lean2/library/data/num.lean
Leonardo de Moura dbaf81e16d refactor(library): remove unnecessary 'standard' subdirectory
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-08-23 18:08:09 -07:00

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-- Copyright (c) 2014 Microsoft Corporation. All rights reserved.
-- Released under Apache 2.0 license as described in the file LICENSE.
-- Author: Leonardo de Moura
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import logic.classes.inhabited
namespace num
-- pos_num and num are two auxiliary datatypes used when parsing numerals such as 13, 0, 26.
-- The parser will generate the terms (pos (bit1 (bit1 (bit0 one)))), zero, and (pos (bit0 (bit1 (bit1 one)))).
-- This representation can be coerced in whatever we want (e.g., naturals, integers, reals, etc).
inductive pos_num : Type :=
one : pos_num,
bit1 : pos_num → pos_num,
bit0 : pos_num → pos_num
inductive num : Type :=
zero : num,
pos : pos_num → num
theorem inhabited_pos_num [instance] : inhabited pos_num :=
inhabited_mk one
theorem num_inhabited [instance] : inhabited num :=
inhabited_mk zero
end num