50 lines
2.3 KiB
Text
50 lines
2.3 KiB
Text
/-
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Copyright (c) 2018 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.uint init.platform init.data.fin
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def usize_sz : nat := (2:nat) ^ system.platform.nbits
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structure usize :=
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(val : fin usize_sz)
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def usize.of_nat (n : nat) : usize := ⟨fin.of_nat n⟩
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def usize.to_nat : usize → nat | ⟨a⟩ := a.val
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def usize.add : usize → usize → usize | ⟨a⟩ ⟨b⟩ := ⟨a + b⟩
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def usize.sub : usize → usize → usize | ⟨a⟩ ⟨b⟩ := ⟨a - b⟩
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def usize.mul : usize → usize → usize | ⟨a⟩ ⟨b⟩ := ⟨a * b⟩
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def usize.div : usize → usize → usize | ⟨a⟩ ⟨b⟩ := ⟨a / b⟩
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def usize.mod : usize → usize → usize | ⟨a⟩ ⟨b⟩ := ⟨a % b⟩
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def usize.modn : usize → nat → usize | ⟨a⟩ b := ⟨a %ₙ b⟩
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def usize.lt : usize → usize → Prop | ⟨a⟩ ⟨b⟩ := a < b
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def usize.le : usize → usize → Prop | ⟨a⟩ ⟨b⟩ := a ≤ b
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instance : has_zero usize := ⟨⟨fin.of_nat 0⟩⟩
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instance : has_one usize := ⟨⟨fin.of_nat 1⟩⟩
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instance : has_add usize := ⟨usize.add⟩
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instance : has_sub usize := ⟨usize.sub⟩
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instance : has_mul usize := ⟨usize.mul⟩
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instance : has_mod usize := ⟨usize.mod⟩
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instance : has_modn usize := ⟨usize.modn⟩
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instance : has_div usize := ⟨usize.div⟩
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instance : has_lt usize := ⟨usize.lt⟩
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instance : has_le usize := ⟨usize.le⟩
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instance : inhabited usize := ⟨0⟩
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def usize.dec_eq : Π (a b : usize), decidable (a = b)
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| ⟨a⟩ ⟨b⟩ := if h : a = b then is_true (h ▸ rfl) else is_false (λ h', usize.no_confusion h' (λ h', absurd h' h))
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def usize.dec_lt : Π (a b : usize), decidable (a < b)
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| ⟨a⟩ ⟨b⟩ := infer_instance_as (decidable (a < b))
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def usize.dec_le : Π (a b : usize), decidable (a ≤ b)
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| ⟨a⟩ ⟨b⟩ := infer_instance_as (decidable (a ≤ b))
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instance : decidable_eq usize := {dec_eq := usize.dec_eq}
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instance usize.has_decidable_lt (a b : usize) : decidable (a < b) := usize.dec_lt a b
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instance usize.has_decidable_le (a b : usize) : decidable (a ≤ b) := usize.dec_le a b
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theorem usize.modn_lt {m : nat} : ∀ (u : usize), m > 0 → usize.to_nat (u %ₙ m) < m
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| ⟨u⟩ h := fin.modn_lt u h
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