Related papers: A Practical Formalization of Monadic Equational Re…
Free monads (and their variants) have become a popular general-purpose tool for representing the semantics of effectful programs in proof assistants. These data structures support the compositional definition of semantics parameterized by…
Real world programming languages crucially depend on the availability of computational effects to achieve programming convenience and expressive power as well as program efficiency. Logical frameworks rely on predicates, or dependent types,…
In this paper, a monad-based denotational model is introduced and shown adequate for the Proto-Quipper family of calculi, themselves being idealized versions of the Quipper programming language. The use of a monadic approach allows us to…
The modern theory of functional programming languages uses monads for encoding computational side-effects and side-contexts, beyond bare-bone program logic. Even though quantum computing is intrinsically side-effectful (as in quantum…
CoqQ is a framework for reasoning about quantum programs in the Coq proof assistant. Its main components are: a deeply embedded quantum programming language, in which classic quantum algorithms are easily expressed, and an expressive…
Sharing of notations and theories across an inheritance hierarchy of mathematical structures, e.g., groups and rings, is important for productivity when formalizing mathematics in proof assistants. The packed classes methodology is a…
Several relational program logics have been introduced for integrating reasoning about relational properties of programs and measurement of quantitative difference between computational effects. Towards a general framework for such logics,…
We show how to smoothly incorporate in the object-oriented paradigm constructs to raise, compose, and handle effects in an arbitrary monad. The underlying pure calculus is meant to be a representative of the last generation of OO languages,…
The paper presents algebraic and logical developments. From the algebraic viewpoint, we introduce Monadic Equational Systems as an abstract enriched notion of equational presentation. From the logical viewpoint, we provide Equational…
Monads have become a powerful tool for structuring effectful computations in functional programming, because they make the order of effects explicit. When translating pure code to a monadic version, we need to specify evaluation order…
The ever-growing complexity of mathematical proofs makes their manual verification by mathematicians very cognitively demanding. Autoformalization seeks to address this by translating proofs written in natural language into a formal…
Dynamic evaluation is a paradigm in computer algebra which was introduced for computing with algebraic numbers. In linear algebra, for instance, dynamic evaluation can be used to apply programs which have been written for matrices with…
Monads govern computational side-effects in programming semantics. They can be combined in a ''bottom-up'' way to handle several instances of such effects. Indexed monads and graded monads do this in a modular way. Here, instead, we equip…
We describe a formalization of higher-order rewriting theory and formally prove that an AFS is strongly normalizing if it can be interpreted in a well-founded domain. To do so, we use Coq, which is a proof assistant based on dependent type…
Functional logic languages are a high-level approach to programming by combining the most important declarative features. They abstract from small-step operational details so that programmers can concentrate on the logical aspects of an…
This thesis revolves around an area of computer science called "semantics". We work with operational semantics, equational theories, and denotational semantics. The first contribution of this thesis is a study of the commutativity of…
We give a new presentation of interactive realizability with a more explicit syntax. Interactive realizability is a realizability semantics that extends the Curry-Howard correspondence to (sub-)classical logic, more precisely to first-order…
This paper describes a formal proof library, developed using the Coq proof assistant, designed to assist users in writing correct diagrammatic proofs, for 1-categories. This library proposes a deep-embedded, domain-specific formal language,…
Recent advances in programming languages study and design have established a standard way of grounding computational systems representation in category theory. These formal results led to a better understanding of issues of control and…
We present an extension of Logic Programming (under stable models semantics) that, not only allows concluding whether a true atom is a cause of another atom, but also deriving new conclusions from these causal-effect relations. This is…