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Diffstat (limited to 'theories/Numbers/AltBinNotations.v')
-rw-r--r-- | theories/Numbers/AltBinNotations.v | 69 |
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diff --git a/theories/Numbers/AltBinNotations.v b/theories/Numbers/AltBinNotations.v new file mode 100644 index 00000000..c7e39996 --- /dev/null +++ b/theories/Numbers/AltBinNotations.v @@ -0,0 +1,69 @@ +(************************************************************************) +(* * The Coq Proof Assistant / The Coq Development Team *) +(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *) +(* <O___,, * (see CREDITS file for the list of authors) *) +(* \VV/ **************************************************************) +(* // * This file is distributed under the terms of the *) +(* * GNU Lesser General Public License Version 2.1 *) +(* * (see LICENSE file for the text of the license) *) +(************************************************************************) + +(** * Alternative Binary Numeral Notations *) + +(** Faster but less safe parsers and printers of [positive], [N], [Z]. *) + +(** By default, literals in types [positive], [N], [Z] are parsed and + printed via the [Numeral Notation] command, by conversion from/to + the [Decimal.int] representation. When working with numbers with + thousands of digits and more, conversion from/to [Decimal.int] can + become significantly slow. If that becomes a problem for your + development, this file provides some alternative [Numeral + Notation] commmands that use [Z] as bridge type. To enable these + commands, just be sure to [Require] this file after other files + defining numeral notations. + + Note: up to Coq 8.8, literals in types [positive], [N], [Z] were + parsed and printed using a native ML library of arbitrary + precision integers named bigint.ml. From 8.9, the default is to + parse and print using a Coq library converting sequences of + digits, hence reducing the amount of ML code to trust. But this + method is slower. This file then gives access to the legacy + method, trading efficiency against a larger ML trust base relying + on bigint.ml. *) + +Require Import BinNums. + +(** [positive] *) + +Definition pos_of_z z := + match z with + | Zpos p => Some p + | _ => None + end. + +Definition pos_to_z p := Zpos p. + +Numeral Notation positive pos_of_z pos_to_z : positive_scope. + +(** [N] *) + +Definition n_of_z z := + match z with + | Z0 => Some N0 + | Zpos p => Some (Npos p) + | Zneg _ => None + end. + +Definition n_to_z n := + match n with + | N0 => Z0 + | Npos p => Zpos p + end. + +Numeral Notation N n_of_z n_to_z : N_scope. + +(** [Z] *) + +Definition z_of_z (z:Z) := z. + +Numeral Notation Z z_of_z z_of_z : Z_scope. |