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Some effects are considered to be higher-level than others. High-leveleffects provide expressive and succinct abstraction of programming concepts,while low-level effects allow more fine-grained control over program executionand resources. Yet, often it is desirable to write programs using theconvenient abstraction offered by high-level effects, and meanwhile stillbenefit from the optimisations enabled by low-level effects. One solution is totranslate high-level effects to low-level ones.  This paper studies how algebraic effects and handlers allow us to simulatehigh-level effects in terms of low-level effects. In particular, we focus onthe interaction between state and nondeterminism known as the local state, asprovided by Prolog. We map this high-level semantics in successive steps onto alow-level composite state effect, similar to that managed by Prolog's WarrenAbstract Machine. We first give a translation from the high-level local-statesemantics to the low-level global-state semantics, by explicitly restoringstate updates on backtracking. Next, we eliminate nondeterminsm altogether infavor of a lower-level state containing a choicepoint stack. Then we avoidcopying the state by restricting ourselves to incremental, reversible stateupdates. We show how these updates can be stored on a trail stack with anotherstate effect. We prove the correctness of all our steps using programcalculation where the fusion laws of effect handlers play a central role.

From High to Low: Simulating Nondeterminism and State with State