DeepAI AI Chat
Log In Sign Up

Semantic Analysis of Normalisation by Evaluation for Typed Lambda Calculus

07/18/2022
by   Marcelo Fiore, et al.
0

This paper studies normalisation by evaluation for typed lambda calculus from a categorical and algebraic viewpoint. The first part of the paper analyses the lambda definability result of Jung and Tiuryn via Kripke logical relations and shows how it can be adapted to unify definability and normalisation, yielding an extensional normalisation result. In the second part of the paper the analysis is refined further by considering intensional Kripke relations (in the form of Artin glueing) and shown to provide a function for normalising terms, casting normalisation by evaluation in the context of categorical glueing. The technical development includes an algebraic treatment of the syntax and semantics of the typed lambda calculus that allows the definition of the normalisation function to be given within a simply typed metatheory. A normalisation-by-evaluation program in a dependently-typed functional programming language is synthesised.

READ FULL TEXT

page 1

page 2

page 3

page 4

05/04/2022

Semimodules and the (syntactically-)linear lambda calculus

In a recent paper, the ℒ^𝒮-calculus has been defined. It is a proof-lang...
04/18/2019

Realizability in the Unitary Sphere

In this paper we present a semantics for a linear algebraic lambda-calcu...
05/25/2023

On the Simply-Typed Functional Machine Calculus: Categorical Semantics and Strong Normalisation

The Functional Machine Calculus (FMC) was recently introduced as a gener...
07/09/2020

Logic of computational semi-effects and categorical gluing for equivariant functors

In this paper, we revisit Moggi's celebrated calculus of computational e...
05/01/2023

The algebraic λ-calculus is a conservative extension of the ordinary λ-calculus

The algebraic λ-calculus is an extension of the ordinary λ-calculus with...
04/03/2018

The Logical Essentials of Bayesian Reasoning

This chapter offers an accessible introduction to the channel-based appr...
10/20/2020

Evaluation of Logic Programs with Built-Ins and Aggregation: A Calculus for Bag Relations

We present a scheme for translating logic programs, which may use aggreg...