# Crate logru[−][src]

## Expand description

## Logic programming in Rust

Logru is an embeddable and fast solver for a subset of Prolog. At the core of the solver is the Universe type which holds all known facts and rules.

The Universe type represents all identifiers using IDs, there is no textual representation. For a more Prolog-like syntax, and an example on how to use the Universe type to build higher-level abstractions, have a look at the textual module.

## Example

As an example, let’s define a few predicates for solving Peano arithmetic expressions. In Prolog, these could be written like this:

```
is_natural(z).
is_natural(s(P)) :- is_natural(P).
add(P, z, P) :- is_natural(P).
add(P, s(Q), s(R)) :- add(P, Q, R).
```

The `is_natural`

predicate defines that zero (z) is a natural number, and each successor (s) of
a natural number is also a natural number.

Addition is also defined recursively. An expression `add(P, Q, R)`

should be read as the
statement `P + Q = R`

. The first case expresses that `P + 0 = P`

for all natural numbers P,
while the second case expresses that `P + s(Q) = s(R)`

where `P + Q = R`

(i.e. we add one on
both sides).

Using the Universe type, we can encode these rules as follows:

```
use logru::ast::{self, Rule};
let mut u = logru::Universe::new();
// Obtain IDs for t he symbols we want to use in our terms.
// The order of these calls doesn't matter.
let s = u.alloc_symbol();
let z = u.alloc_symbol();
let is_natural = u.alloc_symbol();
let add = u.alloc_symbol();
// is_natural(z).
u.add_rule(Rule::fact(is_natural, vec![z.into()]));
// is_natural(s(P)) :- is_natural(P).
u.add_rule(ast::forall(|[p]| {
Rule::fact(is_natural, vec![ast::app(s, vec![p.into()])])
.when(is_natural, vec![p.into()])
}));
// add(P, z, P) :- is_natural(P).
u.add_rule(ast::forall(|[p]| {
Rule::fact(add, vec![p.into(), z.into(), p.into()])
.when(is_natural, vec![p.into()])
}));
// add(P, s(Q), s(R)) :- add(P, Q, R).
u.add_rule(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 then execute queries against this universe, e.g. having the solver compute the solution
for `X + 2 = 3`

. In our relational interpretation, this boils down to proving the statement
“there exists an X such that `add(X, s(s(z)), s(s(s(z))))`

holds”.

```
let query = ast::exists(|[x]| {
ast::Query::new(
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()])])]),
],
)
});
// Obtain an iterator that allows us to exhaustively search the solution space:
let solutions = logru::query_dfs(&u, &query);
// Sanity check that there is only one solution, and it is the expected one
assert_eq!(
solutions.collect::<Vec<_>>(),
vec![vec![Some(ast::app(s, vec![z.into()]))],]
);
```

Logru provides the query_dfs solver for proving such statements. It performs a left-to-right depth first search through the solution space. This means that it processes goals (both in the original query and in matching rules) from left to right, and eagerly recurses into the first available goal until it is fully resolved.

To my knowledge, this strategy is also used by SWI Prolog. It is efficient to implement, but it requires some care in how the predicates are set up in order to avoid infinite recursion.

While not provided by Logru itself, it is possible to build custom solvers using different search strategies on top of the universe abstraction.

## Re-exports

## Modules

An abstract syntax tree for logic terms

A DFS solver for queries

Arena allocation for terms

A Prolog-like syntax

Universe