Related papers: Coherent Explicit Dictionary Application for Haske…
G\"odel's Dialectica interpretation was designed to obtain a relative consistency proof for Heyting arithmetic, to be used in conjunction with the double negation interpretation to obtain the consistency of Peano arithmetic. In recent…
We introduce OpSets, an executable framework for specifying and reasoning about the semantics of replicated datatypes that provide eventual consistency in a distributed system, and for mechanically verifying algorithms that implement these…
2-Theories are a canonical way of describing categories with extra structure. 2-theory-morphisms are used when discussing how one structure can be replaced with another structure. This is central to categorical coherence theory. We place a…
Document coherence describes how much sense text makes in terms of its logical organisation and discourse flow. Even though coherence is a relatively difficult notion to quantify precisely, it can be approximated automatically. This type of…
Exact sequences are a well known notion in homological algebra. We investigate here the more vague properties of 'homotopical exactness', appearing for instance in the fibre or cofibre sequence of a map. Such notions of exactness can be…
We present a lattice of distributed program specifications, whose ordering represents implementability/refinement. Specifications are modelled by families of subsets of relative execution traces, which encode the local orderings of state…
Contextual refinement (CR) is one of the standard notions of specifying open programs. CR has two main advantages: (i) (horizontal and vertical) compositionality that allows us to decompose a large contextual refinement into many smaller…
We introduce a condition for the strong decoherence of a set of alternative histories of a closed quantum-mechanical system such as the universe. The condition applies, for a pure initial state, to sets of homogeneous histories that are…
Exact real computation is an alternative to floating-point arithmetic where operations on real numbers are performed exactly, without the introduction of rounding errors. When proving the correctness of an implementation, one can focus…
The proof of a program property can be reduced to the proof of satisfiability of a set of constrained Horn clauses (CHCs) which can be automatically generated from the program and the property. In this paper we have conducted a case study…
In this work we present a definition for coherence and compatibility of multilinear mappings and homogenous polynomial classes. These definitions are more restricted than the ones proposed before. We began analyzing this new definition in a…
Recursive coalgebras provide an elegant categorical tool for modelling recursive algorithms and analysing their termination and correctness. By considering coalgebras over categories of suitably indexed families, the correctness of the…
A general framework is proposed for integration of rules and external first order theories. It is based on the well-founded semantics of normal logic programs and inspired by ideas of Constraint Logic Programming (CLP) and constructive…
Universal identifiers and hashing have been widely adopted in computer science from distributed financial transactions to data science. This is a consequence of their capability to avoid many shortcomings of relative identifiers, such as…
We deepen the study of conjoined and disjoined conditional events in the setting of coherence. These objects, differently from other approaches, are defined in the framework of conditional random quantities. We show that some well known…
Formal verification provides strong guarantees of correctness of software, which are especially important in safety or security critical systems. Hoare logic is a widely used formalism for rigorous verification of software against…
A new categorical setting is defined in order to characterize the subrecursive classes belonging to complexity hierarchies. This is achieved by means of coercion functors over a symmetric monoidal category endowed with certain recursion…
We study the generalization abilities of language models when translating natural language into formal specifications with complex semantics. In particular, we fine-tune language models on three datasets consisting of English sentences and…
Constraint Handling Rules (CHR) is a rule-based programming language which is typically embedded into a general-purpose language. There exists a plethora of implementations for numerous host languages. However, the existing implementations…
Unifying theories distil common features of programming languages and design methods by means of algebraic operators and their laws. Several practical concerns --- e.g., improvement of a program, conformance of code with design, correctness…