2014-09-15 17:25:07 +00:00
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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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2014-10-05 17:50:13 +00:00
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import logic.inhabited
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2014-09-15 17:25:07 +00:00
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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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2015-02-26 01:00:10 +00:00
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one : pos_num|
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bit1 : pos_num → pos_num|
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2014-09-15 17:25:07 +00:00
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bit0 : pos_num → pos_num
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theorem pos_num.is_inhabited [instance] : inhabited pos_num :=
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inhabited.mk pos_num.one
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namespace pos_num
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definition inc (a : pos_num) : pos_num :=
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rec (bit0 one) (λn r, bit0 r) (λn r, bit1 n) a
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definition num_bits (a : pos_num) : pos_num :=
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rec one (λn r, inc r) (λn r, inc r) a
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end 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 num.is_inhabited [instance] : inhabited num :=
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inhabited.mk num.zero
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namespace num
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definition inc (a : num) : num :=
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rec (pos pos_num.one) (λp, pos (pos_num.inc p)) a
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definition num_bits (a : num) : num :=
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rec (pos pos_num.one) (λp, pos (pos_num.num_bits p)) a
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end num
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