In April 2020, just as the Covid pandemic began, Annie Liu, a professor at Stony Brook University, emailed me to chat about programming language history. She suggested that Python, with its antecedents SETL, ABC, and C, would be a good topic for historical study and preservation. I mentioned that I’d considered SETL as an interesting topic back in the early 2000s, but unfortunately had not acted. After a few more rounds of email with her, I began looking around the web and Annie introduced me to several SETL people. Starting with these people, a few other personal contacts, and some persistence, I was soon in touch with much of the small but friendly SETL community, who very generously pored through their files and donated a wide variety of materials. The result is an historical archive of materials on the SETL programming language, including source code, documentation, and an extensive set of design notes that is available at the Software Preservation Group web site:
In addition, the digital artifacts and some of the physical artifacts are now part of the Computer History Museum’s permanent collection.
The SETL programming language was designed by Jack Schwartz at the Courant Institute of Mathematical Sciences at New York University. Schwartz was an accomplished mathematician who became interested in computer science during the 1960s. While working with John Cocke to learn and document a variety of compiler optimization algorithms, he got the idea of a high-level programming language able to describe such complex algorithms and data structures.  It occurred to him that set theory could be the basis for such a language since it was rich enough to serve as a foundation for all of mathematics. As his colleagues Martin Davis and Edward Schonberg described it in their biographical memoir to him: 
The central feature of the language is the use of sets and mappings over arbitrary domains, as well as the use of universally and existentially quantified expressions to describe predicates and iterations over composite structures. This set-theoretic core is embedded in a conventional imperative language with familiar control structures, subprograms, recursion, and global state in order to make the language widely accessible. Conservative for its time, it did not include higher-order functions. The final version of the language incorporated a backtracking mechanism (with success and fail primitives) as well as database operations. The popular scripting and general purpose programming language Python is understood to be a descendent of SETL, and its lineage is apparent in Python’s popularization of the use of mappings over arbitrary domains.
Schwartz viewed SETL first as a specification language allowing complex algorithms and data structures to be written down, conveyed to other humans, and executed as a part of algorithm development or even as a component of a complete prototype system. Actual production use would typically require reprogramming in terms of data structures closer to the machine such as arrays and lists. Schwartz believed that SETL programs could be optimized “by a combination of automatic and programmer-assisted procedures.” [3, page 70] He wrote several memos about his ideas for SETL [4, 5], and began assembling a project team — mostly graduate students. A series of design notes and memos called the SETL Newsletter was launched.  Malcolm Harrison, another NYU professor, had designed an extensible LISP-like language called BALM; in the first SETL Newsletter he sketched a simple prototype of SETL as a BALM extension. 
Over the following years the SETL Newsletters chronicled a long and confusing series of SETL implementations implemented with various versions of BALM and also with LITTLE, a low-level systems programming language.
- BALMSETL (1971-1972) consisted of a runtime library of procedures corresponding to the various SETL operations, and a modification of BALM which replaced the standard BALM syntactic forms with calls to the appropriate procedures in the library. This runtime library used a hash-based representation of sets (earlier prototypes had used lists).
- SETLB (spring 1972) consisted of a preprocessor (written in Fortran) that translated a simplified subset of SETL to BALMSETL. BALM was converted from producing interpretative code for a generalized BALM machine to producing CDC 6600 machine code.
- SETLB.2 (1973?) was based upon a version of the BALM interpreter written in LITTLE, plus the SETL Run Time Library. It offered a limited capability for variation of the semantics of subroutine and function invocation by the SETLB programmer.
- SETLA (1974?)’s input language was closer to SETL, but it still used the BALMSETL-based runtime library and BALM-based name scoping.
- SETLC (1975?) consisted of a lexical scanner and syntactic analyzer (written in LITTLE), tree-walking routines (written in BALM) that built BALM parse trees), a translator that emitted LITTLE from the parse trees (written in BALM), and the LITTLE compiler. The generated LITTLE code used the SETL Run Time Library.
- SETL/LITTLE (1977-1978?) consisted of a SETL-to-LITTLE translator, a runtime library, and a LITTLE-to-CDC 6600 machine code compiler (all written in LITTLE).
The final system (the only one for which source code is available) was ported to the IBM System/370, Amdahl UTS, DECsystem-10, and DEC VAX. There was also a sophisticated optimizer, itself written in SETL, which however was too large and slow to use in production. Work stopped around the end of 1984 as Schwartz’s focus moved to other fields such as parallel computing and robotics and many of the graduate students received their degrees. A follow-on SETL2 project produced more SETL Newsletters but no system.
Other SETL implementations
Starting in the mid 1970s, SETL-influenced languages were implemented at other institutions including Akademgorodok in Novosibirsk, and then at NYU itself. After a 30-year gestation period, GNU SETL was released in 2022. See https://www.softwarepreservation.org/projects/SETL/#Dialects for more.
Many reports and theses were written and papers were published. Perhaps the most well-known result was the NYUAda project, which was an “executable specification” for Ada that was the first validated Ada implementation. The project members went on to found AdaCore and GNAT Ada compiler.
In addition to Annie Liu, many people helped me on this project; see https://www.softwarepreservation.org/projects/SETL/#Acknowledgments .
 John Cocke and Jacob T. Schwartz. Programming Languages and Their Compilers. Preliminary Notes. 1968-1969; second revised version, Apri1 1970. Courant Institute of Mathematical Sciences, New York University. PDF at software preservation.org
 Martin Davis and Edmond Schonberg. Jacob Theodore Schwartz 1930-2009: A Biographical Memoir. National Academy of Science, 2011. PDF at nasonline.org
 Jacob T. Schwartz. On Programming: An Interim Report on the SETL Project. Installment 1: Generalities; Installment 2: The SETL Language, and Examples of Its Use. Computer Science Department, Courant Institute of Mathematical Sciences, New York University, 1973; revised June 1975. PDF at softwarepreservation.org
 Jacob T. Schwartz. Abstract algorithms and a set theoretic language for their expression. Computer Science Department, Courant Institute of Mathematical Sciences, New York University. Preliminary draft, first part. 1970-1971, 16+289 pages. PDF at softwarepreservation.org
 M. C. Harrison. BALM-SETL: A simple implementation of SETL. SETL Newsletter #1, 5 November 1970. PDF at softwarepreservation.org