# Re: Another code sample - symbolic derivatives

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• To: "David A. Wheeler" <dwheeler@xxxxxxxxxxxx>
• Subject: Re: Another code sample - symbolic derivatives
• From: Alan Manuel Gloria <almkglor@xxxxxxxxx>
• Date: Tue, 9 Apr 2013 21:16:59 +0800
• Cc: srfi-110 <srfi-110@xxxxxxxxxxxxxxxxx>
• Delivered-to: srfi-110@xxxxxxxxxxxxxxxxx
• References: <E1UPOkb-0002Mc-Iv@xxxxxxxxxxxxxxxxxxxxx>

On Tue, Apr 9, 2013 at 10:57 AM, David A. Wheeler wrote:
Here's a version of the "Wizard book" symbolic derivative calculation, using sweet-expressions.
I've placed it below and put it in an attachment.

Unsurprisingly, sweet-_expression_'s ability to accept infix makes infix expressions nicer. E.G.:
deriv '{{x * y} * {x + 3}} 'x

My goal of working out examples like this is to see if there are any serious problems with the sweet-_expression_ notation.  I don't see any problems with the notation in this case.  Granted, this has a bunch of especially short and simple definitions, but I don't see any sign of trouble.

--- David A. Wheeler

#!/usr/bin/env sweet-run
;#!guile -s
;!#

; Code to generate derivatives from the "Wizard Book" -
; Hal Abelson's, Jerry Sussman's and Julie Sussman's
; "Structure and Interpretation of Computer Programs"
; (MIT Press, 1984; ISBN 0-262-01077-1),
; http://mitpress.mit.edu/sicp/full-text/sicp/book/node39.html
; http://mitpress.mit.edu/sicp/code/index.html
;;; SECTION 2.3.2

define deriv(exp var)
cond
number?(exp) 0
variable?(exp)
if same-variable?(exp var) 1 0
sum?(exp)
product?(exp)
make-sum
make-product multiplier(exp) deriv(multiplicand(exp) var)
make-product deriv(multiplier(exp) var) multiplicand(exp)
else error("unknown _expression_ type -- DERIV" exp)

;; representing algebraic expressions

define variable?(x) symbol?(x)

define same-variable?(v1 v2)
{variable?(v1) and variable?(v2) and eq?(v1 v2)}

I'd rather:

define {v1 same-variable? v2}
{variable?(v1) and variable?(v2) and {v1 eq? v2}}

define sum?(x)
{pair?(x) and eq?(car(x) '+)}

define product?(x)
{pair?(x) and eq?(car(x) '*)}

;; Simplification

define make-sum(a1 a2)
cond
=number?(a1 0) a2
=number?(a2 0) a1
{number?(a1) and number?(a2)} {a1 + a2}
else list('+ a1 a2)

Every binary predicate is a good place to use { } on:

define make-sum(a1 a2) \$ cond
{a1 =number? 0} \$ a2
{a2 =number? 0} \$ a1
{number?(a1) and number?(a2)} \$ {a1 + a2}
else \$ `{,a1 + ,a2}

... and so on...