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Church’s formal system of lambda-calculus

  • Duccio Pianigiani

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”.

  • Keywords:
  • Lambda calculus,
  • Type Theory,
  • Cartesian Closed Categories,
  • normalization,
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Duccio Pianigiani

University of Siena, Italy - ORCID: 0000-0001-9441-7226

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  • Publication Year: 2025
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Chapter Information

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

CC BY-SA 4.0

Metadata License

CC0 1.0

Bibliographic Information

Book Title

Lectures in Proof Theory and Complexity

Authors

Duccio Pianigiani

Peer Reviewed

Publication Year

2025

Copyright Information

© 2025 Author(s)

Content License

CC BY-SA 4.0

Metadata License

CC0 1.0

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

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