Concepts inA note on elimination of simplest recursions
Recursion
Recursion is the process of repeating items in a self-similar way. For instance, when the surfaces of two mirrors are exactly parallel with each other the nested images that occur are a form of infinite recursion. The term has a variety of meanings specific to a variety of disciplines ranging from linguistics to logic.
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Recursive definition
In mathematical logic and computer science, a recursive definition (or inductive definition) is used to define an object in terms of itself . A recursive definition of a function defines values of the functions for some inputs in terms of the values of the same function for other inputs. For example, the factorial function n! is defined by the rules 0! = 1. (n+1)! = (n+1)·n!. This definition is valid because, for all n, the recursion eventually reaches the base case of 0.
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Definition
A definition (¿) is a passage that explains the meaning of a term, or a type of thing. The term to be defined is the definiendum. A term may have many different senses or meanings. For each such specific sense, a definiens is a cluster of words that defines that term. A chief difficulty in managing definition is the need to use other terms that are already understood or whose definitions are easily obtainable. The use of the term in a simple example may suffice.
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Partial function
In mathematics, a partial function from X to Y is a function ¿: X' ¿ Y, where X' is a subset of X. It generalizes the concept of a function by not forcing f to map every element of X to an element of Y (only some subset X' of X). If X' = X, then ¿ is called a total function and is equivalent to a function. Partial functions are often used when the exact domain, X', is not known (e.g. many functions in computability theory).
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Program transformation
A program transformation is any operation that takes a computer program and generates another program. In many cases the transformed program is required to be semantically equivalent to the original, relative to a particular formal semantics and in fewer cases the transformations result in programs that semantically differ from the original in predictable ways.
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Computer program
A computer program (also software, or just a program) is a sequence of instructions written to perform a specified task with a computer. A computer requires programs to function, typically executing the program's instructions in a central processor. The program has an executable form that the computer can use directly to execute the instructions.
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Graph (mathematics)
In mathematics, a graph is an abstract representation of a set of objects where some pairs of the objects are connected by links. The interconnected objects are represented by mathematical abstractions called vertices, and the links that connect some pairs of vertices are called edges. Typically, a graph is depicted in diagrammatic form as a set of dots for the vertices, joined by lines or curves for the edges. Graphs are one of the objects of study in discrete mathematics.
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