Capturing the Future by Replaying the Past

TL;DR

This paper introduces thermometer continuations, a novel method to implement delimited continuations using exceptions and state by replaying computations, enabling monadic effects in languages lacking native support.

Contribution

It presents a new construction of delimited continuations from exceptions and state, expanding their applicability in programming languages.

Findings

Thermometer continuations can implement any monadic effect.

The method allows capturing intermediate states by replaying computations.

An elegant special-case for nondeterminism is provided.

Abstract

Delimited continuations are the mother of all monads! So goes the slogan inspired by Filinski's 1994 paper, which showed that delimited continuations can implement any monadic effect, letting the programmer use an effect as easily as if it was built into the language. It's a shame that not many languages have delimited continuations. Luckily, exceptions and state are also the mother of all monads! In this Pearl, we show how to implement delimited continuations in terms of exceptions and state, a construction we call $\textit{thermometer continuations}$. While traditional implementations of delimited continuations require some way of "capturing" an intermediate state of the computation, the insight of thermometer continuations is to reach this intermediate state by replaying the entire computation from the start, guiding it using a recording it so that the same thing happens until the captured point. Along the way, we explain delimited continuations and monadic reflection, show how the Filinski construction lets thermometer continuations express any monadic effect, share an elegant special-case for nondeterminism, and discuss why our construction is not prevented by theoretical results that exceptions and state cannot macro-express continuations.