Related papers: Incoherent coherences
interpreters are tools to compute approximations for behaviors of a program. These approximations can then be used for optimisation or for error detection. In this paper, we show how to describe an abstract interpreter using the type-theory…
It is often useful, if not necessary, to reason about the syntactic structure of an expression in an interpreted language (i.e., a language with a semantics). This paper introduces a mathematical structure called a syntax framework that is…
We present an approach for representing abstract argumentation frameworks based on an encoding into classical higher-order logic. This provides a uniform framework for computer-assisted assessment of abstract argumentation frameworks using…
Abstract predicates are considered in this paper as abstraction technique for heap-separated configurations, and as genuine Prolog predicates which are translated straight into a corresponding formal language grammar used as validation…
In previous work ("From signatures to monads in UniMath"), we described a category-theoretic construction of abstract syntax from a signature, mechanized in the UniMath library based on the Coq proof assistant. In the present work, we…
The operational semantics of interactive systems is usually described by labeled transition systems. Abstract semantics (that is defined in terms of bisimilarity) is characterized by the final morphism in some category of coalgebras. Since…
General coherence theorems are constructed that yield explicit presentations of categorical and algebraic objects. The categorical structures involved are finitary discrete Lawvere 2-theories, though they are approached within the language…
We introduce a novel approach to secure compilation based on maps of distributive laws. We demonstrate through four examples that the coherence criterion for maps of distributive laws can potentially be a viable alternative for compiler…
SYNTAGMA is a rule-based parsing system, structured on two levels: a general parsing engine and a language specific grammar. The parsing engine is a language independent program, while grammar and language specific rules and resources are…
I introduce a formalism for representing the syntax of recursively structured graph-like patterns. It does not use production rules, like a conventional graph grammar, but represents the syntactic structure in a more direct and declarative…
In this report, we introduce observation algebras, constructed by considering the downclosed subsets of a coherence space ordered by reverse inclusion. These may be interpreted as specifications of sets of events via some predicates with…
An abstract mathematical framework is presented in this paper as a unification of several deformed or generalized algebra proposed recently in the context of generalized statistical theories intended to treat certain complex thermodynamic…
We present a device for specifying and reasoning about syntax for datatypes, programming languages, and logic calculi. More precisely, we study a notion of "signature" for specifying syntactic constructions. In the spirit of Initial…
The traditional abstract domain framework for imperative programs suffers from several shortcomings; in particular it does not allow precise symbolic abstractions. To solve these problems, we propose a new abstract interpretation framework,…
Coherence phenomena appear in two different situations. In the context of category theory the term `coherence constraints' refers to a set of diagrams whose commutativity implies the commutativity of a larger class of diagrams. In the…
We provide a novel notion of what it means to be interpretable, looking past the usual association with human understanding. Our key insight is that interpretability is not an absolute concept and so we define it relative to a target model,…
We present the first definition of strictly associative and unital $\infty$-category. Our proposal takes the form of a type theory whose terms describe the operations of such structures, and whose definitional equality relation enforces…
This work introduces a general theory of universal pseudomorphisms and develops their connection to diagrammatic coherence. The main results give hypotheses under which pseudomorphism coherence is equivalent to the coherence theory of…
Some personal recollections on the introduction of `abstract proof systems' as a framework for formulating syntax-independent, general results about rule derivability and admissibility. With a particular eye on the inspiration I owe to Roel…
We propose a formalization of generic algorithms that includes analog algorithms. This is achieved by reformulating and extending the framework of abstract state machines to include continuous-time models of computation. We prove that every…