Domains test

.gitmodules

@@ -0,0 +1,4 @@
+[submodule "winnow"]
+	path = winnow
+	url = git@github.com:supersurviveur/winnow.git
+	branch = operator-in-expression

1.pl

@@ -1,9 +1,22 @@
+:- use_module(library(clpfd)).
+
 entier(zero).
 entier(s(X)) :- entier(X).
 
 add(X, zero, X).
 add(X, s(Y), Z) :- add(s(X), Y, Z).
 
+inf(zero, X) :- entier(X).
+inf(s(X), s(Y)) :- inf(X, Y).
+
 mult(zero, X, zero).
 mult(s(Y), X, Z) :- mult(Y, X, W), add(W, X, Z).
 
+div(A, B) :- inf(A, B), inf(X, B), mult(X, A, B).
+div_w(X, Y) :- inf(s(X), Y), inf(s(s(zero)), X), div(X, Y).
+prime(X) :- entier(X), \+ div_w(_, X).
+
+peano(X, zero) :- X #= 0.
+peano(X, s(P)) :- X #> 0, X #= Y + 1, peano(Y, P).
+
+

Cargo.lock

@@ -11,6 +11,12 @@ dependencies = [
  "memchr",
 ]
 
+[[package]]
+name = "allocator-api2"
+version = "0.2.21"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "683d7910e743518b0e34f1186f92494becacb047c7b6bf616c96772180fef923"
+
 [[package]]
 name = "anstream"
 version = "0.6.21"
@@ -61,6 +67,12 @@ dependencies = [
  "windows-sys",
 ]
 
+[[package]]
+name = "bimap"
+version = "0.6.3"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "230c5f1ca6a325a32553f8640d31ac9b49f2411e901e427570154868b46da4f7"
+
 [[package]]
 name = "colorchoice"
 version = "1.0.4"
@@ -90,6 +102,29 @@ dependencies = [
  "log",
 ]
 
+[[package]]
+name = "equivalent"
+version = "1.0.2"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "877a4ace8713b0bcf2a4e7eec82529c029f1d0619886d18145fea96c3ffe5c0f"
+
+[[package]]
+name = "foldhash"
+version = "0.2.0"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "77ce24cb58228fbb8aa041425bb1050850ac19177686ea6e0f41a70416f56fdb"
+
+[[package]]
+name = "hashbrown"
+version = "0.16.1"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "841d1cc9bed7f9236f321df977030373f4a4163ae1a7dbfe1a51a2c1a51d9100"
+dependencies = [
+ "allocator-api2",
+ "equivalent",
+ "foldhash",
+]
+
 [[package]]
 name = "is_terminal_polyfill"
 version = "1.70.2"
@@ -120,18 +155,21 @@ dependencies = [
  "syn",
 ]
 
-[[package]]
-name = "litemap"
-version = "0.8.1"
-source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "6373607a59f0be73a39b6fe456b8192fcc3585f602af20751600e974dd455e77"
-
 [[package]]
 name = "log"
 version = "0.4.29"
 source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "5e5032e24019045c762d3c0f28f5b6b8bbf38563a65908389bf7978758920897"
 
+[[package]]
+name = "lru"
+version = "0.16.3"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "a1dc47f592c06f33f8e3aea9591776ec7c9f9e4124778ff8a3c3b87159f7e593"
+dependencies = [
+ "hashbrown",
+]
+
 [[package]]
 name = "memchr"
 version = "2.8.0"
@@ -144,13 +182,21 @@ version = "1.70.2"
 source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "384b8ab6d37215f3c5301a95a4accb5d64aa607f1fcb26a11b5303878451b4fe"
 
+[[package]]
+name = "owo-colors"
+version = "4.2.3"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "9c6901729fa79e91a0913333229e9ca5dc725089d1c363b2f4b4760709dc4a52"
+
 [[package]]
 name = "picolog"
 version = "0.1.0"
 dependencies = [
+ "bimap",
  "env_logger",
- "litemap",
  "log",
+ "lru",
+ "owo-colors",
  "winnow",
 ]
 
@@ -277,8 +323,6 @@ dependencies = [
 [[package]]
 name = "winnow"
 version = "0.7.14"
-source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "5a5364e9d77fcdeeaa6062ced926ee3381faa2ee02d3eb83a5c27a8825540829"
 dependencies = [
  "memchr",
 ]

Cargo.toml

@@ -4,7 +4,9 @@ version = "0.1.0"
 edition = "2024"
 
 [dependencies]
+bimap = "0.6.3"
 env_logger = "0.11.8"
-litemap = "0.8.1"
 log = "0.4.29"
-winnow = "0.7.14"
+winnow = { version = "0.7.14", path = "./winnow" }
+lru = "0.16.3"
+owo-colors = "4.2.3"

rustfmt.toml

@@ -0,0 +1,5 @@
+brace_style="AlwaysNextLine"
+control_brace_style="AlwaysNextLine"
+combine_control_expr=false
+
+

src/ast.rs

@@ -1,6 +1,11 @@
+use owo_colors::{OwoColorize, colors::css::Gray};
+
 use std::fmt::Display;
 
-pub type Variable = String;
+use crate::domain::Domain;
+
+#[derive(Clone, PartialEq, Eq, Debug, Hash)]
+pub struct Variable(pub String, pub Option<usize>);
 
 #[derive(Clone, Debug)]
 pub struct Module
@@ -15,7 +20,7 @@ pub struct Clause
     pub body: Option<Body>,
 }
 
-#[derive(Clone, Debug)]
+#[derive(Clone, Debug, PartialEq, Eq, Hash)]
 pub enum Body
 {
     Term(Predicate),
@@ -23,11 +28,48 @@ pub enum Body
     Or(Vec<Body>),
 }
 
-#[derive(Clone, Debug, PartialEq)]
+#[derive(Clone, Debug, Eq, PartialEq, Hash)]
 pub enum Predicate
 {
     Variable(Variable), // Upercase variable like X
-    Fixed(String, Vec<Predicate>),
+    Fixed(Functor, Vec<Predicate>),
+    Domain(Domain),
+}
+
+#[derive(Clone, Debug, PartialEq, Eq, Hash)]
+pub enum Functor
+{
+    Operator(Operator),
+    Functor(String),
+}
+
+#[derive(Clone, Debug, PartialEq, Eq, Hash)]
+pub struct Operator
+{
+    pub op: String,
+    pub precedence: usize,
+    pub op_type: OperatorType,
+}
+
+impl Operator
+{
+    pub fn new(op: String, precedence: usize, op_type: OperatorType) -> Self
+    {
+        Self {
+            op,
+            precedence,
+            op_type,
+        }
+    }
+}
+
+#[derive(Clone, Debug, PartialEq, Eq, Hash)]
+pub enum OperatorType
+{
+    Prefix,
+    Postfix,
+    LeftInfix,
+    RightInfix,
 }
 
 impl Display for Body
@@ -54,6 +96,19 @@ impl Display for Body
     }
 }
 
+impl Display for Variable
+{
+    fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result
+    {
+        write!(f, "{}", self.0)?;
+        if let Some(num) = self.1
+        {
+            write!(f, "{}", format!("[{}]", num).fg::<Gray>())?;
+        }
+        Ok(())
+    }
+}
+
 impl Display for Predicate
 {
     fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result
@@ -83,6 +138,7 @@ impl Display for Predicate
                     Ok(())
                 }
             }
+            Predicate::Domain(domain) => write!(f, "{domain}"),
         }
     }
 }
@@ -110,3 +166,23 @@ impl Display for Module
         Ok(())
     }
 }
+
+impl Display for Functor
+{
+    fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result
+    {
+        match self
+        {
+            Functor::Operator(op) => write!(f, "{}", op),
+            Functor::Functor(name) => write!(f, "{}", name),
+        }
+    }
+}
+
+impl Display for Operator
+{
+    fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result
+    {
+        write!(f, "{}", self.op)
+    }
+}

src/domain.rs

@@ -0,0 +1,512 @@
+use std::{cmp, fmt::Display};
+
+use crate::domain;
+
+#[derive(Clone, Debug, PartialEq, Eq, Hash)]
+pub struct Domain
+{
+    pub union: Vec<DomainRange>,
+}
+
+#[derive(Clone, Copy, Debug, PartialEq, Eq, Hash)]
+pub struct DomainRange
+{
+    pub start: DomainBound,
+    pub end: DomainBound,
+}
+
+#[derive(Clone, Copy, Debug, PartialEq, Eq, Hash)]
+pub enum DomainBound
+{
+    Unbounded,
+    Bounded(i64),
+}
+
+impl Domain
+{
+    pub fn all() -> Domain
+    {
+        Domain {
+            union: vec![DomainRange {
+                start: DomainBound::Unbounded,
+                end: DomainBound::Unbounded,
+            }],
+        }
+    }
+
+    pub fn included_in(&self, domain: &Domain) -> bool
+    {
+        self.union(domain) == *domain
+    }
+
+    pub fn empty(&self) -> bool
+    {
+        self.union.len() == 0
+    }
+
+    pub fn disjoint(&self, domain: &Domain) -> bool
+    {
+        self.intersection(domain).union.len() == 0
+    }
+
+    pub fn intersection(&self, domain: &Domain) -> Domain
+    {
+        let mut i = 0;
+        let mut j = 0;
+        let mut stack = vec![];
+
+        while i < self.union.len() || j < domain.union.len()
+        {
+            if i < self.union.len() && j < domain.union.len()
+            {
+                let a = self.union[i];
+                let b = domain.union[j];
+
+                if a.disjoint(&b)
+                {
+                    if a < b
+                    {
+                        i += 1;
+                    }
+                    else
+                    {
+                        j += 1;
+                    }
+                }
+                else
+                {
+                    let inter = a.intersection(&b);
+                    if let Some(range) = inter
+                    {
+                        stack.push(range);
+                    };
+                    if a.ends_furthest(&b)
+                    {
+                        i += 1;
+                    }
+                    else
+                    {
+                        j += 1;
+                    }
+                }
+            }
+            else
+            {
+                break;
+            }
+        }
+
+        Domain { union: stack }
+    }
+
+    pub fn union(&self, domain: &Domain) -> Domain
+    {
+        let mut i = 0;
+        let mut j = 0;
+        let mut stack = vec![];
+
+        while i < self.union.len() || j < domain.union.len()
+        {
+            if i < self.union.len() && j < domain.union.len()
+            {
+                let a = self.union[i];
+                let b = domain.union[j];
+
+                let (min, max) = (a.min(b), a.max(b));
+
+                if let DomainBound::Bounded(end) = min.end
+                    && let DomainBound::Bounded(start) = max.start
+                    && end == start
+                {
+                    let union = a.union(&b);
+                    stack.extend_from_slice(union.union.as_slice());
+                    i += 1;
+                    j += 1;
+                }
+                else if a.disjoint(&b)
+                {
+                    if a < b
+                    {
+                        stack.push(a);
+                        i += 1;
+                    }
+                    else
+                    {
+                        stack.push(b);
+                        j += 1;
+                    }
+                }
+                else
+                {
+                    let union = a.union(&b);
+                    stack.extend_from_slice(union.union.as_slice());
+                    i += 1;
+                    j += 1;
+                }
+            }
+            else if i < self.union.len()
+            {
+                stack.extend_from_slice(&self.union[i..]);
+                i = self.union.len();
+            }
+            else
+            {
+                stack.extend_from_slice(&domain.union[j..]);
+                j = self.union.len();
+            }
+        }
+
+        Domain { union: stack }
+    }
+}
+
+impl From<DomainRange> for Domain
+{
+    fn from(value: DomainRange) -> Self
+    {
+        Domain { union: vec![value] }
+    }
+}
+
+impl DomainBound
+{
+    pub fn min_start(&self, bound: DomainBound) -> DomainBound
+    {
+        match (self, bound)
+        {
+            (DomainBound::Unbounded, DomainBound::Unbounded) => DomainBound::Unbounded,
+            (DomainBound::Bounded(_), DomainBound::Unbounded)
+            | (DomainBound::Unbounded, DomainBound::Bounded(_)) => DomainBound::Unbounded,
+            (DomainBound::Bounded(a), DomainBound::Bounded(b)) => DomainBound::Bounded(*a.min(&b)),
+        }
+    }
+
+    pub fn max_end(&self, bound: DomainBound) -> DomainBound
+    {
+        match (self, bound)
+        {
+            (DomainBound::Unbounded, DomainBound::Unbounded) => DomainBound::Unbounded,
+            (DomainBound::Bounded(_), DomainBound::Unbounded)
+            | (DomainBound::Unbounded, DomainBound::Bounded(_)) => DomainBound::Unbounded,
+            (DomainBound::Bounded(a), DomainBound::Bounded(b)) => DomainBound::Bounded(*a.max(&b)),
+        }
+    }
+}
+
+impl PartialOrd for DomainRange
+{
+    fn partial_cmp(&self, other: &Self) -> Option<cmp::Ordering>
+    {
+        Some(self.cmp(other))
+    }
+}
+
+impl Ord for DomainRange
+{
+    fn cmp(&self, other: &Self) -> std::cmp::Ordering
+    {
+        match (self.start, other.start)
+        {
+            (DomainBound::Unbounded, DomainBound::Unbounded) => cmp::Ordering::Equal,
+            (DomainBound::Unbounded, DomainBound::Bounded(_)) => cmp::Ordering::Less,
+            (DomainBound::Bounded(_), DomainBound::Unbounded) => cmp::Ordering::Greater,
+            (DomainBound::Bounded(a), DomainBound::Bounded(b)) => a.cmp(&b),
+        }
+    }
+}
+
+impl DomainRange
+{
+    pub fn intersection(&self, range: &DomainRange) -> Option<DomainRange>
+    {
+        let (min, max) = (self.min(range), self.max(range));
+        match (min.end, max.start)
+        {
+            (DomainBound::Unbounded, DomainBound::Unbounded) => Some(DomainRange {
+                start: DomainBound::Unbounded,
+                end: DomainBound::Unbounded,
+            }),
+            (DomainBound::Unbounded, DomainBound::Bounded(a)) => Some(DomainRange {
+                start: DomainBound::Bounded(a),
+                end: max.end,
+            }),
+            (DomainBound::Bounded(a), DomainBound::Unbounded) => Some(DomainRange {
+                start: max.start,
+                end: DomainBound::Bounded(a),
+            }),
+            (DomainBound::Bounded(a), DomainBound::Bounded(b)) if b < a => Some(DomainRange {
+                start: DomainBound::Bounded(b),
+                end: DomainBound::Bounded(a),
+            }),
+            _ => None,
+        }
+    }
+
+    pub fn union(&self, range: &DomainRange) -> Domain
+    {
+        if self.disjoint(range)
+        {
+            let (a, b) = (self.min(range), self.max(range));
+            if let DomainBound::Bounded(end) = a.end
+                && let DomainBound::Bounded(start) = b.start
+                && end == start
+            {
+                Domain {
+                    union: vec![DomainRange {
+                        start: a.start,
+                        end: b.end,
+                    }],
+                }
+            }
+            else
+            {
+                Domain {
+                    union: vec![*self.min(range), *self.max(range)],
+                }
+            }
+        }
+        else
+        {
+            let (a, b) = (self.min(range), self.max(range));
+            let range = DomainRange {
+                start: match (a.start, b.start)
+                {
+                    (DomainBound::Bounded(a), DomainBound::Bounded(b)) =>
+                    {
+                        DomainBound::Bounded(a.min(b))
+                    }
+                    (DomainBound::Unbounded, DomainBound::Bounded(_))
+                    | (DomainBound::Bounded(_), DomainBound::Unbounded)
+                    | (DomainBound::Unbounded, DomainBound::Unbounded) => DomainBound::Unbounded,
+                },
+                end: match (a.end, b.end)
+                {
+                    (DomainBound::Bounded(a), DomainBound::Bounded(b)) =>
+                    {
+                        DomainBound::Bounded(a.max(b))
+                    }
+                    (DomainBound::Unbounded, DomainBound::Bounded(_))
+                    | (DomainBound::Bounded(_), DomainBound::Unbounded)
+                    | (DomainBound::Unbounded, DomainBound::Unbounded) => DomainBound::Unbounded,
+                },
+            };
+
+            Domain { union: vec![range] }
+        }
+    }
+
+    pub fn ends_furthest(&self, end: &DomainRange) -> bool
+    {
+        match (self.end, end.end)
+        {
+            (DomainBound::Unbounded, DomainBound::Unbounded) => true,
+            (DomainBound::Unbounded, DomainBound::Bounded(_)) => true,
+            (DomainBound::Bounded(_), DomainBound::Unbounded) => false,
+            (DomainBound::Bounded(a), DomainBound::Bounded(b)) => a >= b,
+        }
+    }
+
+    pub fn disjoint(&self, range: &DomainRange) -> bool
+    {
+        let (a, b) = (self.min(range), self.max(range));
+        matches!((a.end, b.start), (DomainBound::Bounded(a), DomainBound::Bounded(b)) if a <= b)
+    }
+
+    pub fn singleton(value: i64) -> DomainRange
+    {
+        DomainRange {
+            start: DomainBound::Bounded(value),
+            end: DomainBound::Bounded(value + 1),
+        }
+    }
+
+    pub fn from(value: i64) -> DomainRange
+    {
+        DomainRange {
+            start: DomainBound::Bounded(value),
+            end: DomainBound::Unbounded,
+        }
+    }
+
+    pub fn to(value: i64) -> DomainRange
+    {
+        DomainRange {
+            start: DomainBound::Unbounded,
+            end: DomainBound::Bounded(value),
+        }
+    }
+
+    pub fn closed(start: i64, end: i64) -> DomainRange
+    {
+        DomainRange {
+            start: DomainBound::Bounded(start),
+            end: DomainBound::Bounded(end),
+        }
+    }
+}
+
+impl Display for Domain
+{
+    fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result
+    {
+        let len = self.union.len();
+        for (i, range) in self.union.iter().enumerate()
+        {
+            write!(f, "{}", range)?;
+            if i != len - 1
+            {
+                write!(f, " ∪ ")?;
+            }
+        }
+        Ok(())
+    }
+}
+
+impl Display for DomainRange
+{
+    fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result
+    {
+        match (self.start, self.end)
+        {
+            (DomainBound::Bounded(a), DomainBound::Bounded(b)) if b == a + 1 => write!(f, "{}", a),
+            (a, b) => write!(f, "{}..{}", a, b),
+        }
+    }
+}
+
+impl Display for DomainBound
+{
+    fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result
+    {
+        match self
+        {
+            DomainBound::Unbounded => Ok(()),
+            DomainBound::Bounded(n) => write!(f, "{}", n),
+        }
+    }
+}
+
+mod test
+{
+    #[allow(unused_imports)]
+    use crate::domain::{Domain, DomainBound, DomainRange};
+
+    #[test]
+    pub fn domain_range_parse()
+    {
+        let a: DomainRange = "..".into();
+        assert_eq!(
+            a,
+            DomainRange {
+                start: DomainBound::Unbounded,
+                end: DomainBound::Unbounded
+            }
+        );
+
+        let a: DomainRange = "42..".into();
+        assert_eq!(
+            a,
+            DomainRange {
+                start: DomainBound::Bounded(42),
+                end: DomainBound::Unbounded
+            }
+        );
+
+        let a: DomainRange = "..42".into();
+        assert_eq!(
+            a,
+            DomainRange {
+                start: DomainBound::Unbounded,
+                end: DomainBound::Bounded(42),
+            }
+        );
+
+        let a: DomainRange = "0..42".into();
+        assert_eq!(
+            a,
+            DomainRange {
+                start: DomainBound::Bounded(0),
+                end: DomainBound::Bounded(42),
+            }
+        );
+    }
+
+    #[test]
+    pub fn domain_range_union()
+    {
+        let inf: DomainRange = "..".into();
+        let inf_b: DomainRange = "..42".into();
+        let a_inf: DomainRange = "0..".into();
+        let a_b: DomainRange = "10..20".into();
+        let a_b2: DomainRange = "30..50".into();
+        let a_b3: DomainRange = "20..30".into();
+
+        assert_eq!(inf.union(&inf), "..".into());
+        assert_eq!(inf.union(&inf_b), "..".into());
+        assert_eq!(inf.union(&a_inf), "..".into());
+        assert_eq!(inf.union(&a_b), "..".into());
+
+        assert_eq!(inf.union(&inf), "..".into());
+        assert_eq!(inf_b.union(&inf), "..".into());
+        assert_eq!(a_inf.union(&inf), "..".into());
+        assert_eq!(a_b.union(&inf), "..".into());
+
+        assert_eq!(inf.union(&inf), "..".into());
+        assert_eq!(inf_b.union(&inf_b), "..42".into());
+        assert_eq!(a_inf.union(&a_inf), "0..".into());
+        assert_eq!(a_b.union(&a_b), "10..20".into());
+
+        assert_eq!(
+            a_b.union(&a_b2),
+            Domain {
+                union: vec!["10..20".into(), "30..50".into()]
+            }
+        );
+
+        assert_eq!(a_b.union(&a_b3), "10..30".into());
+    }
+
+    #[test]
+    pub fn domain_union()
+    {
+        let k: Domain = "2..5".into();
+        let k2: Domain = "5..10".into();
+        assert_eq!(
+            k.union(&k2),
+            Domain {
+                union: vec![DomainRange {
+                    start: DomainBound::Bounded(2),
+                    end: DomainBound::Bounded(10)
+                }]
+            }
+        );
+    }
+
+    #[test]
+    pub fn domain_intersection()
+    {
+        let k: Domain = "0..5".into();
+        let k2: Domain = "10..15".into();
+
+        let k3: Domain = "3..7".into();
+        let k4: Domain = "13..17".into();
+
+        let a = k.union(&k2);
+        let b = k3.union(&k4);
+        assert_eq!(
+            a.intersection(&b),
+            Domain {
+                union: vec![
+                    DomainRange {
+                        start: DomainBound::Bounded(3),
+                        end: DomainBound::Bounded(5)
+                    },
+                    DomainRange {
+                        start: DomainBound::Bounded(13),
+                        end: DomainBound::Bounded(15)
+                    }
+                ]
+            }
+        );
+    }
+}

src/lib.rs

@@ -1,3 +1,4 @@
 pub mod ast;
+pub mod domain;
 pub mod parsing;
 pub mod prover;

src/main.rs

@@ -1,7 +1,7 @@
-use log::info;
 use picolog::ast::Body;
 use picolog::ast::Module;
 use picolog::ast::Predicate;
+use picolog::domain::Domain;
 
 fn main()
 {
@@ -10,31 +10,67 @@ fn main()
         .format_timestamp(None)
         .init();
     //println!("{:#?}", Module::parse_from_file("1.pl"));
+    // let module: Module = "
+    //     integer(zero).
+    //     integer(s(X)) :- integer(X).
+    //
+    //     add(X, zero, X).
+    //     add(X, s(Y), Z) :- add(s(X), Y, Z).
+    //
+    //     mult(zero, X, zero).
+    //     mult(s(Y), X, Z) :- mult(Y, X, W), add(W, X, Z).
+    //
+    //     op(10, yfx, +).
+    //     op(8, yfx, ^).
+    //     op(6, xfy, ::).
+    //     op(2, fx, [).
+    //     op(2, xf, ]).
+    //     op(3, yfx, |).
+    //
+    //     A + B :- test.
+    //
+    //     A ^ B + C :- test.
+    //     A::B::C :- A.
+    //     [Hd|Tl] :- Hd::Tl.
+    //
+    //     l(X) :- in(X, 3..7).
+    // "
+    // .into();
+
+    let d1: Domain = "5..10".into();
+    let d2: Domain = "7..18".into();
+
     let module: Module = "
-        integer(zero).
-        integer(s(X)) :- integer(X).
-
-        add(X, zero, X).
-        add(X, s(Y), Z) :- add(s(X), Y, Z).
-
-        mult(zero, X, zero).
-        mult(s(Y), X, Z) :- mult(Y, X, W), add(W, X, Z).
+        hello(5..10).
+        world(7..18).
     "
     .into();
 
-    //let prop: Body = "integer(s(X))".into();
-    let prop: Body = "mult(X, s(s(s(zero))), s(s(s(s(s(s(s(s(s(zero))))))))))".into();
-    for c in module.prove(&prop)
+    //let pred: Predicate = "hello(0..10).".into();
+    let show: Body = "hello(X), world(X)".into();
+
+    for c in module.prove(&show)
     {
         println!("true:");
         println!("{}", c.simplified());
         let _ = std::io::stdin().read_line(&mut String::new());
     }
-
+    //println!("{}", module.prove(&pred).unwrap());
+    // let prop: Body = "mult(X, s(s(s(zero))), s(s(s(s(s(s(s(s(s(zero))))))))))".into();
+    //let prop: Body = "integer(s(X))".into();
+    //let prop: Body = "mult(X, s(s(zero)), s(s(s(s(zero)))))".into();
+    //let prop: Body = "mult(X, Y, Z)".into();
+    //let prop: Body = "mult(s(s(zero)), s(s(zero)), X)".into();
+    // for c in module.prove(&prop)
+    // {
+    //     println!("true:");
+    //     println!("{}", c.simplified());
+    //     let _ = std::io::stdin().read_line(&mut String::new());
+    // }
+    //
     // let p: Predicate = "add(s(zero), zero, Y)".into();
     // let p1: Predicate = "add(X, zero, X)".into();
     // // let p: Predicate = "integer(s(zero))".into();
     // // let p1: Predicate = "integer(s(X))".into();
     // println!("{}", p.matches(&p1).unwrap());
-    //
 }

src/parsing.rs

@@ -1,29 +1,234 @@
-use std::path::Path;
+use std::{collections::HashMap, path::Path};
 
-use winnow::Parser;
-use winnow::Result;
-use winnow::ascii::alphanumeric0;
-use winnow::ascii::multispace0;
-use winnow::combinator::alt;
-use winnow::combinator::delimited;
-use winnow::combinator::opt;
-use winnow::combinator::separated;
-use winnow::combinator::seq;
-use winnow::error::ContextError;
+use winnow::{
+    Parser, Result, Stateful,
+    ascii::{self, alphanumeric1, dec_int, multispace0},
+    combinator::{
+        Infix, Postfix, Prefix, alt, delimited, expression, opt, preceded, repeat, separated, seq,
+        terminated,
+    },
+    error::ContextError,
+    token::literal,
+};
 
-use crate::ast::Body;
 use crate::ast::Clause;
+use crate::ast::Functor;
 use crate::ast::Module;
+use crate::ast::Operator;
 use crate::ast::Predicate;
+use crate::ast::Variable;
+use crate::ast::{Body, OperatorType};
+use crate::domain::{Domain, DomainBound, DomainRange};
 
-pub fn predicate_parse(input: &mut &str) -> Result<Predicate>
+impl Operator
 {
-    let ident = alphanumeric0.parse_next(input)?;
+    pub fn get_precedence(&self) -> usize
+    {
+        self.precedence
+    }
+    pub fn make_infix_operator<'a>(self) -> Infix<Stream<'a>, Predicate, Operator, ContextError>
+    {
+        fn make_predicate(
+            _: &mut Stream,
+            a: Predicate,
+            op: Operator,
+            b: Predicate,
+        ) -> Result<Predicate>
+        {
+            Ok(Predicate::Fixed(Functor::Operator(op), vec![a, b]))
+        }
+        let precedence = self.get_precedence() as i64;
+        match self.op_type
+        {
+            OperatorType::LeftInfix => Infix::Left(precedence, self, make_predicate),
+            OperatorType::RightInfix => Infix::Right(precedence, self, make_predicate),
+            _ => unreachable!(),
+        }
+    }
+}
+
+impl Operator
+{
+    fn infix(value: String, state: &State) -> Result<Self>
+    {
+        state
+            .custom_operators
+            .get(&(value.clone(), OperatorType::RightInfix))
+            .or_else(|| {
+                state
+                    .custom_operators
+                    .get(&(value, OperatorType::LeftInfix))
+            })
+            .ok_or(ContextError::new())
+            .cloned()
+    }
+    fn prefix(value: String, state: &State) -> Result<Self>
+    {
+        state
+            .custom_operators
+            .get(&(value, OperatorType::Prefix))
+            .ok_or(ContextError::new())
+            .cloned()
+    }
+    fn postfix(value: String, state: &State) -> Result<Self>
+    {
+        state
+            .custom_operators
+            .get(&(value, OperatorType::Postfix))
+            .ok_or(ContextError::new())
+            .cloned()
+    }
+}
+
+const OPERATORS: [&str; 9] = [":", "-", "+", "|", "/", "*", "[", "]", "^"];
+
+#[derive(Debug)]
+pub struct State
+{
+    custom_operators: HashMap<(String, OperatorType), Operator>,
+}
+
+impl Default for State
+{
+    fn default() -> Self
+    {
+        Self::new()
+    }
+}
+
+impl State
+{
+    pub fn new() -> Self
+    {
+        Self {
+            custom_operators: HashMap::new(),
+        }
+    }
+}
+
+type Stream<'is> = Stateful<&'is str, State>;
+
+pub fn domain_range_parse(input: &mut Stream) -> Result<DomainRange>
+{
+    let start = opt(dec_int.map(DomainBound::Bounded))
+        .map(|v| v.unwrap_or(DomainBound::Unbounded))
+        .parse_next(input)?;
+    literal("..").parse_next(input)?;
+    let end = opt(dec_int.map(DomainBound::Bounded))
+        .map(|v| v.unwrap_or(DomainBound::Unbounded))
+        .parse_next(input)?;
+    Ok(DomainRange { start, end })
+}
+
+pub fn domain_parse(input: &mut Stream) -> Result<Domain>
+{
+    // Domain is either a..b, ..
+    alt((domain_range_parse, dec_int.map(DomainRange::singleton)))
+        .map(|domain| Domain {
+            union: vec![domain],
+        })
+        .parse_next(input)
+}
+
+pub fn operator_parse(input: &mut Stream) -> Result<String>
+{
+    delimited(multispace0, repeat(1.., alt(OPERATORS)), multispace0)
+        .map(|op: String| Ok(op))
+        .parse_next(input)?
+}
+
+pub fn operator_parse_infix(input: &mut Stream) -> Result<Operator>
+{
+    operator_parse(input).map(|op| Operator::infix(op, &input.state))?
+}
+pub fn operator_parse_postfix(input: &mut Stream) -> Result<Operator>
+{
+    operator_parse(input).map(|op| Operator::postfix(op, &input.state))?
+}
+pub fn operator_parse_prefix(input: &mut Stream) -> Result<Operator>
+{
+    operator_parse(input).map(|op| Operator::prefix(op, &input.state))?
+}
+
+pub fn operator_definition_parse(input: &mut Stream) -> Result<()>
+{
+    let (precedence, op_type, op) = preceded(
+        "op",
+        delimited(
+            ("(", multispace0),
+            seq! {
+                ascii::dec_uint,
+                _: (multispace0, ",", multispace0),
+                alt(("xfx", "xfy", "yfx", "xf", "yf", "fy", "fx")),
+                _: (multispace0, ",", multispace0),
+                operator_parse,
+            },
+            (multispace0, ")", multispace0, "."),
+        ),
+    )
+    .parse_next(input)?;
+    let op_type = match op_type
+    {
+        "xf" | "yf" => OperatorType::Postfix,
+        "fx" | "fy" => OperatorType::Prefix,
+        "xfx" => unimplemented!(),
+        "yfx" => OperatorType::LeftInfix,
+        "xfy" => OperatorType::RightInfix,
+        _ => unreachable!(),
+    };
+    input.state.custom_operators.insert(
+        (op.clone(), op_type.clone()),
+        Operator::new(op, precedence, op_type),
+    );
+    Ok(())
+}
+
+pub fn predicate_parse_infix_expression<'a>(
+    input: &mut Stream<'a>,
+) -> Result<Infix<Stream<'a>, Predicate, Operator, ContextError>>
+{
+    let op = operator_parse_infix.parse_next(input)?;
+    Ok(op.make_infix_operator())
+}
+
+pub fn predicate_parse_prefix_expression<'a>(
+    input: &mut Stream<'a>,
+) -> Result<Prefix<Stream<'a>, Predicate, Operator, ContextError>>
+{
+    let op = operator_parse_prefix.parse_next(input)?;
+    let precedence = op.get_precedence() as i64;
+    Ok(Prefix(precedence, op, |_, op, a| {
+        Ok(Predicate::Fixed(Functor::Operator(op), vec![a]))
+    }))
+}
+pub fn predicate_parse_postfix_expression<'a>(
+    input: &mut Stream<'a>,
+) -> Result<Postfix<Stream<'a>, Predicate, Operator, ContextError>>
+{
+    let op = operator_parse_postfix.parse_next(input)?;
+    let precedence = op.get_precedence() as i64;
+    Ok(Postfix(precedence, op, |_, a, op| {
+        Ok(Predicate::Fixed(Functor::Operator(op), vec![a]))
+    }))
+}
+
+pub fn predicate_parse_expression(input: &mut Stream) -> Result<Predicate>
+{
+    expression(predicate_parse_recursive)
+        .infix(predicate_parse_infix_expression)
+        .postfix(predicate_parse_postfix_expression)
+        .prefix(predicate_parse_prefix_expression)
+        .parse_next(input)
+}
+
+pub fn predicate_parse_variable_or_functor(input: &mut Stream) -> Result<Predicate>
+{
+    let ident = alphanumeric1.parse_next(input)?;
 
     // Check if output is a variable
     if ident.chars().next().is_some_and(|char| char.is_uppercase())
     {
-        Ok(Predicate::Variable(String::from(ident)))
+        Ok(Predicate::Variable(Variable(String::from(ident), None)))
     }
     else
     {
@@ -34,11 +239,29 @@ pub fn predicate_parse(input: &mut &str) -> Result<Predicate>
         )
         .parse_next(input)
         .unwrap_or(Vec::new());
-        Ok(Predicate::Fixed(String::from(ident), arguments))
+        Ok(Predicate::Fixed(
+            Functor::Functor(String::from(ident)),
+            arguments,
+        ))
     }
 }
 
-fn body_parse_or(input: &mut &str) -> Result<Body>
+pub fn predicate_parse_recursive(input: &mut Stream) -> Result<Predicate>
+{
+    alt((
+        delimited("(", predicate_parse, ")"),
+        domain_parse.map(Predicate::Domain),
+        predicate_parse_variable_or_functor,
+    ))
+    .parse_next(input)
+}
+
+pub fn predicate_parse(input: &mut Stream) -> Result<Predicate>
+{
+    alt((predicate_parse_expression, predicate_parse_recursive)).parse_next(input)
+}
+
+fn body_parse_or(input: &mut Stream) -> Result<Body>
 {
     separated(
         1..,
@@ -52,7 +275,7 @@ fn body_parse_or(input: &mut &str) -> Result<Body>
     .parse_next(input)
 }
 
-pub fn body_parse(input: &mut &str) -> Result<Body>
+pub fn body_parse(input: &mut Stream) -> Result<Body>
 {
     // Parse and
     separated(1.., body_parse_or, (multispace0, ",", multispace0))
@@ -60,7 +283,7 @@ pub fn body_parse(input: &mut &str) -> Result<Body>
         .parse_next(input)
 }
 
-pub fn clause_parse(input: &mut &str) -> Result<Clause>
+pub fn clause_parse(input: &mut Stream) -> Result<Clause>
 {
     seq! {
         Clause
@@ -74,12 +297,19 @@ pub fn clause_parse(input: &mut &str) -> Result<Clause>
     .parse_next(input)
 }
 
-pub fn module_parse(input: &mut &str) -> Result<Module>
+pub fn module_parse(input: &mut Stream) -> Result<Module>
 {
     let _: Result<&str, ContextError> = multispace0.parse_next(input);
-    separated(0.., clause_parse, multispace0)
-        .map(|clauses| Module { clauses })
-        .parse_next(input)
+    separated(
+        0..,
+        preceded::<_, (), _, _, _, _>(
+            repeat(0.., terminated(operator_definition_parse, multispace0)),
+            clause_parse,
+        ),
+        multispace0,
+    )
+    .map(|clauses| Module { clauses })
+    .parse_next(input)
 }
 
 impl<T> From<T> for Module
@@ -88,8 +318,13 @@ where
 {
     fn from(value: T) -> Self
     {
-        let mut str: &str = value.as_ref();
-        module_parse.parse_next(&mut str).unwrap()
+        let str: &str = value.as_ref();
+        module_parse
+            .parse_next(&mut Stream {
+                input: str,
+                state: State::new(),
+            })
+            .unwrap()
     }
 }
 
@@ -107,8 +342,13 @@ where
 {
     fn from(value: T) -> Self
     {
-        let mut str: &str = value.as_ref();
-        predicate_parse.parse_next(&mut str).unwrap()
+        let str: &str = value.as_ref();
+        predicate_parse
+            .parse_next(&mut Stream {
+                input: str,
+                state: State::new(),
+            })
+            .unwrap()
     }
 }
 
@@ -118,7 +358,44 @@ where
 {
     fn from(value: T) -> Self
     {
-        let mut str: &str = value.as_ref();
-        body_parse.parse_next(&mut str).unwrap()
+        let str: &str = value.as_ref();
+        body_parse
+            .parse_next(&mut Stream {
+                input: str,
+                state: State::new(),
+            })
+            .unwrap()
+    }
+}
+
+impl<T> From<T> for Domain
+where
+    T: AsRef<str>,
+{
+    fn from(value: T) -> Self
+    {
+        let str: &str = value.as_ref();
+        domain_parse
+            .parse_next(&mut Stream {
+                input: str,
+                state: State::new(),
+            })
+            .unwrap()
+    }
+}
+
+impl<T> From<T> for DomainRange
+where
+    T: AsRef<str>,
+{
+    fn from(value: T) -> Self
+    {
+        let str: &str = value.as_ref();
+        domain_range_parse
+            .parse_next(&mut Stream {
+                input: str,
+                state: State::new(),
+            })
+            .unwrap()
     }
 }

src/prover.rs

@@ -1,21 +1,24 @@
+pub mod and;
+pub mod body;
 pub mod constraints;
+pub mod not;
+pub mod or;
+pub mod predicate;
 pub mod tracing;
 pub mod unification;
 
 use std::cell::Cell;
+use std::collections::HashMap;
 use std::rc::Rc;
 
-use litemap::LiteMap;
-use log::info;
-
 use crate::ast::Body;
 use crate::ast::Clause;
 use crate::ast::Module;
 use crate::ast::Predicate;
+use crate::ast::Variable;
+use crate::prover::body::BodyProver;
 use crate::prover::constraints::Constraints;
-use crate::prover::tracing::ProofType;
-use crate::prover::tracing::SimpleTracer;
-use crate::prover::tracing::Tracer;
+use crate::prover::tracing::IndentedTracer;
 
 #[derive(Clone, Copy, Debug, Default)]
 pub struct Counter(usize);
@@ -27,7 +30,12 @@ impl GlobalCounter
 {
     pub fn new() -> GlobalCounter
     {
-        GlobalCounter(Rc::new(Cell::new(0)))
+        Self::with(0)
+    }
+
+    pub fn with(n: usize) -> GlobalCounter
+    {
+        GlobalCounter(Rc::new(Cell::new(n)))
     }
 
     pub fn get(&self) -> usize
@@ -48,290 +56,18 @@ impl GlobalCounter
     }
 }
 
-pub struct BodyProver<'a, T: Tracer + 'a>
-{
-    module: &'a Module,
-    constraints: Constraints,
-    tracer: Option<T>,
-    prover: Box<dyn Iterator<Item = Constraints> + 'a>,
-}
-
-pub struct PredicateProver<'a, T: Tracer>
-{
-    module: &'a Module,
-    predicate: Predicate,
-    constraints: Constraints,
-    counter_snapshot: Counter,
-    tracer: T,
-
-    global_counter: GlobalCounter,
-    current_clause: usize,
-    sub_proof: Option<BodyProver<'a, T>>,
-}
-
-pub struct AndProver<'a, T: Tracer>
-{
-    module: &'a Module,
-    bodies: Vec<Body>,
-    constraints: Constraints,
-    tracer: T,
-
-    global_counter: GlobalCounter,
-    sub_proofs: Vec<(Counter, BodyProver<'a, T>)>,
-}
-
-impl<'a, T: Tracer + 'a> BodyProver<'a, T>
-{
-    pub fn new(
-        module: &'a Module,
-        global_counter: GlobalCounter,
-        body: Body,
-        constraints: Constraints,
-        tracer: &T,
-    ) -> BodyProver<'a, T>
-    {
-        let body_tracer = if let Body::And(_) = body
-        {
-            Some(tracer.begin_proof(ProofType::Body, format!("Proving {}", body)))
-        }
-        else
-        {
-            None
-        };
-        let prover: Box<dyn Iterator<Item = Constraints>> = match &body
-        {
-            Body::Term(predicate) => Box::new(PredicateProver::new(
-                module,
-                global_counter,
-                predicate.clone(),
-                constraints.clone(),
-                tracer,
-            )),
-            Body::And(items) => Box::new(AndProver::new(
-                module,
-                global_counter,
-                items.clone(),
-                constraints.clone(),
-                tracer,
-            )),
-            Body::Or(items) => Box::new(BodyProver::new(
-                module,
-                global_counter,
-                items[0].clone(),
-                constraints.clone(),
-                tracer,
-            )),
-        };
-        //info!(target: "BodyProver", "Proving {}", body);
-        BodyProver {
-            tracer: body_tracer,
-            module,
-            constraints,
-            prover,
-        }
-    }
-}
-
-impl<'a, T: Tracer + 'a> PredicateProver<'a, T>
-{
-    pub fn new(
-        module: &'a Module,
-        global_counter: GlobalCounter,
-        predicate: Predicate,
-        constraints: Constraints,
-        tracer: &T,
-    ) -> PredicateProver<'a, T>
-    {
-        //info!(target: "PredicateProver", "Proving {}", predicate);
-        PredicateProver {
-            module,
-            tracer: tracer.begin_proof(ProofType::Predicate, format!("Proving {}", &predicate)),
-            predicate,
-            constraints,
-            current_clause: 0,
-            sub_proof: None,
-            counter_snapshot: global_counter.snapshot(),
-            global_counter,
-        }
-    }
-}
-
-impl<T: Tracer> AndProver<'_, T>
-{
-    pub fn new<'a>(
-        module: &'a Module,
-        global_counter: GlobalCounter,
-        bodies: Vec<Body>,
-        constraints: Constraints,
-        tracer: &T,
-    ) -> AndProver<'a, T>
-    where
-        T: 'a,
-    {
-        assert!(!bodies.is_empty());
-
-        AndProver {
-            tracer: tracer.begin_proof(ProofType::And),
-            module,
-            sub_proofs: vec![(
-                global_counter.snapshot(),
-                BodyProver::new(
-                    module,
-                    global_counter.clone(),
-                    bodies[0].clone(),
-                    constraints.clone(),
-                    tracer,
-                ),
-            )],
-            bodies,
-            constraints,
-            global_counter,
-        }
-    }
-}
-
-impl<'a, T: Tracer + 'a> Iterator for PredicateProver<'a, T>
-{
-    type Item = Constraints;
-
-    fn next(&mut self) -> Option<Self::Item>
-    {
-        match self.sub_proof.as_mut()
-        {
-            None =>
-            {
-                if self.current_clause == self.module.clauses.len()
-                {
-                    None
-                }
-                else
-                {
-                    let clause = &self.module.clauses[self.current_clause]
-                        .make_unique(self.global_counter.clone());
-                    //info!(target: "PredicateProver", "Unifying '{}' against '{}'", self.predicate, clause);
-                    let uni = self.predicate.matches(&clause.head);
-                    let full_constraints = uni.and_then(|x| x.and(&self.constraints));
-
-                    if let Some(c) = &full_constraints
-                    {
-                        //info!(target: "PredicateProver", " => {}", c);
-                    }
-                    else
-                    {
-                        //info!(target: "PredicateProver", " => (Can't unify)");
-                    }
-                    match full_constraints
-                    {
-                        Some(constraints) if clause.body.is_none() =>
-                        {
-                            self.current_clause += 1;
-                            Some(constraints)
-                        }
-                        Some(constraints) =>
-                        {
-                            self.current_clause += 1;
-                            self.counter_snapshot = self.global_counter.snapshot();
-                            self.sub_proof = Some(BodyProver::new(
-                                self.module,
-                                self.global_counter.clone(),
-                                clause.body.clone().unwrap(),
-                                constraints,
-                                &self.tracer,
-                            ));
-                            self.next()
-                        }
-                        None =>
-                        {
-                            self.current_clause += 1;
-                            self.next()
-                        }
-                    }
-                }
-            }
-            Some(prover) =>
-            {
-                let next = prover.next();
-                match next
-                {
-                    Some(constraints) => Some(constraints),
-                    None =>
-                    {
-                        self.global_counter.restore(self.counter_snapshot);
-                        self.sub_proof = None;
-                        self.next()
-                    }
-                }
-            }
-        }
-    }
-}
-
-impl<'a, T: Tracer + 'a> Iterator for BodyProver<'a, T>
-{
-    type Item = Constraints;
-    fn next(&mut self) -> Option<Constraints>
-    {
-        self.prover.next()
-    }
-}
-
-impl<'a, T: Tracer + 'a> Iterator for AndProver<'a, T>
-{
-    type Item = Constraints;
-
-    fn next(&mut self) -> Option<Self::Item>
-    {
-        if self.sub_proofs.is_empty()
-        {
-            return None;
-        }
-
-        let (current_proof_snap, mut current_proof) = self.sub_proofs.pop().unwrap();
-
-        match current_proof.next()
-        {
-            Some(constraints) =>
-            {
-                if self.sub_proofs.len() == self.bodies.len() - 1
-                {
-                    self.sub_proofs.push((current_proof_snap, current_proof));
-                    Some(constraints)
-                }
-                else
-                {
-                    self.sub_proofs.push((current_proof_snap, current_proof));
-                    self.sub_proofs.push((
-                        self.global_counter.snapshot(),
-                        BodyProver::new(
-                            self.module,
-                            self.global_counter.clone(),
-                            self.bodies[self.sub_proofs.len()].clone(),
-                            constraints,
-                            &self.tracer,
-                        ),
-                    ));
-                    self.next()
-                }
-            }
-            None =>
-            {
-                self.global_counter.restore(current_proof_snap);
-                self.next()
-            }
-        }
-    }
-}
-
 impl Module
 {
-    pub fn prove<'a>(&'a self, body: &'a Body) -> BodyProver<'a, SimpleTracer>
+    pub fn prove<'a>(&'a self, body: &'a Body) -> BodyProver<'a>
     {
         BodyProver::new(
             self,
             GlobalCounter::new(),
             body.clone(),
             Constraints::none(),
-            &SimpleTracer::new(ProofType::Body),
+            //&mut EmptyTracer,
+            &mut IndentedTracer::new(),
+            //&SimpleTracer::new(ProofType::Body),
         )
     }
 }
@@ -340,7 +76,7 @@ impl Clause
 {
     pub fn make_unique(&self, counter: GlobalCounter) -> Clause
     {
-        let mut unique_map = LiteMap::new();
+        let mut unique_map = HashMap::new();
         Clause {
             head: self.head.make_unique(counter.clone(), &mut unique_map),
             body: self
@@ -356,7 +92,7 @@ impl Body
     pub fn make_unique(
         &self,
         counter: GlobalCounter,
-        unique_map: &mut LiteMap<String, usize>,
+        unique_map: &mut HashMap<Variable, usize>,
     ) -> Body
     {
         match self
@@ -383,18 +119,15 @@ impl Predicate
     pub fn make_unique(
         &self,
         counter: GlobalCounter,
-        unique_map: &mut LiteMap<String, usize>,
+        unique_map: &mut HashMap<Variable, usize>,
     ) -> Self
     {
         match self
         {
-            Predicate::Variable(name) => Predicate::Variable(format!(
-                "_{}[{}]",
-                name,
-                unique_map
-                    .entry(name.clone())
-                    .or_insert_with(|| counter.get())
-            )),
+            Predicate::Variable(var) =>
+            {
+                Predicate::Variable(var.make_unique(counter.clone(), unique_map))
+            }
             Predicate::Fixed(name, predicates) => Predicate::Fixed(
                 name.clone(),
                 predicates
@@ -402,6 +135,26 @@ impl Predicate
                     .map(|x| x.make_unique(counter.clone(), unique_map))
                     .collect(),
             ),
+            Predicate::Domain(domain) => Predicate::Domain(domain.clone()),
         }
     }
 }
+
+impl Variable
+{
+    pub fn make_unique(
+        &self,
+        counter: GlobalCounter,
+        unique_map: &mut HashMap<Variable, usize>,
+    ) -> Self
+    {
+        Variable(
+            self.0.clone(),
+            Some(
+                *unique_map
+                    .entry(self.clone())
+                    .or_insert_with(|| counter.get()),
+            ),
+        )
+    }
+}

src/prover/and.rs

@@ -0,0 +1,172 @@
+use std::fmt::Write;
+
+use owo_colors::OwoColorize;
+
+use crate::ast::Body;
+use crate::ast::Module;
+use crate::prover::Counter;
+use crate::prover::GlobalCounter;
+use crate::prover::body::BodyProver;
+use crate::prover::constraints::Constraints;
+use crate::prover::tracing::ProofType;
+use crate::prover::tracing::Tracer;
+
+pub struct AndProver<'a, T: Tracer>
+{
+    module: &'a Module,
+    bodies: Vec<Body>,
+    tracer: T,
+
+    global_counter: GlobalCounter,
+    sub_proofs: Vec<(Counter, BodyProver<'a>)>,
+}
+impl<T: Tracer> AndProver<'_, T>
+{
+    pub fn new<'a>(
+        module: &'a Module,
+        global_counter: GlobalCounter,
+        bodies: Vec<Body>,
+        constraints: Constraints,
+        tracer: &mut T,
+    ) -> AndProver<'a, T>
+    where
+        T: 'a,
+    {
+        assert!(!bodies.is_empty());
+
+        // Pretty logging
+        let mut tracer = tracer.begin_proof(ProofType::And);
+        let mut next = String::new();
+        for x in bodies.iter().skip(1)
+        {
+            let _ = next.write_str(&format!("{}, ", x));
+        }
+
+        let mut conjuction = String::new();
+        let len = bodies.len();
+        for (i, x) in bodies.iter().enumerate()
+        {
+            let _ = conjuction.write_str(&format!("{}", x));
+            if i != len - 1
+            {
+                let _ = conjuction.write_str(" ∧ ");
+            }
+        }
+
+        tracer.print_step(format!("Proving conjuction {}", conjuction));
+        tracer.print_step(format!("{}  :", "Proved".fg::<owo_colors::colors::Green>(),));
+        tracer.print_step(format!(
+            "{} : {}",
+            "Proving".fg::<owo_colors::colors::Yellow>(),
+            bodies[0]
+        ));
+        tracer.print_step(format!(
+            "{}    : {}",
+            "Next".fg::<owo_colors::colors::Red>(),
+            next
+        ));
+        tracer.print_step(format!("With constraints : {}", constraints.simplified()));
+        // End pretty logging
+
+        AndProver {
+            module,
+            sub_proofs: vec![(
+                global_counter.snapshot(),
+                BodyProver::new(
+                    module,
+                    global_counter.clone(),
+                    bodies[0].clone(),
+                    constraints.clone(),
+                    &mut tracer,
+                ),
+            )],
+            tracer,
+            bodies,
+            global_counter,
+        }
+    }
+}
+impl<'a, T: Tracer + 'a> Iterator for AndProver<'a, T>
+{
+    type Item = Constraints;
+
+    fn next(&mut self) -> Option<Self::Item>
+    {
+        if self.sub_proofs.is_empty()
+        {
+            return None;
+        }
+
+        let (current_proof_snap, mut current_proof) = self.sub_proofs.pop().unwrap();
+
+        match current_proof.next()
+        {
+            Some(constraints) =>
+            {
+                if self.sub_proofs.len() == self.bodies.len() - 1
+                {
+                    self.sub_proofs.push((current_proof_snap, current_proof));
+                    Some(constraints)
+                }
+                else
+                {
+                    // Pretty logging
+                    let mut proved = String::new();
+                    let mut proving = String::new();
+                    let mut next = String::new();
+                    for (i, x) in self.bodies.iter().enumerate()
+                    {
+                        let dest;
+                        if i == self.sub_proofs.len() + 1
+                        {
+                            dest = &mut proving;
+                        }
+                        else if i < self.sub_proofs.len() + 1
+                        {
+                            dest = &mut proved;
+                        }
+                        else
+                        {
+                            dest = &mut next;
+                        }
+                        let _ = dest.write_str(&format!("{}, ", x));
+                    }
+                    self.tracer.print_step(format!(
+                        "{}  : {}",
+                        "Proved".fg::<owo_colors::colors::Green>(),
+                        proved
+                    ));
+                    self.tracer.print_step(format!(
+                        "{} : {}",
+                        "Proving".fg::<owo_colors::colors::Yellow>(),
+                        proving
+                    ));
+                    self.tracer.print_step(format!(
+                        "{}    : {}",
+                        "Next".fg::<owo_colors::colors::Red>(),
+                        next
+                    ));
+                    // End pretty logging
+
+                    self.sub_proofs.push((current_proof_snap, current_proof));
+                    self.sub_proofs.push((
+                        self.global_counter.snapshot(),
+                        BodyProver::new(
+                            self.module,
+                            self.global_counter.clone(),
+                            self.bodies[self.sub_proofs.len()].clone(),
+                            constraints,
+                            &mut self.tracer,
+                        ),
+                    ));
+                    self.next()
+                }
+            }
+            None =>
+            {
+                self.global_counter.restore(current_proof_snap);
+                self.next()
+            }
+        }
+    }
+}

src/prover/body.rs

@@ -0,0 +1,70 @@
+use crate::ast::Body;
+use crate::ast::Module;
+use crate::prover::GlobalCounter;
+use crate::prover::and::AndProver;
+use crate::prover::constraints::Constraints;
+use crate::prover::predicate::PredicateProver;
+use crate::prover::tracing::Tracer;
+
+pub struct BodyProver<'a>
+{
+    prover: Box<dyn Iterator<Item = Constraints> + 'a>,
+}
+
+impl<'a> BodyProver<'a>
+{
+    pub fn new<T: Tracer + 'a>(
+        module: &'a Module,
+        global_counter: GlobalCounter,
+        body: Body,
+        constraints: Constraints,
+        tracer: &mut T,
+    ) -> BodyProver<'a>
+    {
+        let prover: Box<dyn Iterator<Item = Constraints>> = match &body
+        {
+            Body::Term(predicate) => Box::new(PredicateProver::new(
+                module,
+                global_counter,
+                predicate.clone(),
+                constraints.clone(),
+                tracer,
+            )),
+
+            // Shortcut And & Or prover if it contains only one element to simplify proofs
+            Body::And(items) | Body::Or(items) if items.len() == 1 => Box::new(BodyProver::new(
+                module,
+                global_counter,
+                items[0].clone(),
+                constraints.clone(),
+                tracer,
+            )),
+
+            Body::And(items) => Box::new(AndProver::new(
+                module,
+                global_counter,
+                items.clone(),
+                constraints.clone(),
+                tracer,
+            )),
+            Body::Or(items) => Box::new(BodyProver::new(
+                module,
+                global_counter,
+                items[0].clone(),
+                constraints.clone(),
+                tracer,
+            )),
+        };
+
+        BodyProver { prover }
+    }
+}
+
+impl<'a> Iterator for BodyProver<'a>
+{
+    type Item = Constraints;
+    fn next(&mut self) -> Option<Constraints>
+    {
+        self.prover.next()
+    }
+}

src/prover/constraints.rs

@@ -1,15 +1,18 @@
+use std::collections::HashMap;
 use std::fmt::Display;
 
-use litemap::LiteMap;
-
 use crate::ast::Body;
 use crate::ast::Predicate;
 use crate::ast::Variable;
+use crate::domain;
+use crate::domain::Domain;
+use crate::prover::predicate;
 
 #[derive(Clone, Debug)]
 pub struct Constraints
 {
-    set: LiteMap<Variable, Predicate>,
+    pub(crate) predicates: HashMap<Variable, Predicate>,
+    pub(crate) domains: HashMap<Variable, Domain>,
 }
 
 impl Constraints
@@ -17,20 +20,33 @@ impl Constraints
     pub fn none() -> Self
     {
         Constraints {
-            set: LiteMap::new(),
+            predicates: HashMap::new(),
+            domains: HashMap::new(),
         }
     }
 
-    pub fn with(variable: Variable, predicate: Predicate) -> Self
+    pub fn with(variable: Variable, predicate: Option<Predicate>, domain: Option<Domain>) -> Self
     {
         let mut c = Constraints::none();
-        c.set.insert(variable, predicate);
+        if let Some(predicate) = predicate
+        {
+            c.predicates.insert(variable.clone(), predicate);
+        }
+        if let Some(domain) = domain
+        {
+            c.domains.insert(variable, domain);
+        }
         c
     }
 
-    pub fn try_append(&mut self, variable: &Variable, predicate: &Predicate) -> bool
+    pub fn try_append(
+        &mut self,
+        variable: &Variable,
+        predicate: &Predicate,
+        domain: &Domain,
+    ) -> bool
     {
-        if let Some(other_predicate) = self.set.get(variable)
+        let predicates = if let Some(other_predicate) = self.predicates.get(variable)
         {
             if predicate == other_predicate
             {
@@ -47,7 +63,7 @@ impl Constraints
                 // We can try adding the unification contraints which is implicitely the same
                 if self.try_merge(&unification_contraints)
                 {
-                    self.set.insert(variable.clone(), predicate.clone());
+                    self.predicates.insert(variable.clone(), predicate.clone());
                     true
                 }
                 else
@@ -64,18 +80,40 @@ impl Constraints
         else
         {
             // No constraint
-            self.set.insert(variable.clone(), predicate.clone());
+            self.predicates
+                .insert(variable.clone(), (predicate.clone(), domain.clone()));
             true
+        };
+
+        // Check if domains are compatible
+        let domains = if let Some((_, other_domain)) = self.predicates.get_mut(variable)
+        {
+            let intersection = domain.intersection(other_domain);
+            if intersection.empty()
+            {
+                false
+            }
+            else
+            {
+                *other_domain = intersection;
+                true
+            }
         }
+        else
+        {
+            true
+        };
+
+        domains && predicates
     }
 
     pub fn try_merge(&mut self, constraints: &Constraints) -> bool
     {
         // Trying to merge, is just trying to add all of the constraints into self
         let mut ok = self.clone();
-        for (var, pred) in constraints.set.iter()
+        for (var, (pred, domain)) in constraints.predicates.iter()
         {
-            if !ok.try_append(var, pred)
+            if !ok.try_append(var, pred, domain)
             {
                 return false;
             }
@@ -94,24 +132,26 @@ impl Constraints
     pub fn simplified(&self) -> Constraints
     {
         let mut max_sub = Constraints::none();
-        for (var, pred) in self.set.iter()
+        for (var, (pred, domain)) in self.predicates.iter()
         {
-            max_sub.set.insert(var.clone(), pred.substitute(self));
+            max_sub
+                .predicates
+                .insert(var.clone(), (pred.substitute(self), domain.clone()));
         }
 
         let mut stripped = max_sub.clone();
-        'outer: for (var, _) in max_sub.set.iter()
+        'outer: for (var, _) in max_sub.predicates.iter()
         {
-            if var.chars().next().is_some_and(|x| x == '_')
+            if var.0.chars().next().is_some_and(|x| x == '_') || var.1.is_some()
             {
-                for (_, other_pred) in max_sub.set.iter()
+                for (_, (other_pred, _)) in max_sub.predicates.iter()
                 {
                     if other_pred.contains_variable(var)
                     {
                         continue 'outer;
                     }
                 }
-                stripped.set.remove(var);
+                stripped.predicates.remove(var);
             }
         }
 
@@ -127,7 +167,7 @@ impl Predicate
         {
             Predicate::Variable(name) =>
             {
-                if let Some(pred) = constraints.set.get(name)
+                if let Some((pred, _)) = constraints.predicates.get(name)
                 {
                     pred.substitute(constraints)
                 }
@@ -143,15 +183,17 @@ impl Predicate
                     .map(|x| x.substitute(constraints))
                     .collect(),
             ),
+            Predicate::Domain(domain) => Predicate::Domain(domain.clone()),
         }
     }
 
-    pub fn contains_variable(&self, name: &String) -> bool
+    pub fn contains_variable(&self, name: &Variable) -> bool
     {
         match self
         {
             Predicate::Variable(var_name) => name == var_name,
             Predicate::Fixed(_, predicates) => predicates.iter().any(|x| x.contains_variable(name)),
+            Predicate::Domain(_) => false,
         }
     }
 }
@@ -184,8 +226,8 @@ impl Display for Constraints
 {
     fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result
     {
-        let len = self.set.len();
-        for (i, (var, pred)) in self.set.iter().enumerate()
+        let len = self.predicates.len();
+        for (i, (var, (pred, _))) in self.predicates.iter().enumerate()
         {
             write!(f, "{} = {}", var, pred)?;
             if i != len - 1
@@ -193,6 +235,15 @@ impl Display for Constraints
                 write!(f, ", ")?;
             }
         }
+        write!(f, " ;; ")?;
+        for (i, (var, (_, domain))) in self.predicates.iter().enumerate()
+        {
+            write!(f, "{} in {}", var, domain)?;
+            if i != len - 1
+            {
+                write!(f, ", ")?;
+            }
+        }
         Ok(())
     }
 }

src/prover/internal_operators.rs

@@ -0,0 +1,50 @@
+use crate::{ast::Predicate, prover::constraints::Constraints};
+
+impl Constraints
+{
+    pub fn collapsed_operators(&self) -> Constraints
+    {
+        let mut new_constraints = Constraints::none();
+        for (var, pred) in self.set.iter()
+        {
+            new_constraints
+                .set
+                .insert(var.clone(), pred.substitute(self).collapsed_operators());
+        }
+        new_constraints
+    }
+}
+
+impl Predicate
+{
+    pub fn collapsed_operators(&self) -> Predicate
+    {
+        match self
+        {
+            Predicate::Variable(variable) => Predicate::Variable(variable.clone()),
+            Predicate::Fixed(crate::ast::Functor::Operator(op), predicates)
+                if op.op == "+" && predicates.len() == 2 =>
+            {
+                match (predicates[0].clone(), predicates[1].clone())
+                {
+                    (Predicate::Number(a), Predicate::Number(b)) => Predicate::Number(a + b),
+                    _ => self.clone(),
+                }
+            }
+            Predicate::Fixed(crate::ast::Functor::Operator(op), predicates)
+                if op.op == "-" && predicates.len() == 2 =>
+            {
+                match (predicates[0].clone(), predicates[1].clone())
+                {
+                    (Predicate::Number(a), Predicate::Number(b)) => Predicate::Number(a - b),
+                    _ => self.clone(),
+                }
+            }
+            Predicate::Fixed(functor, predicates) => Predicate::Fixed(
+                functor.clone(),
+                predicates.iter().map(|x| x.collapsed_operators()).collect(),
+            ),
+            Predicate::Number(n) => Predicate::Number(*n),
+        }
+    }
+}

src/prover/not.rs

@@ -0,0 +1,71 @@
+use crate::ast::Body;
+use crate::ast::Module;
+use crate::prover::GlobalCounter;
+use crate::prover::body::BodyProver;
+use crate::prover::constraints::Constraints;
+use crate::prover::tracing::ProofType;
+use crate::prover::tracing::Tracer;
+
+pub struct NotProver<'a, T: Tracer + 'a>
+{
+    prover: Option<BodyProver<'a>>,
+    constraints: Constraints,
+    tracer: T,
+}
+
+impl<'a, T: Tracer + 'a> NotProver<'a, T>
+{
+    pub fn new(
+        module: &'a Module,
+        global_counter: GlobalCounter,
+        body: Body,
+        constraints: Constraints,
+        tracer: &mut T,
+    ) -> NotProver<'a, T>
+    {
+        let mut not_tracer = tracer.begin_proof(ProofType::Body);
+        NotProver {
+            prover: Some(BodyProver::new(
+                module,
+                global_counter,
+                body,
+                constraints.clone(),
+                &mut not_tracer,
+            )),
+            tracer: not_tracer,
+            constraints: constraints.clone(),
+        }
+    }
+}
+
+impl<'a, T: Tracer + 'a> Iterator for NotProver<'a, T>
+{
+    type Item = Constraints;
+    fn next(&mut self) -> Option<Constraints>
+    {
+        if let Some(x) = self.prover.as_mut()
+        {
+            match &mut x.next()
+            {
+                Some(_) =>
+                {
+                    // The prover showed that the proof is true.
+                    // Thus the negation is never true
+                    self.prover = None;
+                    None
+                }
+                None =>
+                {
+                    // The prover did not find any proof
+                    // Thus the negation is true
+                    self.prover = None;
+                    Some(self.constraints.clone())
+                }
+            }
+        }
+        else
+        {
+            None
+        }
+    }
+}

src/prover/or.rs

@@ -0,0 +1,124 @@
+use std::fmt::Write;
+
+use crate::ast::Body;
+use crate::ast::Module;
+use crate::prover::Counter;
+use crate::prover::GlobalCounter;
+use crate::prover::body::BodyProver;
+use crate::prover::constraints::Constraints;
+use crate::prover::tracing::ProofType;
+use crate::prover::tracing::Tracer;
+
+pub struct OrProver<'a, T: Tracer>
+{
+    module: &'a Module,
+    bodies: Vec<Body>,
+    constraints: Constraints,
+    tracer: T,
+
+    current_proving: usize,
+    global_counter: GlobalCounter,
+    counter_snapshot: Counter,
+    sub_proof: Option<BodyProver<'a>>,
+}
+
+impl<T: Tracer> OrProver<'_, T>
+{
+    pub fn new<'a>(
+        module: &'a Module,
+        global_counter: GlobalCounter,
+        bodies: Vec<Body>,
+        constraints: Constraints,
+        tracer: &mut T,
+    ) -> OrProver<'a, T>
+    where
+        T: 'a,
+    {
+        assert!(!bodies.is_empty());
+
+        // Pretty logging
+        let mut tracer = tracer.begin_proof(ProofType::And);
+
+        let mut next = String::new();
+        for x in bodies.iter().skip(1)
+        {
+            let _ = next.write_str(&format!("{}, ", x));
+        }
+
+        let mut disjunction = String::new();
+        let len = bodies.len();
+        for (i, x) in bodies.iter().enumerate()
+        {
+            let _ = disjunction.write_str(&format!("{}", x));
+            if i != len - 1
+            {
+                let _ = disjunction.write_str(" ∨ ");
+            }
+        }
+
+        // End pretty logging
+
+        OrProver {
+            module,
+            sub_proof: Some(BodyProver::new(
+                module,
+                global_counter.clone(),
+                bodies[0].clone(),
+                constraints.clone(),
+                &mut tracer,
+            )),
+            tracer,
+            current_proving: 0,
+            counter_snapshot: global_counter.snapshot(),
+            bodies,
+            constraints,
+            global_counter,
+        }
+    }
+}
+
+impl<'a, T: Tracer + 'a> Iterator for OrProver<'a, T>
+{
+    type Item = Constraints;
+
+    fn next(&mut self) -> Option<Self::Item>
+    {
+        let proof = match &mut self.sub_proof
+        {
+            Some(sub_proof) => sub_proof.next(),
+            None =>
+            {
+                return None;
+            }
+        };
+
+        match proof
+        {
+            Some(x) => Some(x),
+            None =>
+            {
+                // Advance to next possibility
+                if self.current_proving == self.bodies.len() - 1
+                {
+                    self.sub_proof = None;
+                    None
+                }
+                else
+                {
+                    self.current_proving += 1;
+                    self.global_counter.restore(self.counter_snapshot);
+                    self.tracer
+                        .print_step(format!("Tring with {}", self.bodies[self.current_proving]));
+                    self.sub_proof = Some(BodyProver::new(
+                        self.module,
+                        self.global_counter.clone(),
+                        self.bodies[self.current_proving].clone(),
+                        self.constraints.clone(),
+                        &mut self.tracer,
+                    ));
+                    self.next()
+                }
+            }
+        }
+    }
+}

src/prover/predicate.rs

@@ -0,0 +1,132 @@
+use owo_colors::OwoColorize;
+use owo_colors::colors::Green;
+
+use crate::ast::{Module, Predicate};
+use crate::prover::body::BodyProver;
+use crate::prover::constraints::Constraints;
+use crate::prover::tracing::{ProofType, Tracer};
+use crate::prover::{Counter, GlobalCounter};
+
+pub struct PredicateProver<'a, T: Tracer>
+{
+    module: &'a Module,
+    predicate: Predicate,
+    constraints: Constraints,
+    counter_snapshot: Counter,
+    tracer: T,
+
+    global_counter: GlobalCounter,
+    current_clause: usize,
+    sub_proof: Option<BodyProver<'a>>,
+}
+
+impl<'a, T: Tracer + 'a> PredicateProver<'a, T>
+{
+    pub fn new(
+        module: &'a Module,
+        global_counter: GlobalCounter,
+        predicate: Predicate,
+        constraints: Constraints,
+        tracer: &mut T,
+    ) -> PredicateProver<'a, T>
+    {
+        //info!(target: "PredicateProver", "Proving {}", predicate);
+        let mut predicate_prover = tracer.begin_proof(ProofType::Predicate);
+        predicate_prover.print_step(format!(
+            "{} '{}'",
+            "Proving predicate".fg::<Green>(),
+            predicate
+        ));
+        PredicateProver {
+            module,
+            tracer: predicate_prover,
+            predicate,
+            constraints,
+            current_clause: 0,
+            sub_proof: None,
+            counter_snapshot: global_counter.snapshot(),
+            global_counter,
+        }
+    }
+}
+
+impl<'a, T: Tracer + 'a> Iterator for PredicateProver<'a, T>
+{
+    type Item = Constraints;
+
+    fn next(&mut self) -> Option<Self::Item>
+    {
+        match self.sub_proof.as_mut()
+        {
+            None =>
+            {
+                if self.current_clause == self.module.clauses.len()
+                {
+                    None
+                }
+                else
+                {
+                    let clause = &self.module.clauses[self.current_clause]
+                        .make_unique(self.global_counter.clone());
+                    let uni = self.predicate.matches(&clause.head);
+                    let full_constraints = uni.and_then(|x| x.and(&self.constraints));
+
+                    if let Some(c) = &full_constraints
+                    {
+                        self.tracer.print_step(format!(
+                            "Unifying '{}' aginst '{}'",
+                            self.predicate, clause
+                        ));
+                        self.tracer.print_step(format!(
+                            "↳ {}: {}",
+                            "Matches".fg::<Green>(),
+                            c.simplified()
+                        ));
+                    }
+
+                    match full_constraints
+                    {
+                        Some(constraints) if clause.body.is_none() =>
+                        {
+                            self.current_clause += 1;
+                            Some(constraints)
+                        }
+                        Some(constraints) =>
+                        {
+                            self.current_clause += 1;
+                            self.counter_snapshot = self.global_counter.snapshot();
+                            self.sub_proof = Some(BodyProver::new(
+                                self.module,
+                                self.global_counter.clone(),
+                                clause.body.clone().unwrap(),
+                                constraints,
+                                &mut self.tracer,
+                            ));
+                            self.next()
+                        }
+                        None =>
+                        {
+                            self.global_counter.restore(self.counter_snapshot);
+                            self.current_clause += 1;
+                            self.next()
+                        }
+                    }
+                }
+            }
+            Some(prover) =>
+            {
+                let next = prover.next();
+                match next
+                {
+                    Some(constraints) => Some(constraints),
+                    None =>
+                    {
+                        self.global_counter.restore(self.counter_snapshot);
+                        self.sub_proof = None;
+                        self.next()
+                    }
+                }
+            }
+        }
+    }
+}

src/prover/tracing.rs

@@ -1,6 +1,9 @@
-use std::{default, fmt::Display};
-
 use log::info;
+use owo_colors::colors::css::DarkGray;
+use owo_colors::colors::css::Gray;
+use owo_colors::OwoColorize;
+use owo_colors::Style;
+use std::fmt::Display;
 
 #[derive(Clone, Copy)]
 pub enum ProofType
@@ -25,8 +28,8 @@ impl Display for ProofType
 
 pub trait Tracer
 {
-    fn begin_proof<T: Display>(&self, proof_type: ProofType) -> Self;
-    fn print_step<T: Display>(&self, show: T);
+    fn begin_proof(&mut self, proof_type: ProofType) -> Self;
+    fn print_step<T: Display>(&mut self, show: T);
     fn end_proof(self);
 }
 
@@ -45,12 +48,12 @@ impl SimpleTracer
 
 impl Tracer for SimpleTracer
 {
-    fn begin_proof<T: Display>(&self, proof_type: ProofType) -> Self
+    fn begin_proof(&mut self, proof_type: ProofType) -> Self
     {
         SimpleTracer { proof_type }
     }
 
-    fn print_step<T: Display>(&self, show: T)
+    fn print_step<T: Display>(&mut self, show: T)
     {
         let str = format!("{}", self.proof_type);
         info!(target: &str, "{}", show);
@@ -61,3 +64,83 @@ impl Tracer for SimpleTracer
         todo!()
     }
 }
+
+pub struct IndentedTracer
+{
+    first: bool,
+    depth: usize,
+}
+
+impl IndentedTracer
+{
+    pub fn new() -> IndentedTracer
+    {
+        IndentedTracer {
+            first: true,
+            depth: 0,
+        }
+    }
+}
+
+impl Tracer for IndentedTracer
+{
+    fn begin_proof(&mut self, _proof_type: ProofType) -> Self
+    {
+        IndentedTracer {
+            first: true,
+            depth: self.depth + 1,
+        }
+    }
+
+    fn print_step<T: Display>(&mut self, show: T)
+    {
+        for i in 0..self.depth
+        {
+            let style = if i % 2 == 0
+            {
+                Style::new().fg::<Gray>()
+            }
+            else
+            {
+                Style::new().fg::<DarkGray>()
+            };
+            print!("{}", "│".style(style));
+        }
+        self.first = false;
+        println!("{}", show);
+        // let _ = std::io::stdin().read_line(&mut String::new());
+        // println!("\x1b[2A");
+    }
+
+    fn end_proof(self)
+    {
+        drop(self);
+    }
+}
+
+impl Drop for IndentedTracer
+{
+    fn drop(&mut self) {}
+}
+
+impl Default for IndentedTracer
+{
+    fn default() -> Self
+    {
+        Self::new()
+    }
+}
+
+pub struct EmptyTracer;
+
+impl Tracer for EmptyTracer
+{
+    fn begin_proof(&mut self, _proof_type: ProofType) -> Self
+    {
+        EmptyTracer
+    }
+
+    fn print_step<T: Display>(&mut self, _show: T) {}
+
+    fn end_proof(self) {}
+}

src/prover/unification.rs

@@ -1,6 +1,7 @@
-use log::debug;
+use std::clone;
 
 use crate::ast::Predicate;
+use crate::domain::{self, Domain};
 use crate::prover::constraints::Constraints;
 
 impl Predicate
@@ -18,9 +19,20 @@ impl Predicate
                 //debug!("Unifying var {} against {}", self, other);
                 // We are trying to see if X (any) matches the other Predicate.
                 // This is always true if X = other_predicate
-                Some(Constraints::with(variable.clone(), other.clone()))
+                match other
+                {
+                    Predicate::Domain(domain) => Some(Constraints::with(
+                        variable.clone(),
+                        other.clone(),
+                        domain.clone(),
+                    )),
+                    _ => Some(Constraints::with(
+                        variable.clone(),
+                        other.clone(),
+                        Domain::all(),
+                    )),
+                }
             }
-
             Predicate::Fixed(name, arguments) =>
             {
                 match other
@@ -31,7 +43,7 @@ impl Predicate
                         // (any)
                         // This is always true
                         //debug!("Unifying pred {} against var {}", self, other);
-                        Some(Constraints::with(var.clone(), self.clone()))
+                        Some(Constraints::with(var.clone(), self.clone(), Domain::all()))
                     }
                     // Match pred(X, Y, Z, ...) with pred(_X, _Y, _Z, ...)
                     Predicate::Fixed(other_name, other_arguments)
@@ -60,6 +72,20 @@ impl Predicate
                     _ => None,
                 }
             }
+            Predicate::Domain(domain) => match other
+            {
+                Predicate::Variable(variable) => Some(Constraints::with(
+                    variable.clone(),
+                    other.clone(),
+                    domain.clone(),
+                )),
+                Predicate::Fixed(_, _) => None,
+                Predicate::Domain(other_domain) if !domain.intersection(other_domain).empty() =>
+                {
+                    Some(Constraints::none())
+                }
+                Predicate::Domain(_) => None,
+            },
         }
     }
 }