30 lines
558 B
Idris
30 lines
558 B
Idris
module Quox.OPE.Length
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import Quox.OPE.Basics
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%default total
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public export
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data Length : Scope a -> Type where
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Z : Length [<]
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S : (s : Length xs) -> Length (xs :< x)
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%name Length s
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%builtin Natural Length
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public export
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(.nat) : Length xs -> Nat
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(Z).nat = Z
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(S s).nat = S s.nat
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%transform "Length.nat" Length.(.nat) xs = believe_me xs
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export
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0 ok : (s : Length xs) -> s.nat = length xs
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ok Z = Refl
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ok (S s) = cong S $ ok s
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public export %hint
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toLength : (xs : Scope a) -> Length xs
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toLength [<] = Z
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toLength (sx :< x) = S (toLength sx)
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