From windley@cheetah  Thu Aug 17 08:41:44 1989
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Subject: report on higher-order logic
Date: Thu, 17 Aug 89 08:43:14 -0800
From: Phil Windley <windley@cheetah>

The following report discusses a new formulation of higher-order logic
which has been implemented using the Isabelle system. It can be ordered
from Computing Service Bookshop, University of Cambridge, Pembroke
Street, Cambridge CB2 3QG, England.

                   Technical Report 175

    A Formulation of the Simple Theory of Types (for Isabelle)

                            by

    Lawrence C. Paulson, Computer Laboratory, University of Cambridge

                         ABSTRACT
Simple type theory is formulated for use with the generic theorem prover
Isabelle.  This requires explicit type inference rules.  There are
function, product, and subset types, which may be empty. Descriptions (the
$\eta$-operator) introduce the Axiom of Choice.  Higher-order logic is
obtained through reflection between formulae and terms of type bool.
Recursive types and functions can be formally constructed.

Isabelle proof procedures are described. The logic appears suitable for
general mathematics as well as computational problems.


