I've always wondered if there's more to FP than (more or less) point-free style with an associated algebra. TFA seems to stop just when it might get interesting. Did Backus ever develop (or aim for) a notion of semantic completeness, e.g. Cartesian closure or whatever works [0] for Hughes's Arrows? The last has the interesting property of being foundationally point-free but also supporting a syntax with variables (with non-standard scoping rules). Which perhaps refutes Backus's original concerns.

[0] https://en.wikipedia.org/wiki/Arrow_(computer_science)

Author here. This is work-in-progress, not linked from top level. I'll keep working.

Remembering John Backus:

> [...] At that time, John was interested in pure functional programming, with no side-effects on storage or the external world. I advocated extending the language to allow writing complete interactive applications. John conceded the importance of this, and came up with a scheme in which one would write a function to express the complete transformation of an application on the global state. I struggled with John’s variable free style, and suggested we allow lambda variables when defining a new functional form (higher-order function), but he stuck to his guns.

(In my project) I’ve reduced extensibility to the meta-composition rule, and I’m using an IO monad for interaction because I believe all functions should remain as simple as possible.

Is this your project: https://github.com/metazip/pointfrip ?

I have looked at the diagrams. If a side effect occurs between Program A and Program B, then referential transparency is violated. Referential transparency is the "sacred principle" of algebra; if it is violated, no algebraic transformation is possible—unless I am mistaken or we are talking about a monadic continuation.

Can we move this conversation to email? I am not sure what diagrams you are referring to.

In that first diagram (https://softwarepreservation.computerhistory.org/FP/Composin...), A and B are supposed to be pure functional programs; side-effects are modeled by each one outputting a new version of each modified input. In the second diagram (https://softwarepreservation.computerhistory.org/FP/Strict_H...), as actually implemented in FL, they stick to strictly leftmost-innermost evaluation order so that side-effects are at consistent (but this presumably prevents parallel evaluation).

some Plasm files https://github.com/metazip/plasmfiles/blob/main/Function-Lev...

Yes, it started with https://esolangs.org/wiki/FP_trivia in Delphi, and the project using the Lazarus-IDE was Pointfrip.

Thanks for the extensive collection. Valuable work. I’ve included a reference to the link collection on https://github.com/function-level/function-level.github.io

Thanks very much; I in turn will add a link the Related Resources section. If you'd like to be recognized as other than metazip then let me know via email.

Videos to FL and FP: John Backus: Function Level Programming and the FL Language 1987 (https://www.youtube.com/watch?v=FxcT4vK01-w&t=15s), John Backus Group Meeting - IBM Research - 5 July 1989 (https://www.youtube.com/watch?v=KzBkb-bvNK4), Backus on functional programming (https://www.youtube.com/watch?v=OxuPZXXiwKk) from Original: Oral History of John Backus (https://www.youtube.com/watch?v=dDsWTyLEgbk)

The first video is the same as https://softwarepreservation.computerhistory.org/FP/#Backus1... .

I hadn't seen the Group Meeting video; I will add it (even though it's very rough).

I will change the entry for [Booch2007] to include the video as well as the transcript.

TFA contains a great number of links to downloadable interesting research papers.