Implementing Logic Programming
btmc.substack.com
btmc.substack.com
The most astonishing result of miniKanren is a Scheme interpreter that you can run forwards, backwards, or both. http://webyrd.net/quines/quines.pdf demonstrates using it to generate a Scheme quine, that is, a Scheme program whose output when run is itself ("miniKanren, Live and Untagged: Quine Generation via Relational Interpreters (Programming Pearl)", Byrd, Holk, and Friedman).
§4.4 of SICP http://sarabander.github.io/sicp/html/4_002e4.xhtml also has an implementation of logic programming in Scheme which is extremely approachable.
Unlike the post, I don't think Datalog is the place to look for deep insights about logic programming. Instead, it's the place to look for deep insights about databases.
I looked at how to implement Prolog and was stumped until I found that SICP section.
So I ported it to JavaScript and gave it a Prolog-like syntax and made a web page where you could run the assignment but also exposed the inner workings, and it was one of the neatest things I've ever handed in as coursework.
(Thank you for reading the article, I also implemented microKanren before and it's insane how little code it takes to get full a logic programming engine going)
Same approach. I think an older version of the book it's freely available, or maybe the one on Scheme itself.
Scheme being homoiconic makes far easier to create quines.
I'll note there is a really shallow version of naive datalog I rather like if you're willing to compromise on syntax and nonlinear variable use.
edge = {(1,2), (2,3)}
path = set()
for i in range(10):
# path(x,y) :- edge(x,y).
path |= edge
# path(x,z) :- edge(x,y), path(y,z).
path |= {(x,z) for x,y in edge for (y1,z) in path if y == y1}
I wrote a small datalog from the Z3 AST to sqlite recently along these lines https://github.com/philzook58/knuckledragger/blob/main/kdrag...
I am currently implementing a Datalog to PostgreSQL query engine at work as we want to experiment with modeling authorization rules in Datalog and then run authorization queries directly in the database. As I want to minimize the round trips to the database I use a different approach than yours and translate Datalog programs to recursive CTEs. These are a bit limited, so we have to restrict ourselves to linearly recursive Datalog programs, but for the purpose of modeling authorization rules that seems to be enough (e.g. you can still model things such as "permissions propagate from groups to group members").
I am really unhappy about the design of CTEs, and frankly I think it is a clunky hack designed by someone who was not aware of all the research on Datalog evaluation, which Ullman and others had already written excellent textbooks about at the time. CTEs are simultaneously too powerful - Turing-completeness in a declarative query language is a sure way to tell that the designers screwed up - and too restricted because being stuck in the Turing tarpit rules out so many techniques for optimization.
I didn't know about DuckDB's approach, but it seems to be a way to mark your relations as moded and exploit that during the evaluation. It appears to improve performance, but unfortunately the design it builds on is inherently flawed. I wish SQL would get a proper pure Datalog fragment in the future.
(Also added a link to your article on what you can do with Datalog, excellent stuff, couldn't have written it better myself)
https://github.com/true-grue/python-dsls/blob/main/datalog/d...
https://codeberg.org/ashton314/microKanren
By the end of it, I implement a small type checker that, when you run it backwards (by giving the checker a type), it proceeds to enumerate programs that inhabit that type!
Discussed on HN at the time: https://news.ycombinator.com/item?id=43978357
This window manager implemented in Prolog popped up here recently. It's really cool!
I jumped to it as a new daily driver in the hope that I'd learn some Prolog, and it's been quite the success, actually. The developer is really nice, and he's generously helped me with some basic questions and small PRs.
Definitely recommended. I have a Guix package for it if anyone's interested.
Any reading recommendations for high quality logic programming codebases?
I gave OpenAI Codex a single prompt with a sample like:
fact parent("Alice", "Bob")
rule grandparent(x, z) :- parent(x, y), parent(y, z)
let gps = query grandparent(x, z)
- fact storage + recursive rule support
- bottom-up fixpoint evaluation
- unification and `!=` constraints
- FFI bindings to expose `fact`, `rule`, and `query` to scripts
Total implementation was ~250 LOC. Genuinely amazed how effective the LLM was at helping bootstrap a real logic layer in one go.
The PR is here https://github.com/mochilang/mochi/pull/616
It’s not very easy to get into, but it’s very fast on rule resolution and being pure C is easy to integrate. I’m trying to get smart code parsing using logic language and this seems promising. I’m also a Lisp nerd so that works for me :)
Knowing how to implement a small logic programming language from scratch really feels like a superpower sometimes.
This bit at the end of the article seems to imply it’s possible, maybe with some tricks?
> We could also add support for arithmetic and composite atoms (like lists), which introduce some challenges if we wish to stay “Turing-incomplete”.
Twelf is quite elegant, although not as powerful as other proof assistants such as Coq. Proofs in Twelf are simply logic programs which have been checked to be total and terminating.
Edit: Here's a link to a short page in the manual which shows how termination checking works: https://twelf.org/wiki/percent-terminates/
The syntax of Twelf is a bit different from other logic languages, but just note that every rule must have a name and that instead of writing `head :- subgoal1, subgoal2, ..., subgoaln` you write `ruleName : head <- subgoal1 <- subgoal2 <- ... <- subgoaln`.
Also note that this approach only works for top-down evaluation because it still allows you to define infinite relations (e.g. the successor relation for natural numbers is infinite). Bottom-up evaluation will fail to terminate unless restricted to only derive facts that contribute to some ground query. I don't know if anyone have looked into that problem, but that seems interesting. It is probably related to the "magic sets" transformation for optimizing bottom-up queries, but as far as I understand that does not give any hard guarantees to performance, and I don't know how it would apply to this problem.
Look into Datafun: A total functional language that generalizes Datalog. Also be sure to watch Datafun author Michael Arntzenius's Strangeloop talk.
Yes you can add support for integers in various ways where termination is still guaranteed. The simplest trick is to distinguish predicates (like pred(X, 42)) from constraints (like X > 7). Predicates have facts, constraints do not. When checking that every variable in the head of a rule appears in the body, add the condition that it appears in a predicate in the body.
So if you have a predicate like age(X:symbol, Y:int), you can use its facts to limit the set of integers under consideration. Then, if you write:
age(X, A), A + 1 >= 18.
You'd get everyone that becomes an adult next year. Fancier solutions are also possible, for example by employing techniques from finite domain constraint solving.
Respectfully I would encourage you to consider this comment is confusing bad Prolog with all Prolog, and you are really missing out on some elegant and powerful concepts if you believe Prolog stops here.
I would love this to be an invitation for you to reevaluate modern Prolog and see what the language is really capable of.
I'll throw you right in the deep end with Prolog Definite Clause Grammars[1] and meta-interpreters[2].
There are a few things which are very special and magical to Prolog which are quite mind expanding. I hope you enjoy the resources.
But why wouldn't you use Mercury instead? No extra-logical nonsense like cuts, IO done properly with linear types, much better performance, etc. DCGs aren't exclusive to Prolog, why suffer the janky bits?
And while they're not built-in to it, Soufflé Datalog supports algebraic datatypes (so you can model difference lists), and you could preprocess a DCG into the native clause form plus a length tracking argument to prevent it from creating an infinitely sized database.
I've never worked with meta-interpreters so I can't comment on those, but I will try to watch the video you posted later.
Additionally, there is nothing stopping you from writing pure monotonic Prolog, which does not involve cuts and uses pure IO.
Circling back to DCGs, the combination of DCGs plus interpreters, which can be expressed in a handful of lines of code, allows for powerful language crafting.
While constraint solvers are not unique to Prolog, CS+DCG+MI is a killer combination I've only ever seen in Prolog that when combined allow you to solve some wicked problems rather elegantly.
That being said, thanks for the reminder about Mercury, that looks like it could come in handy on some Java-only projects.
This is DCG+CS only, still quite powerful and I have adapted it for GOAP and Hierarchical Task Networks quite successfully: https://www.metalevel.at/zurg/
Finally, I will agree with you that there is a LOT of jank Prolog, but not ALL Prolog is jank, and some Prolog is truly exquisite-- I hope you will keep an eye out for it.
Though even in that video we see a display of "jank", e.g., needing to ensure that rules don't overlap, being careful with introducing redundant choicepoints, permission errors, the trick with +, etc. in the vanilla meta-interpreter and the workarounds to get efficient tail recursion in the list-based meta-interpreter.
However, I don't think there's any way to avoid such "jank" when implementing something this powerful. The "jank" is the price to be able to do this. So fair point that this is something Prolog, and only Prolog, can do.
The fact that we were able to have this exchange was great. I appreciate your points and look forward to incorporating your work into mine!
> In this article, we study the convergence of datalog when it is interpreted over an arbitrary semiring. We consider an ordered semiring, define the semantics of a datalog program as a least fixpoint in this semiring, and study the number of steps required to reach that fixpoint, if ever. We identify algebraic properties of the semiring that correspond to certain convergence properties of datalog programs. Finally, we describe a class of ordered semirings on which one can use the semi-naïve evaluation algorithm on any datalog program.
It’s quite neat since this allows them to represent linear regression, gradient decent, shortest path (APSP) within a very similar framework as regular Datalog.
They have a whole section on the necessary condition for convergence (i.e. termination).
> For practical usage, Soufflé extends Datalog to make it Turing-equivalent through arithmetic functors. This results in the ability of the programmer to write programs that may never terminate.
I haven't found an excuse to really use it though!
I found it pretty interesting for that use case, although the learning curve isn't trivial for traditional devs.
For an easy example to consider, what would the logical program look like that described any common fractal? https://rosettacode.org/wiki/Koch_curve#Prolog shows that... it is not necessarily a win for this idea.
For the general task asked in the OP here, I would hope you could find an example in rosettacode that shows prolog gets a good implementation. Unfortunately, I get the impression some folks prefer code golf for these more so than they do "makes the problem obvious."
For fractals you’ll want to be able to recognize and generate the structures. It’s a great use case for Definite Clause Grammars (DCGs). A perfect example of this would be Triska’s Dragon Curve implementation. https://www.youtube.com/watch?v=DMdiPC1ZckI
I would still agree that you can do better than the examples I'm finding, but I am not entirely clear why/how the dragon curve is honestly any better here? The prolog, notably, does not draw the curve. Just being used to generate the sequence of characters that describes it. But... that is already trivial in normal code.
Actually drawing it will get you something like this: https://rosettacode.org/wiki/Dragon_curve#Prolog. Contrast that with the Logo version and you can see how the paradigm of the programming language can make a giant difference in how the code solution looks.
Note that I'm not an expert in any of this, I've just been reading about this kind of AI recently. I haven't actually done this myself.
Another example would be something like an Entity Component System. The moment it starts getting complex (i.e., you have fancy queries and joins), then you're actually implementing a really shitty relational programming engine, and you might as well just implement Datalog instead at that point and reap the benefits.
Other kinds of search problems are probably better tackled by constraint programming instead.
It's a golfing language that I used on codegolf.SE, so my experience is probably very different from that of someone who used logic programming for "real" coding. But I found the experience very pleasurable: the fun in codegolfing is largely from bending your mind in unusual ways to approach the problem (and its sub-problems) differently to solve it with terser code. Brachylog added to this by providing its own set of (what to me were) unusual approaches, thus making sure that the process was always fresh and weird enough to be fun.
Before Microkanren, the rite of passage for logic programming was to build a Prolog using Warren's Abstract Machine (WAM).
https://direct.mit.edu/books/monograph/4253/Warren-s-Abstrac...
Is implementing a Kanren and embedding it as suggested by the author really the recommended approach? Back in the day I used Sicstus mostly but tried to use SWI whenever possible (because I'm a FLOSS guy at heart). I'm asking because we went the opposite direction and used Prolog as the first language and called Java or C when needed (io, GUI). I'd describe the result as a "hot mess".
Random note: "Art of Prolog" and "Craft of Prolog" remain two of my favorite CS books to this day.
I'd be curious what the "state of the art" is these days and would love ve to hear from some folks using Prolog in the trenches.
Funny enough, I made the same mistake you did back in the day. Used Prolog as the "boss" that just called back to Java as needed. My professor gave me a shitty grade because the idea was to make the opposite, a Java program that queries a Prolog database to make decisions, the Prolog part itself wasn't directly supposed to make any.
I was pissed at the time since I was showing off my Prolog skills which in a Logic Programming course I expected would give me a good grade, but that professor was 100% right. The power of logic programming is tainted when you mix it with IO and expect a specific ordering to the rule applications. Cuts are a sin.
It's not that cuts themselves are a problem, they're a symptom of a larger problem, of which unrestricted IO is another. They both exist because a Prolog implementation is intimately tied to a specific search strategy. One that you, as a programmer, must learn and exploit.
And because you can use cuts and IO, the search strategy must remain what it is. It's an ouroboros. A snake eating its own tail. This enforced search strategy makes Prolog a poor declarative language (despite all the neat parlor tricks you can do with it).
Why? As we climb the abstraction ladder, we relinquish control. This is a double-edged sword. We can express problems orders of magnitude more succinctly, but we must trust the machine to arrive at the solution efficiently and with limited guidance.
For example, C might be considered low level in comparison to most languages, but it is extremely high level compared to assembly.
C compilers can generate efficient machine code precisely because certain details are abstracted away: register allocation, function inlining, loop unrolling, constant-folding, dead-code elimination, etc.
These are only possible thanks to various higher-level concepts being available (variables, constants, functions, loops, conditionals, etc.) and lower-level concepts being unavailable (e.g., unrestricted goto). You have inline assembly, but it's restricted to function bodies, and you have to tell the compiler which registers you touch, or you'd prevent it from applying many optimizations entirely.
Many of the supposedly higher-level languages (like Java, C#, etc.), aren't really higher-level than C. You can express the same things in C, just slightly more verbose. Garbage Collection? You can bolt a garbage collector to C. Generators (yield)? I can implement that with macros. Generics? If void* is too cumbersome, a template file and some include tricks is a few lines of code away. They're just a pile of admittedly nice conveniences.
A pure functional language though? That could allow us to go a level higher. It's not the pattern matching or the higher order functions, however, those are still things C can express. No, the key is the referential transparency and lack of sequencing. Referential transparency means order of execution no longer matters. And if order of execution no longer matters, then we can parallelize everything.
We don't have a good strategy for automating this in a compiler yet, but the capability is there. Large scale MapReduce is only possible because we've abstracted away loops into those higher-level operations (map & reduce) calling referentially transparent functions.
Prolog didn't relinquish enough control. We can't express certain problems without resorting to weird dances to appease the poor search algorithm, same as how I might have to contort the way I write a C program so the compiler can vectorize the code.
If we relinquish enough control to arrive at Datalog (not even Turing-complete), we can make use of all the tools available to the relational model. The sort of dynamic query planning and optimization database engines use. A human can write a better query plan than a database engine, but a human cannot write a tailored query plan every few microseconds.
In Datalog I don't have to worry much about how I write my rules. I can have them be mutually recursive, I can have multiple rules with the same pattern in the head, I can write the body in a really inefficient order. A Datalog engine is free to optimize all of that out. I can't use higher-order predicates, but I can in ASP, which also has massively more efficient search than Prolog.
Even in other Turing-complete logic programming languages, like Mercury and Curry, I have a lot more freedom in how I express the problem because they have the freedom to optimize the code in a way that allows the solution to be arrived at efficiently. Curry can guarantee a solution will be arrived at if one exists, Prolog cannot.
The extra-logical control Prolog provides (like cuts) only serves as a tool to work around the poor search algorithm it uses, one it cannot change because of the control it gives. To me it's just an evolutionary dead-end, albeit one of great historical importance.
>> We don't have a good strategy for automating this in a compiler yet, but the capability is there
And it's been "there" since the 1960s, but it's still not here. Looks pretty on paper, doesn't work on metal. Close, but no cigar.
>> They both exist because a Prolog implementation is intimately tied to a specific search strategy.
That is not right. There are different execution stategies for Prolog, other than DFS. In fact, Datalog's bottom-up evaluation with a TP-operator, is one of those: you can apply it to Polog programs just fine, except without the nice termination guarantees; but then, Church-Turing thesis.
Another execution strategy is SLG-Resolution with tabulation, a.k.a. tabling, which I mentioned in my other comment. I copy the link to SWI-Prolog's implementation here again:
https://www.swi-prolog.org/pldoc/man?section=tabling
Tablng is as old as nails in the Prolog community [1]. Besides which there is a ton of computer science knowledge you can bring to bear on the problem of avoiding non-termination, or unnecessary backtacking. If that is, indeed, the problem. Like I say, I don't understand from your comment what is your real-life, real-world, practical problem with using cuts.
>> Prolog didn't relinquish enough control. We can't express certain problems without resorting to weird dances to appease the poor search algorithm, same as how I might have to contort the way I write a C program so the compiler can vectorize the code.
I don't understand what that means. Prolog is FOL running on a digital computer. One is a computational paradigm, the other is a computational device. There is a mismatch between the two, unfortunately and inevitably, because the difference between theory and practice etc etc, and there are concessions that had to be made to be able to run one on top of the other. Messrs Kowalksi and Colmerauer (the man whose name not even French Computer Scientists can pronounce- true story) alighted on a set of choices that had the advantage of being the most practical possible, for the purpose of having a real language, that one can write real code in, to run on real computers; unlike, say, Haskell.
And you can do a lot more than just "write code". Prolog, because its interpreter is an implementation of SLD-Resolution, is not just a programming language but a sound and (refutation-) complete deductive inference system for FOL. And with recent advances in Inductive Logic Programming, it turns out it's also a sound and refutation complete inductive inference system, too.
Another couple of points:
DFS is not a poor choice of a search algorithm. It's an efficient one. You say ASP is "massively more efficient" than Prolog. It's not. ASP interpreters must first solve an NP-complete problem, which they only do thanks to powerful, special-purpose solvers. Those solvers are fast [2], but efficiency is a whole oher ball game (we don't have efficient algorithms for NP-complete problems). The NP-complete problem is that, because of ASP's bottom-up interpretation, the entire Herbrand base of a predicate must be fully ground. That's why ASP also has no functions [3]; so, no lists. The big advantage of Resolution, its One Neat Trick as an algorithm, is exactly that it doesn't have to ground the entire Herbrand base before finding a proof, if one exists. That's thanks to unification. More to the point, as Resolution proceeds, it prunes the search space of proofs, just by discarding branches starting at goals that fail unification. ASP can't do that [4,5].
See, every time anyone has tried to "fix" Prolog's not-fully-100%-declarativeness, they've just broken it.
Or, as I like to say about logic programming in general; sound, complete, efficient: choose two.
_______________
[1] OLD-Resolution with Tabulation; Tamaki and Sato, 1986 https://dl.acm.org/doi/10.5555/12069.12075
[2] And cool.
[3] Because functions turn a predicate's Herbrand base infinite, and then it takes an infinite amount of time to ground it.
[4] Well, ish. Standard, bottom-up ASP can't but there are different ways to evaluate ASP ... programs, too. For instance, you can evaluate them top-down, with unification, just like in Prolog. See sCASP (first link I could find; dig deeper):
http://platon.etsii.urjc.es/~jarias/slides/gde21-tutorial.pd...
[5] It's not just unification pruning the search space of proofs, either. It's that the cardinality of the resolution closure of a set of Horn clauses decreases monotonically until either the empty clause is constructed by resolution, or... well, infinity.
So what follows is purely anecdotal of course, but it can't be anything else really. At my university we were exposed to all the 4 major paradigms: Procedural (C), OOP (Java), Functional (Haskell), Logic (Prolog).
When I first got exposed to Prolog, I was amazed. "Wow, you can just write the rules and it figures out the solution!". That didn't last long. It was slow and clunky, I had to be careful how I wrote the rules, and debugging was an exercise in frustration. Sometimes it ran forever, sometimes it gave repeated answers, sometimes it gave all the right answers and then ran forever.
Cuts were introduced as the solution to the performance issues, and to me they were witchcraft more than they were engineering. Something you threw around at random in the hopes of making it work. I tried to go all in with it, make the whole class project as much as possible in Prolog (it was a Java/Prolog mix).
My professor actually ended up giving me a bad grade because that's not how he wanted Prolog to have been used. He actually wanted us to use it more like one might use Datalog (with good reason, but Datalog was never explicitly mentioned).
At the time I didn't get it, the whole paradigm just felt like a complete joke to me. Something researchers liked to play with but unfit for any real work. That was also the perception of the vast majority of my colleagues.
Same was true of functional programming by the way, though to a lesser extent. I (and others) could definitely see the benefits of referential transparency, higher order functions and lazy evaluation. But I'd just apply them in whatever language I was already using. Same as how if I wanted to do search, I'd just write a depth first search algorithm myself, no reason to bother with Prolog.
All examples were either trivial nonsense, ridiculous contortions of the paradigm (a window manager? really?), or "irrelevant" research (research about Prolog using Prolog to do more Prolog).
But the problem is that my perception of Prolog extended to my perception of logic programming in general. I saw them as one and the same. The "best" and "most famous" logic programming language is jank, so the whole paradigm must be jank.
Only after I was later exposed to SMT solvers did it finally "click" that different programming paradigms can be truly transformative. That they can provide truly massive productivity boosts. Z3 added a Datalog mode at some point, which was when I realized my perception of the logic paradigm was clouded.
From Z3 Datalog I moved on to Souffle Datalog and Datomic (that syntax though, ugh), where I got to experience how poor SQL truly is. I already knew it was a poor showing of the relational paradigm, but I didn't realize the relational paradigm itself was so much weaker than the real deal: logic programming.
So that convinced me logic programming had value. Real, undeniable, practical value, not "parlor tricks". But that was still "the non-Turing-complete fragment of logic programming is useful", not "logic programming is useful". Because full logic programming still meant "Prolog" to me, the slow, janky language I used in university.
But then I got to experience Mercury and Curry. Full, Turing-complete logic programming languages with massively better performance than Prolog, that don't need cuts to perform well. Mercury has its determinism modes which make debugging the behavior of rules so much easier (much as how static typing in general makes everything easier to debug).
Curry's "needed narrowing" semantics also means if there is a solution, it will find it. This is true even though Curry is also a Turing-complete logic programming language. Prolog can get stuck in a branch of the search tree that cannot lead to a solution.
Mercury and Curry are both strong evidence to me that "every time anyone has tried to fix Prolog's not-fully-100%-declarativeness, they've just broken it." is not really accurate.
Can you give me a serious example that would not be expressible in either? Another commenter mentioned meta-interpreters but while they're incredibly cool, I'd still classify them more as a great research tool than a practical one. How often do you need one?
Great, but that's aesthetics. You'd save a lot of time by being upfront about that. De gustibus non est disputandum.
I note that your aversion for Prolog comes from a course you had in -undergrad, I think? I fell in love with Prolog in my undergrad course and even undertook a substantial project in it, where I loved it even more- but I didn't really get it until my PhD where I had the time to really sit down and study, not just Prolog as a programming language, but logic programming, as a thing unto itself. I didn't even know what sources to read, and I had read all the Prolog textbooks I could find. That's not to gatekeep, or pull rank, but logic programming is a deep and old subject and one really needs guidance to get to grips with it which you just don't get in undergrad (not least because many tutors themselves aren't that deeply knowledgeable in the subject).
I note also that you seem to have been introduced to Prolog in terms of its vaunted declarative qualities: "you just write the rules". That's probably the worst lie one can tell to students and the worst possible way to introduce Prolog, because, as you found out, Prolog just doesn't work that way. For example, back in my undergrad, I only learned about the "declarative paradigm" much later on and even then I thought it was more of a gimmick, the kind of argument people reach for when they try to convince others to be excited about the same things they're excited. This kind of argument is supposed to go beyond aesthetics, but it fails to do so. For example, why is declarative programming better than procedural? It isn't. It's just a matter of taste.
The first thing I paid attention to about Prolog was "automated theorem proving", which was what blew my mind. I had just noticed the way manual theorem proving proceeds in a very mechanical manner and was thinking it should be possible to write a program to do it, when I found out someone had done it, for real, and much better than I ever could. I don't think that's aesthetics. It's a real, and distinct, capability, that you don't find e.g. in C or Haskell. How important it is, that's again a personal matter. For me, plenty. For others, not so much. De gustibus etc.
The right way to introduce Prolog is the long way around, starting with propositional logic, then FOL, then logic programming, then Resolution, and then only at the end introducing Prolog and other logic programming languages. The way Prolog is taught now, it just doesn't work and everyone leaves university without understanding a thing about it.
I can't give a "serious example" of using Mercury or Curry because I have only checked them out once or twice and don't have experience with them. I don't have anything against them, to be clear, as I don't have anything against Datalog. I prefer Prolog because it's more mature, and its implementations more feature-rich. SWI-Prolog in particular is bedecked with libraries like a swiss army knife and its maintainer is a programming super-hero. But if you like Mercury then you could possibly help with its development, which I understand has slowed down for lack of interest, which is a big shame.
On meta-interpreters, I use one all the time. The Inductive Logic Programming system that I created during my PhD is based on an inductive, second-order Prolog meta-interpreter:
https://github.com/stassa/louise
You'll find the early version of that meta-interpreter in https://github.com/stassa/louise/blob/master/src/vanilla.pl A new version, decoupled from any specific learning system, is in a private repo. Let me know if you're very very interested. A write up is here:
https://hmlr-lab.github.io/pdfs/Second_Order_SLD_ILP2024.pdf
>> Prolog can get stuck in a branch of the search tree that cannot lead to a solution.
There's more ways to execute Prolog than DFS so that you don't get stuck in loops. Obviously there'll always be infinite proof branches because Church-Turing. I'm not sure you fully appreciate that?
That might seem like an annoying limitation, but to me it is not. Most problems fit well within the bounds, and you get to reap the benefits.
>> There's more ways to execute Prolog than DFS so that you don't get stuck in loops. Obviously there'll always be infinite proof branches because Church-Turing. I'm not sure you fully appreciate that?
It doesn't have to do with Church-Turing. The issue is with DFS specifically which can get stuck in an unproductive search branch. This is mitigated by Mercury with termination checks and mode determinism, and entirely solved by Curry through an execution semantics that guarantees fair search (only way to not terminate is if there is no solution).
If you can execute Prolog in a different manner then I'm happy that's the case but I find it hard to believe that's still Prolog. How would the IO come out in the same order?
>> But if you like Mercury then you could possibly help with its development, which I understand has slowed down for lack of interest, which is a big shame.
Sadly I lack the skillset...
>> I prefer Prolog because it's more mature, and its implementations more feature-rich
My preference for the semantics of the far less popular logic programming languages likely clouds my judgements towards Prolog more than I'd like to admit.
See my link to SWI-Prolog's implementation of tabling above. Copied here again (third time) for your convenience:
Folks, really, using GitHub pages with static website generator is all you need. Your content will be nice and truly freely accessible to everyone.
Is that really a criticism?
We really wanted a model that could convincingly handle and reasonably schedule arbitrary combinations of schema change statements that are valid in Postgres. Unlike mysql postgres offers transactional schema changes. Unlike Postgres, cockroach strives to implement online schema changes in a protocol inspired by f1 [0]. Also, you want to make sure you can safely roll back (until you’ve reached the point where you know it can’t fail, then only metadata updates are allowed).
The model we came up with was to decompose all things that can possibly change into “elements” [1] and each element had a schedule of state transitions that move the element through a sequence of states from public to absent or vice versa [2]. Each state transitions has operations [3].
Anyway, you end up wanting to define rules that say that certain element states have to be entered before other if the elements are related in some way. Or perhaps some transitions should happen at the same time. To express these rules I created a little datalog-like framework I called rel [4]. This lets you embed in go a rules engine that then you can add indexes to so that you can have sufficiently efficient implementation and know that all your lookups are indexed statically. You write the rules in Go [5]. To be honest it could be more ergonomic.
The rules are written in Go but for testing and visibility they produce a datomic-inspired format [6]. There’s a lot of rules now!
The internal implementation isn’t too far off from the search implementation presented here [7]. Here’s unify [8]. The thing has some indexes and index selection for acceleration. It also has inverted indexes for set containment queries.
It was fun to make a little embedded logic language and to have had a reason to!
0: https://static.googleusercontent.com/media/research.google.c... 1: https://github.com/cockroachdb/cockroach/blob/f48b3438a296aa... 2: https://github.com/cockroachdb/cockroach/blob/f48b3438a296aa... 3: https://github.com/cockroachdb/cockroach/blob/f48b3438a296aa... 4: https://github.com/cockroachdb/cockroach/blob/f48b3438a296aa... 5: https://github.com/cockroachdb/cockroach/blob/f48b3438a296aa... 6: https://github.com/cockroachdb/cockroach/blob/master/pkg/sql... 7: https://github.com/cockroachdb/cockroach/blob/f48b3438a296aa... 8: https://github.com/cockroachdb/cockroach/blob/f48b3438a296aa...
Yeah, sounds like a real show-stopper. Prolog is not 100% declarative, which is really what every programmer wants from a programming language.
Better use a language like C# or Java, or Python, which are 0% declarative. Or try to implement datalog (only not really) so that you can't even use lists because that's what real-word programmers are looking for in a real-world programming language: 100% declarative, 0% real-world uses.
Ah well, at least the author has heard of SLD-Resolution which is more than one can say about the authors of SICP. But they haven't heard of SLG Resolution with tabulation (a.k.a. "tabling") which is a way to execute Prolog programs while preserving the Turing-completeness but without getting stuck in left-recursions. Among other things.
https://www.swi-prolog.org/pldoc/man?section=tabling
Edit:
>> Prolog also allows IO, so the order in which things get executed is critical.
I paid €7 to make this post because I'm on a boat in the middle of the Adriatic sea and my Vodafone contract is AWOL, so listen closely: no, Prolog's IO is not what makes it Turing Complete. That comes from definite logic, i.e. a fragment of the First Order Predicate Calculus (a.k.a. First Order Logic) restricted to formulae in clausal form with at most one positive literal a.k.a Horn clauses, that nevertheless retains the full expressivity of full FOL. Definite logic is semi-decidable and when evaluated by Resolution, as SLD-Resolution (restricted to definite program clauses and Horn goals), it is refutation-complete (and sound, to boot). Meaning, in summary, that any true sentence can be proved true but if a sentence is false then it cannot always be proved false, by SLD-Resolution. So far, so theoretically good.
What Prolog does which is really dangerous and makes the order of execution "critical" is that it allows the programmer to edit the program database i.e. the database of facts and rules, in other words, the program itself, programmatically, i.e from the program itself. This means that not all your program's state is known before the program runs and database operations are completed. That sucks hairy balls but it is also a very useful mechanism that requires experience and understanding of the language, its core concepts, and programming in general, to use right.
But Prolog's Turing completeness has nothing to do with IO, or database ops. That was not worth €7.