SETL

---

title: "SETL" type: doc version: 1 created: 2026-02-28 author: "Wikipedia contributors" status: active scope: public tags: ["academic-programming-languages", "set-theoretic-programming-languages", "programming-languages-created-in-1969", "articles-with-example-code"] description: "Programming language" topic_path: "linguistics" source: "https://en.wikipedia.org/wiki/SETL" license: "CC BY-SA 4.0" wikipedia_page_id: 0 wikipedia_revision_id: 0

::summary Programming language ::

::data[format=table title="Infobox programming language"]

Field	Value
name	SETL
paradigm	multi-paradigm: imperative, procedural, structured, object-oriented
designer	(Jack) Jacob T. Schwartz
developer	Courant Institute of Mathematical Sciences
released
latest release version	1.1
latest release date
typing	Dynamic
platform	CDC 6600, CDC Cyber, DEC VAX, IBM/370, Sun workstation, Apollo, BESM-6, ES EVM, others
website
influenced by	ALGOL 60
influenced	SETL2, ISETL, SETLX, Starset, ABC
::

| name = SETL | logo = | paradigm = multi-paradigm: imperative, procedural, structured, object-oriented | designer = (Jack) Jacob T. Schwartz | developer = Courant Institute of Mathematical Sciences | released = | latest release version = 1.1 | latest release date = | typing = Dynamic | platform = CDC 6600, CDC Cyber, DEC VAX, IBM/370, Sun workstation, Apollo, BESM-6, ES EVM, others | operating system = | website = | implementations = | dialects = | influenced by = ALGOL 60 | influenced = SETL2, ISETL, SETLX, Starset, ABC

SETL (SET Language) is a very high-level programming language based on the mathematical theory of sets. It was originally developed at the New York University (NYU) Courant Institute of Mathematical Sciences in the late 1960s, by a group including (Jack) Jacob T. Schwartz, R.B.K. Dewar, and E. Schonberg. Schwartz is credited with designing the language.

Design

SETL provides two basic aggregate data types: (unordered) sets, and tuples. The elements of sets and tuples can be of any arbitrary type, including sets and tuples themselves, except the undefined value om (sometimes capitalized: OM). Maps are provided as sets of pairs (i.e., tuples of length 2) and can have arbitrary domain and range types. Primitive operations in SETL include set membership, union, intersection, and power set construction, among others.

SETL provides quantified boolean expressions constructed using the universal and existential quantifiers of first-order predicate logic.

SETL provides several iterators to produce a variety of loops over aggregate data structures.

Examples

Print all prime numbers from 2 to N: print([n in [2..N] | forall m in {2..n - 1} | n mod m 0]); The notation is similar to list comprehension.

A factorial procedure definition: procedure factorial(n); -- calculates the factorial n! return if n = 1 then 1 else n * factorial(n - 1) end if; end factorial;

A more conventional SETL expression for factorial (n 0):

• /[1..n]

Uses

Implementations of SETL were available on the CDC 6600, CDC Cyber, DEC VAX, IBM/370, Sun workstation and Apollo.{{cite book |last1=Schwartz |first1=J.T. |last2=Dewar |first2=R.B.K. |last3=Dubinsky |first3=E. |last4=Schonberg |first4=E. |year=1986 |url=https://books.google.com/books?id=4pfbBwAAQBAJ&pg=PR6 |title=Programming with sets: An Introduction to SETL |publisher=Springer-Verlag |place=New York, New York |isbn=978-1-4613-9577-5 In the 1970s, SETL was ported to the BESM-6, ES EVM and other Russian computer systems.{{cite book |editor=И.В. Поттосин |year=2001 |title=Становление новосибирской школы программирования (мозаика воспоминаний) |trans-title=Formation of the Novosibirsk school of programming (mosaic of memories) |location=Новосибирск |publisher=Институт систем информатики им. А. П. Ершова СО РАН |pages=106–113 |url=https://www.iis.nsk.su/files/articles/mozaika.pdf |language=ru

SETL was used for an early implementation of the programming language Ada, named the NYU Ada/ED translator. This later became the first validated Ada implementation, certified on April 11, 1983.

According to Guido van Rossum, "Python's predecessor, ABC, was inspired by SETL – Lambert Meertens spent a year with the SETL group at NYU before coming up with the final ABC design!"

Language variants

SET Language 2 (SETL2), a backward incompatible descendant of SETL, was created by Kirk Snyder of the Courant Institute of Mathematical Sciences at New York University in the late 1980s. Like its predecessor, it is based on the theory and notation of finite sets, but has also been influenced in syntax and style by the Ada language.

Interactive SET Language (ISETL) is a variant of SETL used in discrete mathematics.

GNU SETL is a command-line utility that implements and extends SETL.

References

References

1. (1986). "Programming with Sets".
2. "GNU SETL Om".
3. (2009-03-04). "Jacob T. Schwartz, 79, Restless Scientist, Dies". The New York Times.
4. (2011). "Computational Logic and Set Theory".
5. "Chapter 2".
6. "Chapter 3".
7. "Chapter 4".
8. (November 1980). "Proceeding of the ACM-SIGPLAN symposium on Ada programming language – SIGPLAN '80".
9. SofTech Inc.. (1983-04-11). "Ada Compiler Validation Summary Report: NYU Ada/ED, Version 19.7 V-001".
10. [http://mail.python.org/pipermail/python-dev/2000-August/008881.html Python-Dev: SETL (was: Lukewarm about range literals)]
11. "SETL2 – EDM2".
12. (1989). "Learning discrete mathematics with ISETL". Springer-Verlag.
13. "GNU SETL".

::callout[type=info title="Wikipedia Source"] This article was imported from Wikipedia and is available under the Creative Commons Attribution-ShareAlike 4.0 License. Content has been adapted to SurfDoc format. Original contributors can be found on the article history page. ::