Declarative programming

Constraint programming states relations between variables in the form of constraints that specify the properties of the target solution. The set of constraints is solved by giving a value to each variable so that the solution is consistent with the maximum number of constraints. Constraint programming often complements other paradigms: functional, logical, or even imperative programming.

Well-known examples of declarative domain-specific languages (DSLs) include the yacc parser generator input language, QML, the Make build specification language, Puppet's configuration management language, regular expressions, Datalog, answer set programming and a subset of SQL (SELECT queries, for example). DSLs have the advantage of being useful while not necessarily needing to be Turing-complete, which makes it easier for a language to be purely declarative.

Many markup languages such as HTML, MXML, XAML, XSLT or other user-interface markup languages are often declarative. HTML, for example, only describes what should appear on a webpage - it specifies neither control flow for rendering a page nor the page's possible interactions with a user.

As of 2013, some software systems combine traditional user-interface markup languages (such as HTML) with declarative markup that defines what (but not how) the back-end server systems should do to support the declared interface. Such systems, typically using a domain-specific XML namespace, may include abstractions of SQL database syntax or parameterized calls to web services using representational state transfer (REST) and SOAP.

Functional programming languages such as Haskell, Scheme, and ML evaluate expressions via function application. Unlike the related but more imperative paradigm of procedural programming, functional programming places little emphasis on explicit sequencing. For example, in Scheme, the order of evaluation of many kinds of sub-expressions is undefined or implicit.[7] Instead, computations are characterised by various kinds of recursive higher-order function application and composition, and as such can be regarded simply as a set of mappings between domains and codomains. Many functional languages, including most of those in the ML and Lisp families, are not purely functional, and thus allow the introduction of stateful effects in programs.

Makefiles, for example, specify dependencies in a declarative fashion,[8] but include an imperative list of actions to take as well. Similarly, yacc specifies a context free grammar declaratively, but includes code snippets from a host language, which is usually imperative (such as C).

Logic programming languages, such as Prolog, Datalog and answer set programming, compute by proving that a goal is a logical consequence of the program, or by showing that the goal is true in a model defined by the program. Prolog computes by reducing goals to subgoals, top-down using backward reasoning, whereas most Datalog systems compute bottom-up using forward reasoning. Answer set programs typically use SAT solvers to generate a model of the program.

Models, or mathematical representations, of physical systems may be implemented in computer code that is declarative. The code contains a number of equations, not imperative assignments, that describe ("declare") the behavioral relationships. When a model is expressed in this formalism, a computer is able to perform algebraic manipulations to best formulate the solution algorithm. The mathematical causality is typically imposed at the boundaries of the physical system, while the behavioral description of the system itself is declarative or acausal. Declarative modeling languages and environments include Analytica, Modelica and Simile.[9]

Lisp (1958) stands for "LISt Processor."[10] It is tailored to process lists. A data structure is formed by building lists of lists. In memory, this forms a tree data structure. Internally, the tree structure of typical Lisp data lends itself nicely to processing with recursive functions.[11] The syntax to build a tree is to enclose the whitespace-separated elements within parenthesis. The following is a list of three elements. The first two elements are themselves lists of two elements each:

((A B) (HELLO WORLD) 94)

Lisp has functions to extract and reconstruct elements.[12] The function car (sometimes called first) returns the first element in the list. The function cdr (sometimes called rest) returns a list containing everything but the first element. The function cons returns a list that is the second argument with the first prepended to it. Therefore, if X is a non-empty list, the following expression evaluates to the list X:

(cons (car x) (cdr x))

The code itself returns a copy of the list X. As is typical in functional languages, operations in Lisp often copy data when asked to produce new data from old. The tree structure of Lisp data facilitates this as well: a new structure made from pre-existing data shares as much of its internal structure with its antecedents as possible, with new additions stored as branches of the tree, and references to the original structure under its original name will return exactly that and no more.

One drawback of Lisp is when many functions are nested, the parentheses may look confusing.[13] Modern Lisp environments help ensure parenthesis match. As an aside, Lisp does support the imperative language operations of the assignment statement and goto loops.[14] Also, Lisp is not concerned with the datatype of the elements at compile time. Instead, it assigns the datatypes at runtime. This may lead to programming errors not being detected early in the development process. To counteract this, Lisp development is typically carried out in an extremely incremental manner, with functions and higher-order functions built up and tested live during development. Additionally, through the use of macros, which are Lisp functions that operate upon Lisp programs as data structures, type checking may be performed discretionally at any point the programmer wishes.

Writing large, reliable, and readable Lisp programs requires forethought. If properly planned, the program may be much shorter than an equivalent imperative language program.[13] Lisp is widely used in artificial intelligence. However, its usage has been accepted only because it has imperative language operations, making unintended side-effects possible.[15]

ML (1973)[16] stands for "Meta Language." ML is statically typed, and function arguments and return types may be annotated.[17]

fun times_10(n : int) : int = 10 * n;

ML is not as bracket-centric as Lisp, and instead uses a wider variety of syntax to codify the relationship between code elements, rather than appealing to list ordering and nesting to express everything. The following is an application of times_10:

times_10 2

It returns "20 : int", that is, 20, a value of type int.

Like Lisp, ML is tailored to process lists, though all elements of a list must be the same type.[18]

Prolog (1972) stands for "PROgramming in LOGic." It was developed for natural language question answering,[19] using SL resolution[20] both to deduce answers to queries and to parse and generate natural language sentences.

The building blocks of a Prolog program are facts and rules. Here is a simple example:

cat(tom).                        % tom is a cat
mouse(jerry).                    % jerry is a mouse

animal(X) :- cat(X).             % each cat is an animal
animal(X) :- mouse(X).           % each mouse is an animal

big(X)   :- cat(X).              % each cat is big
small(X) :- mouse(X).            % each mouse is small

eat(X,Y) :- mouse(X), cheese(Y). % each mouse eats each cheese
eat(X,Y) :- big(X),   small(Y).  % each big being eats each small being

Given this program, the query eat(tom,jerry) succeeds, while eat(jerry,tom) fails. Moreover, the query eat(X,jerry) succeeds with the answer substitution X=tom.

Prolog executes programs top-down, using SLD resolution to reason backwards, reducing goals to subgoals. In this example, it uses the last rule of the program to reduce the goal of answering the query eat(X,jerry) to the subgoals of first finding an X such that big(X) holds and then of showing that small(jerry) holds. It repeatedly uses rules to further reduce subgoals to other subgoals, until it eventually succeeds in unifying all subgoals with facts in the program. This backward reasoning, goal-reduction strategy treats rules in logic programs as procedures, and makes Prolog both a declarative and procedural programming language.[21]

The broad range of Prolog applications is highlighted in the Year of Prolog Book,[22] celebrating the 50 year anniversary of Prolog.

The origins of Datalog date back to the beginning of logic programming, but it was identified as a separate area around 1977. Syntactically and semantically, it is a subset of Prolog. But because it does not have compound terms, it is not Turing-complete.

Most Datalog systems execute programs bottom-up, using rules to reason forwards, deriving new facts from existing facts, and terminating when there are no new facts that can be derived, or when the derived facts unify with the query. In the above example, a typical Datalog system would first derive the new facts:

animal(tom).
animal(jerry).
big(tom).
small(jerry).

Using these facts, it would then derive the additional fact:

eats(tom, jerry).

It would then terminate, both because no new, additional facts can be derived, and because the newly derived fact unifies with the query

eats(X, jerry).

Datalog has been applied to such problems as data integration, information extraction, networking, security, cloud computing and machine learning.[23][24]

Answer set programming (ASP) evolved in the late 1990s, based on the stable model (answer set) semantics of logic programming. Like Datalog, it is a subset of Prolog; and, because it does not have compound terms, it is not Turing-complete.

Most implementations of ASP execute a program by first "grounding" the program, replacing all variables in rules by constants in all possible ways, and then using a propositional SAT solver, such as the DPLL algorithm to generate one or more models of the program.

Its applications are oriented towards solving difficult search problems and knowledge representation.[25][26]