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<title>Function-level programming</title>

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<span id="openzim-page-title" class="mw-page-title-main"><span class="mw-page-title-main">Function-level programming</span></span>

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</style><div role="note" class="hatnote navigation-not-searchable">"function-level" redirects here. For the term in mental health assessments, see <a href="Global_Assessment_of_Functioning" title="Global Assessment of Functioning">Global Assessment of Functioning</a>.</div>

<div role="note" class="hatnote navigation-not-searchable">Not to be confused with <a href="Functional_programming" title="Functional programming">functional programming</a>.</div>

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<p>In computer science, <b>function-level</b> programming refers to one of the two contrasting <a href="Programming_paradigm" title="Programming paradigm">programming paradigms</a> identified by <a href="John_Backus" title="John Backus">John Backus</a> in his work on programs as mathematical objects, the other being <a href="Value-level_programming" title="Value-level programming">value-level programming</a>.

</p><p>In his 1977 <a href="Turing_Award" title="Turing Award">Turing Award</a> lecture, Backus set forth what he considered to be the need to switch to a different philosophy in programming language design:<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup>

</p>

<blockquote><p>Programming languages appear to be in trouble. Each successive language incorporates, with a little cleaning up, all the features of its predecessors plus a few more. [...] Each new language claims new and fashionable features... but the plain fact is that few languages make programming sufficiently cheaper or more reliable to justify the cost of producing and learning to use them.</p></blockquote>

<p>He designed <a href="FP_(programming_language)" title="FP (programming language)">FP</a> to be the first <a href="Programming_language" title="Programming language">programming language</a> to specifically support the function-level programming style.

</p><p>A <i>function-level</i> program is <b>variable-free</b> (cf. <a href="Point-free_programming" class="mw-redirect" title="Point-free programming"><i>point-free</i> programming</a>), since <a href="Variable_(programming)" class="mw-redirect" title="Variable (programming)">program variables</a>, which are essential in value-level definitions, are not needed in function-level programs.

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<div class="mw-heading mw-heading2"><h2 id="Introduction">Introduction</h2></div>

<p>In the function-level style of programming, a program is built directly from programs that are given at the outset, by combining them with <b>program-forming operations</b> or <b>functionals</b>. Thus, in contrast with the value-level approach that applies the given programs to values to form a <i>succession of values</i> culminating in the desired result value, the function-level approach applies program-forming operations to the given programs to form a <i>succession of programs</i> culminating in the desired result program.

</p><p>As a result, the function-level approach to programming invites study of the <i>space of programs under program-forming operations</i>, looking to derive useful algebraic properties of these program-forming operations. The function-level approach offers the possibility of making the set of programs a mathematical space by emphasizing the algebraic properties of the program-forming operations over the <i>space of programs</i>.

</p><p>Another potential advantage of the function-level view is the ability to use only <a href="Strict_function" title="Strict function">strict functions</a> and thereby have bottom-up semantics, which are the simplest kind of all. Yet another is the existence of function-level definitions that are not the <i>lifted</i> (that is, <i>lifted</i> from a lower value-level to a higher function-level) image of any existing value-level one: these (often terse) function-level definitions represent a more powerful style of programming not available at the value-level.

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<div class="mw-heading mw-heading2"><h2 id="Contrast_to_functional_programming">Contrast to functional programming</h2></div>

<p>When Backus studied and publicized his function-level style of programming, his message was mostly misunderstood<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> as supporting the traditional <a href="Functional_programming" title="Functional programming">functional programming</a> style languages instead of his own <a href="FP_(programming_language)" title="FP (programming language)">FP</a> and its successor <a href="FL_programming_language" class="mw-redirect" title="FL programming language">FL</a>.

</p><p>Backus calls functional programming <a href="Applicative_programming" class="mw-redirect" title="Applicative programming">applicative programming</a>; his function-level programming is a particular, constrained type.

</p><p>A key distinction from functional languages is that Backus' language has the following hierarchy of types:

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<ul><li>atoms</li>

<li>functions, which take atoms to atoms</li>

<li><a href="Higher-order_function" title="Higher-order function">Higher-order functions</a> (which he calls "functional forms"), which take one or two functions to functions</li></ul>

<p>...and the only way to generate new functions is to use one of the functional forms, which are fixed: you cannot build your own functional form (at least not within FP; you can within FFP (<a href="Formal_FP" class="mw-redirect" title="Formal FP">Formal FP</a>)).

</p><p>This restriction means that functions in FP are a <a href="Module_(mathematics)" title="Module (mathematics)">module</a> (generated by the built-in functions) over the algebra of functional forms, and are thus algebraically tractable. For instance, the general question of equality of two functions is equivalent to the <a href="Halting_problem" title="Halting problem">halting problem</a>, and is undecidable, but equality of two functions in FP is just equality in the algebra, and thus (Backus imagines) easier.

</p><p>Even today, many users of <a href="Lambda_calculus" title="Lambda calculus">lambda style</a> languages often misinterpret Backus' function-level approach as a restrictive variant of the lambda style, which is a <i>de facto</i> value-level style. In fact, Backus would not have disagreed with the 'restrictive' accusation: he argued that it was <i>precisely</i> due to such restrictions that a well-formed mathematical space could arise, in a manner analogous to the way <a href="Structured_programming" title="Structured programming">structured programming</a> limits programming to a <i>restricted</i> version of all the control-flow possibilities available in plain, unrestricted <a href="Unstructured_programming" class="mw-redirect" title="Unstructured programming">unstructured programs</a>.

</p><p>The value-free style of FP is closely related to the equational logic of a <a href="Cartesian-closed_category" class="mw-redirect" title="Cartesian-closed category">cartesian-closed category</a>.

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<div class="mw-heading mw-heading2"><h2 id="Example_languages">Example languages</h2></div>

<p>The canonical function-level programming language is <a href="FP_(programming_language)" title="FP (programming language)">FP</a>. Others include <a href="FL_(programming_language)" title="FL (programming language)">FL</a>, and <a href="J_(programming_language)" title="J (programming language)">J</a>.

</p>

<ul><li><a href="Concatenative_programming_language" title="Concatenative programming language">Concatenative programming language</a></li>

<li><a href="Functional_programming" title="Functional programming">Functional programming</a>, <a href="Declarative_programming" title="Declarative programming">declarative programming</a> (compare)</li>

<li><a href="Tacit_programming" title="Tacit programming">Tacit programming</a></li>

<li><a href="Value-level_programming" title="Value-level programming">Value-level programming</a>, <a href="Imperative_programming" title="Imperative programming">imperative programming</a> (contrast)</li></ul>

<div class="mw-heading mw-heading2"><h2 id="References">References</h2></div>

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</style><cite id="CITEREFBackus1978" class="citation journal cs1">Backus, John (1978). <a rel="nofollow" class="external text" href="https://www.cs.ucf.edu/~dcm/Teaching/COT4810-Fall%202012/Literature/Backus.pdf">"Can programming be liberated from the von Neumann style?: A functional style and its algebra of programs"</a> <span class="cs1-format">(PDF)</span>. <i>Communications of the ACM</i>. <b>21</b> (8): <span class="nowrap">613–</span>641. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1145%2F359576.359579">10.1145/359576.359579</a></span>.</cite></span>

</li>

<li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text"><cite id="CITEREFHudak1989" class="citation journal cs1">Hudak, Paul (1989). "Conception, evolution, and application of functional programming languages". <i>ACM Computing Surveys</i>. <b>21</b> (3): <span class="nowrap">359–</span>411. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1145%2F72551.72554">10.1145/72551.72554</a>. <a href="S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:207637854">207637854</a>.</cite></span>

</li>

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<div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2></div>

<ul><li><a rel="nofollow" class="external text" href="https://dl.acm.org/doi/pdf/10.1145/800223.806757">Function Level Programs As Mathematical Objects</a> from John Backus</li>

<li>From Function Level Semantics to Program Transformation and Optimization <a rel="nofollow" class="external text" href="https://link.springer.com/content/pdf/10.1007/3-540-15198-2_5.pdf?pdf=inline%20link">SpringerLink</a> see point 1.2 and 1.3</li>

<li><a rel="nofollow" class="external text" href="http://dirkgerrits.com/publications/john-backus.pdf#section.8">Closed applicative languages, FP and FL</a>, in John W. Backus (Publications) or the original <a rel="nofollow" class="external text" href="https://dl.acm.org/doi/pdf/10.1145/512927.512934">Programming Language Semantics and Closed Applicative Languages</a></li>

<li>Instance variables, a <a rel="nofollow" class="external text" href="https://esolangs.org/wiki/FP_trivia">way out</a> of the variable abstinence</li></ul>

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</style><div id="Programming_paradigms_(Comparison_by_language)368" style="font-size:114%;margin:0 4em"><a href="Programming_paradigm" title="Programming paradigm">Programming paradigms</a> (<a href="Comparison_of_multi-paradigm_programming_languages" title="Comparison of multi-paradigm programming languages">Comparison by language</a>)</div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Imperative_programming" title="Imperative programming">Imperative</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Structured_programming" title="Structured programming">Structured</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Jackson_structured_programming" title="Jackson structured programming">Jackson structures</a></li>

<li><a href="Block_(programming)" title="Block (programming)">Block-structured</a></li>

<li><a href="Modular_programming" title="Modular programming">Modular</a></li>

<li><a href="Non-structured_programming" title="Non-structured programming">Non-structured</a></li>

<li><a href="Procedural_programming" title="Procedural programming">Procedural</a></li>

<li><a href="Programming_in_the_large_and_programming_in_the_small" title="Programming in the large and programming in the small">Programming in the large and in the small</a></li>

<li><a href="Design_by_contract" title="Design by contract">Design by contract</a></li>

<li><a href="Invariant-based_programming" title="Invariant-based programming">Invariant-based</a></li>

<li><a href="Nested_function" title="Nested function">Nested function</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Object-oriented_programming" title="Object-oriented programming">Object-oriented</a><br>(<a href="Comparison_of_programming_languages_(object-oriented_programming)" title="Comparison of programming languages (object-oriented programming)">comparison</a>, <a href="List_of_object-oriented_programming_languages" title="List of object-oriented programming languages">list</a>)</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Class-based_programming" title="Class-based programming">Class-based</a>, <a href="Prototype-based_programming" title="Prototype-based programming">Prototype-based</a>, <a href="Object-based_language" title="Object-based language">Object-based</a></li>

<li><a href="Agent-oriented_programming" title="Agent-oriented programming">Agent</a></li>

<li><a href="Immutable_object" title="Immutable object">Immutable object</a></li>

<li><a href="Persistent_programming_language" title="Persistent programming language">Persistent</a></li>

<li><a href="Uniform_function_call_syntax" title="Uniform function call syntax">Uniform function call syntax</a></li></ul>

</div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Declarative_programming" title="Declarative programming">Declarative</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Functional_programming" title="Functional programming">Functional</a><br>(<a href="Comparison_of_functional_programming_languages" title="Comparison of functional programming languages">comparison</a>)</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Recursion_(computer_science)" title="Recursion (computer science)">Recursive</a></li>

<li><a href="Anonymous_function" title="Anonymous function">Anonymous function</a> (<a href="Partial_application" title="Partial application">Partial application</a>)</li>

<li><a href="Higher-order_programming" title="Higher-order programming">Higher-order</a></li>

<li><a href="Purely_functional_programming" title="Purely functional programming">Purely functional</a></li>

<li><a href="Total_functional_programming" title="Total functional programming">Total</a></li>

<li><a href="Strict_programming_language" title="Strict programming language">Strict</a></li>

<li><a href="Generalized_algebraic_data_type" title="Generalized algebraic data type">GADTs</a></li>

<li><a href="Dependent_type" title="Dependent type">Dependent types</a></li>

<li><a href="Functional_logic_programming" title="Functional logic programming">Functional logic</a></li>

<li><a href="Tacit_programming" title="Tacit programming">Point-free style</a></li>

<li><a href="Expression-oriented_programming_language" title="Expression-oriented programming language">Expression-oriented</a></li>

<li><a href="Applicative_programming_language" title="Applicative programming language">Applicative</a>, <a href="Concatenative_programming_language" title="Concatenative programming language">Concatenative</a></li>

<li>, <a href="Value-level_programming" title="Value-level programming">Value-level</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Dataflow_programming" title="Dataflow programming">Dataflow</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Flow-based_programming" title="Flow-based programming">Flow-based</a></li>

<li><a href="Reactive_programming" title="Reactive programming">Reactive</a> (<a href="Functional_reactive_programming" title="Functional reactive programming">Functional reactive</a>)</li>

<li><a href="Signal_programming" class="mw-redirect" title="Signal programming">Signals</a></li>

<li><a href="Stream_processing" title="Stream processing">Streams</a></li>

<li><a href="Synchronous_programming_language" title="Synchronous programming language">Synchronous</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Logic_programming" title="Logic programming">Logic</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Abductive_logic_programming" title="Abductive logic programming">Abductive logic</a></li>

<li><a href="Answer_set_programming" title="Answer set programming">Answer set</a></li>

<li><a href="Constraint_programming" title="Constraint programming">Constraint</a> (<a href="Constraint_logic_programming" title="Constraint logic programming">Constraint logic</a>)</li>

<li><a href="Inductive_logic_programming" title="Inductive logic programming">Inductive logic</a></li>

<li><a href="Nondeterministic_programming" title="Nondeterministic programming">Nondeterministic</a></li>

<li><a href="Ontology_language" title="Ontology language">Ontology</a></li>

<li><a href="Probabilistic_logic_programming" title="Probabilistic logic programming">Probabilistic logic</a></li>

<li><a href="Query_language" title="Query language">Query</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Domain-specific_language" title="Domain-specific language">DSL</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Algebraic_modeling_language" title="Algebraic modeling language">Algebraic modeling</a></li>

<li><a href="Array_programming" title="Array programming">Array</a></li>

<li><a href="Automata-based_programming" title="Automata-based programming">Automata-based</a> (<a href="Action_language" title="Action language">Action</a>)</li>

<li><a href="Command_language" title="Command language">Command</a> (<a href="Spacecraft_command_language" title="Spacecraft command language">Spacecraft</a>)</li>

<li><a href="Differentiable_programming" title="Differentiable programming">Differentiable</a></li>

<li><a href="Grammar-oriented_programming" title="Grammar-oriented programming">Grammar-oriented</a></li>

<li><a href="Interface_description_language" title="Interface description language">Interface description</a></li>

<li><a href="Language-oriented_programming" title="Language-oriented programming">Language-oriented</a></li>

<li><a href="List_comprehension" title="List comprehension">List comprehension</a></li>

<li><a href="Modeling_language" title="Modeling language">Modeling</a></li>

<li><a href="Natural-language_programming" class="mw-redirect" title="Natural-language programming">Natural language</a></li>

<li><a href="Non-English-based_programming_languages" title="Non-English-based programming languages">Non-English-based</a></li>

<li><a href="Page_description_language" title="Page description language">Page description</a></li>

<li><a href="Pipeline_(software)" title="Pipeline (software)">Pipes</a> and <a href="Filter_(software)" title="Filter (software)">filters</a></li>

<li><a href="Probabilistic_programming" title="Probabilistic programming">Probabilistic</a></li>

<li><a href="Quantum_programming" title="Quantum programming">Quantum</a></li>

<li><a href="Scientific_programming_language" title="Scientific programming language">Scientific</a></li>

<li><a href="Scripting_language" title="Scripting language">Scripting</a></li>

<li><a href="Set_theoretic_programming" title="Set theoretic programming">Set-theoretic</a></li>

<li><a href="Simulation_language" title="Simulation language">Simulation</a></li>

<li><a href="Stack-oriented_programming" title="Stack-oriented programming">Stack-based</a></li>

<li><a href="System_programming_language" title="System programming language">System</a></li>

<li><a href="Tactile_programming_language" title="Tactile programming language">Tactile</a></li>

<li><a href="Template_processor" title="Template processor">Templating</a></li>

<li><a href="Transformation_language" title="Transformation language">Transformation</a> (<a href="Graph_rewriting" title="Graph rewriting">Graph rewriting</a>, <a href="Production_system_(computer_science)" title="Production system (computer science)">Production</a>, <a href="Pattern_matching" title="Pattern matching">Pattern</a>)</li>

<li><a href="Visual_programming_language" title="Visual programming language">Visual</a></li></ul>

</div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Concurrent_computing" title="Concurrent computing">Concurrent</a>,<br><a href="Distributed_computing" title="Distributed computing">distributed</a>,<br><a href="Parallel_computing" title="Parallel computing">parallel</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Actor_model" title="Actor model">Actor-based</a></li>

<li><a href="Automatic_mutual_exclusion" title="Automatic mutual exclusion">Automatic mutual exclusion</a></li>

<li><a href="Choreographic_programming" title="Choreographic programming">Choreographic programming</a></li>

<li><a href="Concurrent_logic_programming" title="Concurrent logic programming">Concurrent logic</a> (<a href="Concurrent_constraint_logic_programming" title="Concurrent constraint logic programming">Concurrent constraint logic</a>)</li>

<li><a href="Concurrent_object-oriented_programming" title="Concurrent object-oriented programming">Concurrent OO</a></li>

<li><a href="Macroprogramming" title="Macroprogramming">Macroprogramming</a></li>

<li><a href="Multitier_programming" title="Multitier programming">Multitier programming</a></li>

<li><a href="Organic_computing" title="Organic computing">Organic computing</a></li>

<li><a href="Parallel_programming_model" title="Parallel programming model">Parallel programming models</a></li>

<li><a href="Partitioned_global_address_space" title="Partitioned global address space">Partitioned global address space</a></li>

<li><a href="Process-oriented_programming" title="Process-oriented programming">Process-oriented</a></li>

<li><a href="Relativistic_programming" title="Relativistic programming">Relativistic programming</a></li>

<li><a href="Service-oriented_programming" title="Service-oriented programming">Service-oriented</a></li>

<li><a href="Structured_concurrency" title="Structured concurrency">Structured concurrency</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Metaprogramming" title="Metaprogramming">Metaprogramming</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Attribute-oriented_programming" title="Attribute-oriented programming">Attribute-oriented</a></li>

<li><a href="Automatic_programming" title="Automatic programming">Automatic</a> (<a href="Inductive_programming" title="Inductive programming">Inductive</a>)</li>

<li><a href="Dynamic_programming_language" title="Dynamic programming language">Dynamic</a></li>

<li><a href="Extensible_programming" title="Extensible programming">Extensible</a></li>

<li><a href="Generic_programming" title="Generic programming">Generic</a></li>

<li><a href="Homoiconicity" title="Homoiconicity">Homoiconicity</a></li>

<li><a href="Interactive_programming" title="Interactive programming">Interactive</a></li>

<li><a href="Macro_(computer_science)" title="Macro (computer science)">Macro</a> (<a href="Hygienic_macro" title="Hygienic macro">Hygienic</a>)</li>

<li><a href="Metalinguistic_abstraction" title="Metalinguistic abstraction">Metalinguistic abstraction</a></li>

<li><a href="Multi-stage_programming" title="Multi-stage programming">Multi-stage</a></li>

<li><a href="Program_synthesis" title="Program synthesis">Program synthesis</a> (<a href="Bayesian_program_synthesis" title="Bayesian program synthesis">Bayesian</a>, <a href="Inferential_programming" title="Inferential programming">Inferential</a>, <a href="Programming_by_demonstration" title="Programming by demonstration">by demonstration</a>, <a href="Programming_by_example" title="Programming by example">by example</a>)</li>

<li><a href="Reflective_programming" title="Reflective programming">Reflective</a></li>

<li><a href="Self-modifying_code" title="Self-modifying code">Self-modifying code</a></li>

<li><a href="Symbolic_programming" title="Symbolic programming">Symbolic</a></li>

<li><a href="Template_metaprogramming" title="Template metaprogramming">Template</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Separation_of_concerns" title="Separation of concerns">Separation<br>of concerns</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Aspect-oriented_programming" title="Aspect-oriented programming">Aspects</a></li>

<li><a href="Component-based_software_engineering" title="Component-based software engineering">Components</a></li>

<li><a href="Data-driven_programming" title="Data-driven programming">Data-driven</a></li>

<li><a href="Data-oriented_design" title="Data-oriented design">Data-oriented</a></li>

<li><a href="Event-driven_programming" title="Event-driven programming">Event-driven</a></li>

<li><a href="Feature-oriented_programming" title="Feature-oriented programming">Features</a></li>

<li><a href="Literate_programming" title="Literate programming">Literate</a></li>

<li><a href="Role-oriented_programming" title="Role-oriented programming">Roles</a></li>

<li><a href="Subject-oriented_programming" title="Subject-oriented programming">Subjects</a></li></ul>

</div></td></tr></tbody></table></div></div><div><div class="zim-footer">

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