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We describe several views of the semantics of a simple programming language as formal documents in the calculus of inductive constructions that can be verified by the Coq proof system. Covered aspects are natural semantics, denotational…
Artificial intelligence assisted mathematical proof has become a highly focused area nowadays. One key problem in this field is to generate formal mathematical proofs from natural language proofs. Due to historical reasons, the formal proof…
While Chain-of-Thought (CoT) prompting enhances the reasoning capabilities of large language models, the faithfulness of the generated rationales remains an open problem for model interpretability. We propose a novel theoretical lens for…
We sketch a simple language of concurrent objects which explores the design space between type systems and continuous testing. In our language, programs are collections of communicating automata checked automatically for multiparty…
Game Logic is an excellent setting to study proofs-about-programs via the interpretation of those proofs as programs, because constructive proofs for games correspond to effective winning strategies to follow in response to the opponent's…
In purely functional programming languages imperative features, more generally computational effects are prohibited. However, non-functional lan- guages do involve effects. The theory of decorated logic provides a rigorous for- malism (with…
We present the PML 2 language, which provides a uniform environment for programming, and for proving properties of programs in an ML-like setting. The language is Curry-style and call-by-value, it provides a control operator (interpreted in…
Algorithms are ways of mapping problems to solutions. An algorithm is invertible precisely when this mapping is injective, such that the initial problem can be uniquely inferred from its solution. While invertible algorithms can be…
Many logic programming based approaches can be used to describe and solve combinatorial search problems. On the one hand there is constraint logic programming which computes a solution as an answer substitution to a query containing the…
Formal verification provides strong guarantees of correctness of software, which are especially important in safety or security critical systems. Hoare logic is a widely used formalism for rigorous verification of software against…
We propose a general framework to allow: (a) specifying the operational semantics of a programming language; and (b) stating and proving properties about program correctness. Our framework is based on a many-sorted system of hybrid modal…
Design patterns are distilled from many real systems to catalog common programming practice. However, some object-oriented design patterns are distorted or overly complicated because of the lack of supporting programming language constructs…
An attempt at unifying logic and functional programming is reported. As a starting point, we take the view that "logic programs" are not about logic but constitute inductive definitions of sets and relations. A skeletal language design…
Logic languages based on the theory of rational, possibly infinite, trees have much appeal in that rational trees allow for faster unification (due to the safe omission of the occurs-check) and increased expressivity (cyclic terms can…
The predominant challenge in weakly supervised semantic parsing is that of spurious programs that evaluate to correct answers for the wrong reasons. Prior work uses elaborate search strategies to mitigate the prevalence of spurious…
Software contracts allow programmers to state rich program properties using the full expressive power of an object language. However, since they are enforced at runtime, monitoring contracts imposes significant overhead and delays error…
In this paper we propose an approach to reasoning about properties of imperative programs. We assume in this context that the meanings of program constructs are described using rules in the natural semantics style with the additional…
Loop invariants are fundamental to reasoning about programs with loops. They establish properties about a given loop's behavior. When they additionally are inductive, they become useful for the task of formal verification that seeks to…
Modern language models (LMs) exhibit strong deductive reasoning capabilities, yet standard evaluations emphasize correctness while overlooking a key aspect of reasoning: efficiency. In real-world reasoning scenarios, much of the available…
Programming languages are engineered languages that allow to instruct a machine and share algorithmic information; they have a great influence on the society since they underlie almost every information technology artefact, and they are at…