Higher-order demand-driven symbolic evaluation

Symbolic backwards execution (SBE) is a useful variation on standard forward symbolic evaluation; it allows a symbolic evaluation to start anywhere in the program and proceed by executing in reverse to the program start. SBE brings goal-directed reasoning to symbolic evaluation and has proven effective in e.g. automated test generation for imperative languages. In this paper we define DDSE, a novel SBE which operates on a functional as opposed to imperative language; furthermore, it is defined as a natural extension of a backwards-executing interpreter. We establish the soundness of DDSE and define a test generation algorithm for this toy language. We report on an initial reference implementation to confirm the correctness of the principles. CCS Concepts: • Software and its engineering → Software testing and debugging; Formal software verification; • Theory of computation → Programming logic; Logic and verification; Verification by model checking.

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Higher-order demand-driven symbolic evaluation

Palmer

Park

Smith

et al. 2020

Proc. ACM Program. Lang.

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A Pure Demand Operational Semantics with Applications to Program Analysis

Smith,

Zhang

2024

Proc. ACM Program. Lang.

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This paper develops a novel minimal-state operational semantics for higher-order functional languages that uses only the call stack and a source program point or a lexical level as the complete state information: there is no environment, no substitution, no continuation, etc. We prove this form of operational semantics equivalent to standard presentations. We then show how this approach can open the door to potential new applications: we define a program analysis as a direct finitization of this operational semantics. The program analysis that naturally emerges has a number of novel and interesting properties compared to standard program analyses for higher-order programs: for example, it can infer recurrences and does not need value widening. We both give a formal definition of the analysis and describe our current implementation.

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Story of Your Lazy Function’s Life: A Bidirectional Demand Semantics for Mechanized Cost Analysis of Lazy Programs

Xia,

Israel,

Kramarz

et al. 2024

Proc. ACM Program. Lang.

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Lazy evaluation is a powerful tool that enables better compositionality and potentially better performance in functional programming, but it is challenging to analyze its computation cost. Existing works either require manually annotating sharing, or rely on separation logic to reason about heaps of mutable cells. In this paper, we propose a bidirectional demand semantics that allows for extrinsic reasoning about the computation cost of lazy programs without relying on special program logics. To show the effectiveness of our approach, we apply the demand semantics to a variety of case studies including insertion sort, selection sort, Okasaki's banker's queue, and the implicit queue. We formally prove that the banker's queue and the implicit queue are both amortized and persistent using the Rocq Prover (formerly known as Coq). We also propose the reverse physicist's method, a novel variant of the classical physicist's method, which enables mechanized, modular and compositional reasoning about amortization and persistence with the demand semantics.

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Higher-order demand-driven symbolic evaluation

Cited by 4 publications

References 25 publications