Lambda Calculus with Explicit Read-back

TL;DR

This paper presents a simplified term rewriting system for lambda calculus with explicit read-back, proving its correctness, uniqueness of reduction sequences, and representation of the normalizing leftmost strategy.

Contribution

It introduces a more accessible rewriting system for lambda calculus with explicit read-back, facilitating analysis and verification of properties.

Findings

Correctly represents lambda calculus.

Ensures unique reduction sequences for any term.

Models the normalizing leftmost reduction strategy.

Abstract

This paper introduces a new term rewriting system that is similar to the embedded read-back mechanism for interaction nets presented in our previous work, but is easier to follow than in the original setting and thus to analyze its properties. Namely, we verify that it correctly represents the lambda calculus. Further, we show that there is exactly one reduction sequence that starts with any term in our term rewriting system. Finally, we represent the leftmost strategy which is known to be normalizing.