An expression is any combination of variables, constants, and functions linked by operators that can be evaluated. The section Rules for Name Resolution in JSL Building Blocks 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.
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.
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;
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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
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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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.
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.
";
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 ) ) );
dist;
For( i = 0, i < 3, i = i + 1, dist );
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 ) ) ) );
Formula( Eval( Substitute( Expr( Log( xxx ) ), Expr( xxx ), Column Name( i ) ) ) );
Formula( Eval( Column Name( i ) ) + 10 );
Formula(Eval(Substitute(Expr(xxx+10), Expr(xxx), column name(i))))
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.
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) )
a = 1; b = 2; c = 3;
x = Expr( a + b + c );
x; 6 |
Evaluates x to the expression a+b+c, and then evaluates the expression, returning the result, 6 (unpacks all layers).
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Eval( x );
6 |
Evaluates x to the expression a+b+c, and then evaluates the expression, returning the result, 6 (unpacks all layers).
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NameExpr( x );
a+b+c |
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Expr( x );
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.
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 (Expr(expression)) returns the number of arguments to literal expression.
For example, if aExpr = {a+b,c,d,e+f+g};
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NArg(aExpr) results in 4.
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NArg(Arg(aExpr,4)) results in 3.
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NArg(Expr({1,2,3,4})) results in 4.
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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);
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r = Head(aExpr) results in Add().
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r = Head (Expr(sqrt(r))) results in Sqrt().
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r = Head({1,2,3}) results in {} .
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Arg(expressionArg,indexArg) extracts the specified argument of the symbolic expression, resulting in an expression.
The expressionArg can be a name holding an expression, an expression evaluated to an expression, or a literal expression quoted by Expr().
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As another example, if aExpr = Expr(12+13*sqrt(14-15));
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Arg(aExpr,1) yields 12
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Arg(aExpr,2) yields 13*sqrt(14-15)
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Arg(Expr(12+13*sqrt(14-15)),2) yields 13*sqrt(14-15)
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Arg(Arg(aExpr,2),1) yields the first argument within the second argument of aExpr, or 13.
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Arg(Arg(aExpr,2),2) yields Sqrt( 14 - 15 )
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Arg(Arg(Arg(aExpr,2),2),1) yields 14 - 15
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Arg(Arg(Arg(aExpr,2),2),3) yields Empty()
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1.
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The inner Arg statement is evaluated.
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Arg(aExpr,2)
13 * Sqrt( 14 - 15 )
Arg(Arg(aExpr,2),2)
// this is equivalent to Arg(Expr (13 * Sqrt( 14 - 15 ) ), 2)
Sqrt( 14 - 15 )
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);
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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);
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r = HeadName (aExpr) results in "Add".
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r = HeadName (Expr(sqrt(r))) results in "Sqrt".
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r = HeadName ({1,2,3}) results in "List".
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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.
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.
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" ); // results in "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","%" ); // result is "abcdefghi";
// with different start and end delimiters
r = Eval Insert( "abc[xstring]ghi","[","]" ); // result is "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
Eval List evaluates expressions inside a list and returns a list with the results:
x = { 1 + 2, 3 + 4 };
y = Eval List( x ); // result in 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.
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 7.3 to learn what would happen if you tried to use Eval directly on x without first doing Eval Expr.
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 ); // results in "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 ); // results in 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) ); // results in 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 );
Char |
Char(Expr(expression)) Char(name) |
Converts an expression into a character string. The expression must be quoted with Expr; otherwise its evaluation is converted to a string.
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string = char(number, width, decimal) |
Converts a number into its character representation. Width and decimal are optional arguments to specify formatting; the default is 18 for width and 99 for decimal.
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Eval |
Eval(x) |
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Eval Expr |
Eval Expr(x) |
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Eval List |
Eval List(list) |
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Expr |
Expr(x) |
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NameExpr |
NameExpr(x) |
Returns the unevaluated expression of x rather than the evaluation of x. NameExpr is like Expr except that if x is a name, NameExpr returns the unevaluated expression stored in the name rather than the unevaluated name x.
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Num |
Num("string") |
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Parse |
Parse("string") |
Table 7.3 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;