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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]
| Paradigm | multi-paradigm: imperative, procedural, structured, object-oriented |
|---|---|
| Designed by | (Jack) Jacob T. Schwartz |
| Developer | Courant Institute of Mathematical Sciences |
| First appeared | 1969 |
| Stable release | 1.1
/ January 7, 2005 |
| Typing discipline | Dynamic |
| Website | setl |
| Influenced by | |
| ALGOL 60 | |
| Influenced | |
| SETL2, ISETL, SETLX, Starset, ABC | |
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):
*/[1..n]
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]
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]
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