From 578ed1ba98510058cf48f897a9bf4e3391684120 Mon Sep 17 00:00:00 2001 From: William Carroll Date: Thu, 30 Jan 2020 16:00:29 +0000 Subject: Move move .emacs.d out of configs/shared Moving all of my Emacs-related files into their own directory at the root of this repository. --- emacs/.emacs.d/wpc/number.el | 153 +++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 153 insertions(+) create mode 100644 emacs/.emacs.d/wpc/number.el (limited to 'emacs/.emacs.d/wpc/number.el') diff --git a/emacs/.emacs.d/wpc/number.el b/emacs/.emacs.d/wpc/number.el new file mode 100644 index 000000000000..f496349050d9 --- /dev/null +++ b/emacs/.emacs.d/wpc/number.el @@ -0,0 +1,153 @@ +;;; number.el --- Functions for working with numbers -*- lexical-binding: t -*- +;; Author: William Carroll + +;;; Commentary: +;; +;; Classifications of numbers: +;; - Natural: (a.k.a positive integers, counting numbers); {1, 2, 3, ... } +;; +;; - Whole: Natural Numbers, plus zero; {0, 1, 2, 3, ...} +;; +;; - Integers: Whole numbers plus all the negatives of the natural numbers; +;; {... , -2, -1, 0, 1, 2, ...} +;; +;; - Rational numbers: (a.k.a. fractions) where the top and bottom numbers are +;; integers; e.g., 1/2, 3/4, 7/2, ⁻4/3, 4/1. Note: The denominator cannot be +;; 0, but the numerator can be. +;; +;; - Real numbers: All numbers that can be written as a decimal. This includes +;; fractions written in decimal form e.g., 0.5, 0.75 2.35, ⁻0.073, 0.3333, or +;; 2.142857. It also includes all the irrational numbers such as π, √2 etc. +;; Every real number corresponds to a point on the number line. +;; +;; The functions defined herein attempt to capture the mathematical definitions +;; of numbers and their classifications as defined above. + +;;; Code: + +;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; +;; Dependencies +;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; + +(require 'prelude) +(require 'dash) + +;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; +;; Library +;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; + +(defconst number/test? t + "When t, run the test suite defined herein.") + +;; TODO: What about int.el? + +;; TODO: How do we handle a number typeclass? + +(defun number/positive? (x) + "Return t if `X' is a positive number." + (> x 0)) + +(defun number/negative? (x) + "Return t if `X' is a positive number." + (< x 0)) + +;; TODO: Don't rely on this. Need to have 10.0 and 10 behave similarly. +(defun number/float? (x) + "Return t if `X' is a floating point number." + (floatp x)) + +(defun number/natural? (x) + "Return t if `X' is a natural number." + (and (number/positive? x) + (not (number/float? x)))) + +(defun number/whole? (x) + "Return t if `X' is a whole number." + (or (= 0 x) + (number/natural? x))) + +(defun number/integer? (x) + "Return t if `X' is an integer." + (or (number/whole? x) + (number/natural? (- x)))) + +;; TODO: How defensive should these guards be? Should we assert that the inputs +;; are integers before checking evenness or oddness? + +;; TODO: Look up Runar (from Unison) definition of handling zero as even or odd. + +;; TODO: How should rational numbers be handled? Lisp is supposedly famous for +;; its handling of rational numbers. +;; TODO: `calc-mode' supports rational numbers as "1:2" meaning "1/2" +;; (defun number/rational? (x)) + +;; TODO: Can or should I support real numbers? +;; (defun number/real? (x)) + +(defun number/even? (x) + "Return t if `X' is an even number." + (or (= 0 x) + (= 0 (mod x 2)))) + +(defun number/odd? (x) + "Return t if `X' is an odd number." + (not (number/even? x))) + +(defun number/dec (x) + "Subtract one from `X'. +While this function is undeniably trivial, I have unintentionally done (- 1 x) + when in fact I meant to do (- x 1) that I figure it's better for this function + to exist, and for me to train myself to reach for it and its inc counterpart." + (- x 1)) + +(defun number/inc (x) + "Add one to `X'." + (+ x 1)) + +;; TODO: Does this belong in a math module? Is math too vague? Or is number +;; too vague? +;; TODO: Resolve the circular dependency that this introduces with series.el, +;; and then re-enable this function and its tests below. +;; (defun number/factorial (x) +;; "Return factorial of `X'." +;; (cond +;; ((number/negative? x) (error "Will not take factorial of negative numbers")) +;; ((= 0 x) 1) +;; ;; NOTE: Using `series/range' introduces a circular dependency because: +;; ;; series -> number -> series. Conceptually, however, this should be +;; ;; perfectly acceptable. +;; (t (->> (series/range 1 x) +;; (list/reduce 1 #'*))))) + +;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; +;; Tests +;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; + +(when number/test? + (prelude/assert + (number/positive? 10)) + (prelude/assert + (number/natural? 10)) + (prelude/assert + (number/whole? 10)) + (prelude/assert + (number/whole? 0)) + (prelude/assert + (number/integer? 10)) + ;; (prelude/assert + ;; (= 120 (number/factorial 5))) + (prelude/assert + (number/even? 6)) + (prelude/refute + (number/odd? 6)) + (prelude/refute + (number/positive? -10)) + (prelude/refute + (number/natural? 10.0)) + (prelude/refute + (number/natural? -10)) + (prelude/refute + (number/natural? -10.0))) + +(provide 'number) +;;; number.el ends here -- cgit 1.4.1