DeepAI AI Chat
Log In Sign Up

Nominal Matching Logic

07/28/2022
by   James Cheney, et al.
King's College London
0

We introduce Nominal Matching Logic (NML) as an extension of Matching Logic with names and binding following the Gabbay-Pitts nominal approach. Matching logic is the foundation of the 𝕂 framework, used to specify programming languages and automatically derive associated tools (compilers, debuggers, model checkers, program verifiers). Matching logic does not include a primitive notion of name binding, though binding operators can be represented via an encoding that internalises the graph of a function from bound names to expressions containing bound names. This approach is sufficient to represent computations involving binding operators, but has not been reconciled with support for inductive reasoning over syntax with binding (e.g., reasoning over λ-terms). Nominal logic is a formal system for reasoning about names and binding, which provides well-behaved and powerful principles for inductive reasoning over syntax with binding, and NML inherits these principles. We discuss design alternatives for the syntax and the semantics of NML, prove meta-theoretical properties and give examples to illustrate its expressive power. In particular, we show how induction principles for λ-terms (α-structural induction) can be defined and used to prove standard properties of the λ-calculus.

READ FULL TEXT

page 1

page 2

page 3

page 4

06/12/2018

Syntax and Semantics of Cedille

This document presents the syntax, classification rules, realizability s...
01/26/2021

A program logic for fresh name generation

We present a program logic for Pitts and Stark's ν-calculus, an extensio...
01/02/2023

Nominal Recursors as Epi-Recursors

We study nominal recursors from the literature on syntax with bindings a...
07/16/2021

Countability of Inductive Types Formalized in the Object-Logic Level

The set of integer number lists with finite length, and the set of binar...
02/11/2022

Inference with System W Satisfies Syntax Splitting

In this paper, we investigate inductive inference with system W from con...
07/15/2020

Computational Logic for Biomedicine and Neurosciences

We advocate here the use of computational logic for systems biology, as ...