deriving in common lisp

derive.lisp

(ql:quickload "fare-matcher")

(defpackage :derive
  (:use :common-lisp
        :fare-matcher))

(in-package :derive)

(defvar *variable*)

(defun independentp (n)
  (or (eq n 'e) (numberp n)))

(defun dependentp (n)
  (eq n *variable*))

(defun derive-expr (expr)
  (match expr
    ; with respect to some variable
    (`(lambda (,x) ,e) (let ((*variable* x)) (derive-expr e)))


    ; exponentiation
    (`(,x ^ ,y)
      (cond
        ((independentp y) `(,y * (,x ^ (,y - 1)) * ,(derive-expr x)))
        ((independentp x) `((,x ^ ,y) * ,(derive-expr y)))
        (t                (derive-expr `(e ^ (,y * (ln ,x)))))))

    ; simple transformations
    (`(sqrt ,x) (derive-expr `(,x ^ 1/2)))
    (`(ln ,x) `(1 / ,x))
    (`(log ,x ,a) `(1 / (,x * (ln ,a))))

    ; division
    (`(,x / ,y) `(((,(derive-expr x) * ,y) - (,x * ,(derive-expr y))) / (,y ^ 2)))

    ; multiplication
    (`(,x * ,y) `((,x * ,(derive-expr y)) + (,(derive-expr x) * ,y)))

    ; addition
    (`(,a + ,b) `(,(derive-expr a) + ,(derive-expr b)))

    ; subtraction
    (`(,a + ,b) `(,(derive-expr a) - ,(derive-expr b)))

    ; trigonometry
    (`(sin ,x) `((cos ,x) * ,(derive-expr x)))
    (`(cos ,x) `(-1 * (sin ,x) * ,(derive-expr x)))
    (`(tan ,x) `((sec ,x) ^ 2))

    (x (cond
         ((independentp x) 0)
         ((dependentp x) 1)
         (t x)))))

(defmacro derive (v e)
  `',(derive-expr `(lambda (,v) ,e)))

(format t "~A~%" (derive x (x ^ 2)))
(format t "~A~%" (derive x (3 * (x ^ 3/2))))
(format t "~A~%" (derive x (x ^ x)))