29 lines
1 KiB
Text
29 lines
1 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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-- Author: Leonardo de Moura
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----------------------------------------------------------------------------------------------------
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import logic.classes.inhabited
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namespace num
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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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theorem inhabited_pos_num [instance] : inhabited pos_num :=
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inhabited_mk one
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theorem num_inhabited [instance] : inhabited num :=
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inhabited_mk zero
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end num
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