Parser implementation

* Adaptation of the grammar to make more regular w.r.t reference space
   names placement.

 * Implemented Type check

 * Implemented prediction of the result set cardinality. This assumes:
    + A space is not infinite, this is required to compute complementary
      sets as we can compute the whole space volume.
    + Density is mostly uniform, this allows us to assume the number of
      results is related with a constant factor to the volume in space
      of the selection.
    + The prediction is approximated by using the most pessimistic
      resulting cardinality for each operator, in order to keep the
      operation simple, and fast, at the expense of the precision.

 * Implemented execution, which calls into a DB abstraction layer. That
   layer is currently mostly empty. Execution is also implemented in a
   naive way, and should most likely be optimised.

Cargo.toml

@@ -17,6 +17,7 @@ path = "src/main.rs"
 lalrpop-util = "0.17.0"
 regex = "0.2.1"
 measure_time = "0.6" # To mesure parsing time, only required by binary
+lazy_static = "1.3.0" # for space.rs, might be removed once the full data model is provided by the use of the crate
 
 # Logging macros API
 log = { version = "0.4", features = ["max_level_trace", "release_max_level_debug"] }

Grammars/filters.g4

@@ -134,33 +134,38 @@ hyperrectangle
     : 'hyperrectangle' '{'
           position ',' position
           ( ',' position ',' position )*
+          ( ',' STRING )?
        '}'
     ;
 
 /* A hypersphere is defined by its center and a radius, independantly
  * of the number of dimensions of the space. */
 hypersphere
-    : 'hypersphere' '{' position ( ',' positive_number ) '}'
+    : 'hypersphere' '{'
+           position
+           ',' positive_number
+           ( ',' STRING )?
+        '}'
     ;
 
 point
-    : 'point' '{' position '}'
+    : 'point' '{' position ( ',' STRING )? '}'
     ;
 
 /* Define a shape as the non-zero values in a NIfTI object, defined by
  *   nifti{
- *     spaceId: string,
  *     lower_corner: position,  // Optional, default to the origin
  *     rotation: [ position+ ], // Optional, no rotation by default
- *     bytes: uri(STRING)       // uri to the NIfTI object
+ *     bytes: uri(STRING),      // uri to the NIfTI object
+ *     spaceId: string
  *   }
  */
 nifti
     : 'nifti' '{'
-        STRING ','
         (position ',' )?
         ( '[' position ( ',' position )* ']' ',' )?
-        byte_provider
+        byte_provider ','
+        STRING
       '}'
     ;
 

Grammars/queries.g4

@@ -18,11 +18,11 @@ projection_operators
  *
  * If it is provided, it MUST resolve to a NUMBER. */
 nifti_operator
-    : 'nifti' '(' ( selector ',' )? bag_expression ')'
+    : 'nifti' '(' ( STRING ',' )? ( selector ',' )? bag_expression ')'
     ;
 
 json_operator
-    : 'json' '(' jslt ',' bag_expression ')'
+    : 'json' '(' jslt ',' bag_expression ( ',' STRING )? ')'
     ;
 
 jslt

src/ast.rs

@@ -1,113 +0,0 @@
-trait Expression {
-    fn check_type();
-    fn predict();
-    fn execute();
-}
-
-/**********************************************************************/
-/* FORMATTING DATA                                                    */
-/**********************************************************************/
-#[derive(Clone, Debug)]
-pub enum Projection {
-    Nifti(LiteralSelector, Bag),
-    JSON(JsonValue, Bag),
-}
-
-// JSON FORMAT
-#[derive(Clone, Debug)]
-pub enum JsonValue {
-    String(String),
-    JsonNumber(LiteralNumber),
-    Bool(bool),
-    Null,
-    Object(Vec<(String, JsonValue)>),
-    Array(Vec<JsonValue>),
-    Selector(LiteralSelector),
-    Aggregation(Aggregation),
-}
-
-#[derive(Clone, Debug)]
-pub enum Aggregation {
-    Count(bool, LiteralSelector),
-    Sum(LiteralSelector),
-    Min(LiteralSelector),
-    Max(LiteralSelector),
-}
-
-// NIFTI
-#[derive(Clone, Debug)]
-struct Transform {
-    reference: String,
-    offset: Vec<LiteralNumber>,
-    rotation: Vec<Vec<LiteralNumber>>,
-}
-
-/**********************************************************************/
-/* SELECTING / FILTERING DATA                                         */
-/**********************************************************************/
-#[derive(Clone, Debug)]
-pub enum Bag {
-    Distinct(Box<Bag>),
-    Filter(Option<Predicate>, Option<Box<Bag>>),
-    Complement(Box<Bag>),
-    Intersection(Box<Bag>, Box<Bag>),
-    Union(Box<Bag>, Box<Bag>),
-    Bag(Vec<Bag>),
-    Inside(Shape),
-    Outside(Shape),
-}
-
-/**********************************************************************/
-/* BAG OPERATORS                                                      */
-/**********************************************************************/
-#[derive(Clone, Debug)]
-pub enum Predicate {
-    Less(Position, LiteralPosition),
-    Greater(Position, LiteralPosition),
-    Equal(Position, LiteralPosition),
-    Not(Box<Predicate>),
-    And(Box<Predicate>, Box<Predicate>),
-    Or(Box<Predicate>, Box<Predicate>),
-}
-
-/**********************************************************************/
-/* SPATIAL OPERATORS                                                  */
-/**********************************************************************/
-
-/**********************************************************************/
-/* SHAPES                                                             */
-/**********************************************************************/
-#[derive(Clone, Debug)]
-pub enum Shape {
-    Point(LiteralPosition),
-    HyperRectangle(Vec<LiteralPosition>),
-    HyperSphere(LiteralPosition, LiteralNumber),
-    Nifti(),
-}
-
-/**********************************************************************/
-/* POSITIONS                                                          */
-/**********************************************************************/
-#[derive(Clone, Debug)]
-pub enum Position {
-    StrCmpICase(LiteralSelector, String),
-    StrCmp(LiteralSelector, String),
-    Selector(LiteralSelector),
-    LiteralPosition(LiteralPosition),
-}
-
-/**********************************************************************/
-/* Literals / TOKENS                                                  */
-/**********************************************************************/
-
-#[derive(Clone, Debug)]
-pub struct Field(pub String, pub Option<usize>);
-
-#[derive(Clone, Debug)]
-pub enum LiteralNumber {
-    Int(i64),
-    Float(f64),
-}
-
-pub type LiteralPosition = Vec<LiteralNumber>;
-pub type LiteralSelector = Vec<Field>;

src/database/mod.rs

@@ -0,0 +1,57 @@
+use crate::executors::ResultSet;
+use crate::symbols::*;
+
+//use ironsea_index::*;
+
+pub fn get_all(_space_id: &String) -> ResultSet {
+    //space::get_all(space_id)
+    Err("not yet implemented".to_string())
+}
+
+pub fn get_by_bounding_box(_space_id: &String, _bounding_box: &Vec<LiteralPosition>) -> ResultSet {
+    Err("not yet implemented".to_string())
+}
+
+pub fn get_by_position(_space_id: &String, _position: &LiteralPosition) -> ResultSet {
+    Err("not yet implemented".to_string())
+}
+
+pub fn get(_point: &Object, _fields: &Vec<Field>) -> Result<LiteralPosition, String> {
+    Err("not yet implemented".to_string())
+}
+
+#[derive(PartialEq, Eq, Hash, Clone, Debug)]
+pub struct Object {
+    id: u32,
+}
+
+impl Object {
+    pub fn length(&self) -> f64 {
+        0.0
+    }
+
+    pub fn eval(&self, _predicate: &Predicate) -> bool {
+        false
+    }
+}
+
+impl Position {
+    pub fn eval(&self, point: &Object) -> LiteralPosition {
+        match self {
+            Position::StrCmpICase(_selector, _string) => LiteralPosition(vec![]), //TODO
+            Position::StrCmp(_selector, _string) => LiteralPosition(vec![]),      //TODO
+            Position::Selector(selector) => selector.eval(point),
+            Position::Literal(position) => position.clone(),
+        }
+    }
+}
+
+impl LiteralSelector {
+    pub fn eval(&self, point: &Object) -> LiteralPosition {
+        let LiteralSelector(fields) = self;
+        match get(point, fields) {
+            Err(_) => LiteralPosition(vec![]),
+            Ok(p @ LiteralPosition(_)) => p,
+        }
+    }
+}

src/database/space.rs

@@ -0,0 +1,86 @@
+use std::collections::HashMap;
+
+use crate::types::LiteralTypes;
+
+//FIXME: Improve, as this should not be static, but coming from DB.
+lazy_static! {
+    static ref UNIVERSE: String = "Universe".to_string();
+    static ref SPACES: HashMap<&'static str, Space> = {
+        let mut m = HashMap::new();
+        m.insert(
+            "Universe",
+            Space {
+                space_type: LiteralTypes::Vector(vec![
+                    LiteralTypes::Float,
+                    LiteralTypes::Float,
+                    LiteralTypes::Float,
+                ]),
+                bounding_box: vec![
+                    vec![0, 0, 0],
+                    vec![
+                        std::u32::MAX as i64,
+                        std::u32::MAX as i64,
+                        std::u32::MAX as i64,
+                    ],
+                ],
+            },
+        );
+
+        m
+    };
+}
+
+struct Space {
+    space_type: LiteralTypes,
+    bounding_box: Vec<Vec<i64>>,
+}
+
+impl Space {
+    pub fn max_volume(&self) -> f64 {
+        let mut volume = 1.0;
+        for max in &self.bounding_box[1] {
+            volume *= *max as f64;
+        }
+
+        volume
+    }
+}
+
+pub fn name() -> &'static String {
+    lazy_static! {
+        static ref UNIVERSE: String = "Universe".to_string();
+    };
+
+    &UNIVERSE
+}
+
+#[inline]
+pub fn get_type(space_id: &String) -> &LiteralTypes {
+    lazy_static! {
+        static ref EMPTY_TYPE: LiteralTypes = LiteralTypes::Vector(Vec::new());
+    };
+
+    match SPACES.get(space_id.as_str()) {
+        None => &EMPTY_TYPE,
+        Some(space) => &space.space_type,
+    }
+}
+
+#[inline]
+pub fn bounding_box(space_id: &String) -> &Vec<Vec<i64>> {
+    lazy_static! {
+        static ref EMPTY_BOX: Vec<Vec<i64>> = Vec::new();
+    };
+    match SPACES.get(space_id.as_str()) {
+        None => &EMPTY_BOX,
+        Some(space) => &space.bounding_box,
+    }
+}
+
+#[inline]
+pub fn max_volume(space_id: &String) -> f64 {
+    match SPACES.get(space_id.as_str()) {
+        None => 0.0,
+        Some(space) => space.max_volume(),
+    }
+}

src/executors.rs

@@ -0,0 +1,314 @@
+use std::collections::HashSet;
+
+use super::database;
+use super::expression::*;
+use super::symbols::*;
+
+pub type ResultSet = Result<Vec<database::Object>, String>;
+
+impl Executor for Projection {
+    type ResultSet = self::ResultSet;
+
+    fn execute(&self) -> ResultSet {
+        match self {
+            Projection::Nifti(_, _, _bag) => Err("not yet implemented".to_string()),
+            Projection::JSON(_, _format, bag) => bag.execute(), // FIXME: Add projections here
+        }
+    }
+}
+
+impl Executor for Bag {
+    type ResultSet = self::ResultSet;
+
+    fn execute(&self) -> ResultSet {
+        fn get_bounding_box(
+            position: &LiteralPosition,
+            radius: &LiteralNumber,
+        ) -> Result<Vec<LiteralPosition>, String> {
+            let LiteralPosition(position) = position;
+            let mut low = vec![];
+            let mut high = vec![];
+            match radius {
+                LiteralNumber::Int(r) => {
+                    for x in position {
+                        match x {
+                            LiteralNumber::Int(x) => {
+                                low.push(LiteralNumber::Int(x - r));
+                                high.push(LiteralNumber::Int(x + r));
+                            }
+                            LiteralNumber::Float(x) => {
+                                low.push(LiteralNumber::Float(x - (*r as f64)));
+                                high.push(LiteralNumber::Float(x + (*r as f64)));
+                            }
+                        };
+                    }
+                }
+                LiteralNumber::Float(r) => {
+                    for x in position {
+                        match x {
+                            LiteralNumber::Int(_) => {
+                                return Err(format!("The radius provided is a floating point value, which is incompatible with integer coordinates components: radius {:?}, coordinates {:?}", radius, position));
+                            }
+                            LiteralNumber::Float(x) => {
+                                low.push(LiteralNumber::Float(x - r));
+                                high.push(LiteralNumber::Float(x + r));
+                            }
+                        };
+                    }
+                }
+            }
+
+            Ok(vec![LiteralPosition(low), LiteralPosition(high)])
+        };
+
+        match self {
+            Bag::Distinct(bag) => match bag.execute() {
+                e @ Err(_) => e,
+                Ok(mut v) => {
+                    let set: HashSet<_> = v.drain(..).collect(); // dedup
+                    v.extend(set.into_iter());
+
+                    Ok(v)
+                }
+            },
+            Bag::Filter(predicate, bag) => match predicate {
+                None => bag.execute(),
+                Some(predicate) => match bag.execute() {
+                    e @ Err(_) => e,
+                    Ok(source) => {
+                        let mut filtered = Vec::new();
+
+                        for point in source {
+                            if point.eval(predicate) {
+                                filtered.push(point);
+                            }
+                        }
+
+                        Ok(filtered)
+                    }
+                },
+            },
+            Bag::Complement(bag) => match bag.execute() {
+                // The complement of a set is computed within its definition space.
+                e @ Err(_) => e,
+                Ok(inside) => {
+                    let mut outside = Vec::new();
+                    match database::get_all(bag.space()) {
+                        e @ Err(_) => e,
+                        Ok(points) => {
+                            for point in points {
+                                if !inside.contains(&point) {
+                                    outside.push(point)
+                                }
+                            }
+
+                            Ok(outside)
+                        }
+                    }
+                }
+            },
+            Bag::Intersection(lh, rh) => {
+                let l = lh.execute();
+                if let Ok(l) = l {
+                    let r = rh.execute();
+                    if let Ok(r) = r {
+                        let mut v = vec![];
+
+                        if rh.predict() < lh.predict() {
+                            for o in r {
+                                if l.contains(&o) {
+                                    v.push(o);
+                                }
+                            }
+                        } else {
+                            for o in l {
+                                if r.contains(&o) {
+                                    v.push(o);
+                                }
+                            }
+                        }
+                        Ok(v)
+                    } else {
+                        r
+                    }
+                } else {
+                    l
+                }
+            }
+            Bag::Union(lh, rh) => {
+                let l = lh.execute();
+                if let Ok(mut l) = l {
+                    let r = rh.execute();
+                    if let Ok(mut r) = r {
+                        if rh.predict() < lh.predict() {
+                            l.append(&mut r);
+                            Ok(l)
+                        } else {
+                            r.append(&mut l);
+                            Ok(r)
+                        }
+                    } else {
+                        r
+                    }
+                } else {
+                    l
+                }
+            }
+            Bag::Bag(bags) => {
+                let mut v = vec![];
+                for bag in bags {
+                    let b = bag.execute();
+                    match b {
+                        e @ Err(_) => {
+                            return e;
+                        }
+                        Ok(mut b) => {
+                            //TODO: SPACE CONVERSIONS IF NOT THE SAME SPACES?
+                            v.append(&mut b);
+                        }
+                    }
+                }
+
+                Ok(v)
+            }
+            Bag::Inside(shape) => match shape {
+                Shape::Point(space_id, position) => database::get_by_position(space_id, position),
+                Shape::HyperRectangle(space_id, bounding_box) => {
+                    database::get_by_bounding_box(space_id, bounding_box)
+                }
+                Shape::HyperSphere(space_id, position, radius) => {
+                    let length = match radius {
+                        LiteralNumber::Int(x) => *x as f64,
+                        LiteralNumber::Float(x) => *x,
+                    };
+
+                    match get_bounding_box(position, radius) {
+                        Err(e) => Err(e),
+                        Ok(inside) => match database::get_by_bounding_box(space_id, &inside) {
+                            e @ Err(_) => e,
+                            Ok(source) => {
+                                let mut filtered = vec![];
+
+                                for point in source {
+                                    // Include the surface of the sphere
+                                    if point.length() <= length {
+                                        filtered.push(point);
+                                    }
+                                }
+                                Ok(filtered)
+                            }
+                        },
+                    }
+                }
+                Shape::Nifti(_space_id) => Err("not yet implemented".to_string()),
+            },
+            Bag::Outside(shape) => {
+                fn outside_set(space_id: &String, inside: Vec<database::Object>) -> ResultSet {
+                    let mut outside = Vec::new();
+                    match database::get_all(space_id) {
+                        e @ Err(_) => e,
+                        Ok(points) => {
+                            for point in points {
+                                if !inside.contains(&point) {
+                                    outside.push(point)
+                                }
+                            }
+
+                            Ok(outside)
+                        }
+                    }
+                }
+
+                match shape {
+                    Shape::Point(space_id, position) => {
+                        match database::get_by_position(space_id, position) {
+                            e @ Err(_) => e,
+                            Ok(inside) => outside_set(space_id, inside),
+                        }
+                    }
+                    Shape::HyperRectangle(space_id, bounding_box) => {
+                        // We need to adapt the bounding_box to ensure the
+                        // surface will not hit as part of the inside set, so we
+                        // compute the biggest bounding box contained within the
+                        // given box.
+
+                        // Smallest increment possible
+                        let mut low: Vec<LiteralNumber> = vec![];
+                        let LiteralPosition(coordinates) = &bounding_box[0];
+                        for coordinate in coordinates {
+                            match coordinate {
+                                LiteralNumber::Int(x) => low.push(LiteralNumber::Int(x + 1)),
+                                LiteralNumber::Float(x) => {
+                                    low.push(LiteralNumber::Float(x + std::f64::EPSILON))
+                                }
+                            };
+                        }
+                        let low = LiteralPosition(low);
+
+                        // Smallest decrement possible
+                        let mut high: Vec<LiteralNumber> = vec![];
+                        let LiteralPosition(coordinates) = &bounding_box[1];
+                        for coordinate in coordinates {
+                            match coordinate {
+                                LiteralNumber::Int(x) => high.push(LiteralNumber::Int(x - 1)),
+                                LiteralNumber::Float(x) => {
+                                    high.push(LiteralNumber::Float(x - std::f64::EPSILON))
+                                }
+                            };
+                        }
+                        let high = LiteralPosition(high);
+
+                        match database::get_by_bounding_box(space_id, &vec![low, high]) {
+                            e @ Err(_) => e,
+                            Ok(inside) => outside_set(space_id, inside),
+                        }
+                    }
+                    Shape::HyperSphere(space_id, position, radius) => {
+                        let length = match radius {
+                            LiteralNumber::Int(x) => *x as f64,
+                            LiteralNumber::Float(x) => *x,
+                        };
+
+                        match get_bounding_box(position, radius) {
+                            Err(e) => Err(e),
+                            Ok(inside) => match database::get_by_bounding_box(space_id, &inside) {
+                                Err(e) => Err(e),
+                                Ok(source) => {
+                                    let mut filtered = vec![];
+
+                                    for point in source {
+                                        // Exclude the surface of the sphere, so
+                                        // that it is included in the
+                                        // complement.
+                                        if point.length() < length {
+                                            filtered.push(point);
+                                        }
+                                    }
+
+                                    outside_set(space_id, filtered)
+                                }
+                            },
+                        }
+                    }
+                    Shape::Nifti(_space_id) => Err("not yet implemented".to_string()),
+                }
+            }
+        }
+    }
+}
+
+impl Predicate {
+    pub fn eval(&self, point: &database::Object) -> bool {
+        match self {
+            Predicate::Not(predicate) => !predicate.eval(point),
+            Predicate::And(lh, rh) => lh.eval(point) && rh.eval(point),
+            Predicate::Or(lh, rh) => lh.eval(point) || rh.eval(point),
+            // I don't know how to evaluate these at this point, so let the DB object take care of that.
+            //            Predicate::Less(selector, literal) => &selector.eval(point) < literal,
+            //            Predicate::Greater(selector, literal) => &selector.eval(point) > literal,
+            //            Predicate::Equal(selector, literal) => &selector.eval(point) == literal,
+            // Redirect to the DB Objet the evaluation of the remaining predicate operators
+            predicate => point.eval(predicate),
+        }
+    }
+}

src/expression.rs

@@ -0,0 +1,15 @@
+pub trait Validator {
+    type ValidationResult;
+
+    fn validate(&self) -> Self::ValidationResult;
+}
+
+pub trait Predictor {
+    fn predict(&self) -> f64;
+}
+
+pub trait Executor {
+    type ResultSet;
+
+    fn execute(&self) -> Self::ResultSet;
+}

src/lib.rs

@@ -1,10 +1,25 @@
+#[macro_use]
+extern crate lazy_static;
+
 #[macro_use]
 extern crate lalrpop_util;
 
 lalrpop_mod!(pub queries); // synthesized by LALRPOP
 
-pub mod ast;
+mod database;
-pub use ast::*;
+mod executors;
+mod expression;
+mod predictors;
+mod validators;
+
+mod symbols;
+mod types;
+
+pub use expression::Executor;
+pub use expression::Predictor;
+pub use expression::Validator;
+pub use queries::FiltersParser;
+pub use queries::QueryParser;
 
 #[cfg(test)]
 mod tests;

src/main.rs

@@ -3,7 +3,8 @@ extern crate measure_time;
 
 extern crate parser;
 
-use parser::queries;
+use parser::QueryParser;
+use parser::{Executor, Predictor, Validator};
 
 use std::io;
 
@@ -15,13 +16,13 @@ fn main() {
     pretty_env_logger::init();
 
     //let parser = queries::FiltersParser::new();
-    let parser = queries::QueryParser::new();
+    let parser = QueryParser::new();
 
     loop {
+        println!();
         info!("Expression to parse (type `quit` to exit): ");
 
         let mut input = String::new();
-
         match io::stdin().read_line(&mut input) {
             Ok(0) => break,    // Catch ^D
             Ok(1) => continue, // Catch \n
@@ -34,11 +35,42 @@ fn main() {
         }
 
         let input = input.as_str();
-        let mut out;
         {
-            debug_time!("Parsing");
+            debug_time!("Interpretation");
-            out = parser.parse(input);
+            let mut parse;
+            {
+                trace_time!("Parsing");
+                parse = parser.parse(input);
+            }
+            trace!("Tree: \n{:?}", parse);
+
+            match parse {
+                Ok(Some(t)) => {
+                    let validate;
+                    {
+                        trace_time!("Type check");
+                        validate = t.validate();
+                    }
+                    info!("Type: \n{:?}", validate);
+
+                    if let Ok(_) = validate {
+                        let predict;
+                        {
+                            trace_time!("Prediction");
+                            predict = t.predict();
+                        }
+                        info!("Predict: \n{:?}", predict);
+
+                        let execute;
+                        {
+                            trace_time!("Exectution");
+                            execute = t.execute();
+                        }
+                        info!("Execution: \n{:?}", execute);
+                    }
+                }
+                _ => (),
+            }
         }
-        info!("Tree: \n{:?}", out);
     }
 }

src/predictors.rs

@@ -0,0 +1,48 @@
+use super::expression::Predictor;
+use super::symbols::*;
+
+use super::database::space;
+
+impl Predictor for Projection {
+    fn predict(&self) -> f64 {
+        match self {
+            Projection::Nifti(_, _, bag) => bag.predict(),
+            Projection::JSON(_, _, bag) => bag.predict(),
+        }
+    }
+}
+
+impl Predictor for Bag {
+    fn predict(&self) -> f64 {
+        match self {
+            Bag::Distinct(bag) => bag.predict(),
+            Bag::Filter(_, bag) => bag.predict(),
+            Bag::Complement(bag) => space::max_volume(bag.space()) - bag.predict(),
+            Bag::Intersection(lh, rh) => {
+                let l = lh.predict();
+                let r = rh.predict();
+                if l < r {
+                    l
+                } else {
+                    r
+                }
+            }
+            Bag::Union(lh, rh) => lh.predict() + rh.predict(),
+            Bag::Bag(bags) => {
+                let mut s = 0.0;
+                for bag in bags {
+                    s += bag.predict();
+                }
+                s
+            }
+            Bag::Inside(shape) => shape.predict(),
+            Bag::Outside(shape) => space::max_volume(shape.space()) - shape.predict(),
+        }
+    }
+}
+
+impl Predictor for Shape {
+    fn predict(&self) -> f64 {
+        self.volume()
+    }
+}

src/queries.lalrpop

@@ -1,7 +1,7 @@
 use std::str::FromStr;
 
-use crate::ast;
+use crate::symbols;
-use crate::ast::*;
+use crate::database::space;
 
 grammar;
 
@@ -10,7 +10,7 @@ grammar;
 //*********************************************************************/
 pub Query = { Projections? };
 
-Projections: ast::Projection = {
+Projections: symbols::Projection = {
     NiftiOperator,
     JsonOperator
 };
@@ -19,18 +19,39 @@ Projections: ast::Projection = {
 // each position where there is a point in bag_expression.
 //
 // If it is provided, it MUST resolve to a NUMBER.
-NiftiOperator: ast::Projection = {
+NiftiOperator: symbols::Projection = {
-    "nifti" "(" <s:( Selector "," )?> <b:Bags> ")" =>
+    "nifti" "("
+        <s:( Selector "," )?>
+        <b:Bags>
+        <rs:( "," <String> )?>
+    ")" => {
+        let space_id = match rs {
+            Some(id) => id,
+            None => space::name().clone(),
+        };
+
         if let Some((sel, _)) = s {
-            Projection::Nifti(sel, b)
+           symbols::Projection::Nifti(space_id, sel, b)
         } else {
-            Projection::Nifti(Vec::new(), b)
+          symbols::Projection::Nifti(space_id, symbols::LiteralSelector(Vec::new()), b)
         }
+
+    }
 };
 
-JsonOperator: ast::Projection = {
+JsonOperator: symbols::Projection = {
-    "json" "(" <f:JsonValues> "," <b:Bags> ")" =>
+    "json" "("
-        Projection::JSON(f, b)
+        <f:JsonValues> ","
+        <b:Bags>
+        <rs:( "," <String> )?>
+    ")" => {
+        let space_id = match rs {
+            Some(id) => id,
+            None => space::name().clone(),
+        };
+
+        symbols::Projection::JSON(space_id, f, b)
+    }
 };
 
 //*********************************************************************/
@@ -41,73 +62,73 @@ JsonOperator: ast::Projection = {
 //  https://github.com/antlr/grammars-v4/blob/master/json/JSON.g4
 //
 // Some of the parser / lexer rules are in the imported grammar as well.
-JsonValues: ast::JsonValue = {
+JsonValues: symbols::JsonValue = {
-    String => JsonValue::String(<>),
+    String => symbols::JsonValue::String(<>),
     JsonNumber => <>,
     JsonObj => <>,
     JsonArray => <>,
-    "true" => JsonValue::Bool(true),
+    "true" => symbols::JsonValue::Bool(true),
-    "false" => JsonValue::Bool(false),
+    "false" => symbols::JsonValue::Bool(false),
-    "null" => JsonValue::Null,
+    "null" => symbols::JsonValue::Null,
     // Support reference to values from the selected bag.
-    Selector => JsonValue::Selector(<>),
+    Selector => symbols::JsonValue::Selector(<>),
-    Aggregations => JsonValue::Aggregation(<>)
+    Aggregations => symbols::JsonValue::Aggregation(<>)
 };
 
-JsonObj: ast::JsonValue = {
+JsonObj: symbols::JsonValue = {
     "{" <exp:( JsonPair ( "," JsonPair )* )?> "}" => {
         if let Some((elem, list)) = exp {
-            let mut values: Vec<(String, JsonValue)> = vec![elem];
+            let mut values = vec![elem];
 
             for v in list {
                 let (_, pair) = v;
                 values.push(pair.clone());
             }
 
-            JsonValue::Object(values)
+            symbols::JsonValue::Object(values)
         } else {
-            JsonValue::Object(Vec::new())
+            symbols::JsonValue::Object(Vec::new())
         }
     }
 };
 
-JsonPair: (String, ast::JsonValue) = {
+JsonPair: (String, symbols::JsonValue) = {
     <s:String> ":" <v:JsonValues> => (s, v)
 };
 
-JsonArray: ast::JsonValue = {
+JsonArray: symbols::JsonValue = {
     "[" <exp:( JsonValues ( "," JsonValues )* )?> "]" => {
         if let Some((elem, list)) = exp {
-            let mut values: Vec<JsonValue> = vec![elem];
+            let mut values = vec![elem];
 
             for v in list.iter() {
                 let (_, val) = v;
                 values.push(val.clone());
             }
 
-            JsonValue::Array(values)
+            symbols::JsonValue::Array(values)
         } else {
-            JsonValue::Array(Vec::new())
+            symbols::JsonValue::Array(Vec::new())
         }
     }
 };
 
 // The bag expression is implicit here, as this is te
 // second argument to the json operator
-Aggregations: ast::Aggregation = {
+Aggregations: symbols::Aggregation = {
     "count" "(" <d:"distinct"?> <s:Selector> ")" => {
             if let Some(_) = d {
-                Aggregation::Count(true, s)
+                symbols::Aggregation::Count(true, s)
             } else {
-                Aggregation::Count(false, s)
+                symbols::Aggregation::Count(false, s)
             }
         },
     "sum" "(" <Selector> ")" =>
-        Aggregation::Sum(<>),
+        symbols::Aggregation::Sum(<>),
     "min" "(" <Selector> ")" =>
-        Aggregation::Min(<>),
+        symbols::Aggregation::Min(<>),
     "max" "(" <Selector> ")" =>
-        Aggregation::Max(<>),
+        symbols::Aggregation::Max(<>),
 };
 
 //*********************************************************************/
@@ -116,7 +137,7 @@ Aggregations: ast::Aggregation = {
 pub Filters = { Bags };
 
 // All these expressions generate bags.
-Bags: ast::Bag = {
+Bags: symbols::Bag = {
     // Bag Operators
     Distinct,
     Filter,
@@ -129,49 +150,65 @@ Bags: ast::Bag = {
     Outside,
     // When used directly here, the inside() operation on the shape is
     // implied.
-    Shapes => Bag::Inside(<>)
+    Shapes => symbols::Bag::Inside(<>)
 };
 
 //*********************************************************************/
 // BAG OPERATORS                                                      */
 //*********************************************************************/
-Distinct: ast::Bag = {
+Distinct: symbols::Bag = {
     "distinct" "(" <Bags> ")" =>
-        Bag::Distinct(Box::new(<>))
+        symbols::Bag::Distinct(Box::new(<>))
 };
 
 // Returns all the points which are NOT part of the bag.
-Complement: ast::Bag = {
+Complement: symbols::Bag = {
     "complement" "(" <Bags> ")" =>
-        Bag::Complement(Box::new(<>))
+        symbols::Bag::Complement(Box::new(<>))
 };
 
 // Returns points which are part of both left and right sets.
-Intersection: ast::Bag = {
+Intersection: symbols::Bag = {
     "intersection" "(" <lh:Bags> "," <rh:Bags> ")" =>
-        Bag::Intersection(Box::new(lh), Box::new(rh))
+        symbols::Bag::Intersection(Box::new(lh), Box::new(rh))
 };
 
 // Returns points which are either part of left or right sets
 // (or both).
-Union: ast::Bag = {
+Union: symbols::Bag = {
     "union" "(" <lh:Bags> "," <rh:Bags> ")" =>
-        Bag::Union(Box::new(lh), Box::new(rh))
+        symbols::Bag::Union(Box::new(lh), Box::new(rh))
 };
 
 // Filters point so that points part of the resulting bag respect
 // the predicate.
-Filter: ast::Bag = {
+Filter: symbols::Bag = {
 //     "filter" "(" <p:Predicates> "," <b:Bags> ")" =>
     "filter" "(" <b:Bags> ")" =>
-        Bag::Filter(None, Some(Box::new(b))),
+        symbols::Bag::Filter(None, Box::new(b)),
     "filter" "(" <p:Predicates> <b:("," <Bags> )?> ")" => match b {
-        Some(b) => Bag::Filter(Some(p), Some(Box::new(b))),
+        Some(b) => symbols::Bag::Filter(Some(p), Box::new(b)),
-        None => Bag::Filter(Some(p), None),
+        None => {
+            let v = space::bounding_box(space::name());
+            let mut positions = Vec::new();
+            for point in v {
+                let mut position = Vec::new();
+                for c in point {
+                    position.push(symbols::LiteralNumber::Int(*c))
+                }
+                positions.push(symbols::LiteralPosition(position));
+            }
+            let bb = symbols::Shape::HyperRectangle(
+                space::name().clone(),
+                positions
+            );
+
+            symbols::Bag::Filter(Some(p), Box::new(symbols::Bag::Inside(bb)))
+        }
     }
 };
 
-Predicates: ast::Predicate = {
+Predicates: symbols::Predicate = {
     Less,
     Greater,
     Equal,
@@ -180,41 +217,41 @@ Predicates: ast::Predicate = {
     Or
 };
 
-Less: ast::Predicate = {
+Less: symbols::Predicate = {
     "<" "(" <v:Positions> "," <literal:Position> ")" => {
-        Predicate::Less(v, literal)
+        symbols::Predicate::Less(v, literal)
     }
 };
 
-Greater: ast::Predicate = {
+Greater: symbols::Predicate = {
     ">" "(" <v:Positions> "," <literal:Position> ")" => {
-        Predicate::Greater(v, literal)
+        symbols::Predicate::Greater(v, literal)
     }
 };
 
-Equal: ast::Predicate = {
+Equal: symbols::Predicate = {
     "=" "(" <v:Positions> "," <literal:Position> ")" => {
-        Predicate::Equal(v, literal)
+        symbols::Predicate::Equal(v, literal)
     }
 };
 
-Not: ast::Predicate = {
+Not: symbols::Predicate = {
     "!" "(" <p:Predicates> ")" =>
-        Predicate::Not(Box::new(p))
+        symbols::Predicate::Not(Box::new(p))
 };
 
-And: ast::Predicate = {
+And: symbols::Predicate = {
     "&" "(" <lh:Predicates> "," <rh:Predicates> ")" =>
-        Predicate::And(Box::new(lh), Box::new(rh))
+        symbols::Predicate::And(Box::new(lh), Box::new(rh))
 };
 
-Or: ast::Predicate = {
+Or: symbols::Predicate = {
     "|" "(" <lh:Predicates> "," <rh:Predicates> ")" =>
-        Predicate::Or(Box::new(lh), Box::new(rh))
+        symbols::Predicate::Or(Box::new(lh), Box::new(rh))
 };
 
 // Arbitrary bag of positions.
-Bag: ast::Bag = {
+Bag: symbols::Bag = {
     "bag" "{" <elem:Bags> <list:("," Bags )*> "}" => {
         let mut bags = vec![elem];
 
@@ -222,7 +259,7 @@ Bag: ast::Bag = {
             bags.push(b);
         }
 
-        Bag::Bag(bags)
+        symbols::Bag::Bag(bags)
     }
 };
 
@@ -240,15 +277,15 @@ Bag: ast::Bag = {
 // of the cube [0,0], [1,1].
 
 // Returns the set of points outside the shape, (face included)
-Outside: ast::Bag = {
+Outside: symbols::Bag = {
     "outside" "(" <Shapes> ")" =>
-        Bag::Outside(<>)
+        symbols::Bag::Outside(<>)
 };
 
 // Returns the set of points inside the shape, (face included)
-Inside: ast::Bag = {
+Inside: symbols::Bag = {
     "inside" "(" <Shapes> ")" =>
-        Bag::Inside(<>)
+        symbols::Bag::Inside(<>)
 };
 
 //*********************************************************************/
@@ -257,7 +294,7 @@ Inside: ast::Bag = {
 
 // Shapes are defined in terms of POSITION, a.k.a a LiteralPosition
 // value, which is not a POSITIONS, which might be a filter for example.
-Shapes: ast::Shape = {
+Shapes: symbols::Shape = {
     Point,
     HyperRectangle,
     HyperSphere,
@@ -266,30 +303,50 @@ Shapes: ast::Shape = {
 
 // If the hyperrectangle is aligned with the axes, then two points are
 // enough, if not we need all the points to be specified.
-HyperRectangle: ast::Shape = {
+HyperRectangle: symbols::Shape = {
     "hyperrectangle" "{"
         <l:Position> "," <h:Position>
         <list:( "," Position "," Position )*>
+        <rs:( "," <String> )?>
     "}" => {
+        let space_id = match rs {
+            Some(id) => id,
+            None => space::name().clone(),
+        };
         let mut pos = vec![l, h];
         for (_, lh, _, rh) in list.iter() {
             pos.push(lh.clone());
             pos.push(rh.clone());
         }
-        Shape::HyperRectangle(pos)
+        symbols::Shape::HyperRectangle(space_id, pos)
     }
 };
 
 // A hypersphere is defined by its center and a radius, independantly
 // of the number of dimensions of the space.
-HyperSphere: ast::Shape = {
+HyperSphere: symbols::Shape = {
-    "hypersphere" "{" <c:Position> "," <r:PositiveNumber> "}" =>
+    "hypersphere" "{"
-        Shape::HyperSphere(c, r)
+        <c:Position> "," <r:PositiveNumber>
+        <rs:( "," <String> )?>
+    "}" => {
+        let space_id = match rs {
+            Some(id) => id,
+            None => space::name().clone(),
+        };
+
+        symbols::Shape::HyperSphere(space_id, c, r)
+    }
 };
 
-Point: ast::Shape = {
+Point: symbols::Shape = {
-    "point" "{" <Position> "}" =>
+    "point" "{" <pos:Position> <rs:( "," <String> )?> "}" => {
-        Shape::Point(<>)
+         let space_id = match rs {
+            Some(id) => id,
+            None => space::name().clone(),
+        };
+
+        symbols::Shape::Point(space_id, pos)
+    }
 };
 
 // Define a shape as the non-zero values in a NIfTI object, defined by
@@ -299,14 +356,18 @@ Point: ast::Shape = {
 //     rotation: [ position+ ], // Optional, no rotation by default
 //     bytes: uri(STRING)       // uri to the NIfTI object
 //   }
-Nifti: ast::Shape = {
+Nifti: symbols::Shape = {
     "nifti" "{"
-        String ","
+        <o:( Position "," )?>
-        ( Position "," )?
+        <rotation:( "[" Position ( "," Position)* "]" "," )?>
-        ( "[" Position ( "," Position)* "]" "," )?
+        <data:ByteProvider>
-        ByteProvider
+        <rs:( "," <String> )?>
     "}" => {
-        Shape::Nifti()
+        let space_id = match rs {
+            Some(id) => id,
+            None => space::name().clone(),
+        };
+        symbols::Shape::Nifti(space_id)
     }
 };
 
@@ -321,44 +382,44 @@ ByteProvider = { "uri" "(" String ")" };
 
 // Always returns a vector of numbers, a.k.a a position (a scalar will
 // be represented as a vector of one element)
-Positions: ast::Position = {
+Positions: symbols::Position = {
     StrCmpICase,
     StrCmp,
-    Selector => Position::Selector(<>),
+    Selector => symbols::Position::Selector(<>),
-    Position => Position::LiteralPosition(<>)
+    Position => symbols::Position::Literal(<>)
 };
 
 // Compare lexicographically two strings, and returns a `position`:
 //  [-1] : String is lexicographically before,
 //  [ 0] : is equal,
 //  [ 1] : is after.
-StrCmp: ast::Position = {
+StrCmp: symbols::Position = {
     "str_cmp" "(" <s:Selector> "," <v:String> ")" => {
-        Position::StrCmp(s, v)
+        symbols::Position::StrCmp(s, v)
     }
 };
 
 // Same, but case insensitive.
-StrCmpICase: ast::Position = {
+StrCmpICase: symbols::Position = {
     "str_cmp_ignore_case" "(" <s:Selector> "," <v:String> ")" => {
-        Position::StrCmpICase(s, v)
+        symbols::Position::StrCmpICase(s, v)
     }
 };
 
 // FIXME: FIELDS are expected to be exisiting in the data model. Root Object is assumed to be the type of the ressource on which the POST call was done.
-Selector = {
+Selector: symbols::LiteralSelector = {
-    ( <Field> )+
+    ( <Field> )+ => symbols::LiteralSelector(<>)
 };
 
-Position: ast::LiteralPosition = {
+Position: symbols::LiteralPosition = {
     "[" <element:Number> <list:( "," <Number>)*> "]" => {
-        let mut pos: LiteralPosition = vec![element];
+        let mut pos = vec![element];
 
         for e in list.iter() {
             pos.push(e.clone());
         }
 
-        pos
+        symbols::LiteralPosition(pos)
     }
 };
 
@@ -370,72 +431,75 @@ Position: ast::LiteralPosition = {
 //  1. start with a dot ('.')
 //  2. optionnally followed by a field name consisting of a letter or
 //     underscore, followed by letters, numbers or underscore,
-//  3. optionnally followed by brakets enclosing an natural number
+//  3. optionnally followed by brakets enclosing a natural number
 //     denoting an offset in a list or array.
-Field: Field = {
+Field: symbols::Field = {
     <n:r"[.]([a-zA-Z_][[a-zA-Z_0-9]]*)?([\[](0|[1-9][0-9]*)[\]])?"> => {
         if let Some(pos) = n.rfind('[') {
             let name = &n[1..pos];
             let index = &n[(pos+1)..(n.len()-1)];
             let index = usize::from_str(index).unwrap();
-            Field(String::from(name), Some(index))
+            symbols::Field(String::from(name), Some(index))
         } else {
             let name = &n[1..];
-            Field(String::from(name), None)
+            symbols::Field(String::from(name), None)
         }
     }
 };
 
 String: String = {
-    r#"["]([\\](["\\/bfnrt]|u[0-9a-fA-F]{4})|[^"\\\u0000-\u001F])*["]"# =>
+    r#"["]([\\](["\\/bfnrt]|u[0-9a-fA-F]{4})|[^"\\\u0000-\u001F])*["]"# => {
-        String::from(<>)
+        let s = <>;
+        let l = s.len() - 1;
+        s[1..l].to_string()
+    }
 };
 
 //*********************************************************************/
 // TOKENS - NUMBERS                                                   */
 //*********************************************************************/
 // We define 3 kinds of number, to avoid ambiguities in the rules.
-JsonNumber: ast::JsonValue = {
+JsonNumber: symbols::JsonValue = {
     <s:"-"?> <v:Num> => match s {
-        None => JsonValue::JsonNumber(v),
+        None => symbols::JsonValue::JsonNumber(v),
         Some(_) => match v {
-            LiteralNumber::Int(x) => JsonValue::JsonNumber(LiteralNumber::Int(-x)),
+            symbols::LiteralNumber::Int(x) => symbols::JsonValue::JsonNumber(symbols::LiteralNumber::Int(-x)),
-            LiteralNumber::Float(x) => JsonValue::JsonNumber(LiteralNumber::Float(-x))
+            symbols::LiteralNumber::Float(x) => symbols::JsonValue::JsonNumber(symbols::LiteralNumber::Float(-x))
         }
     }
 };
 
-PositiveNumber: ast::LiteralNumber = { "+"? <v:Num> => v };
+PositiveNumber: symbols::LiteralNumber = { "+"? <v:Num> => v };
 
-Number: ast::LiteralNumber = {
+Number: symbols::LiteralNumber = {
     "+" <v:Num> => v,
     "-" <v:Num> => match v {
-            LiteralNumber::Int(x) => LiteralNumber::Int(-x),
+            symbols::LiteralNumber::Int(x) => symbols::LiteralNumber::Int(-x),
-            LiteralNumber::Float(x) => LiteralNumber::Float(-x)
+            symbols::LiteralNumber::Float(x) => symbols::LiteralNumber::Float(-x)
         },
     <v:Num> => v
 
 };
 
-Num: ast::LiteralNumber = {
+Num: symbols::LiteralNumber = {
     r"0([.][0-9]+([eE][+\-]?(0|[1-9][0-9]*))?)?"
         => {
            if let Ok(v) = i64::from_str(<>) {
-                LiteralNumber::Int(v)
+                symbols::LiteralNumber::Int(v)
             } else {
                 // Either parsing as a float succeed or we pass along
                 // the error
-                LiteralNumber::Float(f64::from_str(<>).unwrap())
+                symbols::LiteralNumber::Float(f64::from_str(<>).unwrap())
             }
     },
     r"[1-9][0-9]*([.][0-9]+)?([eE][+\-]?(0|[1-9][0-9]*))?"
         => {
             if let Ok(v) = i64::from_str(<>) {
-                LiteralNumber::Int(v)
+                symbols::LiteralNumber::Int(v)
             } else {
                 // Either parsing as a float succeed or we pass along
                 // the error
-                LiteralNumber::Float(f64::from_str(<>).unwrap())
+                symbols::LiteralNumber::Float(f64::from_str(<>).unwrap())
             }
         }
 };

src/symbols.rs

@@ -0,0 +1,319 @@
+use std::cmp::Ordering;
+
+use super::database::space;
+pub use super::types::*;
+
+/**********************************************************************/
+/* FORMATTING DATA                                                    */
+/**********************************************************************/
+#[derive(Clone, Debug)]
+pub enum Projection {
+    Nifti(String, LiteralSelector, Bag),
+    JSON(String, JsonValue, Bag),
+}
+
+impl Projection {
+    pub fn space(&self) -> &String {
+        match self {
+            Projection::Nifti(space, _, _) => &space,
+            Projection::JSON(space, _, _) => &space,
+        }
+    }
+}
+
+// JSON FORMAT
+#[derive(Clone, Debug)]
+pub enum JsonValue {
+    String(String),
+    JsonNumber(LiteralNumber),
+    Bool(bool),
+    Null,
+    Object(Vec<(String, JsonValue)>),
+    Array(Vec<JsonValue>),
+    Selector(LiteralSelector),
+    Aggregation(Aggregation),
+}
+
+#[derive(Clone, Debug)]
+pub enum Aggregation {
+    Count(bool, LiteralSelector),
+    Sum(LiteralSelector),
+    Min(LiteralSelector),
+    Max(LiteralSelector),
+}
+
+// NIFTI
+#[derive(Clone, Debug)]
+struct Transform {
+    reference: String,
+    offset: Vec<LiteralNumber>,
+    rotation: Vec<Vec<LiteralNumber>>,
+}
+
+/**********************************************************************/
+/* SELECTING / FILTERING DATA                                         */
+/**********************************************************************/
+#[derive(Clone, Debug)]
+pub enum Bag {
+    Distinct(Box<Bag>),
+    Filter(Option<Predicate>, Box<Bag>),
+    Complement(Box<Bag>),
+    Intersection(Box<Bag>, Box<Bag>),
+    Union(Box<Bag>, Box<Bag>),
+    Bag(Vec<Bag>),
+    Inside(Shape),
+    Outside(Shape),
+}
+
+impl Bag {
+    pub fn space(&self) -> &String {
+        match self {
+            Bag::Distinct(bag) => bag.space(),
+            Bag::Filter(_, bag) => bag.space(),
+            Bag::Complement(bag) => bag.space(),
+            Bag::Intersection(lh, _) => {
+                // We are assuming lh and rh are in the same space.
+                // Checked as part of the validation.
+                lh.space()
+            }
+            Bag::Union(lh, _) => {
+                // We are assuming lh and rh are in the same space.
+                // Checked as part of the validation.
+                lh.space()
+            }
+            Bag::Bag(_) => {
+                // Bags can be defined in different spaces, thus the output is
+                // always in the universe space.
+                space::name()
+            }
+            Bag::Inside(shape) => shape.space(),
+            Bag::Outside(shape) => shape.space(),
+        }
+    }
+}
+/**********************************************************************/
+/* BAG OPERATORS                                                      */
+/**********************************************************************/
+#[derive(Clone, Debug)]
+pub enum Predicate {
+    Less(Position, LiteralPosition),
+    Greater(Position, LiteralPosition),
+    Equal(Position, LiteralPosition),
+    Not(Box<Predicate>),
+    And(Box<Predicate>, Box<Predicate>),
+    Or(Box<Predicate>, Box<Predicate>),
+}
+
+/**********************************************************************/
+/* SPATIAL OPERATORS                                                  */
+/**********************************************************************/
+
+/**********************************************************************/
+/* SHAPES                                                             */
+/**********************************************************************/
+#[derive(Clone, Debug)]
+pub enum Shape {
+    Point(String, LiteralPosition),
+    HyperRectangle(String, Vec<LiteralPosition>),
+    HyperSphere(String, LiteralPosition, LiteralNumber),
+    Nifti(String),
+}
+
+impl Shape {
+    pub fn space(&self) -> &String {
+        match self {
+            Shape::Point(space, _) => space,
+            Shape::HyperRectangle(space, _) => space,
+            Shape::HyperSphere(space, _, _) => space,
+            Shape::Nifti(space) => space,
+        }
+    }
+
+    pub fn volume(&self) -> f64 {
+        match self {
+            Shape::Point(_, _) => 1.0, // This is the smallest non-zero volume possible //TODO DOUBLE CHECK IT IS TRUE
+            Shape::HyperRectangle(_space, pos) => {
+                //TODO: At this time, only aligned to the axes, defined by two points, hyperrectangles are supported.
+                assert_eq!(pos.len(), 2);
+
+                // We assume the first position is the low point, the second is
+                // the high point, this being true for each dimension. As we add
+                // an even number of points per extra dimension, we assume the
+                // last group is the high end, and the last position is the
+                // highest point.
+                let mut volume = 1.0;
+                let LiteralPosition(low) = &pos[0];
+                let LiteralPosition(high) = &pos[pos.len() - 1];
+
+                // For each dimension, multiply by the length in that dimension
+                for i in 0..low.len() {
+                    let l = match low[i] {
+                        LiteralNumber::Int(x) => x as f64,
+                        LiteralNumber::Float(x) => x,
+                    };
+
+                    let h = match high[i] {
+                        LiteralNumber::Int(x) => x as f64,
+                        LiteralNumber::Float(x) => x,
+                    };
+
+                    let length = if h > l { h - l } else { l - h };
+                    volume *= length;
+                }
+
+                volume
+            }
+            Shape::HyperSphere(_space, pos, r) => {
+                // Formula from https://en.wikipedia.org/wiki/N-sphere#/media/File:N_SpheresVolumeAndSurfaceArea.png
+                let LiteralPosition(p) = pos;
+                let k = p.len(); // Number of dimensions.
+
+                let r = match *r {
+                    LiteralNumber::Int(x) => x as f64,
+                    LiteralNumber::Float(x) => x,
+                };
+
+                let pi = std::f64::consts::PI;
+                let factor = 2.0 * pi;
+
+                // Set starting values for the coefficient
+                let mut a = 2.0;
+                let mut i = 1;
+
+                if (k % 2) == 0 {
+                    a = pi;
+                    i = 2;
+                }
+
+                while i < k {
+                    i += 2;
+                    a *= factor;
+                    a /= i as f64;
+                }
+
+                a * r.powi(i as i32)
+            }
+            Shape::Nifti(_) => unimplemented!(),
+        }
+    }
+}
+
+/**********************************************************************/
+/* POSITIONS                                                          */
+/**********************************************************************/
+#[derive(Clone, Debug)]
+pub enum Position {
+    StrCmpICase(LiteralSelector, String),
+    StrCmp(LiteralSelector, String),
+    Selector(LiteralSelector),
+    Literal(LiteralPosition),
+}
+
+/**********************************************************************/
+/* Literals / TOKENS                                                  */
+/**********************************************************************/
+
+#[derive(Clone, Debug)]
+pub struct Field(pub String, pub Option<usize>);
+
+#[derive(Clone, Debug)]
+pub enum LiteralNumber {
+    Int(i64),
+    Float(f64),
+}
+
+impl PartialEq for LiteralNumber {
+    fn eq(&self, other: &LiteralNumber) -> bool {
+        match self {
+            LiteralNumber::Int(l) => match other {
+                LiteralNumber::Int(r) => l == r,
+                LiteralNumber::Float(_) => false,
+            },
+            LiteralNumber::Float(l) => match other {
+                LiteralNumber::Int(r) => l == &(*r as f64),
+                LiteralNumber::Float(r) => l == r,
+            },
+        }
+    }
+}
+
+#[derive(Clone, Debug)]
+pub struct LiteralPosition(pub Vec<LiteralNumber>);
+
+impl LiteralPosition {
+    pub fn get_type(&self) -> LiteralTypes {
+        let Self(v) = self;
+        let mut t = Vec::new();
+
+        for n in v {
+            t.push(match n {
+                LiteralNumber::Int(_) => LiteralTypes::Int,
+                LiteralNumber::Float(_) => LiteralTypes::Float,
+            });
+        }
+
+        LiteralTypes::Vector(t)
+    }
+
+    pub fn length(&self) -> f64 {
+        let LiteralPosition(v) = self;
+        let mut a = 0.0;
+
+        for x in v {
+            let x = match x {
+                LiteralNumber::Int(x) => (*x) as f64,
+                LiteralNumber::Float(x) => *x,
+            };
+
+            a += x * x;
+        }
+
+        a
+    }
+}
+
+impl PartialOrd for LiteralPosition {
+    fn partial_cmp(&self, other: &LiteralPosition) -> Option<Ordering> {
+        let LiteralPosition(lh) = self;
+        let LiteralPosition(rh) = other;
+
+        if lh.len() != rh.len() {
+            None
+        } else {
+            // Order is defined by the geometric length of the vector between the Origin and the point.
+            let l = self.length();
+            let r = other.length();
+
+            l.partial_cmp(&r)
+        }
+    }
+}
+
+impl PartialEq for LiteralPosition {
+    fn eq(&self, other: &LiteralPosition) -> bool {
+        let LiteralPosition(lh) = self;
+        let LiteralPosition(rh) = other;
+
+        if lh.len() == rh.len() {
+            for i in 0..lh.len() {
+                if lh[i] != rh[i] {
+                    return false;
+                }
+            }
+
+            true
+        } else {
+            false
+        }
+    }
+}
+
+#[derive(Clone, Debug)]
+pub struct LiteralSelector(pub Vec<Field>);
+
+impl LiteralSelector {
+    pub fn get_type(&self) -> LiteralTypes {
+        // FIXME: Pretend for now that everything is a number, needs to be actually looked up in data model.
+        LiteralTypes::Int
+    }
+}

src/types.rs

@@ -0,0 +1,59 @@
+#[derive(Clone, Debug)]
+pub enum LiteralTypes {
+    String,
+    Int,
+    Float,
+    Bag(Vec<LiteralTypes>),          // List of types (heterogeneous)
+    Vector(Vec<LiteralTypes>),       // List of coordinates types (heterogeneous)
+    Array(usize, Box<LiteralTypes>), // Length, homogeneous type
+}
+
+impl PartialEq for LiteralTypes {
+    fn eq(&self, other: &Self) -> bool {
+        match self {
+            LiteralTypes::String => match other {
+                LiteralTypes::String => true,
+                _ => false,
+            },
+            LiteralTypes::Int => match other {
+                LiteralTypes::Int => true,
+                _ => false,
+            },
+            LiteralTypes::Float => match other {
+                LiteralTypes::Float => true,
+                LiteralTypes::Int => true,
+                _ => false,
+            },
+            LiteralTypes::Bag(_) => match other {
+                LiteralTypes::Bag(_) => true,
+                _ => false,
+            },
+            LiteralTypes::Vector(v) => match other {
+                LiteralTypes::Vector(ov) => {
+                    let n = v.len();
+                    if n != ov.len() {
+                        false
+                    } else {
+                        for i in 0..n {
+                            if v[i] != ov[i] {
+                                return false;
+                            }
+                        }
+                        true
+                    }
+                }
+                _ => false,
+            },
+            LiteralTypes::Array(n, t) => match other {
+                LiteralTypes::Array(on, ot) => {
+                    if on == n {
+                        t == ot
+                    } else {
+                        false
+                    }
+                }
+                _ => false,
+            },
+        }
+    }
+}

src/validators.rs

@@ -0,0 +1,171 @@
+use super::database::space;
+use super::expression::Validator;
+use super::symbols::*;
+
+pub type ValidationResult = Result<LiteralTypes, String>;
+
+impl Validator for Projection {
+    type ValidationResult = self::ValidationResult;
+
+    fn validate(&self) -> ValidationResult {
+        match self {
+            Projection::Nifti(_, _, _) => Err("not yet implemented".to_string()),
+            Projection::JSON(_, _format, bag) => bag.validate(),
+            //FIXME: Add support for projections
+            /* match format.validate() {
+                Ok(_) => bag.validate(),
+                Err(_) => Err(()),
+            }*/
+        }
+    }
+}
+
+impl Validator for Bag {
+    type ValidationResult = self::ValidationResult;
+
+    fn validate(&self) -> ValidationResult {
+        fn compare_bag_types(lh: &Box<Bag>, rh: &Box<Bag>) -> ValidationResult {
+            if lh.space().cmp(rh.space()) != std::cmp::Ordering::Equal {
+                return Err(format!(
+                    "left and right sets are defined in different reference spaces: '{}' vs '{}'.",
+                    lh.space(),
+                    rh.space()
+                ));
+            }
+
+            let l = lh.validate();
+            let r = rh.validate();
+
+            match &l {
+                Err(_) => l,
+                Ok(tl) => match r {
+                    e @ Err(_) => e,
+                    Ok(tr) => {
+                        if tl != &tr {
+                            Err(format!(
+                                "Incoherent types between left and right sets: '{:?}' vs '{:?}'",
+                                tl, &tr
+                            ))
+                        } else {
+                            l
+                        }
+                    }
+                },
+            }
+        }
+
+        match self {
+            Bag::Distinct(bag) => bag.validate(),
+            Bag::Filter(_, bag) => bag.validate(),
+            Bag::Complement(bag) => bag.validate(),
+            Bag::Intersection(lh, rh) => compare_bag_types(lh, rh),
+            Bag::Union(lh, rh) => compare_bag_types(lh, rh),
+            Bag::Bag(bags) => {
+                for b in bags {
+                    let t = b.validate();
+                    if t.is_err() {
+                        return t;
+                    }
+                }
+
+                Ok(space::get_type(space::name()).clone())
+            }
+            Bag::Inside(shape) => shape.validate(),
+            Bag::Outside(shape) => shape.validate(),
+        }
+    }
+}
+
+impl Validator for Shape {
+    type ValidationResult = self::ValidationResult;
+
+    fn validate(&self) -> ValidationResult {
+        match self {
+            Shape::Point(_, v) => v.validate(),
+            Shape::HyperRectangle(_space, pos) => {
+                let first = pos[0].get_type();
+                match pos.len() {
+                    2 => {
+                        if first != pos[1].get_type() {
+                            Err(format!(
+                                "HyperRectangle: Incompatible types in points definitions: '{:?}' vs '{:?}'",
+                                first,
+                                pos[1].get_type()
+                            ))
+                        } else {
+                            Ok(first)
+                        }
+                    }
+                    _ => {
+                        //FIXME: Implement arbitrary hypercube definition support. For now reject.
+                        Err("not yet implemented".to_string())
+                        /*
+                        fn check_orthogonal(pos: &Vec<LiteralPosition>) -> bool {
+                            let k = pos.len();
+                            let mut raw_pos = vec![];
+
+                            for s in pos {
+                                match s {
+                                    LiteralTypes::Vector(n) => {
+                                        let mut v = vec![];
+                                        for c in n {
+                                            v.push(match c {
+                                                LiteralNumber::Int(x) => x as f64,
+                                                LiteralNumber::Float(x) => x,
+                                            });
+                                        }
+                                        raw_pos.push(v)
+                                    }
+                                    _ => pass,
+                                }
+                            }
+
+                            for p in raw_pos {}
+                            true
+                        }
+                        match &first {
+                            LiteralTypes::Vector(n) => {
+                                if 2usize.pow(n.len() as u32) == pos.len() {
+                                    // Check we have coherent types for the coordinates.
+                                    for point in pos {
+                                        if first != point.get_type() {
+                                            return Err(());
+                                        }
+                                    }
+
+                                    // We need to check the points define a shape with orthogonal faces.
+                                    if check_orthogonal(pos) {
+                                        Ok(first)
+                                    } else {
+                                        Err(())
+                                    }
+                                } else {
+                                    Err(())
+                                }
+                            }
+                            _ => Err(()),
+                        }*/
+                    }
+                }
+            }
+            Shape::HyperSphere(_, pos, _) => pos.validate(),
+            Shape::Nifti(_) => Err("not yet implemented".to_string()),
+        }
+    }
+}
+
+impl Validator for LiteralPosition {
+    type ValidationResult = self::ValidationResult;
+
+    fn validate(&self) -> ValidationResult {
+        Ok(self.get_type())
+    }
+}
+
+impl Validator for LiteralSelector {
+    type ValidationResult = self::ValidationResult;
+
+    fn validate(&self) -> ValidationResult {
+        Ok(self.get_type())
+    }
+}