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The idea of using unfolding as a way of computing a program semantics has been applied successfully to logic programs and has shown itself a powerful tool that provides concrete, implementable results, as its outcome is actually source…
Formal logic has often been seen as uniquely placed to analyze mathematical argumentation. While formal logic is certainly necessary for a complete understanding of mathematical practice, it is not sufficient. Important aspects of…
Rascal is a high-level transformation language that aims to simplify software language engineering tasks like defining program syntax, analyzing and transforming programs, and performing code generation. The language provides several…
Viewing formal mathematical proofs as logical terms provides a powerful and elegant basis for analyzing how human experts tend to structure proofs and how proofs can be structured by automated methods. We pursue this approach by (1)…
Building software-driven systems that are easily understood becomes a challenge, with their ever-increasing complexity and autonomy. Accordingly, recent research efforts strive to aid in designing explainable systems. Nevertheless, a common…
We introduce MPLSandbox, an out-of-the-box multi-programming language sandbox designed to provide unified and comprehensive feedback from compiler and analysis tools for Large Language Models (LLMs). It can automatically identify the…
This paper analyses the security contribution of typical functional-language features by examining them in the light of accepted information security principles. Imperative and functional code are compared to illustrate various cases. In…
As an approach to a Theory of Everything a framework for developing a coherent theory of mathematics and physics together is described. The main characteristic of such a theory is discussed: the theory must be valid and and sufficiently…
Legislation can be viewed as a body of prescriptive rules expressed in natural language. The application of legislation to facts of a case we refer to as statutory reasoning, where those facts are also expressed in natural language.…
Code sandboxes have emerged as a critical infrastructure for advancing the coding capabilities of large language models, providing verifiable feedback for both RL training and evaluation. However, existing systems fail to provide accurate…
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…
Legal interpretation is a linguistic venture. In judicial opinions, for example, courts are often asked to interpret the text of statutes and legislation. As time has shown, this is not always as easy as it sounds. Matters can hinge on…
The standard approach to logic in the literature in philosophy and mathematics, which has also been adopted in computer science, is to define a language (the syntax), an appropriate class of models together with an interpretation of…
Mathematical text is written using a combination of words and mathematical expressions. This combination, along with a specific way of structuring sentences makes it challenging for state-of-art NLP tools to understand and reason on top of…
Mathematical reasoning is essential for problem-solving in education, science, and industry, serving as a crucial benchmark for evaluating artificial intelligence systems. As Large Language Models (LLMs) improve their reasoning…
Algorithms like those for differentiating functional expressions manipulate the syntactic structure of mathematical expressions in a mathematically meaningful way. A formalization of such an algorithm should include a specification of its…
Term rewriting systems have a simple syntax and semantics and facilitate proofs of correctness. However, they are not as popular in industry or academia as imperative languages. We define a term rewriting based abstract programming language…
Computation is commonly defined as the execution of abstract algorithms over symbolic representations, with physical systems treated as substrates that realise predefined operations. While effective for engineered machines, this separation…
Type soundness is an important property of modern programming languages. In this paper we explore the idea that "well-typed languages are sound": the idea that the appropriate typing discipline over language specifications guarantees that…
Large Language Models (LLMs) have demonstrated impressive capabilities in structured reasoning and symbolic tasks, with coding emerging as a particularly successful application. This progress has naturally motivated efforts to extend these…