Related papers: When Agda met Vampire
We introduce a formal meta-language for probabilistic programming, capable of expressing both programs and the type systems in which they are embedded. We are motivated here by the desire to allow an AGI to learn not only relevant knowledge…
Formally verifying software properties is a highly desirable but labor-intensive task. Recent work has developed methods to automate formal verification using proof assistants, such as Coq and Isabelle/HOL, e.g., by training a model to…
Autoformalization addresses the scarcity of data for Automated Theorem Proving (ATP) by translating mathematical problems from natural language into formal statements. Efforts in recent work shift from directly prompting large language…
Type-preserving (or typed) compilation uses typing derivations to certify correctness properties of compilation. We have designed and implemented a type-preserving compiler for a simply-typed dialect of Prolog we call T-Prolog. The crux of…
This paper presents a combination of several automated reasoning and proof presentation tools with the Mizar system for formalization of mathematics. The combination forms an online service called MizAR, similar to the SystemOnTPTP service…
{log} ('setlog') is a satisfiability solver for formulas of the theory of finite sets and finite set relation algebra (FSTRA). As such, it can be used as an automated theorem prover (ATP) for this theory. {log} is able to automatically…
There is an apparent similarity between the descriptions of small-step operational semantics of imperative programs and the semantics of finite automata, so defining an abstraction mapping from semantics to automata and proving a simulation…
Abstract interpreters are complex pieces of software: even if the abstract interpretation theory and companion algorithms are well understood, their implementations are subject to bugs, that might question the soundness of their…
We present a general and user-extensible equality checking algorithm that is applicable to a large class of type theories. The algorithm has a type-directed phase for applying extensionality rules and a normalization phase based on…
Mella is a minimalistic dependently typed programming language and interactive theorem prover implemented in Haskell. Its main purpose is to investigate the effective integration of automated theorem provers in a pure and simple setting.…
This paper presents the Soda language for verifying multi-agent systems. Soda is a high-level functional and object-oriented language that supports the compilation of its code not only to Scala, a strongly statically typed high-level…
The growing complexity and diversity of models used in the engineering of dependable systems implies that a variety of formal methods, across differing abstractions, paradigms, and presentations, must be integrated. Such an integration…
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,…
A major challenge in applying machine learning to automated theorem proving is the scarcity of training data, which is a key ingredient in training successful deep learning models. To tackle this problem, we propose an approach that relies…
The TPTP World is the well established infrastructure that supports research, development, and deployment of Automated Theorem Proving (ATP) systems. The TPTP World supports a range of classical logics, and since release v9.0.0 has…
A key challenge in abstraction-based verification and control under complex specifications such as Linear Temporal Logic (LTL) is that abstract models retain significantly less information than their original systems. This issue is…
Answer Set Programming (ASP) is an important logic programming paradigm within the field of Knowledge Representation and Reasoning. As a concise, human-readable, declarative language, ASP is an excellent tool for developing trustworthy…
In this work we aim at applying automata techniques to problems studied in Dynamic Epistemic Logic, such as epistemic planning. To do so, we first remark that repeatedly executing ad infinitum a propositional event model from an initial…
The broader goal of this research, on the one hand, is to obtain the State of the Art in Automated Test Production (ATP), to find the open questions and related problems and to track the progress of researchers in the field, and on the…
When writing programs involving matrices or tensors in general, it is desirable to rule out the inconsistency of tensor shapes (i.e., the generalization of matrix sizes) before actual computation. For this purpose, some languages provide…