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Summary: On Irrelevance and Extraction in Type Theory
Andreas Abel
INRIA, Team r2
PPS Lab, Paris
Coq Meeting at JFLA 2010
La Ciotat, Marseille, France
2 February 2010
Andreas Abel (INRIA) Typed Equality Coq Meeting '10 1 / 23
Introduction
Irrelevance and Extraction in Type Theory
Definition (Irrelevance)
A type T is irrelevant if t, t : T implies t = t : T.
Three motivations to consider irrelevance:
1 More powerful type checkers.
More terms type check.
Less proof burden for the user.
2 More efficient type checkers.
Fewer terms to compare for equality.
Erasure of irrelevant parts in internal representation?
3 More dead-code elimination in program extraction.
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