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Demographic and Principles of Electronic Computing
Published in Parveen Berwal, Jagjit Singh Dhatterwal, Kuldeep Singh Kaswan, Shashi Kant, Computer Applications in Engineering and Management, 2022
Parveen Berwal, Jagjit Singh Dhatterwal, Kuldeep Singh Kaswan, Shashi Kant
Philosophical reasoning will lead to a major improvement in software effectiveness and consistency as part of the challenge—Mathematics solutions, for example, Critical Type Theory [1,2], designs huge software systems. This study aims to study the link between the theory of the construction type and the neural networks in a type-based structure by illustrating how two distinct networks may be used. The following are some of the advantages of the application interface suggested:
Using the Lean interactive theorem prover in undergraduate mathematics
Published in International Journal of Mathematical Education in Science and Technology, 2023
The Lean Theorem Prover is based on a version of dependent type theory known as the Calculus of Constructions. Type theory is the study of type systems. In a type system, any object or expression a has a type T, denoted as a:T. Common types include the Boolean type ‘true: bool' or ‘false: bool', the string type ‘"Hello World!": string', the integer type, ‘3:int' and many more. At its core, Lean is known as a type checker (Avigad, Lewis, et al., 2021). In Lean, one can declare mathematical objects and check their types. For example, #Check (a:ℝ)
The class of states of the world as an
Published in International Journal of General Systems, 2018
Fernando Tohmé, Gianluca Caterina, Rocco Gangle
A starting point is to use a type-theoretical language. While there are different varieties, we will focus on Dependent Type Theory (Martin-Löf 1975). The basic elements of its syntax are:Types:Terms:Dependent Types:, , Equations:Inductive Types, defined by a base case and an inductive step.Type Theory has traditionally admitted two classical interpretations:Types are sets and terms are elements.Types are propositions and the terms proofs.where the former is the basis of Bertrand Russell’s interpretation while the latter is called the Curry-Howard correspondence. But there are indeed other possible interpretations. For instance:Types are problems and terms solutions (due to Kolmogorov).Types are seen as data types and terms as instances.A new approach, known as Homotopy Type Theory (HoTT) is based on the homotopical interpretation of types (The Univalent Foundations Program 2013)4:Types are spaces and terms are points in them.This interpretation is particularly useful for the interpretation of dependent types. An expression as can be seen as a fibration. More precisely, a dependent-type B(x) is the fiber on point x : A, i.e. p is a continuous map between B and A (satisfying a certain homotopy lifting property). As a counterpart, we have a section such that .