics for the Stochastic Lambda-Calculus

We define sound and adequate denotational and operational semantics for ...
07/16/2019

Recovering Purity with Comonads and Capabilities

In this paper, we take a pervasively effectful (in the style of ML) type...
07/12/2021

Coherent differentiation

The categorical models of the differential lambda-calculus are additive ...
12/27/2018

Towards a Semantic Measure of the Execution Time in Call-by-Value lambda-Calculus (Long Version)

We investigate the possibility of a semantic account of the execution ti...
04/16/2019

The Geometry of Bayesian Programming

We give a geometry of interaction model for a typed lambda-calculus endo...
04/28/2021

Semantic Bounds and Strong Call-by-Value Normalization

This paper explores two topics at once: the use of denotational semantic...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.