### Example SPARQL Query with SERVICE Clause

Source: https://docs.rs/sparopt

This example shows a SPARQL query that includes a SERVICE clause pointing to a non-existent endpoint. The optimizer might rewrite this to an empty query.

```sparql
SELECT * WHERE { SERVICE <http://example.com/not-found> {} }
```

--------------------------------

### Example of SPARQL Query Rewriting

Source: https://docs.rs/sparopt/latest/sparopt/index.html

Demonstrates how sparopt might rewrite a query containing a non-existent SERVICE endpoint. The optimizer can simplify such queries by removing the problematic SERVICE clause.

```sparql
SELECT * WHERE { SERVICE <http://example.com/not-found> {} }
```

```sparql
SELECT * WHERE {}
```

--------------------------------

### Parsing Literals from Strings

Source: https://docs.rs/sparopt/latest/sparopt/algebra/struct.Literal.html

Demonstrates how to parse different types of literals (simple, language-tagged, typed) from their NTriples serialization using `FromStr`. Includes examples for escaped characters, language tags, and various XSD types.

```rust
use oxrdf::vocab::xsd;
use oxrdf::{Literal, NamedNode};
use std::str::FromStr;

assert_eq!(
    Literal::from_str("\"ex\\n\"")?,
    Literal::new_simple_literal("ex\n")
);
assert_eq!(
    Literal::from_str("\"ex\"@en")?,
    Literal::new_language_tagged_literal("ex", "en")?
);
assert_eq!(
    Literal::from_str("\"2020\"^^<http://www.w3.org/2001/XMLSchema#gYear>")?,
    Literal::new_typed_literal(
        "2020",
        NamedNode::new("http://www.w3.org/2001/XMLSchema#gYear")?
    )
);
assert_eq!(
    Literal::from_str("true")?,
    Literal::new_typed_literal("true", xsd::BOOLEAN)
);
assert_eq!(
    Literal::from_str("+122")?,
    Literal::new_typed_literal("+122", xsd::INTEGER)
);
assert_eq!(
    Literal::from_str("-122.23")?,
    Literal::new_typed_literal("-122.23", xsd::DECIMAL)
);
assert_eq!(
    Literal::from_str("-122e+1")?,
    Literal::new_typed_literal("-122e+1", xsd::DOUBLE)
);
```

--------------------------------

### Convert NamedNode to NamedNodePattern

Source: https://docs.rs/sparopt/latest/sparopt/algebra/enum.NamedNodePattern.html

Demonstrates how to convert a NamedNode into a NamedNodePattern using the `From` trait. This is useful when constructing patterns that start as specific IRIs.

```rust
fn from(node: NamedNode) -> NamedNodePattern
```

--------------------------------

### Estimate Path Size for Property Path Expressions

Source: https://docs.rs/sparopt/latest/src/sparopt/optimizer.rs.html

Estimates the size of a property path expression, handling different types of path constructs like sequences, alternatives, and repetitions. It considers whether the start and end of the path are bound.

```rust
fn estimate_path_size(start_bound: bool, path: &PropertyPathExpression, end_bound: bool) -> usize {
    match path {
        PropertyPathExpression::NamedNode(_) => {
            estimate_triple_pattern_size(start_bound, true, end_bound)
        }
        PropertyPathExpression::Reverse(p) => estimate_path_size(end_bound, p, start_bound),
        PropertyPathExpression::Sequence(a, b) => {
            // We do a for loop join in the best direction
            min(
                estimate_path_size(start_bound, a, false)
                    .saturating_mul(estimate_path_size(true, b, end_bound)),
                estimate_path_size(start_bound, a, true)
                    .saturating_mul(estimate_path_size(false, b, end_bound)),
            )
        }
        PropertyPathExpression::Alternative(a, b) => estimate_path_size(start_bound, a, end_bound)
            .saturating_add(estimate_path_size(start_bound, b, end_bound)),
        PropertyPathExpression::ZeroOrMore(p) => {
            if start_bound && end_bound {
                1
            } else if start_bound || end_bound {
                estimate_path_size(start_bound, p, end_bound).saturating_mul(1000)
            } else {
                1_000_000_000
            }
        }
        PropertyPathExpression::OneOrMore(p) => {
            if start_bound && end_bound {
                1
            } else {
                estimate_path_size(start_bound, p, end_bound).saturating_mul(1000)
            }
        }
        PropertyPathExpression::ZeroOrOne(p) => {
            if start_bound && end_bound {
                1
            } else if start_bound || end_bound {
                estimate_path_size(start_bound, p, end_bound)
            } else {
                1_000_000_000
            }
        }
        PropertyPathExpression::NegatedPropertySet(_) => {
            estimate_triple_pattern_size(start_bound, false, end_bound)
        }
    }
}
```

--------------------------------

### Get NamedNode as String Slice

Source: https://docs.rs/sparopt/latest/sparopt/algebra/struct.NamedNode.html

Provides a string slice view of the IRI contained within the NamedNode.

```rust
pub fn as_str(&self) -> &str
```

--------------------------------

### Variable Creation and Formatting

Source: https://docs.rs/sparopt/latest/sparopt/algebra/struct.Variable.html

Demonstrates how to create a Variable and format it into a SPARQL-compatible string representation.

```APIDOC
## Variable Struct

### Description
A SPARQL query owned variable.

### Usage Example
```rust
use oxrdf::Variable;

// Create a new variable named "foo"
let var = Variable::new("foo").expect("Invalid variable name");

// Format the variable as a SPARQL string
assert_eq!("?foo", var.to_string());
```

### Methods

#### `new(name: impl Into<String>) -> Result<Variable, VariableNameParseError>`
Creates a variable name from a unique identifier. The variable identifier must be valid according to the SPARQL grammar.

#### `new_unchecked(name: impl Into<String>) -> Variable`
Creates a variable name from a unique identifier without validation. It is the caller’s responsibility to ensure that `id` is a valid blank node identifier according to the SPARQL grammar. `Variable::new()` is a safe version of this constructor and should be used for untrusted data.

#### `as_str(&self) -> &str`
Returns the variable name as a string slice.

#### `into_string(self) -> String`
Consumes the `Variable` and returns its name as an owned `String`.

#### `as_ref(&self) -> VariableRef<'_>`
Returns a reference to the variable name.

```

--------------------------------

### impl<T> Any for T

Source: https://docs.rs/sparopt/latest/sparopt/algebra/enum.Expression.html

Provides the `type_id` method to get the unique identifier of a type.

```APIDOC
## fn type_id(&self) -> TypeId

### Description
Gets the `TypeId` of `self`.

### Method
fn

### Parameters
None

### Response
#### Success Response
- **TypeId**: The unique identifier of the type.
```

--------------------------------

### type_id

Source: https://docs.rs/sparopt/latest/sparopt/algebra/enum.Function.html

Gets the TypeId of an object. This is a fundamental method for runtime type identification.

```APIDOC
## fn type_id(&self) -> TypeId

### Description
Gets the `TypeId` of `self`.

### Signature
`fn type_id(&self) -> TypeId`
```

--------------------------------

### Create and Format SPARQL Variable

Source: https://docs.rs/sparopt/latest/sparopt/algebra/struct.Variable.html

Demonstrates creating a Variable from a string and converting it to its SPARQL-compatible string representation. Requires the oxrdf crate.

```rust
use oxrdf::{Variable, VariableNameParseError};

assert_eq!("?foo", Variable::new("foo")?.to_string());
```

--------------------------------

### NamedNode Min Value

Source: https://docs.rs/sparopt/latest/sparopt/algebra/struct.NamedNode.html

Provides a method to get the minimum of two NamedNode values.

```rust
fn min(self, other: Self) -> Self
where Self: Sized,
```

--------------------------------

### impl<T> CloneToUninit for T

Source: https://docs.rs/sparopt/latest/sparopt/algebra/enum.Expression.html

Provides an experimental, nightly-only method for cloning data to an uninitialized memory location.

```APIDOC
## unsafe fn clone_to_uninit(&self, dest: *mut u8)

### Description
🔬This is a nightly-only experimental API. (`clone_to_uninit`)
Performs copy-assignment from `self` to `dest`.

### Method
unsafe fn

### Parameters
- **dest** (*mut u8) - Required - A pointer to the destination memory location.

### Response
None
```

--------------------------------

### RDF Literal String Formatting

Source: https://docs.rs/sparopt/latest/sparopt/algebra/struct.Literal.html

Demonstrates how to format RDF literals into N-Triples, Turtle, and SPARQL compatible strings using different constructors.

```rust
use oxrdf::Literal;
use oxrdf::vocab::xsd;

assert_eq!(
    "\"foo\nbar\"",
    Literal::new_simple_literal("foo\nbar").to_string()
);

assert_eq!(
    r#"\"1999-01-01\"^^<http://www.w3.org/2001/XMLSchema#date>"#,
    Literal::new_typed_literal("1999-01-01", xsd::DATE).to_string()
);

assert_eq!(
    r#"\"foo\"@en"#,
    Literal::new_language_tagged_literal("foo", "en")?.to_string()
);
```

--------------------------------

### NamedNode Max Value

Source: https://docs.rs/sparopt/latest/sparopt/algebra/struct.NamedNode.html

Provides a method to get the maximum of two NamedNode values.

```rust
fn max(self, other: Self) -> Self
where Self: Sized,
```

--------------------------------

### Expression Construction and Conversion

Source: https://docs.rs/sparopt/latest/src/sparopt/algebra.rs.html

Demonstrates the conversion of various expression types into their canonical forms, including logical operations, comparisons, arithmetic, and function calls. This is part of the `From<Expression>` implementation for `Expression`.

```rust
Expression::And(inner) => inner
                .iter()
                .map(Into::into)
                .reduce(|a, b| Self::And(Box::new(a), Box::new(b)))
                .unwrap_or_else(|| Literal::from(true).into()),
            Expression::Equal(left, right) => Self::Equal(
                Box::new(left.as_ref().into()),
                Box::new(right.as_ref().into()),
            ),
            Expression::SameTerm(left, right) => Self::SameTerm(
                Box::new(left.as_ref().into()),
                Box::new(right.as_ref().into()),
            ),
            Expression::Greater(left, right) => Self::Greater(
                Box::new(left.as_ref().into()),
                Box::new(right.as_ref().into()),
            ),
            Expression::GreaterOrEqual(left, right) => Self::GreaterOrEqual(
                Box::new(left.as_ref().into()),
                Box::new(right.as_ref().into()),
            ),
            Expression::Less(left, right) => Self::Less(
                Box::new(left.as_ref().into()),
                Box::new(right.as_ref().into()),
            ),
            Expression::LessOrEqual(left, right) => Self::LessOrEqual(
                Box::new(left.as_ref().into()),
                Box::new(right.as_ref().into()),
            ),
            Expression::Add(left, right) => Self::Add(
                Box::new(left.as_ref().into()),
                Box::new(right.as_ref().into()),
            ),
            Expression::Subtract(left, right) => Self::Subtract(
                Box::new(left.as_ref().into()),
                Box::new(right.as_ref().into()),
            ),
            Expression::Multiply(left, right) => Self::Multiply(
                Box::new(left.as_ref().into()),
                Box::new(right.as_ref().into()),
            ),
            Expression::Divide(left, right) => Self::Divide(
                Box::new(left.as_ref().into()),
                Box::new(right.as_ref().into()),
            ),
            Expression::UnaryPlus(inner) => Self::UnaryPlus(Box::new(inner.as_ref().into())),
            Expression::UnaryMinus(inner) => Self::UnaryMinus(Box::new(inner.as_ref().into())),
            Expression::Not(inner) => Self::Not(Box::new(inner.as_ref().into())),
            Expression::Exists(inner) => Self::Exists(Box::new(inner.as_ref().into())),
            Expression::Bound(variable) => Self::Bound(variable.clone()),
            Expression::If(cond, yes, no) => Self::If(
                Box::new(cond.as_ref().into()),
                Box::new(yes.as_ref().into()),
                Box::new(no.as_ref().into()),
            ),
            Expression::Coalesce(inner) => Self::Coalesce(inner.iter().map(Into::into).collect()),
            Expression::FunctionCall(name, args) => {
                Self::FunctionCall(name.clone(), args.iter().map(Into::into).collect())
            }
        }
    }
}

```

--------------------------------

### Get NamedNodeRef from NamedNode

Source: https://docs.rs/sparopt/latest/sparopt/algebra/struct.NamedNode.html

Obtains a reference to the NamedNode, allowing borrowing without consuming the original.

```rust
pub fn as_ref(&self) -> NamedNodeRef<'_>
```

--------------------------------

### Literal Construction

Source: https://docs.rs/sparopt/latest/sparopt/algebra/struct.Literal.html

Demonstrates how to construct different types of RDF literals: simple, typed, and language-tagged.

```APIDOC
## Literal Construction

### Description

This section details the methods for creating RDF literals.

### Methods

#### `new_simple_literal(value: impl Into<String>) -> Literal`
Builds an RDF simple literal.

#### `new_typed_literal(value: impl Into<String>, datatype: impl Into<NamedNode>) -> Literal`
Builds an RDF literal with a datatype.

#### `new_language_tagged_literal(value: impl Into<String>, language: impl Into<String>) -> Result<Literal, LanguageTagParseError>`
Builds an RDF language-tagged string. Returns an error if the language tag is invalid.

#### `new_language_tagged_literal_unchecked(value: impl Into<String>, language: impl Into<String>) -> Literal`
Builds an RDF language-tagged string without validation. The caller must ensure the language tag is valid BCP47 and lowercase.

#### `new_directional_language_tagged_literal(value: impl Into<String>, language: impl Into<String>, direction: impl Into<BaseDirection>) -> Result<Literal, LanguageTagParseError>`
(Available on `rdf-12` feature only) Builds an RDF directional language-tagged string. Returns an error if the language tag is invalid.

#### `new_directional_language_tagged_literal_unchecked(value: impl Into<String>, language: impl Into<String>, direction: impl Into<BaseDirection>) -> Literal`
(Available on `rdf-12` feature only) Builds an RDF directional language-tagged string without validation. The caller must ensure the language tag is valid BCP47 and lowercase.
```

--------------------------------

### Transform AlGraphPattern::Slice

Source: https://docs.rs/sparopt/latest/src/sparopt/algebra.rs.html

Converts a Slice graph pattern into its internal representation, preserving start and length.

```rust
AlGraphPattern::Slice {
                inner,
                start,
                length,
            } => Self::Slice {
                inner: Box::new(Self::from_sparql_algebra(inner, graph_name, blank_nodes)),
                start: *start,
                length: *length,
            }
```

--------------------------------

### clone_to_uninit

Source: https://docs.rs/sparopt/latest/sparopt/algebra/enum.Function.html

Performs copy-assignment from self to a destination pointer. This is a nightly-only experimental API.

```APIDOC
## unsafe fn clone_to_uninit(&self, dest: *mut u8)

### Description
🔬This is a nightly-only experimental API. (`clone_to_uninit`)
Performs copy-assignment from `self` to `dest`.

### Signature
`unsafe fn clone_to_uninit(&self, dest: *mut u8)`
```

--------------------------------

### Create Slice Operation

Source: https://docs.rs/sparopt/latest/src/sparopt/algebra.rs.html

Translates a Slice graph pattern, which limits the results to a specific range (start and length).

```rust
GraphPattern::Slice {
                inner,
                start,
                length,
            } => Self::Slice {
                inner: Box::new(inner.as_ref().into()),
                start: *start,
                length: *length,
            }
```

--------------------------------

### Convert AlGraphPattern to GraphPattern (Default)

Source: https://docs.rs/sparopt/latest/src/sparopt/algebra.rs.html

Provides a default conversion from AlGraphPattern to GraphPattern using `Self::from_sparql_algebra` with no graph name and an empty HashMap for blank nodes.

```rust
impl From<&AlGraphPattern> for GraphPattern {
    fn from(pattern: &AlGraphPattern) -> Self {
        Self::from_sparql_algebra(pattern, None, &mut HashMap::new())
    }
}
```

--------------------------------

### Slice Operation

Source: https://docs.rs/sparopt/latest/src/sparopt/algebra.rs.html

Constructs a Slice operation. Returns the inner operation if start is 0 and length is None, or an empty operation if the inner operation is empty.

```rust
pub fn slice(inner: Self, start: usize, length: Option<usize>) -> Self {
        if inner.is_empty() {
            return Self::empty();
        }
        if start == 0 && length.is_none() {
            return inner;
        }
        Self::Slice {
            inner: Box::new(inner),
            start,
            length,
        }
    }
```

--------------------------------

### VariableTypes Struct Definition

Source: https://docs.rs/sparopt/latest/src/sparopt/type_inference.rs.html

Defines the `VariableTypes` struct, which holds a map of variables to their inferred types. Provides methods for getting, iterating, intersecting, and unioning type sets.

```rust
#[derive(Default, Clone, Debug)]
pub struct VariableTypes {
    inner: HashMap<Variable, VariableType>,
}

impl VariableTypes {
    pub fn get(&self, variable: &Variable) -> VariableType {
        self.inner
            .get(variable)
            .copied()
            .unwrap_or(VariableType::UNDEF)
    }

    pub fn iter(&self) -> impl Iterator<Item = (&Variable, &VariableType)> {
        self.inner.iter()
    }

    pub fn intersect_with(&mut self, other: Self) {
        for (v, t) in other.inner {
            self.intersect_variable_with(v, t);
        }
    }

    pub fn union_with(&mut self, other: Self) {
        for (v, t) in &mut self.inner {
            if other.get(v).undef {
                t.undef = true; // Might be undefined
            }
        }
        for (v, mut t) in other.inner {
            self.inner
                .entry(v)
                .and_modify(|ex| *ex = *ex | t)
                .or_insert({
                    t.undef = true;
                    t
                });
        }
    }

    fn intersect_variable_with(&mut self, variable: Variable, t: VariableType) {
        let t = self.get(&variable) & t;
        if t != VariableType::UNDEF {
            self.inner.insert(variable, t);
        }
    }
}
```

--------------------------------

### Converting SPARQL Bgp to Graph Patterns

Source: https://docs.rs/sparopt/latest/src/sparopt/algebra.rs.html

Transforms a SPARQL Basic Graph Pattern (BGP) into a sequence of QuadPatterns, joined by a default Join algorithm. If the BGP is empty, it returns an empty singleton or a Graph pattern if a graph name is provided.

```rust
AlGraphPattern::Bgp { patterns } => patterns
    .iter()
    .map(|p| {
        let (subject, predicate, object) =
            Self::triple_pattern_from_algebra(p, blank_nodes);
        Self::QuadPattern {
            subject,
            predicate,
            object,
            graph_name: graph_name.cloned(),
        }
    })
    .reduce(|a, b| Self::Join {
        left: Box::new(a),
        right: Box::new(b),
        algorithm: JoinAlgorithm::default(),
    })
    .unwrap_or_else(|| {
        if let Some(graph_name) = graph_name {
            Self::Graph {
                graph_name: graph_name.clone(),
            }
        } else {
            Self::empty_singleton()
        }
    })
```

--------------------------------

### NamedNode String Representation

Source: https://docs.rs/sparopt/latest/sparopt/algebra/struct.NamedNode.html

Demonstrates how NamedNode's default string formatter produces N-Triples, Turtle, and SPARQL compatible output.

```rust
use oxrdf::NamedNode;

assert_eq!(
    "<http://example.com/foo>",
    NamedNode::new("http://example.com/foo")?.to_string()
);
```

--------------------------------

### try_from

Source: https://docs.rs/sparopt/latest/sparopt/algebra/enum.Function.html

Attempts to perform a conversion from one type to another, returning a `Result`.

```APIDOC
## fn try_from(value: U) -> Result<T, <T as TryFrom<U>>::Error>

### Description
Performs the conversion.

### Signature
`fn try_from(value: U) -> Result<T, <T as TryFrom<U>>::Error>`
```

--------------------------------

### Expression Conversions (From)

Source: https://docs.rs/sparopt/latest/sparopt/algebra/enum.Expression.html

Details the various ways an Expression can be created from other types.

```APIDOC
## From<&Expression> for Expression

### Description
Converts an Expression reference to an owned Expression.

### Method
`from(expression: &Expression) -> Self`

## From<GroundTerm> for Expression

### Description
Converts a GroundTerm into an Expression.

### Method
`from(value: GroundTerm) -> Self`

## From<GroundTermPattern> for Expression

### Description
Converts a GroundTermPattern into an Expression.

### Method
`from(value: GroundTermPattern) -> Self`

## From<Literal> for Expression

### Description
Converts a Literal into an Expression.

### Method
`from(value: Literal) -> Self`

## From<NamedNode> for Expression

### Description
Converts a NamedNode into an Expression.

### Method
`from(value: NamedNode) -> Self`

## From<NamedNodePattern> for Expression

### Description
Converts a NamedNodePattern into an Expression.

### Method
`from(value: NamedNodePattern) -> Self`

## From<Variable> for Expression

### Description
Converts a Variable into an Expression.

### Method
`from(value: Variable) -> Self`

## From<bool> for Expression

### Description
Converts a boolean value into an Expression.

### Method
`from(value: bool) -> Self`
```

--------------------------------

### Build and Validate RDF IRI

Source: https://docs.rs/sparopt/latest/sparopt/algebra/struct.NamedNode.html

Constructs a valid RDF IRI using the `new` function. It returns a Result, indicating potential parsing errors.

```rust
pub fn new(iri: impl Into<String>) -> Result<NamedNode, IriParseError>
```

--------------------------------

### Create Empty Singleton GraphPattern

Source: https://docs.rs/sparopt/latest/src/sparopt/algebra.rs.html

Creates a GraphPattern representing an empty singleton, which is a Values pattern with no variables but one empty binding.

```rust
pub fn empty_singleton() -> Self {
    Self::Values {
        variables: Vec::new(),
        bindings: vec![Vec::new()],
    }
}
```

--------------------------------

### Join Algorithm Enum

Source: https://docs.rs/sparopt/latest/src/sparopt/algebra.rs.html

Defines the HashBuildLeftProbeRight join algorithm. Used in GraphPattern::Join.

```rust
pub enum JoinAlgorithm {
    HashBuildLeftProbeRight { keys: Vec<Variable> },
}

impl Default for JoinAlgorithm {
    fn default() -> Self {
        Self::HashBuildLeftProbeRight {
            keys: Vec::default(),
        }
    }
}
```

--------------------------------

### from

Source: https://docs.rs/sparopt/latest/sparopt/algebra/enum.Function.html

Creates a new instance of a type from a given value. This is a fundamental conversion trait.

```APIDOC
## fn from(t: T) -> T

### Description
Returns the argument unchanged.

### Signature
`fn from(t: T) -> T`
```

--------------------------------

### TryFrom<TermPattern> for GroundTermPattern Conversion

Source: https://docs.rs/sparopt/latest/sparopt/algebra/enum.GroundTermPattern.html

Attempts to convert a TermPattern into a GroundTermPattern. This conversion might fail, returning an error.

```rust
fn try_from( pattern: TermPattern, ) -> Result<GroundTermPattern, <GroundTermPattern as TryFrom<TermPattern>>::Error>
```

--------------------------------

### GraphPattern Methods

Source: https://docs.rs/sparopt/latest/sparopt/algebra/enum.GraphPattern.html

Provides documentation for various methods of the GraphPattern enum, allowing users to construct and manipulate SPARQL graph patterns programmatically.

```APIDOC
## GraphPattern Methods

### `empty()`

Creates an empty graph pattern.

### `empty_singleton()`

Creates an empty singleton graph pattern.

### `is_empty_singleton()`

Checks if the graph pattern is an empty singleton.

### `join(left: GraphPattern, right: GraphPattern, algorithm: JoinAlgorithm)`

Joins two graph patterns using a specified algorithm.

### `lateral(left: GraphPattern, right: GraphPattern)`

Performs a lateral join between two graph patterns. Available on `crate feature 'sep-0006'` only.

### `left_join(left: GraphPattern, right: GraphPattern, expression: Expression, algorithm: LeftJoinAlgorithm)`

Performs a left join between two graph patterns with a specified expression and algorithm.

### `minus(left: GraphPattern, right: GraphPattern, algorithm: MinusAlgorithm)`

Performs a minus operation between two graph patterns using a specified algorithm.

### `union(left: GraphPattern, right: GraphPattern)`

Performs a union operation between two graph patterns.

### `union_all(args: impl IntoIterator<Item = GraphPattern>)`

Performs a union operation on an iterator of graph patterns.

### `filter(inner: GraphPattern, expression: Expression)`

Applies a filter expression to a graph pattern.

### `extend(inner: GraphPattern, variable: Variable, expression: Expression)`

Extends a graph pattern by adding a new variable bound to an expression.

### `values(variables: Vec<Variable>, bindings: Vec<Vec<Option<GroundTerm>>>)`

Creates a graph pattern from a list of variables and bindings.

### `order_by(inner: GraphPattern, expression: Vec<OrderExpression>)`

Orders the results of a graph pattern based on a list of expressions.

### `project(inner: GraphPattern, variables: Vec<Variable>)`

Projects a graph pattern to include only the specified variables.

### `distinct(inner: GraphPattern)`

Removes duplicate solutions from a graph pattern.

### `reduced(inner: GraphPattern)`

Reduces the solutions of a graph pattern.

### `slice(inner: GraphPattern, start: usize, length: Option<usize>)`

Slices the results of a graph pattern, returning a subset of solutions.

### `group(inner: GraphPattern, variables: Vec<Variable>, aggregates: Vec<(Variable, AggregateExpression)>)`

Groups the results of a graph pattern by specified variables and applies aggregate functions.

### `service(inner: GraphPattern, name: NamedNodePattern, silent: bool)`

Applies a SERVICE operation to a graph pattern.

### `lookup_used_variables<'a>(self: &'a GraphPattern, callback: &mut impl FnMut(&'a Variable))`

Looks up and processes all used variables in a graph pattern via a callback function.
```

--------------------------------

### Optimize Graph Pattern

Source: https://docs.rs/sparopt/latest/src/sparopt/optimizer.rs.html

The main entry point for optimizing a graph pattern. It orchestrates normalization, join reordering, and filter pushing.

```rust
pub fn optimize_graph_pattern(pattern: GraphPattern) -> GraphPattern {
        let pattern = Self::normalize_pattern(pattern, &VariableTypes::default());
        let pattern = Self::reorder_joins(pattern, &VariableTypes::default());
        Self::push_filters(pattern, Vec::new(), &VariableTypes::default())
    }
```

--------------------------------

### Create Empty GraphPattern

Source: https://docs.rs/sparopt/latest/src/sparopt/algebra.rs.html

Provides a method to create an empty GraphPattern, represented as a Values pattern with no variables and no bindings.

```rust
pub fn empty() -> Self {
    Self::Values {
        variables: Vec::new(),
        bindings: Vec::new(),
    }
}
```

--------------------------------

### Expression Equality and Hashing

Source: https://docs.rs/sparopt/latest/sparopt/algebra/enum.Expression.html

Covers the equality comparison and hashing implementations for the Expression type.

```APIDOC
## PartialEq for Expression

### Description
Implements partial equality comparison for Expression.

### Methods
- `eq(&self, other: &Expression) -> bool`: Tests for equality.
- `ne(&self, other: &Rhs) -> bool`: Tests for inequality.

## Hash for Expression

### Description
Implements hashing for the Expression type.

### Methods
- `hash<__H: Hasher>(&self, state: &mut __H)`: Feeds this value into the given `Hasher`.
- `hash_slice<H>(data: &[Self], state: &mut H)`: Feeds a slice of this type into the given `Hasher`.
```

--------------------------------

### into

Source: https://docs.rs/sparopt/latest/sparopt/algebra/enum.Function.html

Converts a value into another type by calling the corresponding `From` implementation.

```APIDOC
## fn into(self) -> U

### Description
Calls `U::from(self)`.
That is, this conversion is whatever the implementation of `From<T> for U` chooses to do.

### Signature
`fn into(self) -> U`
```

--------------------------------

### Service Operation

Source: https://docs.rs/sparopt/latest/src/sparopt/algebra.rs.html

Constructs a Service operation, which executes a SPARQL service.

```rust
pub fn service(inner: Self, name: NamedNodePattern, silent: bool) -> Self {
        Self::Service {
            inner: Box::new(inner),
            name,
            silent,
        }
    }
```

--------------------------------

### Create Project Operation

Source: https://docs.rs/sparopt/latest/src/sparopt/algebra.rs.html

Translates a Project graph pattern, which restricts the variables projected from the inner pattern.

```rust
GraphPattern::Project { inner, variables } => Self::Project {
                inner: Box::new(inner.as_ref().into()),
                variables: variables.clone(),
            }
```

--------------------------------

### Parse SPARQL Variable from String

Source: https://docs.rs/sparopt/latest/sparopt/algebra/struct.Variable.html

Shows how to parse a string into a Variable using the FromStr trait. It validates the input against SPARQL grammar. Requires the oxrdf crate.

```rust
use oxrdf::Variable;
use std::str::FromStr;

assert_eq!(Variable::from_str("$foo")?, Variable::new("foo")?);
```

--------------------------------

### Check Suitability for For Loop Join

Source: https://docs.rs/sparopt/latest/src/sparopt/optimizer.rs.html

Determines if a given graph pattern is suitable for a for-loop join optimization. This is a placeholder function with a TODO comment, indicating further refinement is needed.

```rust
fn is_fit_for_for_loop_join(
    pattern: &GraphPattern,
    global_input_types: &VariableTypes,
    entry_types: &VariableTypes,
) -> bool {
    // TODO: think more about it
    match pattern {
        GraphPattern::Values { .. }
        | GraphPattern::QuadPattern { .. }
        | GraphPattern::Path { .. }

```

--------------------------------

### NamedNode::as_str

Source: https://docs.rs/sparopt/latest/sparopt/algebra/struct.NamedNode.html

Returns a string slice view of the IRI.

```APIDOC
## NamedNode::as_str

### Description
Returns a string slice view of the IRI contained within the `NamedNode`.

### Signature
`pub fn as_str(&self) -> &str`

### Returns
A string slice (`&str`) representing the IRI.
```

--------------------------------

### Convert GraphPattern to AlGraphPattern (QuadPattern)

Source: https://docs.rs/sparopt/latest/src/sparopt/algebra.rs.html

Converts a GraphPattern::QuadPattern into an AlGraphPattern::Bgp or AlGraphPattern::Graph. If a graph name is present, it wraps the Bgp in a Graph pattern.

```rust
impl From<&GraphPattern> for AlGraphPattern {
    fn from(pattern: &GraphPattern) -> Self {
        match pattern {
            GraphPattern::QuadPattern {
                subject,
                predicate,
                object,
                graph_name,
            } => {
                let pattern = Self::Bgp {
                    patterns: vec![TriplePattern {
                        subject: subject.clone().into(),
                        predicate: predicate.clone(),
                        object: object.clone().into(),
                    }],
                };
                if let Some(graph_name) = graph_name {
                    Self::Graph {
                        inner: Box::new(pattern),
                        name: graph_name.clone(),
                    }
                } else {
                    pattern
                }
            }
            GraphPattern::Path {
                subject,
                path,
                object,
                graph_name,
            } => {
                let pattern = Self::Path {
                    subject: subject.clone().into(),
                    path: path.clone(),
                    object: object.clone().into(),
                };
                if let Some(graph_name) = graph_name {
                    Self::Graph {
                        inner: Box::new(pattern),
                        name: graph_name.clone(),
                    }
                } else {
                    pattern
                }
            }
            GraphPattern::Graph { graph_name } => Self::Graph {
                inner: Box::new(AlGraphPattern::Bgp {
                    patterns: Vec::new(),
                }),
                name: graph_name.clone(),
            },
            GraphPattern::Join { left, right, .. } => {
                match (left.as_ref().into(), right.as_ref().into()) {

```

--------------------------------

### Variable Conversions

Source: https://docs.rs/sparopt/latest/sparopt/algebra/struct.Variable.html

Illustrates conversions from Variable to other types like NamedNodePattern, GroundTermPattern, and Expression.

```APIDOC
## Variable Conversions

### Description
Demonstrates conversions from `Variable` to other SPARQL-related types.

### Trait Implementations

#### `impl From<Variable> for NamedNodePattern`
Converts a `Variable` into a `NamedNodePattern`.

#### `impl From<Variable> for GroundTermPattern`
Converts a `Variable` into a `GroundTermPattern`.

#### `impl From<Variable> for Expression`
Converts a `Variable` into an `Expression`.

#### `impl<'a> From<VariableRef<'a>> for Variable`
Converts a `VariableRef` into an owned `Variable`.
```

--------------------------------

### Variable Parsing

Source: https://docs.rs/sparopt/latest/sparopt/algebra/struct.Variable.html

Shows how to parse a string into a Variable using the FromStr trait.

```APIDOC
## Variable Parsing

### Description
Parses a variable from its SPARQL serialization using the `FromStr` trait.

### Usage Example
```rust
use oxrdf::Variable;
use std::str::FromStr;

// Parse a string into a Variable
let parsed_var = Variable::from_str("$foo").expect("Failed to parse variable");
let expected_var = Variable::new("foo").expect("Invalid variable name");

assert_eq!(parsed_var, expected_var);
```

### Trait Implementation

#### `impl FromStr for Variable`

##### `from_str(s: &str) -> Result<Variable, <Variable as FromStr>::Err>`
Parses a variable from its SPARQL serialization.

##### `type Err = TermParseError`
The associated error which can be returned from parsing.
```

--------------------------------

### clone_into

Source: https://docs.rs/sparopt/latest/sparopt/algebra/enum.Function.html

Uses borrowed data to replace owned data, typically by cloning.

```APIDOC
## fn clone_into(&self, target: &mut T)

### Description
Uses borrowed data to replace owned data, usually by cloning.

### Signature
`fn clone_into(&self, target: &mut T)`
```

--------------------------------

### Join GraphPatterns

Source: https://docs.rs/sparopt/latest/src/sparopt/algebra.rs.html

Combines two GraphPatterns using a specified JoinAlgorithm. Returns an empty pattern if either input pattern is empty. Returns the non-empty pattern if the other is an empty singleton.

```rust
pub fn join(left: Self, right: Self, algorithm: JoinAlgorithm) -> Self {
    if left.is_empty() || right.is_empty() {
        return Self::empty();
    }
    if left.is_empty_singleton() {
        return right;
    }
    if right.is_empty_singleton() {
        return left;
    }
    Self::Join {
        left: Box::new(left),
        right: Box::new(right),
        algorithm,
    }
}
```

--------------------------------

### Reduce Graph Patterns with Optimal Join Order

Source: https://docs.rs/sparopt/latest/src/sparopt/optimizer.rs.html

Reduces a list of graph patterns into a single pattern by iteratively joining them. It selects the join order based on estimated graph pattern sizes to optimize performance.

```rust
.into_iter()
                    .reduce(|left, right| {
                        let keys = join_key_variables(
                            &infer_graph_pattern_types(&left, input_types.clone()),
                            &infer_graph_pattern_types(&right, input_types.clone()),
                            input_types,
                        );
                        if estimate_graph_pattern_size(&left, input_types)
                            <= estimate_graph_pattern_size(&right, input_types)
                        {
                            GraphPattern::join(
                                left,
                                right,
                                JoinAlgorithm::HashBuildLeftProbeRight { keys },
                            )
                        } else {
                            GraphPattern::join(
                                right,
                                left,
                                JoinAlgorithm::HashBuildLeftProbeRight { keys },
                            )
                        }
                    })
                    .unwrap()
```

--------------------------------

### TryFrom<Term> for GroundTerm

Source: https://docs.rs/sparopt/latest/sparopt/algebra/enum.GroundTerm.html

Attempts to convert a Term into a GroundTerm. This operation may fail and return an error.

```APIDOC
### impl TryFrom<Term> for GroundTerm

#### type Error = ()

#### fn try_from( term: Term, ) -> Result<GroundTerm, <GroundTerm as TryFrom<Term>>::Error>
Performs the conversion.
```

--------------------------------

### Converting SPARQL Join to Graph Patterns

Source: https://docs.rs/sparopt/latest/src/sparopt/algebra.rs.html

Recursively converts SPARQL Join patterns into internal Join operations. Both left and right sides are converted using `from_sparql_algebra`, with a default Join algorithm applied.

```rust
AlGraphPattern::Join { left, right } => Self::Join {
    left: Box::new(Self::from_sparql_algebra(left, graph_name, blank_nodes)),
    right: Box::new(Self::from_sparql_algebra(right, graph_name, blank_nodes)),
    algorithm: JoinAlgorithm::default(),
}
```

--------------------------------

### NamedNode::new

Source: https://docs.rs/sparopt/latest/sparopt/algebra/struct.NamedNode.html

Builds and validates an RDF IRI. This is the safe constructor for creating NamedNode instances from potentially untrusted input.

```APIDOC
## NamedNode::new

### Description
Builds and validates an RDF IRI. This is the safe constructor for creating NamedNode instances from potentially untrusted input.

### Signature
`pub fn new(iri: impl Into<String>) -> Result<NamedNode, IriParseError>`

### Parameters
* `iri`: A string or type that can be converted into a String, representing the IRI to be validated and built.

### Returns
A `Result` containing a `NamedNode` on success, or an `IriParseError` if the IRI is invalid.
```

--------------------------------

### Convert GroundTriple to Expression (SPARQL 1.2)

Source: https://docs.rs/sparopt/latest/src/sparopt/algebra.rs.html

Converts a GroundTriple into an Expression using the Function::Triple call. Requires the 'sparql-12' feature.

```rust
#[cfg(feature = "sparql-12")]
impl From<GroundTriple> for Expression {
    fn from(value: GroundTriple) -> Self {
        Self::FunctionCall(
            Function::Triple,
            vec![
                value.subject.into(),
                value.predicate.into(),
                value.object.into(),
            ],
        )
    }
}
```

--------------------------------

### Convert GroundTriplePattern to Expression (SPARQL 1.2)

Source: https://docs.rs/sparopt/latest/src/sparopt/algebra.rs.html

Converts a GroundTriplePattern into an Expression using the Function::Triple call. Requires the 'sparql-12' feature.

```rust
#[cfg(feature = "sparql-12")]
impl From<GroundTriplePattern> for Expression {
    fn from(value: GroundTriplePattern) -> Self {
        Self::FunctionCall(
            Function::Triple,
            vec![
                value.subject.into(),
                value.predicate.into(),
                value.object.into(),
            ],
        )
    }
}
```

--------------------------------

### Expression Cloning and Debugging

Source: https://docs.rs/sparopt/latest/sparopt/algebra/enum.Expression.html

Documentation for cloning and debugging capabilities of the Expression type.

```APIDOC
## Clone for Expression

### Description
Provides methods for cloning an Expression.

### Methods
- `clone(&self) -> Expression`: Returns a duplicate of the value.
- `clone_from(&mut self, source: &Self)`: Performs copy-assignment from `source`.

## Debug for Expression

### Description
Implements the Debug trait for formatted output of Expression.

### Method
`fmt(&self, f: &mut Formatter<'_>) -> Result`: Formats the value using the given formatter.
```

--------------------------------

### Order Pair for Hashing

Source: https://docs.rs/sparopt/latest/src/sparopt/algebra.rs.html

Orders two hashable items to ensure consistent ordering for hashing purposes.

```rust
fn order_pair<T: Hash>(a: T, b: T) -> (T, T) {
    if hash(&a) <= hash(&b) { (a, b) } else { (b, a) }
}
```

--------------------------------

### Expression Arithmetic Operations

Source: https://docs.rs/sparopt/latest/sparopt/algebra/enum.Expression.html

Provides documentation for the arithmetic operations supported by the Expression type, including addition, subtraction, multiplication, division, and negation.

```APIDOC
## Add for Expression

### Description
Implements the addition operation for Expression.

### Method
`add(self, rhs: Self) -> Expression`

## Sub for Expression

### Description
Implements the subtraction operation for Expression.

### Method
`sub(self, rhs: Self) -> Expression`

## Mul for Expression

### Description
Implements the multiplication operation for Expression.

### Method
`mul(self, rhs: Self) -> Expression`

## Div for Expression

### Description
Implements the division operation for Expression.

### Method
`div(self, rhs: Self) -> Expression`

## Neg for Expression

### Description
Implements the unary negation operation for Expression.

### Method
`neg(self) -> Expression`
```

--------------------------------

### Expression Construction

Source: https://docs.rs/sparopt/latest/sparopt/algebra/enum.Expression.html

Methods for creating new expressions.

```APIDOC
## Expression Construction

### `or_all(args: impl IntoIterator<Item = Self>) -> Self`
Creates an expression that is true if any of the provided arguments are true.

### `and_all(args: impl IntoIterator<Item = Self>) -> Self`
Creates an expression that is true if all of the provided arguments are true.

### `equal(left: Self, right: Self) -> Self`
Creates an expression that checks for equality between two operands.

### `same_term(left: Self, right: Self) -> Self`
Creates an expression that checks if two operands are the same term.

### `greater(left: Self, right: Self) -> Self`
Creates an expression that checks if the left operand is greater than the right operand.

### `greater_or_equal(left: Self, right: Self) -> Self`
Creates an expression that checks if the left operand is greater than or equal to the right operand.

### `less(left: Self, right: Self) -> Self`
Creates an expression that checks if the left operand is less than the right operand.

### `less_or_equal(left: Self, right: Self) -> Self`
Creates an expression that checks if the left operand is less than or equal to the right operand.

### `unary_plus(inner: Self) -> Self`
Creates an expression representing the unary plus of an operand.

### `exists(inner: GraphPattern) -> Self`
Creates an expression that checks for the existence of a graph pattern.

### `if_cond(cond: Self, then: Self, els: Self) -> Self`
Creates a conditional expression that evaluates `then` if `cond` is true, otherwise evaluates `els`.

### `coalesce(args: Vec<Self>) -> Self`
Creates an expression that returns the first non-null value from a list of arguments.

### `call(name: Function, args: Vec<Self>) -> Self`
Creates an expression that calls a named function with provided arguments.
```

--------------------------------

### Create SameTerm SPARQL Expression

Source: https://docs.rs/sparopt/latest/src/sparopt/algebra.rs.html

Creates a SameTerm expression for SPARQL. Similar to Equal, it handles NamedNode and Literal comparisons directly and ensures consistent operand ordering for other types.

```rust
pub fn same_term(left: Self, right: Self) -> Self {
        match (left, right) {
            (Self::NamedNode(left), Self::NamedNode(right)) => (left == right).into(),
            (Self::Literal(left), Self::Literal(right)) if left == right => true.into(),
            (left, right) => {
                let (left, right) = order_pair(left, right);
                Self::SameTerm(Box::new(left), Box::new(right))
            }
        }
    }
```

--------------------------------

### Default Join Graph Pattern (No sep-0006)

Source: https://docs.rs/sparopt/latest/src/sparopt/optimizer.rs.html

Constructs a hash build join operation. This snippet is used when the 'sep-0006' feature is not enabled.

```rust
output = GraphPattern::join(
                                output,
                                next,
                                JoinAlgorithm::HashBuildLeftProbeRight {
                                    keys: join_key_variables(
                                        &output_types,
                                        &to_reorder_types[next_id],
                                        input_types,
                                    ),
                                },
                            );
```

--------------------------------

### Converting SPARQL Graph to Graph Patterns

Source: https://docs.rs/sparopt/latest/src/sparopt/algebra.rs.html

Converts a SPARQL Graph pattern into an internal Graph pattern. The inner pattern is recursively converted, and the graph name is preserved.

```rust
AlGraphPattern::Graph { inner, name } => Self::Graph {
    inner: Box::new(Self::from_sparql_algebra(inner, graph_name, blank_nodes)),
    name: Self::term_pattern_from_algebra(name, blank_nodes),
}
```

--------------------------------

### PartialEq and Eq Implementations for LeftJoinAlgorithm

Source: https://docs.rs/sparopt/latest/sparopt/algebra/enum.LeftJoinAlgorithm.html

Implements equality comparison for LeftJoinAlgorithm.

```rust
fn eq(&self, other: &LeftJoinAlgorithm) -> bool
```

```rust
fn ne(&self, other: &Rhs) -> bool
```

--------------------------------

### impl<V, T> VZip<V> for T

Source: https://docs.rs/sparopt/latest/sparopt/algebra/enum.Expression.html

Provides a method for zipping with a multi-lane vector.

```APIDOC
## fn vzip(self) -> V

### Description
Zips the current value with a multi-lane vector.

### Method
fn

### Parameters
None

### Response
#### Success Response
- **V**: The zipped multi-lane vector.
```

--------------------------------

### Left Join Algorithm Enum

Source: https://docs.rs/sparopt/latest/src/sparopt/algebra.rs.html

Defines the HashBuildRightProbeLeft left join algorithm. Used in GraphPattern::LeftJoin.

```rust
pub enum LeftJoinAlgorithm {
    HashBuildRightProbeLeft { keys: Vec<Variable> },
}

impl Default for LeftJoinAlgorithm {
    fn default() -> Self {
        Self::HashBuildRightProbeLeft {
            keys: Vec::default(),
        }
    }
}
```

--------------------------------

### Create LessOrEqual SPARQL Expression

Source: https://docs.rs/sparopt/latest/src/sparopt/algebra.rs.html

Constructs a LessOrEqual expression for SPARQL, representing the '<=' operator.

```rust
pub fn less_or_equal(left: Self, right: Self) -> Self {
        Self::LessOrEqual(Box::new(left), Box::new(right))
    }
```

--------------------------------

### Create Equal SPARQL Expression

Source: https://docs.rs/sparopt/latest/src/sparopt/algebra.rs.html

Creates an Equal expression for SPARQL. It handles NamedNode and Literal comparisons directly, otherwise creates a generic Equal expression, ensuring consistent ordering of operands.

```rust
pub fn equal(left: Self, right: Self) -> Self {
        match (left, right) {
            (Self::NamedNode(left), Self::NamedNode(right)) => (left == right).into(),
            (Self::Literal(left), Self::Literal(right)) if left == right => true.into(),
            (left, right) => {
                let (left, right) = order_pair(left, right);
                Self::Equal(Box::new(left), Box::new(right))
            }
        }
    }
```

--------------------------------

### Try Convert NamedNodePattern to NamedNode

Source: https://docs.rs/sparopt/latest/sparopt/algebra/enum.NamedNodePattern.html

Demonstrates the attempt to convert a NamedNodePattern back into a NamedNode. This operation can fail if the pattern is actually a Variable, returning an error.

```rust
fn try_from( pattern: NamedNodePattern, ) -> Result<NamedNode, <NamedNode as TryFrom<NamedNodePattern>>::Error>
```

--------------------------------

### Literal Destructuring

Source: https://docs.rs/sparopt/latest/sparopt/algebra/struct.Literal.html

Shows how to extract all components of a literal at once.

```APIDOC
## Literal Destructuring

### Description

This method allows you to extract all components of a literal in a single operation.

### Method

#### `destruct(self) -> (String, Option<NamedNode>, Option<String>, Option<BaseDirection>)`
(Available on `rdf-12` feature only) Extracts the value, datatype, language tag, and base direction from the literal.
```

--------------------------------

### Converting SPARQL Path to Graph Patterns

Source: https://docs.rs/sparopt/latest/src/sparopt/algebra.rs.html

Converts a SPARQL Path pattern into an internal Path representation. It transforms subject and object terms using `term_pattern_from_algebra` and includes the graph name if available.

```rust
AlGraphPattern::Path {
    subject,
    path,
    object,
} => Self::Path {
    subject: Self::term_pattern_from_algebra(subject, blank_nodes),
    path: path.clone(),
    object: Self::term_pattern_from_algebra(object, blank_nodes),
    graph_name: graph_name.cloned(),
}
```

--------------------------------

### Try Convert Term to GroundTerm

Source: https://docs.rs/sparopt/latest/sparopt/algebra/enum.GroundTerm.html

Attempts to convert a generic Term into a GroundTerm. This operation can fail, returning an error.

```rust
impl TryFrom<Term> for GroundTerm {
    type Error = ()
    fn try_from( term: Term, ) -> Result<GroundTerm, <GroundTerm as TryFrom<Term>>::Error>
}
```

--------------------------------

### Project Operation

Source: https://docs.rs/sparopt/latest/src/sparopt/algebra.rs.html

Constructs a Project operation, which selects specific variables from an inner operation.

```rust
pub fn project(inner: Self, variables: Vec<Variable>) -> Self {
        Self::Project {
            inner: Box::new(inner),
            variables,
        }
    }
```

--------------------------------

### try_into

Source: https://docs.rs/sparopt/latest/sparopt/algebra/enum.Function.html

Attempts to convert a value into another type, returning a `Result`.

```APIDOC
## fn try_into(self) -> Result<U, <U as TryFrom<T>>::Error>

### Description
Performs the conversion.

### Signature
`fn try_into(self) -> Result<U, <U as TryFrom<T>>::Error>`
```

--------------------------------

### Create Less SPARQL Expression

Source: https://docs.rs/sparopt/latest/src/sparopt/algebra.rs.html

Constructs a Less expression for SPARQL, representing the '<' operator.

```rust
pub fn less(left: Self, right: Self) -> Self {
        Self::Less(Box::new(left), Box::new(right))
    }
```