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Diffstat (limited to 'theories/Numbers/BinNums.v')
-rw-r--r-- | theories/Numbers/BinNums.v | 61 |
1 files changed, 61 insertions, 0 deletions
diff --git a/theories/Numbers/BinNums.v b/theories/Numbers/BinNums.v new file mode 100644 index 00000000..dfb2c502 --- /dev/null +++ b/theories/Numbers/BinNums.v @@ -0,0 +1,61 @@ +(************************************************************************) +(* v * The Coq Proof Assistant / The Coq Development Team *) +(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2010 *) +(* \VV/ **************************************************************) +(* // * This file is distributed under the terms of the *) +(* * GNU Lesser General Public License Version 2.1 *) +(************************************************************************) + +(** * Binary Numerical Datatypes *) + +Set Implicit Arguments. +(* For compatibility, we will not use generic equality functions *) +Local Unset Boolean Equality Schemes. + +Declare ML Module "z_syntax_plugin". + +(** [positive] is a datatype representing the strictly positive integers + in a binary way. Starting from 1 (represented by [xH]), one can + add a new least significant digit via [xO] (digit 0) or [xI] (digit 1). + Numbers in [positive] can also be denoted using a decimal notation; + e.g. [6%positive] abbreviates [xO (xI xH)] *) + +Inductive positive : Set := + | xI : positive -> positive + | xO : positive -> positive + | xH : positive. + +Delimit Scope positive_scope with positive. +Bind Scope positive_scope with positive. +Arguments xO _%positive. +Arguments xI _%positive. + +(** [N] is a datatype representing natural numbers in a binary way, + by extending the [positive] datatype with a zero. + Numbers in [N] can also be denoted using a decimal notation; + e.g. [6%N] abbreviates [Npos (xO (xI xH))] *) + +Inductive N : Set := + | N0 : N + | Npos : positive -> N. + +Delimit Scope N_scope with N. +Bind Scope N_scope with N. +Arguments Npos _%positive. + +(** [Z] is a datatype representing the integers in a binary way. + An integer is either zero or a strictly positive number + (coded as a [positive]) or a strictly negative number + (whose opposite is stored as a [positive] value). + Numbers in [Z] can also be denoted using a decimal notation; + e.g. [(-6)%Z] abbreviates [Zneg (xO (xI xH))] *) + +Inductive Z : Set := + | Z0 : Z + | Zpos : positive -> Z + | Zneg : positive -> Z. + +Delimit Scope Z_scope with Z. +Bind Scope Z_scope with Z. +Arguments Zpos _%positive. +Arguments Zneg _%positive. |