1,214 research outputs found
Semantics of a Typed Algebraic Lambda-Calculus
Algebraic lambda-calculi have been studied in various ways, but their
semantics remain mostly untouched. In this paper we propose a semantic analysis
of a general simply-typed lambda-calculus endowed with a structure of vector
space. We sketch the relation with two established vectorial lambda-calculi.
Then we study the problems arising from the addition of a fixed point
combinator and how to modify the equational theory to solve them. We sketch an
algebraic vectorial PCF and its possible denotational interpretations
Action semantics in retrospect
This paper is a themed account of the action semantics project, which Peter Mosses has led since the 1980s. It explains his motivations for developing action semantics, the inspirations behind its design, and the foundations of action semantics based on unified algebras. It goes on to outline some applications of action semantics to describe real programming languages, and some efforts to implement programming languages using action semantics directed compiler generation. It concludes by outlining more recent developments and reflecting on the success of the action semantics project
Introduction to the Literature on Semantics
An introduction to the literature on semantics. Included are pointers to the literature on axiomatic semantics, denotational semantics, operational semantics, and type theory
Enriched Lawvere Theories for Operational Semantics
Enriched Lawvere theories are a generalization of Lawvere theories that allow
us to describe the operational semantics of formal systems. For example, a
graph enriched Lawvere theory describes structures that have a graph of
operations of each arity, where the vertices are operations and the edges are
rewrites between operations. Enriched theories can be used to equip systems
with operational semantics, and maps between enriching categories can serve to
translate between different forms of operational and denotational semantics.
The Grothendieck construction lets us study all models of all enriched theories
in all contexts in a single category. We illustrate these ideas with the
SKI-combinator calculus, a variable-free version of the lambda calculus.Comment: In Proceedings ACT 2019, arXiv:2009.0633
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