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'''Value-level programming''' refers to one of the two contrasting [[programming paradigm]]s identified by [[John Backus]] in his work on [[Program (mathematical object)|programs as mathematical objects]], the other being [[function-level programming]].<ref name="s286">{{cite web | title=Concatenative Programming | url=https://web.stanford.edu/class/ee380/Abstracts/171115-slides.pdf |publisher=Stanford University |page=16 | access-date=2025-06-01}}</ref> Backus originally used the term '''object-level programming''' but that term is now prone to confusion with [[object-oriented programming]].<br />
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Value-level programs are those that describe how to combine various ''values'' (i.e., numbers, symbols, strings, etc.) to form other values until the final ''result values'' are obtained. New values are constructed from existing ones by the application of various value-to-value functions, such as addition, concatenation, matrix inversion, and so on.<br />
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Conventional, [[von Neumann programming languages|von Neumann programs]] are value-level: [[expression (programming)|expression]]s on the right side of [[assignment statement]]s are exclusively concerned with building a value that is then to be stored.<br />
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==Connection with Data Types==<br />
The value-level approach to programming invites the study of the space of values under the value-forming operations, and of the algebraic properties of those operations. This is what is called the study of [[data type]]s, and it has advanced from focusing on the '''values''' themselves and their structure, to a primary concern with the value-forming '''operations''' and their structure, as given by certain axioms and algebraic laws, that is, to the ''algebraic study of data types''.<br />
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==Connection with Lambda Calculus languages==<br />
[[Lambda calculus]]-based languages (such as [[Lisp programming language|Lisp]], [[ISWIM programming language|ISWIM]], and [[Scheme (programming language)|Scheme]]) are '''in actual practice''' value-level languages, although they are not thus restricted by design.<br />
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To see why typical ''lambda style'' programs are primarily value-level, consider the usual definition of a value-to-value function, say <br />
'''f''' = λ''x''.'''E'''<br />
here, ''x'' must be a value variable (since the argument of '''f''' is a value by definition) and '''E''' must denote a value too (since '''f''''s result is a value by definition). Typically, '''E''' is an expression involving the application of value-forming functions to value variables and constants; nevertheless, a few value-forming functions having ''both'' function and value arguments do exist and are used for limited purposes{{cn|date=February 2020}}.<br />
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If the term ''values'' is defined to include the value variables themselves, then the value-level view of programming is one of building values by the application of existing programs (value-forming operations/functions) to other values. Lambda-style programming builds a new program from the result-value by lambda-abstracting the value variables.<br />
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==References==<br />
{{Reflist}}<br />
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==See also==<br />
* [[Function-level programming]] (contrast)<br />
* [[Programming paradigm]]s<br />
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==External links==<br />
* [https://dl.acm.org/doi/pdf/10.1145/800223.806757 Function Level Programs As Mathematical Objects] from John Backus<br />
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