Related papers: A Formal Theory of Choreographic Programming
Large language models are increasingly deployed in multi-agent workflows. We introduce Prompt Choreography, a framework that efficiently executes LLM workflows by maintaining a dynamic, global KV cache. Each LLM call can attend to an…
In this chapter, we propose some future directions of work, potentially beneficial to Mathematics and its foundations, based on the recent import of methodology from the theory of programming languages into proof theory. This scientific…
A theory graph is a network of axiomatic theories connected with meaning-preserving mappings called theory morphisms. Theory graphs are well suited for organizing large bodies of mathematical knowledge. Traditional and formal proofs do not…
Automated theorem provers and formal proof assistants are general reasoning systems that are in theory capable of proving arbitrarily hard theorems, thus solving arbitrary problems reducible to mathematics and logical reasoning. In…
Software testing is one of the most popular validation techniques in the software industry. Surprisingly, we can only find a few approaches to testing in the context of logic programming. In this paper, we introduce a systematic approach…
An informal discussion of how the construction problem in algebraic geometry motivates the search for formal proof methods. Also includes a brief discussion of my own progress up to now, which concerns the formalization of category theory…
Autoformalization has emerged as a term referring to the automation of formalization - specifically, the formalization of mathematics using interactive theorem provers (proof assistants). Its rapid development has been driven by progress in…
We present Pyrosome, a generic framework for modular language metatheory that embodies a novel approach to extensible semantics and compilation, implemented in Coq. Common techniques for semantic reasoning are often tied to the specific…
In order to work with mathematical content in computer systems, it is necessary to represent it in formal languages. Ideally, these are supported by tools that verify the correctness of the content, allow computing with it, and produce…
We describe a formalization of higher-order rewriting theory and formally prove that an AFS is strongly normalizing if it can be interpreted in a well-founded domain. To do so, we use Coq, which is a proof assistant based on dependent type…
This article revisits standard theorems from elementary number theory from a constructive, algorithmic, and proof-theoretic perspective, framed within the theory of computable functionals TCF. Key examples include B\'ezout's identity, the…
The free-variable tableau method has been widely used in order to automate proofs in multiple kinds of logics. Many automated theorem provers rely on this approach, either because it is the only available method-e.g., in certain modal…
Passive documents and active programs now widely comingle. Document languages include Turing-complete programming elements, and programming languages include sophisticated document notations. However, there are no formal foundations that…
We discuss a formal framework for using algebraic structures to model a meta-language that can write, compose, and provide interoperability between abstractions of DSLs. The purpose of this formal framework is to provide a verification of…
We study transformational program logics for correctness and incorrectness that we extend to explicitly handle both termination and nontermination. We show that the logics are abstract interpretations of the right image transformer for a…
In this position paper, we propose a reasoning framework that can model the reasoning process underlying natural language inferences. The framework is based on the semantic tableau method, a well-studied proof system in formal logic. Like…
We give a direct and elementary proof of the theorem on formal functions by studying the behaviour of the Godement resolution of a sheaf of modules under completion.
Constructor-Based Conditional Rewriting Logic is a general framework for integrating first-order functional and logic programming which gives an algebraic semantics for non-deterministic functional-logic programs. In the context of this…
Recently, we developed an automated theorem prover for projective incidence geometry. This prover, based on a combinatorial approach using matroids, proceeds by saturation using the matroid rules. It is designed as an independent tool,…
Music and dance have always co-existed as pillars of human activities, contributing immensely to the cultural, social, and entertainment functions in virtually all societies. Notwithstanding the gradual systematization of music and dance…