A. Church in 1936 introduced a formal system based on the operations of function abstraction and application, called the lambda calculus and defined the notion of computable function in this system. Church’s original goal was to construct a formal system for the foundations of mathematics based on functions together with a set of logical notions. When this system was discovered to be inconsistent, Church then separated out the consistent subsystem that is now called lambda calculus and concentrated on it. We we will discuss the three-way isomorphism between typed lambda calculus, intuitionistic Proof Theory and Cartesian Closed Categories of category theory, widely used in Computer Science, sometimes referred as the “computational trinitarianism”.
University of Siena, Italy - ORCID: 0000-0001-9441-7226
Chapter Title
Church’s formal system of lambda-calculus
Authors
Duccio Pianigiani
Language
English
DOI
10.36253/979-12-215-0778-2.06
Peer Reviewed
Publication Year
2025
Copyright Information
© 2025 Author(s)
Content License
Metadata License
Book Title
Lectures in Proof Theory and Complexity
Authors
Duccio Pianigiani
Peer Reviewed
Publication Year
2025
Copyright Information
© 2025 Author(s)
Content License
Metadata License
Publisher Name
Firenze University Press, USiena Press
DOI
10.36253/979-12-215-0778-2
eISBN (pdf)
979-12-215-0778-2
eISBN (xml)
979-12-215-0779-9
Series Title
UNIverSI. Ricerca e Didattica all’Università di Siena
Series ISSN
3035-5915
Series E-ISSN
3035-5931