Formalising formulas-as-types-as-objects

Formalising formulas-as-types-as-objects (2000)

by Qiao Haiyan

Venue:	Types for Proofs and Programs
Citations:	2 - 0 self

Datum	Value	Source
TITLE	Formalising formulas-as-types-as-objects	INFERENCE
AUTHOR NAME	Qiao Haiyan	SVM HeaderParse 0.2
AUTHOR AFFIL	Department of Computing Science; Chalmers University of Technology and Göteborg University	SVM HeaderParse 0.2
AUTHOR ADDR	412 96 Göteborg	SVM HeaderParse 0.2
ABSTRACT	Abstract. We describe a formalisation of the Curry-Howard-Lawvere correspondence between the natural deduction system for minimal logic, the typed lambda calculus and Cartesian closed categories. We formalise the type of natural deduction proof trees as a family of sets Γ ⊢ A indexed by the current assumption list Γ and the conclusion A and organise numerous useful lemmas about proof trees categorically. We prove categorical properties about proof trees up to (syntactic) identity as well as up to βη-convertibility. We prove that our notion of proof trees is equivalent in an appropriate sense to more traditional representations of lambda terms. The formalisation is carried out in the proof assistant ALF for Martin-Löf type theory. 1	SVM HeaderParse 0.2
YEAR	2000	INFERENCE
VENUE	Types for Proofs and Programs	INFERENCE
VENUE TYPE	CONFERENCE	INFERENCE
PAGES	174--194	INFERENCE
VOLUME	1956	INFERENCE
CITATIONS	20 found	ParsCit 1.0