43 lines
931 B
Text
43 lines
931 B
Text
/-- A `Vec` is just a `List α` of statically known size -/
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def Vec (α : Type _) (n : Nat) : Type _
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:= Fin n → α
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abbrev TypeVec : Nat → Type _
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:= Vec (Type _)
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/-- A dependent vector is a heterogeneous list of statically known size -/
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def DVec {n : Nat} (αs : TypeVec n) : Type _
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:= (i : Fin n) → (αs i)
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/-- A vector that repeats a single element `a` -/
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def Vec.const {α : Type _} (a : α) (n : Nat) : Vec α n
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:= fun _ => a
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/- `Vec` is defeq to a `DVec` with constant type -/
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unif_hint (α : Type _) (n : Nat) where
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|- Vec α n =?= DVec (Vec.const α n)
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namespace DVec
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def hd {n : Nat} {αs : TypeVec (n+1)} (v : DVec αs) : (αs 0)
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:= v 0
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end DVec
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namespace Vec
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export DVec (hd)
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end Vec
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def ts : TypeVec 1 := Vec.const Nat 1
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-- works
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example (v : DVec ts) : Nat :=
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v.hd
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-- works
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example (v : Vec Nat 1) : Nat :=
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DVec.hd v
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#check @Vec.hd
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-- works
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example (v : Vec Nat 1) : Nat :=
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v.hd
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