Sökning: "formalized mathematics"
Hittade 5 avhandlingar innehållade orden formalized mathematics.
1. Formalizing Univalent Set-Level Structures in Cubical Agda
Sammanfattning : This licentiate thesis consists of two papers on formalization projects using Cubical Agda, a rather new extension of the Agda proof assistant with constructive support for univalence and higher inductive types. The common denominator of the two papers is that they are concerned with structures on types that are sets in the sense of Homotopy Type Theory or Univalent Foundations (HoTT/UF). LÄS MER
2. Deep learning applied to system identification : A probabilistic approach
Sammanfattning : Machine learning has been applied to sequential data for a long time in the field of system identification. As deep learning grew under the late 00's machine learning was again applied to sequential data but from a new angle, not utilizing much of the knowledge from system identification. LÄS MER
3. Relations in Dependent Type Theory
Sammanfattning : This thesis investigates how to express and reason about relational concepts and methods inside the constructive logical framework of Martin-Löf's monomorphic type theory. We cover several areas where the notion of relation is central, and show how to formalize the basic concepts of each area. LÄS MER
4. Constructive Algebra in Type Theory
Sammanfattning : This thesis contains four papers aiming at bridging the gap between algorithms implemented in computer algebra systems and interactive proof assistants. This is done by implementing and verifying efficient algorithms using the Coq proof assistant together with the SSReflect extension. LÄS MER
5. An Observer-Based Technique with Trace Links for Requirements Validation in Embedded Real-Time Systems
Sammanfattning : With the growing complexity of embedded real-time systems, requirements validation becomes an ever-more critical activity for developing such systems. Studies have revealed that most of the anomalies, discovered in the development of complex systems, belong to requirement and specification phases. LÄS MER