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Summary: Slide 1
Untyped Algorithmic Equality
for Martin-L¨of's Logical Framework
with Surjective Pairs
Andreas Abel
joint work with Thierry Coquand
ProgLog Seminar
Chalmers, G¨oteborg, Sweden
May 11, 2005
Work supported by: TYPES & APPSEM-II (EU), CoVer (SSF)
Slide 2
Background: -equality
· Checking dependent types requires equality test
· One approach: reduce to normal form and compare
syntactically
· Works fine for -equality
· Problem with -reduction: surjective pairing destroys
confluence (Klop 1980)
· Even subject reduction fails:
z : Pair A (x. F x) (z L, z R) : Pair A ( . F (z L))
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