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SETL

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"Setl" redirects here. For the indigenous location in Canada, see Bridge River Rapids.

SETL
Paradigmmulti-paradigm: imperative, procedural, structured, object-oriented
Designed by(Jack) Jacob T. Schwartz
DeveloperCourant Institute of Mathematical Sciences
First appeared1969; 57 years ago
Stable release

1.1 / January 7, 2005; 21 years ago

Typing disciplineDynamic
PlatformCDC 6600, CDC Cyber, DEC VAX, IBM/370, Sun workstation, Apollo, BESM-6, ES EVM, others
Websitesetl.org
Influenced by
ALGOL 60
Influenced
SETL2, ISETL, SETLX, Starset, ABC

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 including (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][6]

SETL provides quantified boolean expressions constructed using the universal and existential quantifiers of first-order predicate logic.[1][6]

SETL provides several iterators to produce a variety of loops over aggregate data structures.[1][7]

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]

Implementations of SETL were available on the CDC 6600, CDC Cyber, DEC VAX, IBM/370, Sun workstation and Apollo.[8] In the 1970s, SETL was ported to the BESM-6, ES EVM and other Russian computer systems.[9]

SETL was used for an early implementation of the programming language Ada, named the NYU Ada/ED translator.[10] This later became the first validated Ada implementation, certified on April 11, 1983.[11]

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!"[12]

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.[13] 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.[13]

Interactive SET Language (ISETL) is a variant of SETL used in discrete mathematics.[14]

GNU SETL is a command-line utility that implements and extends SETL.[15]

  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. pp. v–vii, 2, 48, 53, 57–58, 63, 113ff. doi:10.1007/978-1-4613-9575-1. ISBN 978-1-4613-9577-5.
  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. ^ Schwartz, Jacob T.; Cantone, Domenico; Omodeo, Eugenio G. (2011). Computational Logic and Set Theory. pp. vii. doi:10.1007/978-0-85729-808-9. ISBN 978-0-85729-807-2.
  5. ^ a b "Chapter 2". www.settheory.com. Retrieved 2024-04-24.
  6. ^ a b c "Chapter 3". www.settheory.com. Retrieved 2024-04-24.
  7. ^ "Chapter 4". www.settheory.com. Retrieved 2024-04-24.
  8. ^ Schwartz, J.T.; Dewar, R.B.K.; Dubinsky, E.; Schonberg, E. (1986). Programming with sets: An Introduction to SETL. New York, New York: Springer-Verlag. ISBN 978-1-4613-9577-5.
  9. ^ 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.
  10. ^ 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.
  11. ^ SofTech Inc. (1983-04-11). "Ada Compiler Validation Summary Report: NYU Ada/ED, Version 19.7 V-001". Waltham, Massachusetts. Archived from the original on June 7, 2017. Retrieved 2010-12-16.
  12. ^ Python-Dev: SETL (was: Lukewarm about range literals)
  13. ^ a b "SETL2 – EDM2". www.edm2.com. Retrieved 2024-04-24.
  14. ^ Baxter Hastings, Nancy; Dubinsky, Ed; Levin, Gary (1989). Learning discrete mathematics with ISETL. New York: Springer-Verlag. ISBN 978-0-387-96898-8.
  15. ^ "GNU SETL". setl.org. Retrieved 2024-04-24.