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Register a new userTowards meta-interpretive learning of programming language semantics
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Added by
James Cheney
Publication date
2019
fields
Informatics Engineering
and research's language is
English
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We introduce a new application for inductive logic programming: learning the semantics of programming languages from example evaluations. In this short paper, we explored a simplified task in this domain using the Metagol meta-interpretive learning system. We highlighted the challenging aspects of this scenario, including abstracting over function symbols, nonterminating examples, and learning non-observed predicates, and proposed extensions to Metagol helpful for overcoming these challenges, which may prove useful in other domains.
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We make a formal analogy between random sampling and fresh name generation. We show that quasi-Borel spaces, a model for probabilistic programming, can soundly interpret Starks $ u$-calculus, a calculus for name generation. Moreover, we prove that this semantics is fully abstract up to first-order types. This is surprising for an off-the-shelf model, and requires a novel analysis of probability distributions on function spaces. Our tools are diverse and include descriptive set theory and normal forms for the $ u$-calculus.
It is well-known that big-step semantics is not able to distinguish stuck and non-terminating computations. This is a strong limitation as it makes very difficult to reason about properties involving infinite computations, such as type soundness, which cannot even be expressed. We show that this issue is only apparent: the distinction between stuck and diverging computations is implicit in any big-step semantics and it just needs to be uncovered. To achieve this goal, we develop a systematic study of big-step semantics: we introduce an abstract definition of what a big-step semantics is, we define a notion of computation by formalising the evaluation algorithm implicitly associated with any big-step semantics, and we show how to canonically extend a big-step semantics to characterise stuck and diverging computations. Building on these notions, we describe a general proof technique to show that a predicate is sound, that is, it prevents stuck computation, with respect to a big-step semantics. One needs to check three properties relating the predicate and the semantics and, if they hold, the predicate is sound. The extended semantics are essential to establish this meta-logical result, but are of no concerns to the user, who only needs to prove the three properties of the initial big-step semantics. Finally, we illustrate the technique by several examples, showing that it is applicable also in cases where subject reduction does not hold, hence the standard technique for small-step semantics cannot be used.
CSP-Agda is a library, which formalises the process algebra CSP in the interactive theorem prover Agda using coinductive data types. In CSP-Agda, CSP processes are in monadic form, which sup- ports a modular development of processes. In this paper, we implement two main models of CSP, trace and stable failures semantics, in CSP-Agda, and define the corresponding refinement and equal- ity relations. Because of the monadic setting, some adjustments need to be made. As an example, we prove commutativity of the external choice operator w.r.t. the trace semantics in CSP-Agda, and that refinement w.r.t. stable failures semantics is a partial order. All proofs and definitions have been type checked in Agda. Further proofs of algebraic laws will be available in the CSP-Agda repository.
Algorithmic and data refinement are well studied topics that provide a mathematically rigorous approach to gradually introducing details in the implementation of software. Program refinements are performed in the context of some programming language, but mainstream languages lack features for recording the sequence of refinement steps in the program text. To experiment with the combination of refinement, automated verification, and language design, refinement features have been added to the verification-aware programming language Dafny. This paper describes those features and reflects on some initial usage thereof.
While modern software development heavily uses versioned packages, programming languages rarely support the concept
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