lean2/library/data/num.lean

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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

-- 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 pos_num.one

theorem num_inhabited [instance] : inhabited num :=
inhabited.mk num.zero