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We propose a new approach to formally describing the requirement for statistical inference and checking whether a program uses the statistical method appropriately. Specifically, we define belief Hoare logic (BHL) for formalizing and…
We present a Hoare logic that extends program specifications with regular expressions that capture behaviors in terms of sequences of events that arise during the execution. The idea is similar to session types or process-like behavioral…
The general completeness problem of Hoare logic relative to the standard model $N$ of Peano arithmetic has been studied by Cook, and it allows for the use of arbitrary arithmetical formulas as assertions. In practice, the assertions would…
Artificial intelligence techniques are increasingly being applied to solve control problems, but often rely on black-box methods without transparent output generation. To improve the interpretability and transparency in control systems,…
This paper introduces Isabelle/HoTT, the first development of homotopy type theory in the Isabelle proof assistant. Building on earlier work by Paulson, I use Isabelle's existing logical framework infrastructure to implement essential…
We extend the framework of abstract algebraic logic to weak logics, namely logical systems which are not necessarily closed under uniform substitution. We interpret weak logics by algebras expanded with an additional predicate and we…
Weak-memory models are standard formal specifications of concurrency across hardware, programming languages, and distributed systems. A fundamental computational problem is consistency testing: is the observed execution of a concurrent…
An interactive theorem prover, Isabelle, is under development. In LCF, each inference rule is represented by one function for forwards proof and another (a tactic) for backwards proof. In Isabelle, each inference rule is represented by a…
Modern functional-logic programming languages like Toy or Curry feature non-strict non-deterministic functions that behave under call-time choice semantics. A standard formulation for this semantics is the CRWL logic, that specifies a proof…
We argue that verification of recursive programs by means of the assertional method of C.A.R. Hoare can be conceptually simplified using a modular reasoning. In this approach some properties of the program are established first and…
We present the guarded lambda-calculus, an extension of the simply typed lambda-calculus with guarded recursive and coinductive types. The use of guarded recursive types ensures the productivity of well-typed programs. Guarded recursive…
The multi-valued logic of {\L}ukasiewicz is a substructural logic that has been widely studied and has many interesting properties. It is classical, in the sense that it admits the axiom schema of double negation, [DNE]. However, our…
We consider Hoare-style verification for the graph programming language GP 2. In previous work, graph properties were specified by so-called E-conditions which extend nested graph conditions. However, this type of assertions is not easy to…
A grammar formalism based upon CHR is proposed analogously to the way Definite Clause Grammars are defined and implemented on top of Prolog. These grammars execute as robust bottom-up parsers with an inherent treatment of ambiguity and a…
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…
The code intelligence (CI) models are often black-box and do not offer any insights on the input features that they learn for making correct predictions. This opacity may lead to distrust in their prediction and hamper their wider adoption…
LF is a dependent type theory in which many other formal systems can be conveniently embedded. However, correct use of LF relies on nontrivial metatheoretic developments such as proofs of correctness of decision procedures for LF's…
Scientists form hypotheses and experimentally test them. If a hypothesis fails (is refuted), scientists try to explain the failure to eliminate other hypotheses. The more precise the failure analysis the more hypotheses can be eliminated.…
Write-Once-Memory (WOM) is a model for many modern non-volatile memories, such as flash memories. Recently, several capacity-achieving WOM coding schemes have been proposed based on polar coding. Due to the fact that practical computer…
This paper presents a proof system for reasoning about execution time bounds for a core imperative programming language. Proof systems are defined for three different scenarios: approximations of the worst-case execution time, exact time…