Recursion (computer science) in the context of Nesting (computing)

Lisp (historically LISP, an abbreviation of "list processing") is a family of programming languages with a long history and a distinctive, fully parenthesized prefix notation.Originally specified in the late 1950s, it is the second-oldest high-level programming language still in common use, after Fortran. Lisp has changed since its early days, and many dialects have existed over its history. Today, the best-known general-purpose Lisp dialects are Common Lisp, Scheme, Racket, and Clojure.

Lisp was originally created as a practical mathematical notation for computer programs, influenced by (though not originally derived from) the notation of Alonzo Church's lambda calculus. It quickly became a favored programming language for artificial intelligence (AI) research. As one of the earliest programming languages, Lisp pioneered many ideas in computer science, including tree data structures, automatic storage management, dynamic typing, conditionals, higher-order functions, recursion, the self-hosting compiler, and the read–eval–print loop.

A computer worm is a standalone malware computer program that replicates itself in order to spread to other computers. It often uses a computer network to spread itself, relying on security failures on the target computer to access it. It will use this machine as a host to scan and infect other computers. When these new worm-invaded computers are controlled, the worm will continue to scan and infect other computers using these computers as hosts, and this behavior will continue. Computer worms use recursive methods to copy themselves without host programs and distribute themselves based on exploiting the advantages of exponential growth, thus controlling and infecting more and more computers in a short time. Worms almost always cause at least some harm to the network, even if only by consuming bandwidth, whereas viruses almost always corrupt or modify files on a targeted computer.

Many worms are designed only to spread, and do not attempt to change the systems they pass through. However, as the Morris worm and Mydoom showed, even these "payload-free" worms can cause major disruption by increasing network traffic and other unintended effects.

In computer programming, an automatic variable is a local variable which is allocated and deallocated automatically when program flow enters and leaves the variable's scope. The scope is the lexical context, particularly the function or block in which a variable is defined. Local data is typically (in most languages) invisible outside the function or lexical context where it is defined. Local data is also invisible and inaccessible to a called function, but is not deallocated, coming back in scope as the execution thread returns to the caller.

Automatic local variables primarily applies to recursive lexically scoped languages. Automatic local variables are normally allocated in the stack frame of the procedure in which they are declared. This was originally done to achieve re-entrancy and allowing recursion, a consideration that still applies today. The concept of automatic variables in recursive (and nested) functions in a lexically scoped language was introduced to the wider audience with ALGOL in the late 1950s, and further popularized by its many descendants.

In computer science, a tail call is a subroutine call performed as the final action of a procedure.If the target of a tail is the same subroutine, the subroutine is said to be tail recursive, which is a special case of direct recursion. Tail recursion (or tail-end recursion) is particularly useful, and is often easy to optimize in implementations.

Tail calls can be implemented without adding a new stack frame to the call stack. Most of the frame of the current procedure is no longer needed, and can be replaced by the frame of the tail call, modified as appropriate (similar to overlay for processes, but for function calls). The program can then jump to the called subroutine. Producing such code instead of a standard call sequence is called tail-call elimination or tail-call optimization. Tail-call elimination allows procedure calls in tail position to be implemented as efficiently as goto statements, thus allowing efficient structured programming. In the words of Guy L. Steele, "in general, procedure calls may be usefully thought of as GOTO statements which also pass parameters, and can be uniformly coded as [machine code] JUMP instructions."

In mathematics, the hyperoperation sequence is an infinite sequence of arithmetic operations (called hyperoperations in this context) that starts with a unary operation (the successor function with n = 0). The sequence continues with the binary operations of addition (n = 1), multiplication (n = 2), and exponentiation (n = 3).

After that, the sequence proceeds with further binary operations extending beyond exponentiation, using right-associativity. For the operations beyond exponentiation, the nth member of this sequence is named by Reuben Goodstein after the Greek prefix of n suffixed with -ation (such as tetration (n = 4), pentation (n = 5), hexation (n = 6), etc.) and can be written using n − 2 arrows in Knuth's up-arrow notation.Each hyperoperation may be understood recursively in terms of the previous one by:

A stack register is a computer central processor register whose purpose is to keep track of a call stack. On an accumulator-based architecture machine, this may be a dedicated register. On a machine with multiple general-purpose registers, it may be a register that is reserved by convention, such as on the IBM System/360 through z/Architecture architecture and RISC architectures, or it may be a register that procedure call and return instructions are hardwired to use, such as on the PDP-11, VAX, and Intel x86 architectures. Some designs such as the Data General Eclipse had no dedicated register, but used a reserved hardware memory address for this function.

Machines before the late 1960s—such as the PDP-8 and HP 2100—did not have compilers which supported recursion. Their subroutine instructions typically would save the current location in the jump address, and then set the program counter to the next address. While this is simpler than maintaining a stack, since there is only one return location per subroutine code section, there cannot be recursion without considerable effort on the part of the programmer.