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set versus set-delay

• To: mathgroup at smc.vnet.net
• Subject: [mg75208] set versus set-delay
• From: siewsk at bp.com
• Date: Fri, 20 Apr 2007 00:43:07 -0400 (EDT)

Informative Article
===================

SET versus SETDELAY


Newbie are always told to use SETDELAY instead of SET when they create
a mathematica function.

The objective of this article is to explain the differnce between SET
and SETDELAY using ordinary language (what linguistics call vernacular
language)

The main differences between those two are:

SET       means    CALCULATE FIRST THEN CHANGE
SETDELAY  means    CHANGE FIRST THEN CALCULATE


To explain, consider the following two functions f ang g

f[x_] = Expand[(x+7)^2]           (* Using SET       *)
g[x_]:= Expand[(x+7)^2]          (* Using SETDELAY  *)

The two functions are identical except f uses SET while g uses
SETDELAY. In normal usage there is no difference in the two functions.
However they produce their results using different steps.

================
SET
================

Consider f[4]

(Step 1.  CALCULATE FIRST )

f[x] = Expand[(x+7)^2]

f[x] = x^2 + 14 x + 49

(Step 2. THEN CHANGE )

f[x->4] = x^2 + 14 x + 49

f[4] <- 4^2 + 14 * 4 + 49

f[4] <- 121


================
SETDELAY
================

Consider g[4]

(Step 1.  CHANGE FIRST )

g[x] := Expand[(x+7)^2]

g[x->4] := Expand[(x+7)^2]

g[4] <- Expand[(4+7)^2]

(Step 2. THEN CALCULATE )

g[4] <- Expand[(11)^2]

g[4] <- Expand[121]

g[4] <- 121