Related papers: A Formalization of Operads in Coq
We present a new way of embedding functional languages into the Coq proof assistant by using meta-programming. This allows us to develop the meta-theory of the language using the deep embedding and provides a convenient way for reasoning…
The substitution lemma is a renowned theorem within the realm of lambda-calculus theory and concerns the interactional behaviour of the metasubstitution operation. In this work, we augment the lambda-calculus's grammar with an uninterpreted…
We introduce a large-scale dataset of math word problems and an interpretable neural math problem solver that learns to map problems to operation programs. Due to annotation challenges, current datasets in this domain have been either…
We discuss some aspects of our work on the mechanization of syntax and semantics in the UniMath library, based on the proof assistant Coq. We focus on experiences where Coq (as a type-theoretic proof assistant with decidable typechecking)…
In recent years, a number of lightweight programs have been deployed in critical domains, such as in smart contracts based on blockchain technology. Therefore, the security and reliability of such programs should be guaranteed by the most…
In order to work with mathematical content in computer systems, it is necessary to represent it in formal languages. Ideally, these are supported by tools that verify the correctness of the content, allow computing with it, and produce…
Floating point operations are fast, but require continuous effort on the part of the user in order to ensure that the results are correct. This burden can be shifted away from the user by providing a library of exact analysis in which the…
Using a call-by-value functional language as an example, this article illustrates the use of coinductive definitions and proofs in big-step operational semantics, enabling it to describe diverging evaluations in addition to terminating…
A reliable technique for deductive program verification should be proven sound with respect to the semantics of the programming language. For each different language, the construction of a separate soundness proof is often a laborious…
In this article we present a method for formally proving the correctness of the lazy algorithms for computing homographic and quadratic transformations -- of which field operations are special cases-- on a representation of real numbers by…
As the complexity and heterogeneity of a system grows, the challenge of specifying, documenting and synthesizing correct, machine-readable designs increases dramatically. Separation of the system into manageable parts is needed to support…
This paper introduces a formal metalanguage called the lambda-q calculus for the specification of quantum programming languages. This metalanguage is an extension of the lambda calculus, which provides a formal setting for the specification…
We present a Coq formalisation of the small-step operational semantics of Jafun, a small Java-like language with classes. This format of semantics makes it possible to naturally specify and prove invariants that should hold at each…
Rigorous modelling of natural and industrial systems still conveys various challenges related to abstractions, methods to proceed with and easy-to-use tools to build, compose and reason on models. Operads are mathematical structures that…
Theory of choreographic languages typically includes a number of complex results that are proved by structural induction. The high number of cases and the subtle details in some of them lead to long reviewing processes, and occasionally to…
We show that verification of object-oriented programs by means of the assertional method can be achieved in a simple way by exploiting a syntax-directed transformation from object-oriented programs to recursive programs. This transformation…
Expressive static typing disciplines are a powerful way to achieve high-quality software. However, the adoption cost of such techniques should not be under-estimated. Just like gradual typing allows for a smooth transition from…
We develop a linear logical framework within the Hybrid system and use it to reason about the type system of a quantum lambda calculus. In particular, we consider a practical version of the calculus called Proto-Quipper, which contains the…
Sets and relations are very useful concepts for defining denotational semantics. In the Coq proof assistant, curried functions to Prop are used to represent sets and relations, e.g. A -> Prop, A -> B -> Prop, A -> B -> C -> Prop, etc.…
The stabiliser fragment of quantum theory is a foundational building block for quantum error correction and the fault-tolerant compilation of quantum programs. In this article, we develop a sound, universal and complete denotational…