Related papers: A coinductive semantics of the Unlimited Register …
Recursive definitions of predicates are usually interpreted either inductively or coinductively. Recently, a more powerful approach has been proposed, called flexible coinduction, to express a variety of intermediate interpretations,…
Consider a coring with exact rational functor, and a finitely generated and projective right comodule. We construct a functor (\emph{coinduction functor}) which is right adjoint to the hom-functor represented by this comodule. Using the…
We formally verify an abstract machine for a call-by-value lambda-calculus with de Bruijn terms, simple substitution, and small-step semantics. We follow a stepwise refinement approach starting with a naive stack machine with substitution.…
We employ the Coq proof assistant to develop a mechanically-certified framework for evaluating graph queries and incrementally maintaining materialized graph instances, also called views. The language we use for defining queries and views…
We report the results of the first experiments with learning proof dependencies from the formalizations done with the Coq system. We explain the process of obtaining the dependencies from the Coq proofs, the characterization of formulas…
Complex multi-step reasoning tasks, such as solving mathematical problems, remain challenging for large language models (LLMs). While outcome supervision is commonly used, process supervision via process reward models (PRMs) provides…
Formally reasoning about functional programs is supposed to be straightforward and elegant, however, it is not typically done as a matter of course. Reasoning in a proof assistant requires "reimplementing" the code in those tools, which is…
Validation of a presumably universal theory, such as quantum mechanics, requires a quantum mechanical description of systems that carry out theoretical calculations and experiments. The description of quantum computers is under active…
This book explores an alternative to the current dominant paradigm where a discrete computer model is constructed as an attempt to approximate some continuum theory. We focus on a class of discrete computer models that are based on simple…
We formally verify several computational reductions concerning the Post correspondence problem (PCP) using the proof assistant Coq. Our verifications include a reduction of a string rewriting problem generalising the halting problem for…
Motivated by algorithmic information theory, the problem of program discovery can help find candidates of underlying generative mechanisms of natural and artificial phenomena. The uncomputability of such inverse problem, however,…
The theory of the call-by-value lambda-calculus relies on weak evaluation and closed terms, that are natural hypotheses in the study of programming languages. To model proof assistants, however, strong evaluation and open terms are…
A major difficulty in developing and maintaining very large knowledge bases originates from the variety of forms in which knowledge is made available to the KB builder. The objective of this research is to bring together two complementary…
Some problems of the quantum error-correcting codes theory can be reduced to the investigation of the higher-rank numerical ranges of the operators related to the error operators. We constructively verify a conjecture on the structure of…
Nondeterministic choice is a useful program construct that provides a way to describe the behaviour of a program without specifying the details of possible implementations. It supports the stepwise refinement of programs, a method that has…
We propose an extension of pure type systems with an algebraic presentation of inductive and co-inductive type families with proper indices. This type theory supports coercions toward from smaller sorts to bigger sorts via explicit type…
Matching logic is a logical framework for specifying and reasoning about programs using pattern matching semantics. A pattern is made up of a number of structural components and constraints. Structural components are syntactically matched,…
Robotic designs played an important role in recent advances by providing powerful robots with complex mechanics. Many recent systems rely on parallel actuation to provide lighter limbs and allow more complex motion. However, these emerging…
In recent work we have shown how it is possible to define very precise type systems for object-oriented languages by abstractly compiling a program into a Horn formula f. Then type inference amounts to resolving a certain goal w.r.t. the…
There are several ways to formally represent families of data, such as lambda terms, in a type theory such as the dependent type theory of Coq. Mathematical representations are very compact ones and usually rely on the use of dependent…