Control flow functions

(directly go to documentation on : MaxEvalDepth, Hold, Eval, While, Until, If, SystemCall, Function, Macro, Use, For, ForEach, Apply, MapArgs, Subst, WithValue, /:, /::, TraceStack, TraceExp, TraceRule, Time. )

# 23. Control flow functions

MaxEvalDepth | set the maximum evaluation depth
Hold | keep expression unevaluated
Eval | force evaluation of expression
While | loop while a condition is met
Until | loop until a condition is met
If | branch point
SystemCall | pass a command to the shell
Function | declare or define a function
Macro | declare or define a macro
Use | load a file, but not twice
For | C-style `for` loop
ForEach | loop over all entries in list
Apply | apply a function to arguments
MapArgs | apply a function to all top-level arguments
Subst | perform a substitution
WithValue | temporary assignment during an evaluation
/: | local simplification rules
/:: | local simplification rules
TraceStack | show calling stack after an error occurs
TraceExp | evaluate with tracing enabled
TraceRule | turn on tracing for a particular function
Time | measure the time taken by a function

###

MaxEvalDepth -- set the maximum evaluation depth

##### Internal function

##### Calling format:

    MaxEvalDepth(n)

##### Parameters:

`n` -- new maximum evaluation depth

##### Description:

Use this command to set the maximum evaluation depth to the integer "n". The default value is 1000. The function `MaxEvalDepth` returns `True`.

The point of having a maximum evaluation depth is to catch any infinite recursion. For example, after the definition `f(x) := f(x)`, evaluating the expression `f(x)` would call `f(x)`, which would call `f(x)`, etc. The interpreter will halt if the maximum evaluation depth is reached. Also indirect recursion, e.g. the pair of definitions `f(x) := g(x)` and `g(x) := f(x)`, will be caught.

##### Examples:

An example of an infinite recursion, caught because the maximum evaluation depth is reached.

    In> f(x) := f(x)
    Out> True;
    In> f(x)
    Error on line 1 in file [CommandLine]
    Max evaluation stack depth reached.
    Please use MaxEvalDepth to increase the stack
    size as needed.

However, a long calculation may cause the maximum evaluation depth to be reached without the presence of infinite recursion. The function `MaxEvalDepth` is meant for these cases.

    In> 10 # g(0) <-- 1;
    Out> True;
    In> 20 # g(n_IsPositiveInteger) <-- \
      2 * g(n-1);
    Out> True;
    In> g(1001);
    Error on line 1 in file [CommandLine]
    Max evaluation stack depth reached.
    Please use MaxEvalDepth to increase the stack
    size as needed.

    In> MaxEvalDepth(10000);
    Out> True;
    In> g(1001);
    Out> 21430172143725346418968500981200036211228096234
    1106721488750077674070210224987224498639675763139171
    6255189345835106293650374290571384628087196915514939
    7149607869135549648461970842149210124742283755908364
    3060929499671638825347975351183310878921541258291423
    92955373084335320859663305248773674411336138752;

###

Hold -- keep expression unevaluated

##### Internal function

##### Calling format:

    Hold(expr)

##### Parameters:

`expr` -- expression to keep unevaluated

##### Description:

The expression "expr" is returned unevaluated. This is useful to prevent the evaluation of a certain expression in a context in which evaluation normally takes place.

The function `UnList()` also leaves its result unevaluated. Both functions stop the process of evaluation (no more rules will be applied).

##### Examples:

    In> Echo({ Hold(1+1), "=", 1+1 });
     1+1 = 2
    Out> True;

##### See also:

Eval , HoldArg , UnList .

###

Eval -- force evaluation of expression

##### Internal function

##### Calling format:

    Eval(expr)

##### Parameters:

`expr` -- expression to evaluate

##### Description:

This function explicitly requests an evaluation of the expression "expr", and returns the result of this evaluation.

##### Examples:

    In> a := x;
    Out> x;
    In> x := 5;
    Out> 5;
    In> a;
    Out> x;
    In> Eval(a);
    Out> 5;

The variable `a` is bound to `x`, and `x` is bound to 5. Hence evaluating `a` will give `x`. Only when an extra evaluation of `a` is requested, the value 5 is returned.

Note that the behavior would be different if we had exchanged the assignments. If the assignment `a := x` were given while `x` had the value 5, the variable `a` would also get the value 5 because the assignment operator `:=` evaluates the right-hand side.

##### See also:

Hold , HoldArg , := .

###

While -- loop while a condition is met

##### Internal function

##### Calling format:

    While(pred) body

##### Parameters:

`pred` -- predicate deciding whether to keep on looping

`body` -- expression to loop over

##### Description:

Keep on evaluating "body" while "pred" evaluates to `True`. More precisely, `While` evaluates the predicate "pred", which should evaluate to either `True` or `False`. If the result is `True`, the expression "body" is evaluated and then the predicate "pred" is again evaluated. If it is still `True`, the expressions "body" and "pred" are again evaluated and so on until "pred" evaluates to `False`. At that point, the loop terminates and `While` returns `True`.

In particular, if "pred" immediately evaluates to `False`, the body is never executed. `While` is the fundamental looping construct on which all other loop commands are based. It is equivalent to the `while` command in the programming language C.

##### Examples:

    In> x := 0;
    Out> 0;
    In> While (x! < 10^6) \
      [ Echo({x, x!}); x++; ];
     0  1
     1  1
     2  2
     3  6
     4  24
     5  120
     6  720
     7  5040
     8  40320
     9  362880
    Out> True;

##### See also:

Until , For .

###

Until -- loop until a condition is met

##### Standard library

##### Calling format:

    Until(pred) body

##### Parameters:

`pred` -- predicate deciding whether to stop

`body` -- expression to loop over

##### Description:

Keep on evaluating "body" until "pred" becomes `True`. More precisely, `Until` first evaluates the expression "body". Then the predicate "pred" is evaluated, which should yield either `True` or `False`. In the latter case, the expressions "body" and "pred" are again evaluated and this continues as long as "pred" is `False`. As soon as "pred" yields `True`, the loop terminates and `Until` returns `True`.

The main difference with `While` is that `Until` always evaluates the body at least once, but `While` may not evaluate the body at all. Besides, the meaning of the predicate is reversed: `While` stops if "pred" is `False` while `Until` stops if "pred" is `True`. The command `Until(pred) body;` is equivalent to `pred; While(Not pred) body;`. In fact, the implementation of `Until` is based on the internal command `While`. The `Until` command can be compared to the `do ... while` construct in the programming language C.

##### Examples:

    In> x := 0;
    Out> 0;
    In> Until (x! > 10^6) \
      [ Echo({x, x!}); x++; ];
     0  1
     1  1
     2  2
     3  6
     4  24
     5  120
     6  720
     7  5040
     8  40320
     9  362880
    Out> True;

##### See also:

While , For .

###

If -- branch point

##### Internal function

##### Calling format:

    If(pred, then)
    If(pred, then, else)

##### Parameters:

`pred` -- predicate to test

`then` -- expression to evaluate if "pred" is `True`

`else` -- expression to evaluate if "pred" is `False`

##### Description:

This command implements a branch point. The predicate "pred" is evaluated, which should result in either `True` or `False`. In the first case, the expression "then" is evaluated and returned. If the predicate yields `False`, the expression "else" (if present) is evaluated and returned. If there is no "else" branch (i.e. if the first calling sequence is used), the `If` expression returns `False`.

##### Examples:

The sign function is defined to be 1 if its argument is positive and -1 if its argument is negative. A possible implementation is

    In> mysign(x) := If (IsPositiveReal(x), 1, -1);
    Out> True;
    In> mysign(Pi);
    Out> 1;
    In> mysign(-2.5);
    Out> -1;

Note that this will give incorrect results, if "x" cannot be numerically approximated.

    In> mysign(a);
    Out> -1;

Hence a better implementation would be

    In> mysign(_x)_IsNumber(N(x)) <-- If \
      (IsPositiveReal(x), 1, -1);
    Out> True;

###

SystemCall -- pass a command to the shell

##### Internal function

##### Calling format:

    SystemCall(str)

##### Parameters:

`str` -- string containing the command to call

##### Description:

The command contained in the string "str" is executed by the underlying operating system (OS). The return value of `SystemCall` is `True` or `False` according to the exit code of the command.

The `SystemCall` function is not allowed in the body of the `Secure` command and will lead to an error.

##### Examples:

In a UNIX environment, the command `SystemCall("ls")` would print the contents of the current directory.

    In> SystemCall("ls")
    AUTHORS
    COPYING
    ChangeLog

... (truncated to save space)

    Out> True;

The standard UNIX command `test` returns success or failure depending on conditions. For example, the following command will check if a directory exists:

    In> SystemCall("test -d scripts/")
    Out> True;

Check that a file exists:

    In> SystemCall("test -f COPYING")
    Out> True;
    In> SystemCall("test -f nosuchfile.txt")
    Out> False;

##### See also:

Secure .

###

Function -- declare or define a function

##### Standard library

##### Calling format:

    Function() func(arglist)
    Function() func(arglist, ...)
    Function("op", {arglist}) body
    Function("op", {arglist, ...}) body

##### Parameters:

`func(args)` -- function declaration, e.g. `f(x,y)`

`"op"` -- string, name of the function

`{arglist}` -- list of atoms, formal arguments to the function

`...` -- literal ellipsis symbol "`...`" used to denote a variable number of arguments

`body` -- expression comprising the body of the function

##### Description:

This command can be used to define a new function with named arguments.

The number of arguments of the new function and their names are determined by the list `arglist`. If the ellipsis "`...`" follows the last atom in `arglist`, a function with a variable number of arguments is declared (using `RuleBaseListed`). Note that the ellipsis cannot be the only element of `arglist` and must be preceded by an atom.

A function with variable number of arguments can take more arguments than elements in `arglist`; in this case, it obtains its last argument as a list containing all extra arguments.

The short form of the `Function` call merely declares a `RuleBase` for the new function but does not define any function body. This is a convenient shorthand for `RuleBase` and `RuleBaseListed`, when definitions of the function are to be supplied by rules. If the new function has been already declared with the same number of arguments (with or without variable arguments), `Function` returns false and does nothing.

The second, longer form of the `Function` call declares a function and also defines a function body. It is equivalent to a single rule such as `op(_arg1, _arg2) <-- body`. The rule will be declared at precedence 1025. Any previous rules associated with `"op"` (with the same arity) will be discarded. More complicated functions (with more than one body) can be defined by adding more rules.

##### Examples:

This will declare a new function with two or more arguments, but define no rules for it. This is equivalent to `RuleBase ("f1", {x, y, ...})`.

    In> Function() f1(x,y,...);
    Out> True;
    In> Function() f1(x,y);
    Out> False;

This defines a function `FirstOf` which returns the first element of a list. Equivalent definitions would be `FirstOf(_list) <-- list[1]` or `FirstOf(list) := list[1]`.

    In> Function("FirstOf", {list})  list[1];
    Out> True;
    In> FirstOf({a,b,c});
    Out> a;

The following function will print all arguments to a string:

    In> Function("PrintAll",{x, ...}) If(IsList(x),
      PrintList(x), ToString()Write(x));
    Out> True;
    In> PrintAll(1):
    Out> " 1";
    In> PrintAll(1,2,3);
    Out> " 1 2 3";

##### See also:

TemplateFunction , Rule , RuleBase , RuleBaseListed , := , Retract .

###

Macro -- declare or define a macro

##### Standard library

##### Calling format:

    Macro() func(arglist)
    Macro() func(arglist, ...)
    Macro("op", {arglist}) body
    Macro("op", {arglist, ...}) body

##### Parameters:

`func(args)` -- function declaration, e.g. `f(x,y)`

`"op"` -- string, name of the function

`{arglist}` -- list of atoms, formal arguments to the function

`...` -- literal ellipsis symbol "`...`" used to denote a variable number of arguments

`body` -- expression comprising the body of the function

##### Description:

This does the same as `Function`, but for macros. One can define a macro easily with this function, in stead of having to use `DefMacroRuleBase`.

##### Examples:

the following example defines a looping function.

    In> Macro("myfor",{init,pred,inc,body}) [@init;While(@pred)[@body;@inc;];True;];
    Out> True;
    In> a:=10
    Out> 10;

Here this new macro `myfor` is used to loop, using a variable `a` from the calling environment.

    In> myfor(i:=1,i<10,i++,Echo(a*i))
    10
    20
    30
    40
    50
    60
    70
    80
    90
    Out> True;
    In> i
    Out> 10;

##### See also:

Function , DefMacroRuleBase .

###

Use -- load a file, but not twice

##### Internal function

##### Calling format:

    Use(name)

##### Parameters:

`name` -- name of the file to load

##### Description:

If the file "name" has been loaded before, either by an earlier call to `Use` or via the `DefLoad` mechanism, nothing happens. Otherwise all expressions in the file are read and evaluated. `Use` always returns `True`.

The purpose of this function is to make sure that the file will at least have been loaded, but is not loaded twice.

##### See also:

Load , DefLoad , DefaultDirectory .

###

For -- C-style `for` loop

##### Standard library

##### Calling format:

    For(init, pred, incr) body

##### Parameters:

`init` -- expression for performing the initialization

`pred` -- predicate deciding whether to continue the loop

`incr` -- expression to increment the counter

`body` -- expression to loop over

##### Description:

This commands implements a C style `for` loop. First of all, the expression "init" is evaluated. Then the predicate "pred" is evaluated, which should return `True` or `False`. Next the loop is executed as long as the predicate yields `True`. One traversal of the loop consists of the subsequent evaluations of "body", "incr", and "pred". Finally, the value `True` is returned.

This command is most often used in a form such as `For(i=1, i<=10, i++) body`, which evaluates `body` with `i` subsequently set to 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10.

The expression `For(init, pred, incr) body` is equivalent to `init; While(pred) [body; incr;]`.

##### Examples:

    In> For (i:=1, i<=10, i++) Echo({i, i!});
     1  1
     2  2
     3  6
     4  24
     5  120
     6  720
     7  5040
     8  40320
     9  362880
     10  3628800
    Out> True;

##### See also:

While , Until , ForEach .

###

ForEach -- loop over all entries in list

##### Standard library

##### Calling format:

    ForEach(var, list) body

##### Parameters:

`var` -- looping variable

`list` -- list of values to assign to "var"

`body` -- expression to evaluate with different values of "var"

##### Description:

The expression "body" is evaluated multiple times. The first time, "var" has the value of the first element of "list", then it gets the value of the second element and so on. `ForEach` returns `True`.

##### Examples:

     In> ForEach(i,{2,3,5,7,11}) Echo({i, i!});
     2  2
     3  6
     5  120
     7  5040
     11  39916800
    Out> True;

##### See also:

For .

###

Apply -- apply a function to arguments

##### Standard library

##### Calling format:

    Apply(fn, arglist)

##### Parameters:

`fn` -- function to apply

`arglist` -- list of arguments

##### Description:

This function applies the function "fn" to the arguments in "arglist" and returns the result. The first parameter "fn" can either be a string containing the name of a function or a pure function. Pure functions, modeled after lambda-expressions, have the form "`varlist,body`", where "varlist" is the list of formal parameters. Upon application, the formal parameters are assigned the values in "arglist" (the second parameter of `Apply`) and the "body" is evaluated.

Another way to define a pure function is with the Lambda construct. Here, in stead of passing in "`varlist,body`", one can pass in "Lambda(varlist,body)". Lambda has the advantage that its arguments are not evaluated (using lists can have undesirable effects because lists are evaluated). Lambda can be used everywhere a pure function is expected, in principle, because the function Apply is the only function dealing with pure functions. So all places where a pure function can be passed in will also accept Lambda.

An shorthand for `Apply` is provided by the `@` operator.

##### Examples:

    In> Apply("+", {5,9});
    Out> 14;
    In> Apply({{x,y}, x-y^2}, {Cos(a), Sin(a)});
    Out> Cos(a)-Sin(a)^2;
    In>  Apply(Lambda({x,y}, x-y^2), {Cos(a), Sin(a)});
    Out> Cos(a)-Sin(a)^2
    In>  Lambda({x,y}, x-y^2) @ {Cos(a), Sin(a)}
    Out> Cos(a)-Sin(a)^2

##### See also:

Map , MapSingle , @ .

###

MapArgs -- apply a function to all top-level arguments

##### Standard library

##### Calling format:

    MapArgs(expr, fn)

##### Parameters:

`expr` -- an expression to work on

`fn` -- an operation to perform on each argument

##### Description:

Every top-level argument in "expr" is substituted by the result of applying "fn" to this argument. Here "fn" can be either the name of a function or a pure function (see Apply for more information on pure functions).

##### Examples:

    In> MapArgs(f(x,y,z),"Sin");
    Out> f(Sin(x),Sin(y),Sin(z));
    In> MapArgs({3,4,5,6}, {{x},x^2});
    Out> {9,16,25,36};

##### See also:

MapSingle , Map , Apply .

###

Subst -- perform a substitution

##### Standard library

##### Calling format:

    Subst(from, to) expr

##### Parameters:

`from` -- expression to be substituted

`to` -- expression to substitute for "from"

`expr` -- expression in which the substitution takes place

##### Description:

This function substitutes every occurrence of "from" in "expr" by "to". This is a syntactical substitution: only places where "from" occurs as a subexpression are affected.

##### Examples:

    In> Subst(x, Sin(y)) x^2+x+1;
    Out> Sin(y)^2+Sin(y)+1;
    In> Subst(a+b, x) a+b+c;
    Out> x+c;
    In> Subst(b+c, x) a+b+c;
    Out> a+b+c;

The explanation for the last result is that the expression `a+b+c` is internally stored as `(a+b)+c`. Hence `a+b` is a subexpression, but `b+c` is not.

##### See also:

WithValue , /: .

###

WithValue -- temporary assignment during an evaluation

##### Standard library

##### Calling format:

    WithValue(var, val, expr)
    WithValue({var,...}, {val,...}, expr)

##### Parameters:

`var` -- variable to assign to

`val` -- value to be assigned to "var"

`expr` -- expression to evaluate with "var" equal to "val"

##### Description:

First, the expression "val" is assigned to the variable "var". Then, the expression "expr" is evaluated and returned. Finally, the assignment is reversed so that the variable "var" has the same value as it had before `WithValue` was evaluated.

The second calling sequence assigns the first element in the list of values to the first element in the list of variables, the second value to the second variable, etc.

##### Examples:

    In> WithValue(x, 3, x^2+y^2+1);
    Out> y^2+10;
    In> WithValue({x,y}, {3,2}, x^2+y^2+1);
    Out> 14;

##### See also:

Subst , /: .

###

/: -- local simplification rules

###

/:: -- local simplification rules

##### Standard library

##### Calling format:

    expression /: patterns
    expressions /:: patterns

Precedence: 20000

##### Parameters:

`expression` -- an expression

`patterns` -- a list of patterns

##### Description:

Sometimes you have an expression, and you want to use specific simplification rules on it that are not done by default. This can be done with the `/:` and the `/::` operators. Suppose we have the expression containing things such as `Ln(a*b)`, and we want to change these into `Ln(a)+Ln(b)`, the easiest way to do this is using the `/:` operator, as follows:

    In> Sin(x)*Ln(a*b)
    Out> Sin(x)*Ln(a*b);
    In> % /: { Ln(_x*_y) <- Ln(x)+Ln(y) }
    Out> Sin(x)*(Ln(a)+Ln(b));

A whole list of simplification rules can be built up in the list, and they will be applied to the expression on the left hand side of `/:` .

The forms the patterns can have are one of:

    pattern <- replacement
    {pattern,replacement}
    {pattern,postpredicate,replacement}

Note that for these local rules, `<-` should be used instead of `<--` which would be used in a global rule.

The `/:` operator traverses an expression much as `Subst` does, that is, top down, trying to apply the rules from the beginning of the list of rules to the end of the list of rules. If the rules cannot be applied to an expression, it will try subexpressions of that expression and so on.

It might be necessary sometimes to use the `/::` operator, which repeatedly applies the `/:` operator until the result doesn't change any more. Caution is required, since rules can contradict each other, which could result in an infinite loop. To detect this situation, just use /: repeatedly on the expression. The repetitive nature should become apparent.

##### Examples:

    In> Sin(u)*Ln(a*b) /: {Ln(_x*_y) <- Ln(x)+Ln(y)}
    Out> Sin(u)*(Ln(a)+Ln(b));
    In> Sin(u)*Ln(a*b) /:: { a <- 2, b <- 3 }
    Out> Sin(u)*Ln(6);

##### See also:

Subst .

###

TraceStack -- show calling stack after an error occurs

##### Internal function

##### Calling format:

    TraceStack(expression)

##### Parameters:

`expression` -- an expression to evaluate

##### Description:

TraceStack shows the calling stack after an error occurred. It shows the last few items on the stack, not to flood the screen. These are usually the only items of interest on the stack. This is probably by far the most useful debugging function in Yacas. It shows the last few things it did just after an error was generated somewhere.

For each stack frame, it shows if the function evaluated was a built-in function or a user-defined function, and for the user-defined function, the number of the rule it is trying whether it was evaluating the pattern matcher of the rule, or the body code of the rule.

This functionality is not offered by default because it slows down the evaluation code.

##### Examples:

Here is an example of a function calling itself recursively, causing Yacas to flood its stack:

    In> f(x):=f(Sin(x))
    Out> True;
    In> TraceStack(f(2))
    Debug> 982 :  f (Rule # 0 in body)
    Debug> 983 :  f (Rule # 0 in body)
    Debug> 984 :  f (Rule # 0 in body)
    Debug> 985 :  f (Rule # 0 in body)
    Debug> 986 :  f (Rule # 0 in body)
    Debug> 987 :  f (Rule # 0 in body)
    Debug> 988 :  f (Rule # 0 in body)
    Debug> 989 :  f (Rule # 0 in body)
    Debug> 990 :  f (Rule # 0 in body)
    Debug> 991 :  f (Rule # 0 in body)
    Debug> 992 :  f (Rule # 0 in body)
    Debug> 993 :  f (Rule # 0 in body)
    Debug> 994 :  f (Rule # 0 in body)
    Debug> 995 :  f (User function)
    Debug> 996 :  Sin (Rule # 0 in pattern)
    Debug> 997 :  IsList (Internal function)
    Error on line 1 in file [CommandLine]
    Max evaluation stack depth reached.
    Please use MaxEvalDepth to increase the stack
    size as needed.

##### See also:

TraceExp , TraceRule .

###

TraceExp -- evaluate with tracing enabled

##### Internal function

##### Calling format:

    TraceExp(expr)

##### Parameters:

`expr` -- expression to trace

##### Description:

The expression "expr" is evaluated with the tracing facility turned on. This means that every subexpression, which is evaluated, is shown before and after evaluation. Before evaluation, it is shown in the form `TrEnter(x)`, where `x` denotes the subexpression being evaluated. After the evaluation the line `TrLeave(x,y)` is printed, where `y` is the result of the evaluation. The indentation shows the nesting level.

Note that this command usually generates huge amounts of output. A more specific form of tracing (eg. `TraceRule`) is probably more useful for all but very simple expressions.

##### Examples:

    In> TraceExp(2+3);
      TrEnter(2+3);
        TrEnter(2);
        TrLeave(2, 2);
        TrEnter(3);
        TrLeave(3, 3);
        TrEnter(IsNumber(x));
          TrEnter(x);
          TrLeave(x, 2);
        TrLeave(IsNumber(x),True);
        TrEnter(IsNumber(y));
          TrEnter(y);
          TrLeave(y, 3);
        TrLeave(IsNumber(y),True);
        TrEnter(True);
        TrLeave(True, True);
        TrEnter(MathAdd(x,y));
          TrEnter(x);
          TrLeave(x, 2);
          TrEnter(y);
          TrLeave(y, 3);
        TrLeave(MathAdd(x,y),5);
      TrLeave(2+3, 5);
    Out> 5;

##### See also:

TraceStack , TraceRule .

###

TraceRule -- turn on tracing for a particular function

##### Internal function

##### Calling format:

    TraceRule(template) expr

##### Parameters:

`template` -- template showing the operator to trace

`expr` -- expression to evaluate with tracing on

##### Description:

The tracing facility is turned on for subexpressions of the form "template", and the expression "expr" is evaluated. The template "template" is an example of the function to trace on. Specifically, all subexpressions with the same top-level operator and arity as "template" are shown. The subexpressions are displayed before (indicated with `TrEnter`) and after (`TrLeave`) evaluation. In between, the arguments are shown before and after evaluation (`TrArg`). Only functions defined in scripts can be traced.

This is useful for tracing a function that is called from within another function. This way you can see how your function behaves in the environment it is used in.

##### Examples:

    In> TraceRule(x+y) 2+3*5+4;
        TrEnter(2+3*5+4);
          TrEnter(2+3*5);
              TrArg(2, 2);
              TrArg(3*5, 15);
          TrLeave(2+3*5, 17);
            TrArg(2+3*5, 17);
            TrArg(4, 4);
        TrLeave(2+3*5+4, 21);
    Out> 21;

##### See also:

TraceStack , TraceExp .

###

Time -- measure the time taken by a function

##### Standard library

##### Calling format:

    Time(expr)

##### Parameters:

`expr` -- any expression

##### Description:

The function `Time(expr)` evaluates the expression `expr` and prints the time in seconds needed for the evaluation. The time is printed to the current output stream. The built-in function `GetTime` is used for timing.

The result is the "user time" as reported by the OS, not the real ("wall clock") time. Therefore, any CPU-intensive processes running alongside Yacas will not significantly affect the result of `Time`.

##### Example:

    In> Time(N(MathLog(1000),40))
    0.34 seconds taken
    Out> 6.9077552789821370520539743640530926228033;

##### See also:

GetTime .