Concepts inHigher-order modules and the phase distinction
Type theory
In mathematics, logic and computer science, type theory is any of several formal systems that can serve as alternatives to naive set theory, or the study of such formalisms in general. In programming language theory, a branch of computer science, type theory can refer to the design, analysis and study of type systems, although some computer scientists limit the term's meaning to the study of abstract formalisms such as typed λ-calculi.
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Standard ML
Standard ML (SML) is a general-purpose, modular, functional programming language with compile-time type checking and type inference. It is popular among compiler writers and programming language researchers, as well as in the development of theorem provers. SML is a modern descendant of the ML programming language used in the Logic for Computable Functions (LCF) theorem-proving project.
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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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Dependent type
In computer science and logic, a dependent type is a type that depends on a value. Dependent types play a central role in intuitionistic type theory and in the design of functional programming languages like ATS, Agda and Epigram. An example is the type of n-tuples of real numbers. This is a dependent type because the type depends on the value n. Deciding equality of dependent types in a program may require computations.
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Universal algebra
Universal algebra (sometimes called general algebra) is the field of mathematics that studies algebraic structures themselves, not examples ("models") of algebraic structures. For instance, rather than take particular groups as the object of study, in universal algebra one takes "the theory of groups" as an object of study.
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Compile time
In computer science, compile time refers to either the operations performed by a compiler (the "compile-time operations"), programming language requirements that must be met by source code for it to be successfully compiled (the "compile-time requirements"), or properties of the program that can be reasoned about at compile time. The operations performed at compile time usually include syntax analysis, various kinds of semantic analysis and code generation.
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Run time (program lifecycle phase)
In computer science, run time, run-time, runtime, or execution time is the time during which a program is running, in contrast to other phases of a program's lifecycle such as compile time, link time, load time, etc. A run-time error is detected after or during the execution of a program, whereas a compile-time error is detected by the compiler before the program is ever executed.
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Calculus
Calculus (Latin, calculus, a small stone used for counting) is a branch of mathematics focused on limits, functions, derivatives, integrals, and infinite series. This subject constitutes a major part of modern mathematics education. It has two major branches, differential calculus and integral calculus, which are related by the fundamental theorem of calculus.
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