Archive for the 'Observational Type Theory' Category

OTT by reflecting telescopes

Monday, May 16th, 2005

Starting point: TT with some proper dependency, e.g.

b : Bool
————–
T b : *

T false = Null
T true = One

we assume at least Pi, Sigma, Empty, Null, One, Bool. We also use Prop <= *,
for propositional types.

We introduce telescopes G |- D Tel , e.g.

-----------
G |- () Tel

G |- D Tel G.D |- S : *
-----------------------------
G |- D.S Tel

where

G.() = G
G.(D.S) = (G.D).S

We inhabit telescopes with substitutions, given G |- D Tel
(more…)