MAXDEPTH

Prevent infinite recursion during procedure calls

Description

The environment variable MAXDEPTH determines the maximal recursion depth of nested procedure calls. When this recursion depth is reached, an error occurs.

Possible values: Positive integer; the maximum value depends on the operating system, see below.

The purpose of MAXDEPTH is to provide a heuristic for recognizing infinite recursion with respect to procedure calls, like in p := x -> p(x): p(0). If, in this example, the recursion depth would not be limited, then the procedure p would call itself recursively infinitely often, and the system would "hang".

If during the evaluation of an object the recursion depth MAXDEPTH is reached, then the computation is aborted with an error.

Similarly, the environment variable MAXLEVEL provides a heuristic for recognizing infinite recursion with respect to the substitution of values for identifiers; see the corresponding help page for details and examples.

The default value of MAXDEPTH is 500; MAXDEPTH has this value after starting or resetting the system via reset. Also the command delete MAXDEPTH restores the default value.

MAXDEPTH is a global variable. Use the statement save MAXDEPTH in a procedure to confine any changes to MAXDEPTH to this procedure.

The maximum value of MAXDEPTH depends on the operating system. Under Windows® it is 211 = 2048. Under UNIX® operating systems the maximum value depends on the maximum size of the C-stack. With a default stack size of 8 MB the value is 2048, too; with a bigger stack size it can be bigger (in a bash the stack size can be set with ulimit -s).

Examples

Example 1

Evaluation of objects defined by an infinite recursion produces an error:

p := proc() begin p() end_proc: p()
Error: Recursive definition: the maximal depth for nested procedure calls is reached.
  Evaluating: p

This also works for mutually recursive definitions:

p := proc(x) begin q(x + 1)^2 end_proc:
q := proc(y) begin p(x) + 2 end_proc:
p(0)
Error: Recursive definition: the maximal depth for nested procedure calls is reached.
  Evaluating: p

Example 2

If the maximal recursion depth is reached, then this does not necessarily mean that infinite recursion is involved. The following recursive procedure computes the factorial of a nonnegative integer. If we set the maximal recursion depth to a smaller value than necessary to compute , then an error occurs:

factorial := proc(n) begin
  if n = 0 then 1
  else n*factorial(n - 1)
  end_if
end_proc:
MAXDEPTH := 4: factorial(5)
Error: Recursive definition: the maximal depth for nested procedure calls is reached.
  Evaluating: factorial

If we set MAXDEPTH to 5, then the recursion depth is big enough for computing . The command delete MAXDEPTH resets MAXDEPTH to its default value 500:

MAXDEPTH := 5: factorial(5); delete MAXDEPTH:

See Also

MuPAD Functions

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