String Processing: Validate Email Address Format, Part 1

Here are three approaches to predicates validating that an email address has an "@" sign and a period ".". A true email address validator is much more complicated, so these functions are merely to illustrate some String processing techniques. That said, I did use the first approach to validate thousands of email addresses and flush out bad ones.

The first predicate uses StringMatchQ and the essential idea is to give StringMatchQ a String pattern representing:

1. An "@" wildcard for at least one but an unknown number of characters
2. Followed by the "@" sign as used in an email address to separate localpart from domain
3. Followed by the wildcard again
4. Followed by the period "." used to separate the mail server name from the top-level domain
5. Followed by the wildcard

Note that an asterisk wildcard ("*") would not be suitable since each position in the pattern has at least one character.

The first variation illustrates the use of Verbatim, which tells Mathematica to treat the middle "@" sign as an "@" sign  (read it "verbatim") and not as a pattern wildcard.

Clear@emailAddressQ1;emailAddressQ1@aString_String:=StringMatchQ[aString,"@"~~Verbatim@"@"~~"@.@"]

The second variation of StringMatchQ does the same thing but more concisely, using a double backslash. The first backslash tells Mathematica to treat the second one as an 'escape' character, which then tell Mathematica to treat the "@" sign as an "@" sign and not as a wildcard.

Clear@emailAddressQ1a;emailAddressQ1a@aString_String:=StringMatchQ[aString,"*\\@*.*"]

The second basic approach uses StringContainsQ to detect the presence of the "@" sign and period "." in the address. Since it doesn't require additional characters in the correct positions as does the first approach, it is not as good a validator.

Clear@emailAddressQ2;emailAddressQ2@aString_String:=StringContainsQ[aString,"@"]&&StringContainsQ[aString,"."]

The third approach uses StringFreeQ to see if the address has no "@" sign and period ".", and some logic, and suffers the same limitation as the second approach.

Clear@emailAddressQ3;emailAddressQ3@aString_String:=Not[StringFreeQ[aString,"@"]&&StringFreeQ[aString,"."]]

Test Cases

The test cases are 1) valid email format, 2) missing "@" sign, 3) missing "." and 4) missing both "@" and ".".

testCases={"abc@dwxy.anything","abcdwxy.anything","abc@dwxyanything","abcdwxyanything"};

emailAddressQ1/@testCases

{True,False,False,False}

emailAddressQ1a/@testCases

{True,False,False,False}

emailAddressQ2/@testCases

{True,False,False,False}

emailAddressQ3/@testCases

{True,True,True,False}

Aha! The test cases flushed out a logic error. The way the emailAddressQ3 function is written with the AND (&&) conjunction between the two clauses, only if both StringMatchQ tests are FALSE will AND return FALSE and be negated by NOT into TRUE. We need to change the AND to OR so that if either "@" or "." are missing, the OR returns TRUE and is negated by NOT into FALSE.

Clear@emailAddressQ4;emailAddressQ4@aString_String:=Not[StringFreeQ[aString,"@"]||StringFreeQ[aString,"."]]

emailAddressQ4/@testCases

{True,False,False,False}

String Replacement Methods: StringTemplate

A String Replacement Overview is here.

StringTemplate

StringTemplate saves you the trouble of searching for a String subset within a String to replace or setting up your own marker to flag the StringPosition in the String at which to perform a replacement.

Further, good programming practice dictates that we use selectors and constructors – specialized, dedicated functions to extract a subset of a file or to change a subset of a file – and to always use those rather than ad hoc one liners scattered in our functions and programs.^1,2 StringTemplate conveniently formalizes and enforces the use of selectors and constructors.

StringForm is simpler to understand and use than StringTemplate, so I use StringForm when you need to output a message from your function. I don't end the command with a semi-colon so you can see the InputForm of a TemplateObject including its default Options.

stringTemplate1=StringTemplate@"The quick brown `` jumped over the lazy white ``."

TemplateObject[{The quick brown ,TemplateSlot[1], jumped over the lazy white ,TemplateSlot[2],.},InsertionFunction->TextString,CombinerFunction->StringJoin]

You can directly Apply any StringTemplate as a function to a List of its arguments that fits its requirements, or use TemplateApply to do the same thing.

stringTemplate1@@{"mink","peccadillo"}

The quick brown mink jumped over the lazy white peccadillo.

Equivalently, here StringTemplate is used as a function as you would any other function – use it as the Head of an Expression with its arguments.

stringTemplate1["mink","peccadillo"]

The quick brown mink jumped over the lazy white peccadillo.

Equivalently, using TemplateApply:

TemplateApply[stringTemplate1,{"mink","peccadillo"}]

The quick brown mink jumped over the lazy white peccadillo.

1. Maeder, Roman, Computer Science with Mathematica. Cambridge: Cambridge University Press, 2000. Chapter 5.3. Design of Abstract Data Types.

2. Maeder, Roman, M220: Programming in Mathematica  (course given by Wolfram Education Group, which I have taken twice and recommend).

String Replacement Methods: Overview

Here are String replacement methods that I have used in code from one-liners up to programs producing hundreds of thousands of text and html files. In general, use the simplest method or one that you understand clearly. Use StringForm to output messages from your functions and programs. For longer functions or programs, StringTemplate is the new best practice.

There is a function I don't discuss, StringInsert, which inserts a substring at a given StringPosition in a control String. I don't advocate its use since it's very brittle in that if you add or delete even one character before the StringPosition then the insertion point will be wrong.

StringForm

Literal Replacement, Markers, and Delimiters

StringTemplate

String Replacement Methods: Literal Replacement, Markers, and Delimiters

A String Replacement Overview is here.

Note that the next three methods all use StringReplace. This is in keeping with my principle that the fastest way to learn Mathematica is to become a power user of its 70 or so core functions. In String processing, for instance, StringInsert is not a function you need to know. Instead learn to use the more powerful and robust function, StringReplace.

Literal Replacement

Literal replacement works by using StringReplace to find a literal substring within a String and substitute another substring for it. Literal replacement is very simple and easy to use.

string1="The quick brown fox jumped over the lazy white dog.";

StringReplace[string1,{"fox"->"mink","dog"->"pecadillo"}]

The quick brown mink jumped over the lazy white pecadillo.

Markers

Using markers to indicate the replacement position can improve code legibility. Use StringReplace to replace just the marked text.

string2="The quick brown <animal1> jumped over the lazy white <animal2>.";

StringReplace[string2,{"<animal1>"->"mink","<animal2>"->"pecadillo"}]

The quick brown mink jumped over the lazy white pecadillo.

Delimiters

Use StringReplace to replace text between the delimiters. This is very useful when you want to replace a lot of text in a document, especially in a long document. However, the new function StringTemplate is a superior method overall.

sitemapTemplate="<?xml version=\"1.0\" encoding=\"UTF-8\"?>
<urlset xmlns=\"http://www.sitemaps.org/schemas/sitemap/0.9\">
<!-- put list of urls here with a line feed after each one -->
</urlset>";

urls="<url><loc>http://www.blah.net/page1.html</loc></url>
<url><loc>http://www.blah.net/page2.html</loc></url>";

Note that you use StringExpression (shorthand "~~") to concatenate quoted Strings with Blanks in the String to be found by StringReplace, but you must use StringJoin (shorthand "<>") if you concatenate different Strings in the replacement String.

sitemapTemplateWithURLs=StringReplace[sitemapTemplate,"<!-- put list"~~urlsList__~~"each one -->"->urls]

<?xml version="1.0" encoding="UTF-8"?>
<urlset xmlns="http://www.sitemaps.org/schemas/sitemap/0.9">
<url><loc>http://www.blah.net/page1.html</loc></url>
<url><loc>http://www.blah.net/page2.html</loc></url>
</urlset>

String Operations: The Essential Function StringSplit

Split a String and Gather its Words by Their First Letter

Let's process a nice sonnet I just read in Ray Kurzweil's excellent book on what he thinks is the heart of cognitive science and AI, How to Create a Mind: The Secret of Human Thought Revealed.
To start I copy and paste the text from the web between quotation marks.

In[377]:= sonnet73=
"That time of year thou mayst in me behold,
When yellow leaves, or none, or few, do hang
Upon those boughs which shake against the cold,
Bare ruined choirs, where late the sweet birds sang.
In me thou seest the twilight of such day,
As after sunset fadeth in the west,
Which by and by black night doth take away,
Death's second self, that seals up all in rest.
In me thou seest the glowing of such fire,
That on the ashes of his youth doth lie,
As the death-bed whereon it must expire,
Consumed with that which it was nourished by.
This thou perceiv'st, which makes thy love more strong,
To love that well, which thou must leave ere long.";

Can we use ToLowerCase without Map? Yes, since it's Listable.

In[380]:= sonnet73LowerCase=ToLowerCase@%377

Out[380]= that time of year thou mayst in me behold,
when yellow leaves, or none, or few, do hang
upon those boughs which shake against the cold,
bare ruined choirs, where late the sweet birds sang.
in me thou seest the twilight of such day,
as after sunset fadeth in the west,
which by and by black night doth take away,
death's second self, that seals up all in rest.
in me thou seest the glowing of such fire,
that on the ashes of his youth doth lie,
as the death-bed whereon it must expire,
consumed with that which it was nourished by.
this thou perceiv'st, which makes thy love more strong,
to love that well, which thou must leave ere long.

We need StringSplit, not SplitBy, since we are working with a String. StringSplit is a powerful and essential function when importing and transforming large files to the format you need. Examples in the Doc Center like this one show its versatility:

In[1]:= StringSplit["a-b:c-d:e-f-g",{":","-"}]

Out[1]= {a,b,c,d,e,f,g}

Using WordBoundary as the pattern test for where to split works, but leaves much more "noise". Here is the output. Using InputForm is often handy to see what is going in while processing Strings.

In[409]:= StringSplit[sonnet73LowerCase,WordBoundary]//InputForm

Out[409]//InputForm=
{"that", " ", "time", " ", "of", " ", "year", " ", "thou", " ", "mayst", " ", "in",
 " ", "me", " ", "behold", ",\n", "when", " ", "yellow", " ", "leaves", ", ", "or",
 " ", "none", ", ", "or", " ", "few", ", ", "do", " ", "hang", "\n", "upon", " ",
 "those", " ", "boughs", " ", "which", " ", "shake", " ", "against", " ", "the", " ",
 "cold", ",\n", "bare", " ", "ruined", " ", "choirs", ", ", "where", " ", "late", " ",
 "the", " ", "sweet", " ", "birds", " ", "sang", ".\n", "in", " ", "me", " ", "thou",
 " ", "seest", " ", "the", " ", "twilight", " ", "of", " ", "such", " ", "day", ",\n",
 "as", " ", "after", " ", "sunset", " ", "fadeth", " ", "in", " ", "the", " ", "west",
 ",\n", "which", " ", "by", " ", "and", " ", "by", " ", "black", " ", "night", " ",
 "doth", " ", "take", " ", "away", ",\n", "death", "'", "s", " ", "second", " ",
 "self", ", ", "that", " ", "seals", " ", "up", " ", "all", " ", "in", " ", "rest",
 ".\n", "in", " ", "me", " ", "thou", " ", "seest", " ", "the", " ", "glowing", " ",
 "of", " ", "such", " ", "fire", ",\n", "that", " ", "on", " ", "the", " ", "ashes",
 " ", "of", " ", "his", " ", "youth", " ", "doth", " ", "lie", ",\n", "as", " ", "the",
 " ", "death", "-", "bed", " ", "whereon", " ", "it", " ", "must", " ", "expire",
 ",\n", "consumed", " ", "with", " ", "that", " ", "which", " ", "it", " ", "was", " ",
 "nourished", " ", "by", ".\n", "this", " ", "thou", " ", "perceiv", "'", "st", ", ",
 "which", " ", "makes", " ", "thy", " ", "love", " ", "more", " ", "strong", ",\n",
 "to", " ", "love", " ", "that", " ", "well", ", ", "which", " ", "thou", " ", "must",
 " ", "leave", " ", "ere", " ", "long", "."}

What a mess! And using this lengthy construct to DeleteCases of punctuation still left an imperfect result (which I won't show in case you're about to eat).

%//DeleteCases[#,""|" "|","|", "|" ,"|"'"|"s"|"st"|",\n"|",\n"|".\n"|"\n"|"-"|"."|" . "|"  . "]&

Compare the result from proper use of StringSplit.

In[405]:= sonnet73Split=StringSplit[sonnet73LowerCase,{Whitespace,".",","}]//DeleteCases[#,""]&

Out[405]= {that,time,of,year,thou,mayst,in,me,behold,when,yellow,leaves,or,none,or,few,do,hang,upon,those,boughs,which,shake,against,the,cold,bare,ruined,choirs,where,late,the,sweet,birds,sang,in,me,thou,seest,the,twilight,of,such,day,as,after,sunset,fadeth,in,the,west,which,by,and,by,black,night,doth,take,away,death's,second,self,that,seals,up,all,in,rest,in,me,thou,seest,the,glowing,of,such,fire,that,on,the,ashes,of,his,youth,doth,lie,as,the,death-bed,whereon,it,must,expire,consumed,with,that,which,it,was,nourished,by,this,thou,perceiv'st,which,makes,thy,love,more,strong,to,love,that,well,which,thou,must,leave,ere,long}

Here GatherBy groups sub-lists by the first character of each word.

In[411]:= sonnet73SplitGathered=GatherBy[sonnet73Split,First@Characters@#&]

Out[411]= {{that,time,thou,those,the,the,thou,the,twilight,the,take,that,thou,the,that,the,the,that,this,thou,thy,to,that,thou},{of,or,or,of,of,on,of},{year,yellow,youth},{mayst,me,me,me,must,makes,more,must},{in,in,in,in,in,it,it},{behold,boughs,bare,birds,by,by,black,by},{when,which,where,west,which,whereon,with,which,was,which,well,which},{leaves,late,lie,love,love,leave,long},{none,night,nourished},{few,fadeth,fire},{do,day,doth,death's,doth,death-bed},{hang,his},{upon,up},{shake,sweet,sang,seest,such,sunset,second,self,seals,seest,such,strong},{against,as,after,and,away,all,ashes,as},{cold,choirs,consumed},{ruined,rest},{glowing},{expire,ere},{perceiv'st}}

To see the Lists sorted by their initial letter, we should use SortBy, but this didn't work.

In[412]:= SortBy[%,First@Characters@#&]

We need to add another First to apply the sorting function to the First word in each sublist.

In[413]:= SortBy[%,First@Characters@First@#&]

Out[413]= {{against,as,after,and,away,all,ashes,as},{behold,boughs,bare,birds,by,by,black,by},{cold,choirs,consumed},{do,day,doth,death's,doth,death-bed},{expire,ere},{few,fadeth,fire},{glowing},{hang,his},{in,in,in,in,in,it,it},{leaves,late,lie,love,love,leave,long},{mayst,me,me,me,must,makes,more,must},{none,night,nourished},{of,or,or,of,of,on,of},{perceiv'st},{ruined,rest},{shake,sweet,sang,seest,such,sunset,second,self,seals,seest,such,strong},{that,time,thou,those,the,the,thou,the,twilight,the,take,that,thou,the,that,the,the,that,this,thou,thy,to,that,thou},{upon,up},{when,which,where,west,which,whereon,with,which,was,which,well,which},{year,yellow,youth}}