相关论文: First-order natural deduction in Agda

Real numbers in constructive mathematics have always seemed to require compromises of one form or another. Classical proofs of Cauchy completeness require countable choice, Bishop's setoid construction introduces persistent bookkeeping…

This talk describes how a combination of symbolic computation techniques with first-order theorem proving can be used for solving some challenges of automating program analysis, in particular for generating and proving properties about the…

Our research is part of a wider project that aims to investigate and reason about the correctness of scheme-based source code transformations of Erlang programs. In order to formally reason about the definition of a programming language and…

We describe our Natural Deduction Assistant (NaDeA) and the interfaces between the Isabelle proof assistant and NaDeA. In particular, we explain how NaDeA, using a generated prover that has been verified in Isabelle, provides feedback to…

Existential rules, a.k.a. dependencies in databases, and Datalog+/- in knowledge representation and reasoning recently, are a family of important logical languages widely used in computer science and artificial intelligence. Towards a deep…

Assurance cases can be used to argue for the safety of products in safety engineering. In safety-critical areas, the construction of assurance cases is indispensable. Trustworthiness Derivation Trees (TDTs) enhance assurance cases by…

We propose trace logic, an instance of many-sorted first-order logic, to automate the partial correctness verification of programs containing loops. Trace logic generalizes semantics of program locations and captures loop semantics by…

Using an AI assistant, we developed a method for systematically constructing controlled natural language for requirements based on formal specification patterns containing logical attributes. The method involves three stages: 1) compiling a…

We develop a dependent type theory that is based purely on inductive and coinductive types, and the corresponding recursion and corecursion principles. This results in a type theory with a small set of rules, while still being fairly…

The ability to cast values between related types is a leitmotiv of many flavors of dependent type theory, such as observational type theories, subtyping, or cast calculi for gradual typing. These casts all exhibit a common structural…

First-order linear temporal logic (FOLTL) is a flexible and expressive formalism capable of naturally describing complex behaviors and properties. Although the logic is in general highly undecidable, the idea of using it as a specification…

The expression problem describes how most types can easily be extended with new ways to produce the type or new ways to consume the type, but not both. When abstract syntax trees are defined as an algebraic data type, for example, they can…

For efficiency reasons, the software system designers' will is to use an integrated set of methods and tools to describe specifications and designs, and also to perform analyses such as dependability, schedulability and performance. AADL…

We present a domain-specific type theory for constructions and proofs in category theory. The type theory axiomatizes notions of category, functor, profunctor and a generalized form of natural transformations. The type theory imposes an…

This article presents liquid resource types, a technique for automatically verifying the resource consumption of functional programs. Existing resource analysis techniques trade automation for flexibility -- automated techniques are…

We employ the dependently-typed programming language Agda2 to explore formalisation of untyped and typed term graphs directly as set-based graph structures, via the gs-monoidal categories of Corradini and Gadducci, and as nested…

This paper improves the treatment of equality in guarded dependent type theory (GDTT), by combining it with cubical type theory (CTT). GDTT is an extensional type theory with guarded recursive types, which are useful for building models of…

Incorporating specific knowledge into large language models via retrieval-augmented generation (RAG) is a widespread technique that fuels many of today's industry AI applications. A fundamental problem is to assess if the context retrieved…

The main aim of the paper is to give a short self-contained proof of the decidability of language equivalence for deterministic pushdown automata, which is the famous problem solved by G. Senizergues, for which C. Stirling has derived a…

We introduce a simple functional language foetus (lambda calculus with tuples, constructors and pattern matching) supplied with a termination checker. This checker tries to find a well-founded structural order on the parameters on the given…