Memoisation: Purely, Left-recursively, and with (Continuation Passing) Style

TL;DR

This paper explores various approaches to memoisation, including purely functional, left-recursive, and continuation passing styles, demonstrating a novel implementation in OCaml that preserves functional purity and handles left-recursion effectively.

Contribution

It presents a purely functional implementation of Johnson's continuation passing memoisation approach in OCaml, handling left-recursion without mutation.

Findings

Purely functional memoisation can handle left-recursion effectively.

The OCaml implementation uses a monadic interface to abstract memo table details.

The approach enables compact representation of memo tables after computation.

Abstract

Memoisation, or tabling, is a well-known technique that yields large improvements in the performance of some recursive computations. Tabled resolution in Prologs such as XSB and B-Prolog can transform so called left-recursive predicates from non-terminating computations into finite and well-behaved ones. In the functional programming literature, memoisation has usually been implemented in a way that does not handle left-recursion, requiring supplementary mechanisms to prevent non-termination. A notable exception is Johnson's (1995) continuation passing approach in Scheme. This, however, relies on mutation of a memo table data structure and coding in explicit continuation passing style. We show how Johnson's approach can be implemented purely functionally in a modern, strongly typed functional language (OCaml), presented via a monadic interface that hides the implementation details, yet providing a way to return a compact represention of the memo tables at the end of the computation.