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https://github.com/fatho/logru

Log(ic) programming in Ru(st).
https://github.com/fatho/logru

hacktoberfest logic-programming rust

Last synced: 6 months ago
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Log(ic) programming in Ru(st).

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README 

          
# LogRu



**Log**ic programming in **Ru**st.



![ci badge](https://github.com/fatho/logru/actions/workflows/ci.yml/badge.svg) [![crates.io badge](https://img.shields.io/crates/v/logru)](https://crates.io/crates/logru) [![docs.rs badge](https://img.shields.io/docsrs/logru)](https://docs.rs/logru/)



## Overview



At the heart of this project is a small, efficient Rust library for solving first-order predicate

logic expressions like they can be found in e.g. Prolog. Compare to the latter, this library is much

more simplistic, though extensible.



Additionally, there is a [REPL example](examples/repl.rs) for interactively playing around with the

implementation.



Features that are implemented:

- Standard (compound) terms

- Named variables & wildcards

- DFS-based inference

- A "cut" operation for pruning the search space

- Integer arithmetic

- Extensibility through custom predicate resolvers (e.g. predicates with side effects)



## Showcase



In the REPL you can quickly get started by loading one of the provided test files with some

pre-defined facts and rules, e.g. for [Peano arithmetic](testfiles/arithmetic.lru):



```text

#===================#

# LogRu REPL v0.4.1 #

#===================#



?- :load testfiles/arithmetic.lru

Loaded!

```



We can then ask it to solve 2 + 3 (and find the correct answer 5):



```text

?- add(s(s(z)), s(s(s(z))), X).

Found solution:

  X = s(s(s(s(s(z)))))

No more solutions.

```



It is also possible to enumerate all pairs of terms that add up to five:



```text

?- add(X, Y, s(s(s(s(s(z)))))).

Found solution:

  X = s(s(s(s(s(z)))))

  Y = z

Found solution:

  X = s(s(s(s(z))))

  Y = s(z)

Found solution:

  X = s(s(s(z)))

  Y = s(s(z))

Found solution:

  X = s(s(z))

  Y = s(s(s(z)))

Found solution:

  X = s(z)

  Y = s(s(s(s(z))))

Found solution:

  X = z

  Y = s(s(s(s(s(z)))))

No more solutions.

```



While there is no standard library, using the cut operation, it is possible to build many of the

common combinators, such as `once`:



```text

?- :define once(X) :- X, !.

Defined!

```



Given a predicate producing multiple choices...



```text

?- :define foo(hello). foo(world).

Defined!

?- foo(X).

Found solution:

  X = hello

Found solution:

  X = world

No more solutions.

```



..., we can now restrict it to produce only the first choice:



```text

?- once(foo(X)).

Found solution:

  X = hello

No more solutions.

```



Other combiantors, like negation, can also be implemented using cut.



## Rust API



The core of the API doesn't work with a textual representation of terms like the REPL does, but

encodes everything as semi-opaque IDs. There are then higher-level APIs that provide naming for

those IDs.



### Core API



At the core of the solver are the `logru::SymbolStore` and `logru::RuleSet` types, which

hold all known facts and rules. A few simple rules for [Peano

arithmetic](https://en.wikipedia.org/wiki/Peano_axioms#Addition) can be defined like this:



```rust

use logru::{

    ast::{self, exists, Query, Rule},

    query_dfs,

    resolve::RuleResolver,

    search::Solution,

    SymbolStorage,

};



let mut syms = logru::SymbolStore::new();

let mut r = logru::RuleSet::new();



// Obtain IDs for the symbols we want to use in our terms.

// The order of these calls doesn't matter.

let s = syms.get_or_insert_named("s");

let z = syms.get_or_insert_named("z");



let is_natural = syms.get_or_insert_named("is_natural");

let add = syms.get_or_insert_named("add");



// Define the fact `is_natural(z)`, i.e. that zero is a natural number

r.insert(Rule::fact(is_natural, vec![z.into()]));



// Define the rule `is_natural(s(P)) :- is_natural(P)`, i.e. that

// the successor of P is a natural number if P is also a natural number.

r.insert(ast::forall(|[p]| {

    Rule::fact(is_natural, vec![ast::app(s, vec![p.into()])]).when(is_natural, vec![p.into()])

}));



// Now we define a predicate for addition that we'll call add.

// The statement `add(P, Q, R)` is true if P + Q = R.



// Define the rule `add(P, z, P) :- is_natural(P)`, i.e. that

// adding zero to P is P if P is a natural number.

// This is the base case of Peano addition.

r.insert(ast::forall(|[p]| {

    Rule::fact(add, vec![p.into(), z.into(), p.into()]).when(is_natural, vec![p.into()])

}));



// Finally, define the rule `add(P, s(Q), s(R)) :- add(P, Q, R)`,

// the recursive case of Peano addition.

r.insert(ast::forall(|[p, q, r]| {

    Rule::fact(

        add,

        vec![

            p.into(),

            ast::app(s, vec![q.into()]),

            ast::app(s, vec![r.into()]),

        ],

    )

    .when(add, vec![p.into(), q.into(), r.into()])

}));



// We can now ask the solver to prove statements within this universe, e.g. that "there exists an X

// such that X + 2 = 3". This statement is indeed true for X = 1, and indeed, the solver will provide

// this answer:



let mut r = RuleResolver::new(&r);



// Obtain an iterator that allows us to exhaustively search the solution space:

let solutions = query_dfs(

    &mut r,

    &exists(|[x]| {

        Query::single_app(

            add,

            vec![

                x.into(),

                ast::app(s, vec![ast::app(s, vec![z.into()])]),

                ast::app(s, vec![ast::app(s, vec![ast::app(s, vec![z.into()])])]),

            ],

        )

    }),

);



// Sanity check

assert_eq!(

    solutions.collect::>(),

    vec![Solution(vec![Some(ast::app(s, vec![z.into()]))])],

);

```



The solver uses a left-to-right depth-first search through the provided and derived goals. This is

efficient to implement, but requires some care in how the predicates are set up in order to avoid an

infinite recursion.



### Textual API



For an example of the textual API, see e.g. [`examples/zebra.rs`](examples/zebra.rs), solving a

variant of the famous [Zebra puzzle](https://en.wikipedia.org/wiki/Zebra_Puzzle).



The syntax is very similar to Prolog, but it is far from complete.



### Performance



A rudimentary performance comparison with SWI Prolog has been performed using an inefficient version

of the Zebra puzzle ([`testfiles/zebra-reverse.lru`](testfiles/zebra-reverse.lru)) where the clauses

of the `puzzle` rule are reversed.



For both SWI Prolog and Logru, this makes the Puzzle a lot slower to solve (not surprising since

AFAIK SWI Prolog uses the same search order).



While Logru takes about 48ms to solve the Puzzle and to conclude that there are no further solutions

on the machine at hand, Prolog takes about 13ms to find the solution and an additional 4ms to rule

out any further solutions for a total of 17ms on the same machine.



A large portion of that difference is apparently caused by the occurs check, which seems to be off

by default in Prolog. In a version of Logru compiled without occurs check, the same puzzle is solved

in ~23ms.



Although even with the occurs check enabled, SWI Prolog is only a few milliseconds slower, so there

are likely other optimizations at play, too.



```text

?- :load testfiles/zebra-reverse.lru

Loaded!

?- :time puzzle($0).

Found solution:

  $0 = list(house(yellow, norway, water, diplomat, fox), house(blue, italy, tea, physician, horse), house(red, england, milk, photographer, snails), house(white, spain, juice, violinist, dog), house(green, japan, coffee, painter, zebra))

No more solutions.

Took 0.0603s

```



```text

?- consult('testfiles/zebra-reverse.lru').

true.



?- time(puzzle(Houses)).

% 86,673 inferences, 0.013 CPU in 0.013 seconds (100% CPU, 6567116 Lips)

Houses = list(house(yellow, norway, water, diplomat, fox), house(blue, italy, tea, physician, horse), house(red, england, milk, photographer, snails), house(white, spain, juice, violinist, dog), house(green, japan, coffee, painter, zebra)) ;

% 22,610 inferences, 0.004 CPU in 0.004 seconds (100% CPU, 6459533 Lips)

false.

```



## Future Plans



Without committing to any sort of timeline, additional features that are worth experimenting with

are:

- More natural support for conjunctions and disjunctions (`,` and `;` respectively in Prolog).

- Some sort of standard library.

- Recursion and memory limits.

- A profiling mode that counts some interesting facts and figures about the solver (e.g. number of

  steps taken, number of instantiated rules, peak memory usage).

- Making things even faster by e.g. optimising the occurs check.

- Auto-completion in the REPL.



## License



Licensed under either of



 * Apache License, Version 2.0

   ([LICENSE-APACHE](LICENSE-APACHE) or http://www.apache.org/licenses/LICENSE-2.0)

 * MIT license

   ([LICENSE-MIT](LICENSE-MIT) or http://opensource.org/licenses/MIT)



at your option.



## Contribution



Unless you explicitly state otherwise, any contribution intentionally submitted

for inclusion in the work by you, as defined in the Apache-2.0 license, shall be

dual licensed as above, without any additional terms or conditions.