05f27b8f0e
It seems most of the time these theorems are not used at all. They are just polluting the namespace. Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
85 lines
2 KiB
Text
85 lines
2 KiB
Text
/-
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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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Authors: Leonardo de Moura
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Basic datatypes
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-/
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prelude
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notation `Prop` := Type.{0}
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notation [parsing-only] `Type'` := Type.{_+1}
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notation [parsing-only] `Type₊` := Type.{_+1}
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notation `Type₁` := Type.{1}
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notation `Type₂` := Type.{2}
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notation `Type₃` := Type.{3}
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set_option structure.eta_thm true
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set_option structure.proj_mk_thm true
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inductive unit.{l} : Type.{l} :=
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star : unit
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inductive true : Prop :=
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intro : true
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inductive false : Prop
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inductive empty : Type
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inductive eq {A : Type} (a : A) : A → Prop :=
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refl : eq a a
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inductive heq {A : Type} (a : A) : Π {B : Type}, B → Prop :=
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refl : heq a a
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structure prod (A B : Type) :=
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mk :: (pr1 : A) (pr2 : B)
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inductive and (a b : Prop) : Prop :=
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intro : a → b → and a b
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definition and.elim_left {a b : Prop} (H : and a b) : a :=
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and.rec (λa b, a) H
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definition and.elim_right {a b : Prop} (H : and a b) : b :=
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and.rec (λa b, b) H
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inductive sum (A B : Type) : Type :=
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inl : A → sum A B,
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inr : B → sum A B
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inductive or (a b : Prop) : Prop :=
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intro_left : a → or a b,
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intro_right : b → or a b
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-- pos_num and num are two auxiliary datatypes used when parsing numerals such as 13, 0, 26.
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-- The parser will generate the terms (pos (bit1 (bit1 (bit0 one)))), zero, and (pos (bit0 (bit1 (bit1 one)))).
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-- This representation can be coerced in whatever we want (e.g., naturals, integers, reals, etc).
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inductive pos_num : Type :=
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one : pos_num,
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bit1 : pos_num → pos_num,
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bit0 : pos_num → pos_num
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inductive num : Type :=
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zero : num,
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pos : pos_num → num
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inductive bool : Type :=
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ff : bool,
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tt : bool
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inductive char : Type :=
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mk : bool → bool → bool → bool → bool → bool → bool → bool → char
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inductive string : Type :=
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empty : string,
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str : char → string → string
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inductive nat :=
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zero : nat,
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succ : nat → nat
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inductive option (A : Type) : Type :=
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none {} : option A,
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some : A → option A
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