Concepts inOffline partial evaluation for shift and reset
Continuation-passing style
In functional programming, continuation-passing style (CPS) is a style of programming in which control is passed explicitly in the form of a continuation. Gerald Jay Sussman and Guy L. Steele, Jr. coined the phrase in AI Memo 349 (1975), which sets out the first version of the Scheme programming language. A function written in continuation-passing style takes as an extra argument: an explicit "continuation" i.e. a function of one argument.
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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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Continuation
In computer science and programming, a continuation is an abstract representation of the control state of a computer program. A continuation reifies the program control state, i.e. the continuation is a data structure that represents the computational process at a given point in the process' execution; the created data structure can be accessed by the programming language, instead of being hidden in the runtime environment.
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Type system
A type system associates a type with each computed value. By examining the flow of these values, a type system attempts to ensure or prove that no type errors can occur. The particular type system in question determines exactly what constitutes a type error, but in general the aim is to prevent operations expecting a certain kind of value being used with values for which that operation does not make sense; memory errors will also be prevented.
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Π-calculus
In theoretical computer science, the π-calculus (or pi-calculus) is a process calculus originally developed by Robin Milner, Joachim Parrow and David Walker as a continuation of work on the process calculus CCS. The π-calculus allows channel names to be communicated along the channels themselves, and in this way it is able to describe concurrent computations whose network configuration may change during the computation. The π-calculus is elegantly simple yet very expressive.
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Structural induction
Structural induction is a proof method that is used in mathematical logic (e.g. , in the proof of Łoś' theorem), computer science, graph theory, and some other mathematical fields. It is a generalization of mathematical induction. Structural recursion is a recursion method bearing the same relationship to structural induction as ordinary recursion bears to ordinary mathematical induction.
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Mathematical proof
In mathematics, a proof is a demonstration that if some fundamental statements are assumed to be true, then some mathematical statement is necessarily true. Proofs are obtained from deductive reasoning, rather than from inductive or empirical arguments; a proof must demonstrate that a statement is always true (occasionally by listing all possible cases and showing that it holds in each), rather than enumerate many confirmatory cases.
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