a826de8a3d
I'd previously added an instance from `ForIn'` to `ForIn`, but this then caused some non-defeq duplication. It seems fine to just remove the concrete `ForIn` instances in cases where the `ForIn'` instance exists too. We can even remove a number of type-specific lemmas in favour of the general ones.
74 lines
2.9 KiB
Text
74 lines
2.9 KiB
Text
/-
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Copyright (c) 2020 Microsoft Corporation. All rights reserved.
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Released under Apache 2.0 license as described in the file LICENSE.
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Authors: Leonardo de Moura
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-/
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prelude
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import Init.Meta
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namespace Std
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-- We put `Range` in `Init` because we want the notation `[i:j]` without importing `Std`
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-- We don't put `Range` in the top-level namespace to avoid collisions with user defined types
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structure Range where
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start : Nat := 0
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stop : Nat
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step : Nat := 1
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instance : Membership Nat Range where
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mem r i := r.start ≤ i ∧ i < r.stop
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namespace Range
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universe u v
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@[inline] protected def forIn' {β : Type u} {m : Type u → Type v} [Monad m] (range : Range) (init : β) (f : (i : Nat) → i ∈ range → β → m (ForInStep β)) : m β :=
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let rec @[specialize] loop (start stop step : Nat) (f : (i : Nat) → start ≤ i ∧ i < stop → β → m (ForInStep β)) (fuel i : Nat) (hl : start ≤ i) (b : β) : m β := do
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if hu : i < stop then
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match fuel with
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| 0 => pure b
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| fuel+1 => match (← f i ⟨hl, hu⟩ b) with
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| ForInStep.done b => pure b
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| ForInStep.yield b => loop start stop step f fuel (i + step) (Nat.le_trans hl (Nat.le_add_right ..)) b
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else
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return b
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loop range.start range.stop range.step f range.stop range.start (Nat.le_refl ..) init
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instance : ForIn' m Range Nat inferInstance where
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forIn' := Range.forIn'
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-- No separate `ForIn` instance is required because it can be derived from `ForIn'`.
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@[inline] protected def forM {m : Type u → Type v} [Monad m] (range : Range) (f : Nat → m PUnit) : m PUnit :=
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let rec @[specialize] loop (fuel i stop step : Nat) : m PUnit := do
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if i ≥ stop then
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pure ⟨⟩
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else match fuel with
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| 0 => pure ⟨⟩
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| fuel+1 => f i; loop fuel (i + step) stop step
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loop range.stop range.start range.stop range.step
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instance : ForM m Range Nat where
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forM := Range.forM
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syntax:max "[" withoutPosition(":" term) "]" : term
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syntax:max "[" withoutPosition(term ":" term) "]" : term
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syntax:max "[" withoutPosition(":" term ":" term) "]" : term
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syntax:max "[" withoutPosition(term ":" term ":" term) "]" : term
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macro_rules
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| `([ : $stop]) => `({ stop := $stop : Range })
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| `([ $start : $stop ]) => `({ start := $start, stop := $stop : Range })
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| `([ $start : $stop : $step ]) => `({ start := $start, stop := $stop, step := $step : Range })
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| `([ : $stop : $step ]) => `({ stop := $stop, step := $step : Range })
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end Range
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end Std
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theorem Membership.mem.upper {i : Nat} {r : Std.Range} (h : i ∈ r) : i < r.stop := h.2
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theorem Membership.mem.lower {i : Nat} {r : Std.Range} (h : i ∈ r) : r.start ≤ i := h.1
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theorem Membership.get_elem_helper {i n : Nat} {r : Std.Range} (h₁ : i ∈ r) (h₂ : r.stop = n) :
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i < n := h₂ ▸ h₁.2
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macro_rules
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| `(tactic| get_elem_tactic_trivial) => `(tactic| apply Membership.get_elem_helper; assumption; rfl)
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