Homotopy Type Theory For Dummies
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Identity types<br />
Identity types<br />
Given A : <strong>Type</strong> and a, b : A we can form<br />
a = A b : <strong>Type</strong><br />
the type of proofs that a is equal to b.<br />
The canonical inhabitant is<br />
refl(a) : a = A a<br />
given a : A.<br />
The eliminator for equality types is<br />
J(a) : Π P:Πb:A.a=b→<strong>Type</strong> P(a, refl(a)) → Π x:A,α:a=x P(x, α)<br />
for a : A, with the definitional equality J(P, p, refl(a)) ≡ p.<br />
Thorsten Altenkirch (Nottingham) Edinburgh 13 October 30, 2013 5 / 29
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