Lists and Expressions

Stored expressions

An expression is any combination of variables, constants, and functions linked by operators that can be evaluated. The section Rules for Name Resolution in the JSL Building Blocks section discusses how JMP evaluates expressions. Now you must consider when JMP evaluates expressions. JMP evaluates statements in sequence. Using expressions enables you to assign an expression and then modify or execute that expression when needed.

Quoting and Unquoting Expressions

The operators to control when expressions are evaluated are Expr and Eval, which you should think of as the procrastination and eager operators. Expr just copies its argument as an expression, rather than evaluating it. Eval does the opposite: it evaluates its argument, and then takes that result and evaluates it again.

Expr and Eval can be thought of as quoting and unquoting operators, telling JMP when you mean the expression itself, and when you mean the result of evaluating the expression.

The following examples all assume these two assignments:

x = 1; y = 20;

If you assign the expression x+y to a, quoting it as an expression with Expr, then whenever a is evaluated, it evaluates the expression using the current values of x and y and returns the result. (Exceptions are the utilities Show, Write, and Print, which do not evaluate expressions for pure name arguments.)

x = 1; y = 20;

a = Expr( x + y );

a;

21

If you want the expression that is stored in the name, rather than the result of evaluating the expression, use the NameExpr function. See Retrieve a Stored Expression, Not its Result.

x = 1; y = 20;

Show( Name Expr( a ) );

NameExpr(a) = x + y

If you assign an extra level of expression-quoting, then when a is evaluated, it unpacks one layer and the result is the expression x+y.

x = 1; y = 20;

a = Expr( Expr( x + y ) );

Show( a );

a = Expr(x + y)

If you want the value of the expression, then use Eval to unpack all layers:

x = 1; y = 20;

Show( Eval( a ) );

Eval(a) = 21

You can do this to any level, for example:

x = 1; y = 20;

a = Expr( Expr( Expr( Expr( x + y ) ) ) );

b = a;

Expr( Expr( x + y ) )

c = Eval( a );

Expr( x + y )

d = Eval( Eval( a ) );

x+y

e = Eval( Eval( Eval( a ) ) );

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For more information about expression handling, see Morgan (2010).

Quote an expression as a string

The JSL Quote() function returns the contents of an expression as a quoted string. Comments and white space in the string are preserved. Syntax coloring is also applied to the output.

The following script is an example:

x = JSL Quote( /* Begin quote. */

For (i = 1, i <= 5, i++,

// Print the value of i.

Print( i );

);

// End expression.

);

Show( x );

In the output, the contents of the JSL Quote() function are enclosed in quotes.

x = " /* Begin quote. */

For (i = 1, i <= 5, i++,

// Print the value of i.

Print(i);

);

// End expression.

";

Scripts as Expressions

A common use of the Expr() function is to store a script in a global variable. This could be considered as a macro. Consider the following script:

dist = Expr( Distribution( Column( height ) ) );

To execute the script, use the following expression:

dist;

You can use expressions in a loop to execute it:

For( i = 0, i < 3, i = i + 1, dist );

This loop results in three Distribution platform reports for height.

Use Eval() to evaluate an expression explicitly:

Eval( dist );

Note, however, that in column formulas, Eval() only works if it is outermost in the formula. So, for example,

Formula( Log( Eval( Column Name( i ) ) ) );

would generate an error. Instead, use:

Formula( Eval( Substitute( Expr( Log( xxx ) ), Expr( xxx ), Column Name( i ) ) ) );

As another example,

Formula( Eval( Column Name( i ) ) + 10 );

generates an error, since Eval() is actually under the Add function. Instead, use:

Formula(Eval(Substitute(Expr(xxx+10), Expr(xxx), column name(i))))

Retrieve a Stored Expression, Not its Result

What if you wanted the symbolic value of a global (such as the expression Distribution(Column(height)) stored in dist above), rather than the evaluation of it (the actual launched platform)? The Name Expr function does this. Name Expr retrieves its argument as an expression without evaluating it, but if the argument is a name, it looks up the name’s expression and uses that, unevaluated.

Expr returns its argument exactly, whereas Name Expr looks up the expression stored in its argument. Name Expr “unpacks” just one layer to get the expression, but does not keep unpacking to get the result.

For example, you would need to use this if you had an expression stored in a name and you wanted to edit the expression:

popVar = Expr( Summation( i = 1, N Row(), (y[i] - Col Mean( y )) ^ 2 / N Row() ) );

Summation( i = 1, N Row(), (y[i] - Col Mean( y )) ^ 2 / N Row() )

unbiasedPopVar = Substitute( Name Expr( popVar ), Expr( Wild()/N Row() ), Expr( (y[i] - Col Mean( y )) ^ 2 / ( N Row() - 1 ) ) );

Summation( i = 1, N Row(), (y[i] - Col Mean( y )) ^ 2 / (N Row() - 1) )

Compare x, Expr(x), NameExpr(x), and Eval(x) after submitting this script:

a = 1; b = 2; c = 3;

x = Expr( a + b + c );

x;

Eval( x );

NameExpr( x );

Expr( x );

JSL also supports functions to access and traverse expressions, all of them either a name or a literal expression as an argument. In the following, expressionArg is either a single name or a compound expression to be taken literally.

NArg(expressionArg) finds the number of arguments in expressionArg.

The expressionArg can be a name holding an expression, an expression evaluated to an expression, or a literal expression quoted by Expr().

NArg(name) obtains the expression held in name (it is not evaluated) and returns the number of arguments

NArg(expression) evaluates expression and returns the number of arguments

NArg(Expr(expression)) returns the number of arguments to literal expression.

For example, if aExpr = {a+b,c,d,e+f+g};

• NArg(aExpr) results in 4.

• NArg(Arg(aExpr,4)) results in 3.

• NArg(Expr({1,2,3,4})) results in 4.

Head(expressionArg) returns the head of the expression without any arguments. If the expression is an infix, prefix, or postfix special character operator, then it is returned as the functional equivalent.

The expressionArg can be a name holding an expression, an expression evaluated to an expression, or a literal expression quoted by Expr().

For example, if aExpr = expr(a+b);

• r = Head(aExpr) results in Add().

• r = Head (Expr(sqrt(r))) results in Sqrt().

• r = Head({1,2,3}) results in {} .

Arg(expressionArg,indexArg) extracts the specified argument of the symbolic expression, resulting in an expression.

For example,

Arg(expressionArg,i) extracts the ith argument of expressionArg.

The expressionArg can be a name holding an expression, an expression evaluated to an expression, or a literal expression quoted by Expr().

• Arg(name,i) obtains the expression held in name (it is not evaluated) and finds the ith argument.

• Arg(expression,i) evaluates expression and finds the ith argument.

• Arg(Expr(expression),i) finds the ith argument of expression.

As another example, if aExpr = Expr(12+13*sqrt(14-15));

• Arg(aExpr,1) yields 12.

• Arg(aExpr,2) yields 13*sqrt(14-15).

• Arg(Expr(12+13*sqrt(14-15)),2) yields 13*sqrt(14-15).

To extract an argument of an argument inside an expression, you can nest Arg commands:

• Arg(Arg(aExpr,2),1) yields the first argument within the second argument of aExpr, or 13.

• Arg(Arg(aExpr,2),2) yields Sqrt(14-15).

• Arg(Arg(Arg(aExpr,2),2),1) yields 14-15.

• Arg(Arg(Arg(aExpr,2),2),3) yields Empty()

Here is a description of how the last example line unwraps itself:

1. The inner Arg statement is evaluated.

Arg(aExpr,2)

13 * Sqrt( 14 - 15 )

2. Then the next one is evaluated.

Arg(Arg(aExpr,2),2)

// this is equivalent to Arg(Expr (13 * Sqrt( 14 - 15 ) ), 2)

Sqrt( 14 - 15 )

3. Finally, the outer Arg is evaluated.

Arg(Arg(Arg(aExpr,2),2),3)

// this is equivalent to Arg (Expr (Sqrt( 14 - 15 ) ), 3)

Empty()

There is only one element to the Sqrt expression, so a request for the third argument yields Empty(). To access the two arguments inside the Sqrt expression, try this:

Arg(Arg(Arg(Arg(aExpr,2),2),1),2);

15

HeadName(expressionArg) returns the name of the head of the expression as a string. If the expression is an infix, prefix, postfix, or other special character operator, then it is returned as the functional equivalent.

The expressionArg can be a name holding an expression, an expression evaluated to an expression, or a literal expression quoted by Expr().

For example, if aExpr = expr(a+b);

• r = HeadName (aExpr) results in "Add".

• r = HeadName (Expr(sqrt(r))) results in "Sqrt".

• r = HeadName ({1,2,3}) results in "List".

In previous versions of JMP, other versions of Arg, Narg, Head, and HeadName were implemented, called ArgExpr, NArgExpr, HeadExpr, and HeadNameExpr, respectively. These did the same thing, but did not evaluate their argument. These forms are now deprecated and will not be documented in future versions.

Making Substitutions

Eval Insert is for the situation where you want to make substitutions, by evaluating expressions inside a character string.

With Eval Insert, you specify characters that delimit the start and end of an expression, and everything in between is evaluated and expanded.

There are two functions, one to return the result, the other to do it in-place.

resultString = EvalInsert( string with embedded expressions,startDelimiter,endDelimiter )

EvalInsertInto( string l-value with embedded expressions,startDelimiter,endDelimiter )

The delimiter is optional. The default start delimiter is "^". The default end delimiter is the start delimiter.

xstring = "def";

r = Eval Insert( "abc^xstring^ghi" );  // returns "abcdefghi";

r = "abc^xstring^ghi"; // in-place evaluation

Eval Insert Into( r ); // r now has "abcdefghi";

// with specified delimiter

r = Eval Insert( "abc%xstring%ghi","%" );  // returns "abcdefghi";

// with different start and end delimiters

r = Eval Insert( "abc[xstring]ghi","[","]" );  // returns "abcdefghi";

When a numeric value contains locale-specific formatting, include the <<Use Locale(1) option. The following example substitutes a comma for the decimal point based on the computer’s locale setting.

Eval Insert( "^1.2^", <<Use Locale( 1 ) );

1,2

Evaluate expressions inside lists

Eval List evaluates expressions inside a list and returns a list with the results:

x = { 1 + 2, 3 + 4 };

y = Eval List( x );   // returns y is {3,7}

Eval List is useful for loading the list of user choices returned by Column Dialog or New Window with the Modal argument.

Evaluate expressions inside expressions

Eval Expr() evaluates only the inner expressions and returns an expression that contains the results of the evaluation. By comparison, Eval evaluates the inner expressions, takes the results, and then evaluates it again.

Suppose that a data table contains a column named X3. Here is an example of using Eval Expr() to evaluate the inner expression first:

x = Expr( Distribution( Column( Expr("X"||Char( i ) ) ) ) );

i = 3;

y = Eval Expr( x );   // returns Distribution( Column( "X3" ) )

To evaluate further, you need to either call the result in a subsequent step, or else put Eval() around the Eval Expr(). The following examples create a Distribution report.

// two-step method

x = Expr( Distribution( Column( Expr( "X" || Char( i ) ) ) ) );

i = 3;

y = Eval Expr( x );

y;

// one-step method

x = Expr( Distribution( Column( Expr( "X" || Char( i ) ) ) ) );

i = 3;

Eval( Eval Expr( x ) );

See Table 8.3 to learn what would happen if you tried to use Eval directly on x without first doing Eval Expr.

Parsing Strings into Expressions, and Vice Versa

Parsing is the syntactic scanning of character strings into language expressions. Suppose that you have read in a valid JSL expression into a character string, and now want to evaluate it. The Parse function returns the expression. To evaluate it, use the Eval function.

x = Parse( "a=1" ) ;  // x now has the expression a=1

Eval( Parse( "a=1" ) ); // a now has the value 1

To go in the reverse, use the Char function, which converts an expression into a character string. Usually the argument to a Char function is an Expr function (or a NameExpr of a global variable), since Char evaluates its argument before deparsing it.

y = Char( Expr( a = 1 ) ); // results in y having the character value "a=1"

z = Char( 42 ); // returns "42"

The Char function allows arguments for field width and decimal places if the argument is a number. The default is 18 for width and 99 for decimal (Best format).

Char( 42, 5, 2 ); // returns the character value "42.00"

To preserve locale-specific formatting in the numeric value, include the <<Use Locale(1) option as shown in the following example:

Char( 42, 5, 2, <<Use Locale(1) ); // returns the character value "42,00" in the French locale

The reverse of Char is not quite as simple. To convert a character string into an expression, you use Parse, but to convert a character string into a number value, you use Num.

Parse( y );

Num( z );

Summary

Table 8.3 compares various ways that you can use the evaluation-control functions with x. Assume that a data table contains a column named X3, and x and i have been assigned:

x = Expr( Distribution(Column( Expr("X"||Char( i ) ) ) ) );

i = 3;

Eval(

	EvalExpr(

		Parse(

			Char(

				NameExpr(x)))));