Related papers: From formal proofs to mathematical proofs: a safe,…
Although there are several systems that successfully generate construction steps for ruler and compass construction problems, none of them provides readable synthetic correctness proofs for generated constructions. In the present work, we…
We describe SeCaV, a sequent calculus verifier for first-order logic in Isabelle/HOL, and the SeCaV Unshortener, an online tool that expands succinct derivations into the full SeCaV syntax. We leverage the power of Isabelle/HOL as a proof…
Virtual integration techniques focus on building architectural models of systems that can be analyzed early in the design cycle to try to lower cost, reduce risk, and improve quality of complex embedded systems. Given appropriate…
For performance and verification in machine learning, new methods have recently been proposed that optimise learning systems to satisfy formally expressed logical properties. Among these methods, differentiable logics (DLs) are used to…
Initial Semantics aims at characterizing the syntax associated to a signature as the initial object of some category. We present an initial semantics result for typed higher-order syntax together with its formalization in the Coq proof…
The biggest challenge in hybrid systems verification is the handling of differential equations. Because computable closed-form solutions only exist for very simple differential equations, proof certificates have been proposed for more…
For formulas of the Implicational Propositional Calculus (IPC) that are theorems of the classical Propositional Calculus (PC) we show that PC proofs yield IPC proofs. As a consequence, completeness of PC yields completeness of IPC.
Formalization of real analysis offers a chance to rebuild traditional proofs of important theorems as unambiguous theories that can be interactively explored. This paper provides a comprehensive overview of the Lebesgue Differentiation…
In the context of interactive theorem provers based on a dependent type theory, automation tactics (dedicated decision procedures, call of automated solvers, ...) are often limited to goals which are exactly in some expected logical…
In functional programming, datatypes a la carte provide a convenient modular representation of recursive datatypes, based on their initial algebra semantics. Unfortunately it is highly challenging to implement this technique in proof…
An efficient entailment proof system is essential to compositional verification using separation logic. Unfortunately, existing decision procedures are either inexpressive or inefficient. For example, Smallfoot is an efficient procedure but…
Gradual verification soundly combines static checking and dynamic checking to provide an incremental approach for software verification. With gradual verification, programs can be partially specified first, and then the full specification…
This paper is a brief and informal presentation of cirquent calculus, a novel proof system for resource-conscious logics. As such, it is a refinement of sequent calculus with mechanisms that allow to explicitly account for the possibility…
Cantor's ordinal numbers, a powerful extension of the natural numbers, are a cornerstone of set theory. They can be used to reason about the termination of processes, prove the consistency of logical systems, and justify some of the core…
We propose a call-by-value lambda calculus extended with a new construct inspired by abductive inference and motivated by the programming idioms of machine learning. Although syntactically simple the abductive construct has a complex and…
In the former article "Formal mathematical systems including a structural induction principle" we have presented a unified theory for formal mathematical systems including recursive systems closely related to formal grammars, including the…
We present three projects concerned with applications of proof assistants in the area of programming language theory and mathematics. The first project is about a certified compilation technique for a domain-specific programming language…
Motivated by the transfer of proofs between proof systems, and in particular from first order automated theorem provers (ATPs) to interactive theorem provers (ITPs), we specify an extension of the TPTP derivation text format to describe…
Representing a proof tree by a combinator term that reduces to the tree lets subtle forms of duplication within the tree materialize as duplicated subterms of the combinator term. In a DAG representation of the combinator term these…
We develop foundations for computing Craig-Lyndon interpolants of two given formulas with first-order theorem provers that construct clausal tableaux. Provers that can be understood in this way include efficient machine-oriented systems…