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Value-level programming
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<h2 id="connection-with-data-types">Connection with Data Types</h2> <p>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 <a href="/facts/Data_type/fcx5hgVL">data types</a>, 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 <i>algebraic study of data types</i>. </p> <h2 id="connection-with-lambda-calculus-languages">Connection with Lambda Calculus languages</h2> <p><a href="/facts/Lambda_calculus/DaD3RuQ4">Lambda calculus</a>-based languages (such as <a href="/facts/Lisp_programming_language/xJHA3CrX">Lisp</a>, <a href="/facts/ISWIM_programming_language/fSMk6YbA">ISWIM</a>, and <a href="/facts/Scheme_(programming_language)/0aGdf3SC">Scheme</a>) are in actual practice value-level languages, although they are not thus restricted by design. </p><p>To see why typical <i>lambda style</i> programs are primarily value-level, consider the usual definition of a value-to-value function, say </p> f = λ<i>x</i>.E <p>here, <i>x</i> 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 <i>both</i> function and value arguments do exist and are used for limited purposes. </p><p>If the term <i>values</i> 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. </p> <h2 id="see-also">See also</h2> <ul><li><a href="/facts/Function-level_programming/0uCybhfG">Function-level programming</a> (contrast)</li> <li><a href="/facts/Programming_paradigm/7LwgRpB3">Programming paradigms</a></li></ul> <h2 id="external-links">External links</h2> <ul><li><a href="https://dl.acm.org/doi/pdf/10.1145/800223.806757">Function Level Programs As Mathematical Objects</a> from John Backus</li></ul>