APL's proposed and implemented ideas and tools can be found in many programming-related fields, such as abstract data types, object-oriented programming, functional programming, database and artificial intelligence.
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Key contributions include abstract data types, call-by-sharing, iterators, multiple return values ( a form of parallel assignment ), type-safe parameterized types, and type-safe variant types.
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Thus, in practice a topology on a set is treated like an abstract data type that provides all needed notions ( and constructors ) but hides the distinction between " primary " and " secondary " notions.
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His experiences with object technology through the Simula language, as well as early work on abstract data types and formal specification ( including the Z notation ), provided some of the background for the development of Eiffel.
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Over these two, respectively, collections of " mathematical classes " and of " abstract classes " have been built, the latter encompassing the most commonly used abstract data types in computer science:
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A collection is a concept applicable to abstract data types, and does not prescribe a specific implementation as a concrete data structure, though often there is a conventional choice ( see Container for type theory discussion ).
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The Standard Template Library ( STL ), and the C + + 1998 standard, specifies priority _ queue as one of the STL iteration of its elements ( it strictly adheres to its abstract data type definition ).
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Data reification develops the abstract data types into more concrete data structures, while operation decomposition develops the ( abstract ) implicit specifications of operations and functions into algorithms that can be directly implemented in a computer language of choice.
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LOTOS is an algebraic language that consists of two parts : a part for the description of data and operations, based on abstract data types, and a part for the description of concurrent processes, based on process calculus.
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Term algebras also play a role in the semantics of abstract data types, where an abstract data type declaration provides the signature of a multi-sorted algebraic structure and the term algebra is a concrete model of the abstract declaration.
