Value-level programming
Encyclopedia
Value-level programming refers to one of the two contrasting programming paradigm
s identified by John Backus
in his work on Programs as mathematical objects, the other being function-level programming
. Backus originally used the term object-level programming but that term is now prone to confusion with object-oriented programming
.
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: expression
s on the right side of assignment statements are exclusively concerned with building a value that is then to be stored.
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.
-based languages (such as Lisp
, ISWIM, 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 = λx.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.
Programming paradigm
A programming paradigm is a fundamental style of computer programming. Paradigms differ in the concepts and abstractions used to represent the elements of a program and the steps that compose a computation A programming paradigm is a fundamental style of computer programming. (Compare with a...
s identified by John Backus
John Backus
John Warner Backus was an American computer scientist. He directed the team that invented the first widely used high-level programming language and was the inventor of the Backus-Naur form , the almost universally used notation to define formal language syntax.He also did research in...
in his work on Programs as mathematical objects, the other being function-level programming
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....
. Backus originally used the term object-level programming but that term is now prone to confusion with object-oriented programming
Object-oriented programming
Object-oriented programming is a programming paradigm using "objects" – data structures consisting of data fields and methods together with their interactions – to design applications and computer programs. Programming techniques may include features such as data abstraction,...
.
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
Von Neumann programming languages
A von Neumann language is any of those programming languages that are high-level abstract isomorphic copies of von Neumann architectures . As of 2009, most current programming languages fit into this description, likely as a consequence of the extensive domination of the von Neumann computer...
are value-level: expression
Expression (programming)
An expression in a programming language is a combination of explicit values, constants, variables, operators, and functions that are interpreted according to the particular rules of precedence and of association for a particular programming language, which computes and then produces another value...
s 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 typeData type
In computer programming, a data type is a classification identifying one of various types of data, such as floating-point, integer, or Boolean, that determines the possible values for that type; the operations that can be done on values of that type; the meaning of the data; and the way values of...
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 calculusLambda calculus
In mathematical logic and computer science, lambda calculus, also written as λ-calculus, is a formal system for function definition, function application and recursion. The portion of lambda calculus relevant to computation is now called the untyped lambda calculus...
-based languages (such as Lisp
Lisp programming language
Lisp is a family of computer programming languages with a long history and a distinctive, fully parenthesized syntax. Originally specified in 1958, Lisp is the second-oldest high-level programming language in widespread use today; only Fortran is older...
, ISWIM, 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 = λx.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.
See also
- Function-level programmingFunction-level programmingIn 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....
(contrast) - Programming paradigmProgramming paradigmA programming paradigm is a fundamental style of computer programming. Paradigms differ in the concepts and abstractions used to represent the elements of a program and the steps that compose a computation A programming paradigm is a fundamental style of computer programming. (Compare with a...
s