Relational nullable types with Boolean unification

Type and effect systems have been successfully used to statically reason about effects in many different domains, including region-based memory management, exceptions, and algebraic effects and handlers. Such systems’ soundness is often stated in terms of the absence of effects. Yet, existing systems only admit indirect reasoning about the absence of effects. This is further complicated by effect polymorphism which allows function signatures to abstract over arbitrary, unknown sets of effects. We present a new type and effect system with effect polymorphism as well as union, intersection, and complement effects. The effect system allows us to express effect exclusion as a new class of effect polymorphic functions: those that permit any effects except those in a specific set. This way, we equip programmers with the means to directly reason about the absence of effects. Our type and effect system builds on the Hindley-Milner type system, supports effect polymorphism, and preserves principal types modulo Boolean equivalence. In addition, a suitable extension of Algorithm W with Boolean unification on the algebra of sets enables complete type and effect inference. We formalize these notions in the λ ∁ calculus. We prove the standard progress and preservation theorems as well as a non-standard effect safety theorem: no excluded effect is ever performed. We implement the type and effect system as an extension of the Flix programming language. We conduct a case study of open source projects identifying 59 program fragments that require effect exclusion for correctness. To demonstrate the usefulness of the proposed type and effect system, we recast these program fragments into our extension of Flix.

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Fast and Efficient Boolean Unification for Hindley-Milner-Style Type and Effect Systems

Madsen,

van de Pol,

Henriksen

2023

Proc. ACM Program. Lang.

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As type and effect systems become more expressive there is an increasing need for efficient type inference. We consider a polymorphic effect system based on Boolean formulas where inference requires Boolean unification. Since Boolean unification involves semantic equivalence, conventional syntax-driven unification is insufficient. At the same time, existing Boolean unification techniques are ill-suited for type inference. We propose a hybrid algorithm for solving Boolean unification queries based on Boole’s Successive Variable Elimination (SVE) algorithm. The proposed approach builds on several key observations regarding the Boolean unification queries encountered in practice, including: (i) most queries are simple, (ii) most queries involve a few flexible variables, (iii) queries are likely to repeat due similar programming patterns, and (iv) there is a long tail of complex queries. We exploit these observations to implement several strategies for formula minimization, including ones based on tabling and binary decision diagrams. We implement the new hybrid approach in the Flix programming language. Experimental results show that by reducing the overhead of Boolean unification, the compilation throughput increases from 8,580 lines/sec to 15,917 lines/sec corresponding to a 1.8x speed-up. Further, the overhead on type and effect inference time is only 16% which corresponds to an overhead of less than 7% on total compilation time. We study the hybrid approach and demonstrate that each design choice improves performance.

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Relational nullable types with Boolean unification

Cited by 4 publications

References 39 publications

The Principles of the Flix Programming Language

The Principles of the Flix Programming Language

With or Without You: Programming with Effect Exclusion

Fast and Efficient Boolean Unification for Hindley-Milner-Style Type and Effect Systems

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