Summary: Constructive Type Theory
Notes for Marktoberdorf 1997
July 12, 1997
These notes do not give a fully accurate representation of the planned lectures.
Nevertheless they should provide useful background material which I hope will
supplement the bibliography. The notes focus only on nondependent type theory,
which will be the topic of the first few lectures. The remaining lectures will extend
the material to encompass constructive type theory with dependent types.
The first part of these notes looks at aspects of the nondependent part of
constructive type theory from the foundational point of view, starting with a
quote from Godel's Dialectica paper. The second part of these notes consists
of material prepared for an MSc course at Manchester University on the simply
typed lambda calculus. It includes sections on Deduction and the untyped lambda
calculus. Unfortunately I have not had time to adjust the presentation to properly
serve the purposes of the Summer School. Nevertheless I hope that it may prove
useful as a metatheoretical counterpart to the foundational first part.