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Classical Type Theory Peter B. Andrews
 

Summary: Chapter 15
Classical Type Theory
Peter B. Andrews
Second readers: John Harrison and Michael Kohlhase.
Contents
1 Introduction to type theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 967
1.1 Early versions of type theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . 967
1.2 Type theory with -notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 969
1.3 The Axiom of Choice and Skolemization . . . . . . . . . . . . . . . . . . . . . . 973
1.4 The expressiveness of type theory . . . . . . . . . . . . . . . . . . . . . . . . . 975
1.5 Set theory as an alternative to type theory . . . . . . . . . . . . . . . . . . . . 976
2 Metatheoretical foundations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 977
2.1 The Unifying Principle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 977
2.2 Expansion proofs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 978
2.3 Proof translations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 982
2.4 Higher-order uni cation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 984
2.5 The need for arbitrarily high types . . . . . . . . . . . . . . . . . . . . . . . . . 986
3 Proof search . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 987
3.1 Searching for expansion proofs . . . . . . . . . . . . . . . . . . . . . . . . . . . 988
3.2 Constrained resolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 992

  

Source: Andrews, Peter B. - Department of Mathematical Sciences, Carnegie Mellon University

 

Collections: Mathematics