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Some Lambda Calculus and Type Theory Formalized

By Robert Pollack and James Mckinna and James Mckinna

Abstract

Conversion We have further generalized PTS by parameterizing the rules of table 7 on another relation, (called abstract conversion), occurring in the side condition of rule tConv. In conventional presentations of PTS [Bar92], the actual relation of beta-conversion ( ' ) is used for . There are several reasons to be interested in parameterizing PTS on its conversion relation. For one thing, the type theory ECC, implemented in LEGO, is not actually a PTS because it uses a generalized notion of conversion called cumulativity. ECC is of special interest to us, so we formalize an extension of PTS which includes ECC. Our formal development includes a typechecking algorithm for ECC [Pol94b]. Even for PTS , there is a notorious open problem, the Expansion Postponement problem [vBJMP94, Pol94b], which asks if the conversion relation in table 7 can be replaced by beta-reduction without changing the typability of any terms. We know of one other work on PTS using an abstract conversion relation: [BM]

Topics: y
Publisher: JAR
Year: 1997
DOI identifier: 10.7146/brics.v4i51.19272
OAI identifier: oai:CiteSeerX.psu:10.1.1.16.3787
Provided by: CiteSeerX
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