Value-level programming refers to one of the two contrasting

programming paradigm A programming paradigm is a relatively high-level way to conceptualize and structure the implementation of a computer program. A programming language can be classified as supporting one or more paradigms. Paradigms are separated along and descri ...

s identified by

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

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 Turin ...

. 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''. Objects can contain data (called fields, attributes or properties) and have actions they can perform (called procedures or methods and impl ...

. 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 statement In computer programming, an assignment statement sets and/or re-sets the value stored in the storage location(s) denoted by a variable name; in other words, it copies a value into the variable. In most imperative programming languages, the ass ...

s 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 collection or grouping of data values, usually specified by a set of possible values, a set of allowed operations on these values, and/or a representation of these ...

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 In mathematical logic, the lambda calculus (also written as ''λ''-calculus) is a formal system for expressing computability, computation based on function Abstraction (computer science), abstraction and function application, application using var ...

-based languages (such as

Lisp Lisp (historically LISP, an abbreviation of "list processing") is a family of programming languages with a long history and a distinctive, fully parenthesized Polish notation#Explanation, prefix notation. Originally specified in the late 1950s, ...

ISWIM ISWIM (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 of the ACM ...

, and Scheme) 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.

References

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

References

See also

External links