DeepAI
Log In Sign Up

Sharing Equality is Linear

07/13/2019
by   Deleted, et al.
0

The λ-calculus is a handy formalism to specify the evaluation of higher-order programs. It is not very handy, however, when one interprets the specification as an execution mechanism, because terms can grow exponentially with the number of β-steps. This is why implementations of functional languages and proof assistants always rely on some form of sharing of subterms. These frameworks however do not only evaluate λ-terms, they also have to compare them for equality. In presence of sharing, one is actually interested in the equality---or more precisely α-conversion---of the underlying unshared λ-terms. The literature contains algorithms for such a sharing equality, that are polynomial in the sizes of the shared terms. This paper improves the bounds in the literature by presenting the first linear time algorithm. As others before us, we are inspired by Paterson and Wegman's algorithm for first-order unification, itself based on representing terms with sharing as DAGs, and sharing equality as bisimulation of DAGs.

READ FULL TEXT

page 1

page 2

page 3

page 4

08/10/2018

Proof Nets and the Linear Substitution Calculus

Since the very beginning of the theory of linear logic it is known how t...
11/25/2021

Sketch-Guided Equality Saturation: Scaling Equality Saturation to Complex Optimizations of Functional Programs

Generating high-performance code for diverse hardware and application do...
04/25/2019

The Epsilon Calculus with Equality and Herbrand Complexity

Hilbert's epsilon calculus is an extension of elementary or predicate ca...
07/14/2021

Useful Open Call-by-Need

This paper studies useful sharing, which is a sophisticated optimization...
06/01/2018

The encodability hierarchy for PCF types

Working with the simple types over a base type of natural numbers (inclu...
07/29/2020

Towards a Homotopy Domain Theory (HoDT)

A favourable environment is proposed for the achievement of λ-models wit...
05/17/2022

SCL(EQ): SCL for First-Order Logic with Equality

We propose a new calculus SCL(EQ) for first-order logic with equality th...