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To elaborate further on GrandFather's point that perl uses a reference-counted garbage collector, note that with Perl you get "deterministic destructors" for free; that is, in perl, you are guaranteed that an object is destroyed (and destructor called) immediately its reference count goes to zero. BTW, deterministic destructors are a feature of the C++ RAII idiom yet are problematic when using a tracing garbage collector, such as that used by Java ... which is why Java has a "finally" clause (see also Dispose pattern). See also Finalizer (wikipedia).
You can use deterministic destructors to good effect in Perl with lexical file handles, which are automatically closed when the file handle goes out of scope; for example in:
note that $fh is automatically closed immediately the function exits because the $fh variable goes out of scope at end of function ... and when $fh goes out of scope, its reference count goes to zero and its destructor is automatically and immediately called to close the file handle. No need for an explicit close. (Update: this automatic close at end of scope does not check for errors though, so an explicit close with error checking is advisable for file handles used for writing; see also autodie).
A drawback to reference counting, that tracing GCs solve, is the dreaded circular reference problem. For an example of how to deal with circular references in Perl, see Eliminate circular reference memory leak using weaken (perlmaven). See also Automatic Reference Counting and Weak reference and Circular reference (wikipedia).
As to when malloc'ed memory is actually released back to the OS, see the answers to this question.
What I dislike more than both reference-counting and tracing garbage collectors is Manual memory management, typical in C programs ... which forces you to rely on static and dynamic code analysis tools, such as Coverity, Valgrind, AddressSanitizer and many more, to keep the code clean. See also EXTERNAL TOOLS FOR DEBUGGING PERL section at perlhack.
References Added Later
Updated 2022: Added paragraph about manual memory management.
In reply to Re^2: Do subroutine variables get destroyed? (Deterministic Destructor References)