5c707d936c
This PR renames `Stream` to `Std.Stream` so that the name becomes available to mathlib after a deprecation cycle.
55 lines
1.5 KiB
Text
55 lines
1.5 KiB
Text
namespace Std.Stream
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variable [Std.Stream ρ τ] (s : ρ)
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def take (s : ρ) : Nat → List τ × ρ
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| 0 => ([], s)
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| n+1 =>
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match next? s with
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| none => ([], s)
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| some (x,rest) =>
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let (L,rest) := take rest n
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(x::L, rest)
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def isEmpty : Bool :=
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Option.isNone (next? s)
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def lengthBoundedBy (n : Nat) : Prop :=
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isEmpty (take s n).2
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def hasNext : ρ → ρ → Prop
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:= λ s1 s2 => ∃ x, next? s1 = some ⟨x,s2⟩
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def isFinite : Prop :=
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∃ n, lengthBoundedBy s n
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instance hasNextWF : WellFoundedRelation {s : ρ // isFinite s} where
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rel := λ s1 s2 => hasNext s2.val s1.val
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wf := ⟨λ ⟨s,h⟩ => ⟨Subtype.mk s h, by
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simp only [Subtype.forall]
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cases h with | intro w h
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induction w generalizing s
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case zero =>
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intro s' h' h_next
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simp [hasNext] at h_next
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cases h_next with | intro x h_next
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simp [lengthBoundedBy, isEmpty, Option.isNone, take, h_next] at h
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case succ n ih =>
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intro s' h' h_next
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simp [hasNext] at h_next
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cases h_next with | intro x h_next
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simp [lengthBoundedBy, take, h_next] at h
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have := ih s' h
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exact Acc.intro (⟨s',h'⟩ : {s : ρ // isFinite s}) (by simpa only [Subtype.forall])
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⟩⟩
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def mwe [Stream ρ τ] (acc : α) : {l : ρ // isFinite l} → α
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| ⟨l,h⟩ =>
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match h:next? l with
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| none => acc
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| some (x,xs) =>
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have h_next : hasNext l xs := by exists x
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mwe acc ⟨xs, by sorry⟩
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termination_by l => l
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end Std.Stream
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