λProlog: Logic programming in higher-order logic | Hacker News Reader

λProlog: Logic programming in higher-order logic

lix.polytechnique.fr

167 pointsux26647839 comments

I am a huge fan of the work towards putting this in kanren as λKanren:

https://www.proquest.com/openview/2a5f2e00e8df7ea3f1fd3e8619...

A few of my own experiments in this time with unification over the binders as variables themselves shows there’s almost always a post HM inference sitting there but likely not one that works in total generality.

To me that spot of trying to binding unification in higher order logic constraint equations is the most challenging and interesting problem since it’s almost always decidable or decidably undecidable in specific instances, but provably undecidable in general.

So what gives? Where is this boundary and does it give a clue to bigger gains in higher order unification? Is a more topological approach sitting just behind the veil for a much wider class of higher order inference?

And what of optimal sharing in the presence of backtracking? Lampings algorithm when the unification variables is in the binder has to have purely binding attached path contexts like closures. How does that get shared?

Fun to poke at, maybe just enough modern interest in logic programming to get there too…

I'm surprised how hard I had to dig for an actual example of syntax[1], so here you go.

[1]: https://www.lix.polytechnique.fr/~dale/lProlog/proghol/extra...

There is also an implementation of 99 Bottles of Beer on Rosetta Code: https://rosettacode.org/wiki/99_bottles_of_beer#Lambda_Prolo...

Constantly amused by the split in comments of any moderately innovative language post between ‘I don't care about all this explanation, just show me the syntax!’ and ‘I don't understand any of this syntax, what a useless language!’

If the language is ‘JavaScript but with square brackets instead of braces’ maybe the syntax is relevant. But in general concrete syntax is the least interesting (not least important, but easiest to change) thing in a programming language, and its similarity to other languages a particular reader knows less interesting still. JavaScript is not the ultimate in programming language syntax (I hope!) so it's still worth experimenting, even if the results aren't immediately comprehensible without learning.

In Prolog the syntax is incredibly important. It is designed to be metainterpreted with the same ease in which a for-loop might be written in another language.

https://www.metalevel.at/acomip/

  mi1(true).
  mi1((A,B)) :-
        mi1(A),
        mi1(B).
  mi1(Goal) :-
        Goal \= true,
        Goal \= (_,_),
        clause(Goal, Body),
        mi1(Body).

This can be arbitrarily extended in very interesting, beautiful, and powerful ways. This is extraordinarily hard to achieve and did not happen by accident.

As a challenge, see how easy it is to write a metainterpreter in another language of your choice. Alternately, see if you can think of any way the metainterpretation system in Prolog could be improved.

Finally, think of what would happen to this if we changed the syntax and introduced something like object.field notation.

So while logical programming can be achieved with other syntaxes, the metaintrepretive aspect will be lost. I have yet to see a language that does this better.

Nice link, thank you! I'm not sure it's super related to my comment but it is closely related to some other things I'm thinking about. I'll give it a read :)

There are some examples in this tutorial PDF:

https://www.lix.polytechnique.fr/Labo/Dale.Miller/lProlog/fe...

I have written stuff in Prolog, but I find this lambda Prolog syntax very difficult to grok.

So brainfuck x lisp

Christ... it's incomprehensible... I guess that ones staying in academia :P

I did a few days of AoC in 2020 in λProlog (as a non-expert in the language), using the Elpi implementation. It provides a decent source of relatively digestable toy examples: https://github.com/shonfeder/aoc-2020

(Caveat that I don't claim to be a λProlog or expert.)

All examples showcase the typing discipline that is novel relative to Prolog, and towards day 10, use of the lambda binders, hereditary harrop formulas, and higher order niceness shows up.

There is a great overview of λProlog from 1988: https://repository.upenn.edu/bitstreams/e91f803b-8e75-4f3c-9...

I think that might be my favorite department/lab website I've ever come across. Really fun. Doesn't at all align with the contemporary design status quo and it shows just how good a rich website can be on a large screen. Big fan.

https://www.lix.polytechnique.fr/

Did some modest development on Lambda Prolog back in 1999. I still have a vivid memory of feeling my brain expanding :) like rewiring how I approach programming and opening up new territory in my brain.

It might sound weird and crazy, but it quite literally blew my mind at the time !

Anyone know why there seems to be a Prolog renaissance?

I personally found it by asking for a specific language recommendation from ChatGPT, and one of the suggestions was Prolog.

I remember learning it in univerisity. It's a really weird language to reason with IMO. But really fun. However I've heard the performances are not that good if you wanna make e.g. game AIs with it.

First of all, it helps to actually use a proper compiled Prolog implementation like SWI Prolog.

Second you really need to understand and fine tune cuts, and other search optimization primitives.

Finally in what concerns Game AIs, it is a mixture of algorithms and heuristics, a single paradigm language (first order logic) like Prolog, can't be a tool for all nails.

With λProlog in particular I think it probably finds most of its use in specifying and reasoning about systems/languages/logics, e.g. with Abella. I don't think many people are running it in production as an implementation language.

Yeah the main use of it is probably in ELPI which is a higher order structural reasoning and AST transform tool for Coq/Rocq.

I also learned Prolog in the university.

In the Classsic AI course we had to implement gaming AI algorithms (A*, alpha-beta pruning, etc) and in Prolog for one specific assignment. After trying for a while, I got frustrated and asked the teacher if I could do it in Ruby instead. He agreed: he was the kind of person who just couldn't say no, he was too nice for his own good. I still feel bad about it.

Rest In Peace, Alexandre.

How is this fair to others?!

University is not a competition, others have nothing to do with this? The unfairness here is between me and myself, as I was supposed force myself into doing it in Prolog.

The term "AI" has changed in recent years but if you mean classic game logic such as complex rules and combinatorial opponents then there's plenty of Prolog game code on github eg. for Poker and other card or board games. Prolog is also as natural a choice for adventure puzzles as it gets with repository items and complicated conditions to advance the game. In fact, Amzi! Prolog uses adventure game coding as a topic for its classic (1980s) introductory Prolog learning book Adventure in Prolog ([1]). Based on a cursory look, most code in that book should run just fine on a modern ISO Prolog engine ([2]) in your browser.

[1]: https://www.amzi.com/AdventureInProlog/advtop.php

[2]: https://quantumprolog.sgml.net

> It's a really weird language to reason with IMO

I know you likely mean regular Prolog, but that's actually fairly easy and intuitive to reason with (code dependent). Lambda Prolog is much, much harder to reason about IMO and there's a certain intractability to it because of just how complex the language is.

What would be some applications it handles better than regular Prolog? Something that naturally requires second or higher order logic rather first order logic?

Lambda Prolog isn't a "pure" HOL. It's a very restricted form of HOL using Higher-Order Hereditary Herrop formulas, granting us pretty solid generalized mechanisms of implication and universal quantification, which itself more or less means we get contextual reasoning and scoping rules baked into the grammar for free.

Implementing other programming languages and proving theorems are the low-hanging fruits since you get variable binding without name management, but I genuinely think it has profound implications for expert systems since it essentially removes a massive amount of complexity from contextual reasoning. Being able to account for patient history when providing a diagnosis, for example.

λProlog or Prolog? Probably Prolog I guess?

My bad. Was regular prolog yeah

No. It is actually λProlog which seems to be an extension of Prolog.

I was responding to @TheRoque GP; I know λProlog quite well and I would be pleasantly surprised if they saw that in university, but I think they got taught Prolog. If you mean to say that they saw Lambda Prolog and it is therefor a lot more popular than I believed it to be, then excellent and ignore this reply.

Not at all, it's a completely different language with a very different computational foundation. It's an SML-Haskell type situation.

Learning how to implement Prolog in pg's On Lisp was a fun way to spend multiple weeks programming. Doing this again this year should be a lot of fun.

I'm curious to see how AI is going to reshape research in programming languages. Statically typed languages with expressive type systems should be even more relevant for instance.

Why do you think that?

Because the type system gives you correctness properties, and gives fast feedback to the coding agent. Much faster to type check the code than let say write and run unit tests.

One possible disadvantage of static types is that it can make the code more verbose, but agents really don't care, quite the opposite.

Funnily enough, when programming with agents in statically typed languages I always find myself in need of reminding the agent to check for type errors from the LSP. Seems like it's something they're not so fond of.

when I downloaded the example programs, they open up in my music player but don't play anything

As usual, try mplayer. It can play anything.

(1987)

Reply on news.ycombinator.com