 
Summary: Set Comprehension in Church's Type Theory
Dissertation Description
Chad E. Brown
Universität des Saarlandes, cebrown@ags.unisb.de
1 Introduction
In my doctoral dissertation [11] I studied the role of set comprehension in
Church's formulation of higherorder logic. This work also included extending
the automated theorem prover Tps (see [5, 6]) to search for proofs in extensional
type theory.
Church's type theory [12] is a form of higherorder logic which is suciently
powerful to represent much of traditional mathematics. In order to study au
tomated deduction for higherorder logic, various fragments and formulations
of Church's type theory have been considered. In particular, the higherorder
theorem proving system Tps has traditionally searched for proofs in elementary
type theory. Elementary type theory is Church's type theory without axioms of
extensionality, descriptions, choice, or innity. Miller [13] introduced expansion
proofs as a compact representation for cutfree proofs in elementary type theory.
Tps searches for such compact proofs by combining mating search (a procedure
which applies in rstorder logic) with Huet's preunication algorithm for sim
ply typed #calculus. While this provides a reasonable basis for search, one must
