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Set Comprehension in Church's Type Theory Dissertation Description

Summary: Set Comprehension in Church's Type Theory
Dissertation Description
Chad E. Brown
Universitšt des Saarlandes, cebrown@ags.uni-sb.de
1 Introduction
In my doctoral dissertation [11] I studied the role of set comprehension in
Church's formulation of higher-order 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 higher-order logic which is suciently
powerful to represent much of traditional mathematics. In order to study au-
tomated deduction for higher-order logic, various fragments and formulations
of Church's type theory have been considered. In particular, the higher-order
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 cut-free proofs in elementary type theory.
Tps searches for such compact proofs by combining mating search (a procedure
which applies in rst-order logic) with Huet's pre-unication algorithm for sim-
ply typed #-calculus. While this provides a reasonable basis for search, one must


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


Collections: Mathematics