# Value-level programming

**Value-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 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: 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 types, 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-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.

## See also

- Function-level programming (contrast)
- Programming paradigms