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Paradigmmulti-paradigm: imperative, procedural, structured, object-oriented
Designed by(Jack) Jacob T. Schwartz
DeveloperCourant Institute of Mathematical Sciences
First appeared1969; 55 years ago (1969)
Stable release
1.1 / January 7, 2005; 19 years ago (2005-01-07)
Typing disciplineDynamic
Influenced by

SETL (SET Language) is a very high-level programming language[1] based on the mathematical theory of sets.[2][3] It was originally developed at the New York University (NYU) Courant Institute of Mathematical Sciences in the late 1960s, by a group containing (Jack) Jacob T. Schwartz,[1][3] R.B.K. Dewar, and E. Schonberg.[1] Schwartz is credited with designing the language.[4]


SETL provides two basic aggregate data types: (unordered) sets, and tuples.[1][2][5] The elements of sets and tuples can be of any arbitrary type, including sets and tuples themselves, except the undefined value om[1] (sometimes capitalized: OM).[6] Maps are provided as sets of pairs (i.e., tuples of length 2) and can have arbitrary domain and range types.[1][5] Primitive operations in SETL include set membership, union, intersection, and power set construction, among others.[1][7]

SETL provides quantified boolean expressions constructed using the universal and existential quantifiers of first-order predicate logic.[1][7]

SETL provides several iterators to produce a variety of loops over aggregate data structures.[1][8]


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):



Implementations of SETL were available on the DEC VAX, IBM/370, SUN workstation and APOLLO.[9] In the 1970s, SETL was ported to the BESM-6, ES EVM and other Russian computer systems.[10]

SETL was used for an early implementation of the programming language Ada, named the NYU Ada/ED translator.[11] This later became the first validated Ada implementation, certified on April 11, 1983.[12]

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!"[13]

Language variants[edit]

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.[14] 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.[14]

Interactive SET Language (ISETL) is a variant of SETL used in discrete mathematics.[15]

GNU SETL is a command-line utility that extends and implements SETL.[16]


  1. ^ a b c d e f g h i Schwartz, J. T.; Dewar, R. B. K.; Schonberg, E.; Dubinsky, E. (1986). "Programming with Sets". SpringerLink: v–vii, 2, 48, 53, 57–58, 63, 113ff. doi:10.1007/978-1-4613-9575-1.
  2. ^ a b "GNU SETL Om". setl.org. Retrieved 2024-04-24.
  3. ^ a b Markoff, John (2009-03-04). "Jacob T. Schwartz, 79, Restless Scientist, Dies". The New York Times. ISSN 0362-4331. Retrieved 2024-04-24.
  4. ^ Computational Logic and Set Theory. pp. vii. doi:10.1007/978-0-85729-808-9.
  5. ^ a b "CHAPTER 2". www.settheory.com. Retrieved 2024-04-24.
  6. ^ "CHAPTER 3". www.settheory.com. Retrieved 2024-04-24.
  7. ^ a b "CHAPTER 3". www.settheory.com. Retrieved 2024-04-24.
  8. ^ "CHAPTER 4". www.settheory.com. Retrieved 2024-04-24.
  9. ^ J.T. Schwartz; R.B.K. Dewar; E. Dubinsky; E. Schonberg (1986). Programming with sets. An Introduction to SETL. Springer-Verlag New York Inc. ISBN 978-1-4613-9577-5.
  10. ^ И.В. Поттосин, ed. (2001). Становление новосибирской школы программирования (мозаика воспоминаний) [Formation of the Novosibirsk school of programming (mosaic of memories)] (PDF) (in Russian). Новосибирск: Институт систем информатики им. А. П. Ершова СО РАН. pp. 106–113.
  11. ^ Dewar, Robert B. K.; Fisher Jr., Gerald A.; Schonberg, Edmond; Froelich, Robert; Bryant, Stephen; Goss, Clinton F.; Burke, Michael (November 1980). "The NYU Ada translator and interpreter". Proceeding of the ACM-SIGPLAN symposium on Ada programming language - SIGPLAN '80. Vol. 15. pp. 194–201. doi:10.1145/948632.948659. ISBN 0-89791-030-3. S2CID 10586359.
  12. ^ SofTech Inc., Waltham, MA (1983-04-11). "Ada Compiler Validation Summary Report: NYU Ada/ED, Version 19.7 V-001". Archived from the original on June 7, 2017. Retrieved 2010-12-16.{{cite web}}: CS1 maint: multiple names: authors list (link)
  13. ^ Python-Dev: SETL (was: Lukewarm about range literals)
  14. ^ a b "SETL2 - EDM2". www.edm2.com. Retrieved 2024-04-24.
  15. ^ Baxter Hastings, Nancy; Dubinsky, Ed; Levin, Gary (1989). Learning discrete mathematics with ISETL. New York: Springer-Verlag. ISBN 978-0-387-96898-8.
  16. ^ "GNU SETL". setl.org. Retrieved 2024-04-24.

Further reading[edit]

  • Schwartz, Jacob T., "Set Theory as a Language for Program Specification and Programming". Courant Institute of Mathematical Sciences, New York University, 1970.
  • Schwartz, Jacob T., "On Programming, An Interim Report on the SETL Project", Computer Science Department, Courant Institute of Mathematical Sciences, New York University (1973).
  • Schwartz, Jacob T., Dewar, R.B.K., Dubinsky, E., and Schonberg, E., Programming With Sets: An Introduction to SETL, 1986. ISBN 0-387-96399-5.

External links[edit]