394e0d5f0a
Now, `cmp` is just a fixed helper function. In the future, we will be able to use (more efficient) specialized versions during code generation by defining simp rules.
60 lines
1.5 KiB
Text
60 lines
1.5 KiB
Text
/-
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Copyright (c) 2016 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.data.repr init.data.prod init.data.sum.basic
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universes u v
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inductive ordering
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| lt | eq | gt
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instance : has_repr ordering :=
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⟨(λ s, match s with | ordering.lt := "lt" | ordering.eq := "eq" | ordering.gt := "gt" end)⟩
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namespace ordering
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def swap : ordering → ordering
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| lt := gt
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| eq := eq
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| gt := lt
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@[inline] def or_else : ordering → ordering → ordering
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| lt _ := lt
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| eq o := o
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| gt _ := gt
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theorem swap_swap : ∀ (o : ordering), o.swap.swap = o
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| lt := rfl
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| eq := rfl
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| gt := rfl
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end ordering
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def cmp {α : Type u} [has_lt α] [decidable_rel ((<) : α → α → Prop)] (a b : α) : ordering :=
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if a < b then ordering.lt
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else if b < a then ordering.gt
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else ordering.eq
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instance : decidable_eq ordering :=
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λ a b,
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match a with
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| ordering.lt :=
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match b with
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| ordering.lt := is_true rfl
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| ordering.eq := is_false (λ h, ordering.no_confusion h)
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| ordering.gt := is_false (λ h, ordering.no_confusion h)
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end
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| ordering.eq :=
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match b with
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| ordering.lt := is_false (λ h, ordering.no_confusion h)
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| ordering.eq := is_true rfl
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| ordering.gt := is_false (λ h, ordering.no_confusion h)
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end
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| ordering.gt :=
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match b with
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| ordering.lt := is_false (λ h, ordering.no_confusion h)
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| ordering.eq := is_false (λ h, ordering.no_confusion h)
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| ordering.gt := is_true rfl
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end
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end
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