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Irrelevance in Type Theory Andreas Abel

Summary: Irrelevance in Type Theory
Andreas Abel
Department of Computer Science
Ludwig-Maximilians-University Munich
TCS Oberseminar
LMU Munich
17 December 2010
Andreas Abel (LMU) Irrelevant TT TCS'10 1 / 1
Proof Irrelevance in Agda
-- div' n m computes ceil(n / (m + 1))
div' : {i : Size} Nat i Nat Nat i
div' zero m = zero
div' (suc n) m = suc (div' (n - m) m)
-- div n m computes floor(n / m)
div : Nat (m : Nat) .(zero < m) Nat
div n zero ()
div n (suc m) p = div' (n - m) m
The outcome of division div n m p does not depend on proof
p : 0 < m.


Source: Abel, Andreas - Theoretische Informatik, Ludwig-Maximilians-Universit√§t M√ľnchen


Collections: Computer Technologies and Information Sciences