nLab domain specific embedded programming language




A domain specific programming language is one designed for a specialized kind (“domain”) of applications. A domain specific embedded programming language (DSEL) is a domain specific language realized “inside” a general-purpose high level (typed) programming language.

Relation to synthetic mathematics

There is at least some similarity between DSELs and synthetic mathematics, see for instance (Hudak 98, section 3.2). In (Hudak 98, figure 2) this shows aspects of a real-world DSL for “geometric region analysis” embedded in Haskell which under the relation between type theory and category theory/computational trinitarianism one immediately recognizes as a fragment of synthetic geometry.

Relation to monadic effects

There is a close relation between embedding a domain-specific language and declaring do-notation for monadic effects, see Benton, Hughes & Moggi 2002, §5.3 who write:

Every time a functional programmer designs a combinator library, then, we might as well say that he or she designs a domain specific programming language […]. This is a useful perspective, since it encourages programmers to produce a modular design, with a clean separation between the semantics of the DSL and the program that uses it, rather than mixing combinators and ‘raw’ semantics willy-nilly. And since monads appear so often in programming language semantics, it is hardly surprising that they appear often in combinator libraries also!


Quantum programming

Many existing quantum programming languages are actually domain-specific languages for the description of quantum circuits, and as such many are embedded in ambient type theories.

For instance:

See also Rennela & Staton (2020) for more general discussion.


With emphasis on the relation to monads in computer science:

Discussion for embedding in Haskell:

A list of literature is at

Discussion specifically of quantum programming languages for quantum circuits as domain specific embedded languages:

Last revised on October 14, 2023 at 09:15:54. See the history of this page for a list of all contributions to it.