Topos Semantics for a Higher-Order Temporal Logic of Actions

by   Philip Johnson-Freyd, et al.

TLA is a popular temporal logic for writing stuttering-invariant specifications of digital systems. However, TLA lacks higher-order features useful for specifying modern software written in higher-order programming languages. We use categorical techniques to recast a real-time semantics for TLA in terms of the actions of a group of time dilations, or "stutters," and an extension by a monoid incorporating delays, or "falters." Via the geometric morphism of the associated presheaf topoi induced by the inclusion of stutters into falters, we construct the first model of a higher-order TLA.


page 1

page 2

page 3

page 4


Minimum Model Semantics for Extensional Higher-order Logic Programming with Negation

Extensional higher-order logic programming has been introduced as a gene...

Abstracting Definitional Interpreters

In this functional pearl, we examine the use of definitional interpreter...

Reflections on existential types

Existential types are reconstructed in terms of small reflective subuniv...

RANSAC: Identification of Higher-Order Geometric Features and Applications in Humanoid Robot Soccer

The ability for an autonomous agent to self-localise is directly proport...

An Expressive Probabilistic Temporal Logic

This paper argues that a combined treatment of probabilities, time and a...

Dynamic Symbolic Execution of Higher-Order Functions

The effectiveness of concolic testing deteriorates as the size of progra...

Local Local Reasoning: A BI-Hyperdoctrine for Full Ground Store

Modelling and reasoning about dynamic memory allocation is one of the we...