68 lines
2.5 KiB
Text
68 lines
2.5 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.meta.name init.meta.format
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/- Reflect a C++ level object. The VM replaces it with the C++ implementation. -/
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inductive level
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| zero : level
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| succ : level → level
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| max : level → level → level
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| imax : level → level → level
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| param : name → level
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| global : name → level
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| meta : name → level
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attribute [instance]
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definition level.is_inhabited : inhabited level :=
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inhabited.mk level.zero
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/- TODO(Leo): provide a definition in Lean. -/
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meta_constant level.has_decidable_eq : decidable_eq level
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attribute [instance] level.has_decidable_eq
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meta_constant level.lt : level → level → bool
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meta_constant level.lex_lt : level → level → bool
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meta_constant level.fold {A :Type} : level → A → (level → A → A) → A
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/- Return the given level expression normal form -/
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meta_constant level.normalize : level → level
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/- Return tt iff lhs and rhs denote the same level.
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The check is done by normalization. -/
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meta_constant level.eqv : level → level → bool
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/- Return tt iff the first level occurs in the second -/
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meta_constant level.occurs : level → level → bool
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/- Replace a parameter named n with l in the first level if the list contains the pair (n, l) -/
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meta_constant level.instantiate : level → list (name × level) → list level
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meta_constant level.to_format : level → options → format
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meta_constant level.to_string : level → string
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meta_definition level.cmp (a b : level) : ordering :=
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if level.lt a b = bool.tt then ordering.lt
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else if a = b then ordering.eq
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else ordering.gt
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attribute [instance]
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meta_definition level.has_to_string : has_to_string level :=
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has_to_string.mk level.to_string
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attribute [instance]
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meta_definition level.has_to_format : has_to_format level :=
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has_to_format.mk (λ l, level.to_format l options.mk)
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attribute [instance]
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meta_definition level.has_to_cmp : has_ordering level :=
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has_ordering.mk level.cmp
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meta_definition level.of_nat : nat → level
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| 0 := level.zero
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| (nat.succ n) := level.succ (level.of_nat n)
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open decidable
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meta_definition level.has_param : level → name → bool
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| (level.succ l) n := level.has_param l n
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| (level.max l₁ l₂) n := level.has_param l₁ n || level.has_param l₂ n
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| (level.imax l₁ l₂) n := level.has_param l₁ n || level.has_param l₂ n
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| (level.param n₁) n := to_bool (n₁ = n)
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| l n := ff
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