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Implement checking for sigmas #6

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jonsterling opened this issue Jun 18, 2014 · 0 comments
Closed
4 tasks done

Implement checking for sigmas #6

jonsterling opened this issue Jun 18, 2014 · 0 comments

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@jonsterling
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  • Type formation
  • Introduction: Pair
  • Elimination: Spread
  • Also, Spread needs a first parameter which is the motive. So the elimination rule needs to look like this:
     Γ !-[Σ;E] p : Σ[x:A]B             
     Γ, x : Σ[x:A]B !-[Σ;E] C : U
     Γ, u:A, v:[u/x]B !-[Σ;E] M : [<u,v>/x]C
-----------------------------------------------------
     Γ !-[Σ;E] spread([x]C; [u,v]M; p) : [p/x]C

Therefore, we have in the syntax:

Spread :: (B.Scope () Tm a) -> (B.Scope Bool Tm a) -> Tm a -> Tm a
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