2014-12-04 02:54:24 +00:00
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/-
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Copyright (c) 2014 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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2014-12-15 21:43:42 +00:00
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Module: init.measurable
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2014-12-04 02:54:24 +00:00
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Authors: Leonardo de Moura
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2014-12-15 21:43:42 +00:00
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Types with a nat-valued complexity measure.
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2014-12-04 02:54:24 +00:00
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-/
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prelude
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import init.nat
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open nat
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inductive measurable [class] (A : Type) :=
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mk : (A → nat) → measurable A
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definition size_of {A : Type} [s : measurable A] (a : A) : nat :=
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measurable.rec_on s (λ f, f) a
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definition nat.measurable [instance] : measurable nat :=
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measurable.mk (λ a, a)
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definition option.measurable [instance] (A : Type) (s : measurable A) : measurable (option A) :=
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measurable.mk (λ a, option.cases_on a zero (λ a, size_of a))
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definition prod.measurable [instance] (A B : Type) (sa : measurable A) (sb : measurable B) : measurable (prod A B) :=
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measurable.mk (λ p, prod.cases_on p (λ a b, size_of a + size_of b))
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definition sum.measurable [instance] (A B : Type) (sa : measurable A) (sb : measurable B) : measurable (sum A B) :=
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measurable.mk (λ s, sum.cases_on s (λ a, size_of a) (λ b, size_of b))
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definition bool.measurable [instance] : measurable bool :=
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measurable.mk (λb, zero)
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definition Prop.measurable [instance] : measurable Prop :=
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measurable.mk (λp, zero)
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definition unit.measurable [instance] : measurable unit :=
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measurable.mk (λu, zero)
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definition fn.measurable [instance] (A : Type) (B : A → Type) : measurable (Π x, B x) :=
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measurable.mk (λf, zero)
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