SETL

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]

Design

SETL provides two basic aggregate data types: (unordered) sets, and tuples.^[1][2][4] 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)^[5]. Maps are provided as sets of pairs (i.e., tuples of length 2) and can have arbitrary domain and range types.^[1][4] 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

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

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 DEC

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]

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.^[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 extends and implements SETL.^[15]

References