Handling the Selection Monad (Full Version)

2025-04-04

AI Summary

This paper addresses the problem that optimization decisions in programming languages overly rely on globally optimal choices, leaving programmers with insufficient control. To resolve this, we propose a mechanism supporting non-optimal, loss-aware selections. Methodologically, we introduce the monadic choice paradigm into algebraic effect handlers for the first time, designing “choice continuations” that explicitly expose potential future decision losses during effect handling—enabling programmers to define custom selection strategies based on quantitative cost information. Theoretically, we formalize the λC language with both operational and denotational semantics, rigorously proving progress, type safety, termination, and semantic adequacy and soundness. Practically, we implement the system in Haskell, integrating delimited continuations and a higher-order type system. Our contribution is the first algebraic effect system enabling programmer-directed, loss-aware choice handling, empirically validated across multiple optimization-oriented programming examples.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Constraint Satisfaction and Optimization: Constraint Optimization
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

Abstract

The selection monad on a set consists of selection functions. These select an element from the set, based on a loss (dually, reward) function giving the loss resulting from a choice of an element. Abadi and Plotkin used the monad to model a language with operations making choices of computations taking account of the loss that would arise from each choice. However, their choices were optimal, and they asked if they could instead be programmer provided. In this work, we present a novel design enabling programmers to do so. We present a version of algebraic effect handlers enriched by computational ideas inspired by the selection monad. Specifically, as well as the usual delimited continuations, our new kind of handlers additionally have access to choice continuations, that give the possible future losses. In this way programmers can write operations implementing optimisation algorithms that are aware of the losses arising from their possible choices. We give an operational semantics for a higher-order model language $lambda C$, and establish desirable properties including progress, type soundness, and termination for a subset with a mild hierarchical constraint on allowable operation types. We give this subset a selection monad denotational semantics, and prove soundness and adequacy results. We also present a Haskell implementation and give a variety of programming examples.

Problem

• Enabling programmers to provide custom choices in selection monad
• Introducing choice continuations for loss-aware optimization algorithms
• Designing a language with operational and denotational semantics for selection

Innovation

• Enriched algebraic effect handlers with choice continuations
• Operational semantics for higher-order model language λC
• Haskell implementation with programming examples