272dd5533f
We are considering removing `.` as an alternative for `·` in the lambda dot notation (e.g., `(·+·)`). Reasons: - `.` is not a perfect replacement for `·` (e.g., `(·.insert ·)`) - `.` is too overloaded: `(f.x)` and `(f .x)` and `(f . x)`. We want to keep the first two.
20 lines
659 B
Text
20 lines
659 B
Text
inductive Vector (α : Type u): Nat → Type u where
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| nil : Vector α 0
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| cons (head : α) (tail : Vector α n) : Vector α (n+1)
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namespace Vector
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def mem (a : α) : Vector α n → Prop
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| nil => False
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| cons b l => a = b ∨ mem a l
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def foldr (f : α → β → β) (init : β) : Vector α n → β
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| nil => init
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| cons a l => f a (foldr f init l)
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theorem foldr_max [LE β] [LT β] [DecidableRel (· < · : β → β → Prop)] {v: Vector α n} (f : α → β) (init : β)
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(h: v.mem y):
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f y ≤ v.foldr (λ x acc => max (f x) acc) init := by
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induction v <;> simp only[foldr,max]
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. admit
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. split <;> admit
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end Vector
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