Value-level programming refers to one of the two contrasting

programming paradigm Programming paradigms are a way to classify programming languages based on their features. Languages can be classified into multiple paradigms. Some paradigms are concerned mainly with implications for the execution model of the language, suc ...

s identified by

John Backus John Warner Backus (December 3, 1924 – March 17, 2007) was an American computer scientist. He directed the team that invented and implemented FORTRAN, the first widely used high-level programming language, and was the inventor of the Backu ...

in his work on programs as mathematical objects, the other being

function-level programming In computer science, function-level programming refers to one of the two contrasting programming paradigms identified by John Backus in his work on programs as mathematical objects, the other being value-level programming. In his 1977 Turing ...

. Backus originally used the term object-level programming but that term is now prone to confusion with

object-oriented programming Object-oriented programming (OOP) is a programming paradigm based on the concept of "objects", which can contain data and code. The data is in the form of fields (often known as attributes or ''properties''), and the code is in the form of ...

. 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. Conventional, von Neumann programs are value-level: expressions on the right side of assignment statements are exclusively concerned with building a value that is then to be stored.

Connection with Data Types

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 In computer science and computer programming, a data type (or simply type) is a set of possible values and a set of allowed operations on it. A data type tells the compiler or interpreter how the programmer intends to use the data. Most progra ...

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''.

Connection with Lambda Calculus languages

Lambda calculus Lambda calculus (also written as ''λ''-calculus) is a formal system in mathematical logic for expressing computation based on function abstraction and application using variable binding and substitution. It is a universal model of computation th ...

-based languages (such as

Lisp A lisp is a speech impairment in which a person misarticulates sibilants (, , , , , , , ). These misarticulations often result in unclear speech. Types * A frontal lisp occurs when the tongue is placed anterior to the target. Interdental lispin ...

ISWIM ISWIM (acronym for If you See What I Mean) is an abstract computer programming language (or a family of languages) devised by Peter Landin and first described in his article "The Next 700 Programming Languages", published in the Communications ...

, and

Scheme A scheme is a systematic plan for the implementation of a certain idea. Scheme or schemer may refer to: Arts and entertainment * ''The Scheme'' (TV series), a BBC Scotland documentary series * The Scheme (band), an English pop band * ''The Schem ...

) are in actual practice value-level languages, although they are not thus restricted by design. To see why typical ''lambda style'' programs are primarily value-level, consider the usual definition of a value-to-value function, say f = λ''x''.E 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. 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.

External links

Function Level Programs As Mathematical Objects
from John Backus {{DEFAULTSORT:Value-Level Programming Programming paradigms

Connection with Data Types

Connection with Lambda Calculus languages

See also

External links