Lectures on the Curry-Howard Isomorphism
by Morten Heine B. Sorensen, Pawel Urzyczyn
Publisher: Elsevier Science 2006
Number of pages: 273
The Curry-Howard isomorphism states an amazing correspondence between systems of formal logic as encountered in proof theory and computational calculi as found in type theory. This book give an introduction to parts of proof theory and related aspects of type theory relevant for the Curry-Howard isomorphism. It can serve as an introduction to any or both of typed lambda-calculus and intuitionistic logic.
Download or read it online for free here:
by Hanne Riis Nielson, Flemming Nielson - John Wiley & Sons
The book covers the foundations of structural operational semantics and natural semantics. It shows how to describe the semantics of declarative as well as imperative language constructs and will also touch upon non-sequential constructs.
by D.E. Rydeheard, R.M. Burstall
The book is a bridge-building exercise between computer programming and category theory. Basic constructions of category theory are expressed as computer programs. It is a first attempt at connecting the abstract mathematics with concrete programs.
by Krysia Broda et al - Prentice Hall Trade
The text for advanced undergraduate/graduate students of computer science. It introduces functional, imperative and logic programming and explains how to do it correctly. Functional programming is presented as a programming language in its own right.
by Peter Selinger - Dalhousie University
Topics covered in these notes include the untyped lambda calculus, the Church-Rosser theorem, combinatory algebras, the simply-typed lambda calculus, the Curry-Howard isomorphism, weak and strong normalization, type inference, etc.