Related papers: Formal verification in Coq of program properties i…
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…
An invaluable feature of computer algebra systems is their ability to plot the graph of functions. Unfortunately, when one is trying to design a library of mathematical functions, this feature often falls short, producing incorrect and…
We propose a programming model where effects are treated in a disciplined way, and where the potential side-effects of a function are apparent in its type signature. The type and effect of expressions can also be inferred automatically, and…
We present the syntax and rules of deduction of QPEL (Quantum Program and Effect Language), a language for describing both quantum programs, and properties of quantum programs - effects on the appropriate Hilbert space. We show how…
Formal deductive systems are very common in computer science. They are used to represent logics, programming languages, and security systems. Moreover, writing programs that manipulate them and that reason about them is important and…
Proof assistants are software-based tools that are used in the mechanization of proof construction and validation in mathematics and computer science, and also in certified program development. Different tools are being increasingly used in…
The use of formal methods provides confidence in the correctness of developments. Yet one may argue about the actual level of confidence obtained when the method itself -- or its implementation -- is not formally checked. We address this…
In the paper we introduce graphical objects (called state diagrams) related to functional programs. It is shown that state diagrams of functional programs can be used to solve problems of verification of functional programs. The proposed…
This article describes the development and formal verification (proof of semantic preservation) of a compiler back-end from Cminor (a simple imperative intermediate language) to PowerPC assembly code, using the Coq proof assistant both for…
One of the key steps in quantum algorithms is to prepare an initial quantum superposition state with different kinds of features. These so-called state preparation algorithms are essential to the behavior of quantum algorithms, and…
In this paper we consider the problem of certified static checking of module-like constructs of programming languages. We argue that there are algorithms and properties related to modules that can be defined and proven in an abstract way.…
The use of function contracts to specify the behavior of functions often remains limited to the scope of a single function call. Relational properties link several function calls together within a single specification. They can express more…
We propose a new library to model and verify hardware circuits in the Coq proof assistant. This library allows one to easily build circuits by following the usual pen-and-paper diagrams. We define a deep-embedding: we use a (dependently…
The importance of category theory in recent developments in both mathematics and in computer science cannot be overstated. However, its abstract nature makes it difficult to understand at first. Graphical languages have been developed to…
For performance and verification in machine learning, new methods have recently been proposed that optimise learning systems to satisfy formally expressed logical properties. Among these methods, differentiable logics (DLs) are used to…
We have developed an alternative approach to teaching computer science students how to prove. First, students are taught how to prove theorems with the Coq proof assistant. In a second, more difficult, step students will transfer their…
Proof assistants like Coq are increasingly popular to help mathematicians carry out proofs of the results they conjecture. However, formal proofs remain highly technical and are especially difficult to reuse. In this paper, we present a…
Guarded Interaction Trees are a structure and a fully formalized framework for representing higher-order computations with higher-order effects in Rocq. We present an extension of Guarded Interaction Trees to support formal reasoning about…
Interactive proof assistants make it possible for ordinary mathematicians to write definitions and theorems in a formal proof language, like a programming language, so that a computer can parse them and check them against the rules of a…
Due to their numerous advantages, formal proofs and proof assistants, such as Coq, are becoming increasingly popular. However, one disadvantage of using proof assistants is that the resulting proofs can sometimes be hard to read and…