conjure_cp_core/ast/

expressions.rs

use std::collections::{HashSet, VecDeque};
use std::fmt::{Display, Formatter};
use tracing::trace;

use crate::ast::ReturnType;
use crate::ast::SetAttr;
use crate::ast::SymbolTable;
use crate::ast::literals::AbstractLiteral;
use crate::ast::literals::Literal;
use crate::ast::pretty::{pretty_expressions_as_top_level, pretty_vec};
use crate::ast::sat_encoding::SATIntEncoding;
use crate::ast::{Atom, DomainPtr};
use crate::ast::{GroundDomain, Metadata, UnresolvedDomain};
use crate::ast::{IntVal, Moo};
use crate::ast::{Name, matrix};
use crate::bug;
use conjure_cp_enum_compatibility_macro::document_compatibility;
use itertools::Itertools;
use serde::{Deserialize, Serialize};
use ustr::Ustr;

use polyquine::Quine;
use uniplate::{Biplate, Uniplate};

use super::abstract_comprehension::AbstractComprehension;
use super::ac_operators::ACOperatorKind;
use super::categories::{Category, CategoryOf};
use super::comprehension::Comprehension;
use super::domains::HasDomain as _;
use super::records::RecordValue;
use super::{DeclarationPtr, Domain, Range, Reference, SubModel, Typeable};

// Ensure that this type doesn't get too big
//
// If you triggered this assertion, you either made a variant of this enum that is too big, or you
// made Name,Literal,AbstractLiteral,Atom bigger, which made this bigger! To fix this, put some
// stuff in boxes.
//
// Enums take the size of their largest variant, so an enum with mostly small variants and a few
// large ones wastes memory... A larger Expression type also slows down Oxide.
//
// For more information, and more details on type sizes and how to measure them, see the commit
// message for 6012de809 (perf: reduce size of AST types, 2025-06-18).
//
// You can also see type sizes in the rustdoc documentation, generated by ./tools/gen_docs.sh
//
// https://github.com/conjure-cp/conjure-oxide/commit/6012de8096ca491ded91ecec61352fdf4e994f2e

// TODO: box all usages of Metadata to bring this down a bit more - I have added variants to
// ReturnType, and Metadata contains ReturnType, so Metadata has got bigger. Metadata will get a
// lot bigger still when we start using it for memoisation, so it should really be
// boxed ~niklasdewally

// expect size of Expression to be 112 bytes
static_assertions::assert_eq_size!([u8; 104], Expression);

/// Represents different types of expressions used to define rules and constraints in the model.
///
/// The `Expression` enum includes operations, constants, and variable references
/// used to build rules and conditions for the model.
#[document_compatibility]
#[derive(Clone, Debug, Hash, PartialEq, Eq, Serialize, Deserialize, Uniplate, Quine)]
#[biplate(to=AbstractComprehension)]
#[biplate(to=AbstractLiteral<Expression>)]
#[biplate(to=AbstractLiteral<Literal>)]
#[biplate(to=Atom)]
#[biplate(to=Comprehension)]
#[biplate(to=DeclarationPtr)]
#[biplate(to=DomainPtr)]
#[biplate(to=Literal)]
#[biplate(to=Metadata)]
#[biplate(to=Name)]
#[biplate(to=Option<Expression>)]
#[biplate(to=RecordValue<Expression>)]
#[biplate(to=RecordValue<Literal>)]
#[biplate(to=Reference)]
#[biplate(to=SubModel)]
#[biplate(to=SymbolTable)]
#[biplate(to=Vec<Expression>)]
#[path_prefix(conjure_cp::ast)]
pub enum Expression {
    AbstractLiteral(Metadata, AbstractLiteral<Expression>),
    /// The top of the model
    Root(Metadata, Vec<Expression>),

    /// An expression representing "A is valid as long as B is true"
    /// Turns into a conjunction when it reaches a boolean context
    Bubble(Metadata, Moo<Expression>, Moo<Expression>),

    /// A comprehension.
    ///
    /// The inside of the comprehension opens a new scope.
    // todo (gskorokhod): Comprehension contains a SubModel which contains a bunch of Rc pointers.
    // This makes implementing Quine tricky (it doesnt support Rc, by design). Skip it for now.
    #[polyquine_skip]
    Comprehension(Metadata, Moo<Comprehension>),

    /// Higher-level abstract comprehension
    #[polyquine_skip] // no idea what this is lol but it stops rustc screaming at me
    AbstractComprehension(Metadata, Moo<AbstractComprehension>),

    /// Defines dominance ("Solution A is preferred over Solution B")
    DominanceRelation(Metadata, Moo<Expression>),
    /// `fromSolution(name)` - Used in dominance relation definitions
    FromSolution(Metadata, Moo<Atom>),

    #[polyquine_with(arm = (_, name) => {
        let ident = proc_macro2::Ident::new(name.as_str(), proc_macro2::Span::call_site());
        quote::quote! { #ident.clone().into() }
    })]
    Metavar(Metadata, Ustr),

    Atomic(Metadata, Atom),

    /// A matrix index.
    ///
    /// Defined iff the indices are within their respective index domains.
    #[compatible(JsonInput)]
    UnsafeIndex(Metadata, Moo<Expression>, Vec<Expression>),

    /// A safe matrix index.
    ///
    /// See [`Expression::UnsafeIndex`]
    #[compatible(SMT)]
    SafeIndex(Metadata, Moo<Expression>, Vec<Expression>),

    /// A matrix slice: `a[indices]`.
    ///
    /// One of the indicies may be `None`, representing the dimension of the matrix we want to take
    /// a slice of. For example, for some 3d matrix a, `a[1,..,2]` has the indices
    /// `Some(1),None,Some(2)`.
    ///
    /// It is assumed that the slice only has one "wild-card" dimension and thus is 1 dimensional.
    ///
    /// Defined iff the defined indices are within their respective index domains.
    #[compatible(JsonInput)]
    UnsafeSlice(Metadata, Moo<Expression>, Vec<Option<Expression>>),

    /// A safe matrix slice: `a[indices]`.
    ///
    /// See [`Expression::UnsafeSlice`].
    SafeSlice(Metadata, Moo<Expression>, Vec<Option<Expression>>),

    /// `inDomain(x,domain)` iff `x` is in the domain `domain`.
    ///
    /// This cannot be constructed from Essence input, nor passed to a solver: this expression is
    /// mainly used during the conversion of `UnsafeIndex` and `UnsafeSlice` to `SafeIndex` and
    /// `SafeSlice` respectively.
    InDomain(Metadata, Moo<Expression>, DomainPtr),

    /// `toInt(b)` casts boolean expression b to an integer.
    ///
    /// - If b is false, then `toInt(b) == 0`
    ///
    /// - If b is true, then `toInt(b) == 1`
    #[compatible(SMT)]
    ToInt(Metadata, Moo<Expression>),

    // todo (gskorokhod): Same reason as for Comprehension
    #[polyquine_skip]
    Scope(Metadata, Moo<SubModel>),

    /// `|x|` - absolute value of `x`
    #[compatible(JsonInput, SMT)]
    Abs(Metadata, Moo<Expression>),

    /// `sum(<vec_expr>)`
    #[compatible(JsonInput, SMT)]
    Sum(Metadata, Moo<Expression>),

    /// `a * b * c * ...`
    #[compatible(JsonInput, SMT)]
    Product(Metadata, Moo<Expression>),

    /// `min(<vec_expr>)`
    #[compatible(JsonInput, SMT)]
    Min(Metadata, Moo<Expression>),

    /// `max(<vec_expr>)`
    #[compatible(JsonInput, SMT)]
    Max(Metadata, Moo<Expression>),

    /// `not(a)`
    #[compatible(JsonInput, SAT, SMT)]
    Not(Metadata, Moo<Expression>),

    /// `or(<vec_expr>)`
    #[compatible(JsonInput, SAT, SMT)]
    Or(Metadata, Moo<Expression>),

    /// `and(<vec_expr>)`
    #[compatible(JsonInput, SAT, SMT)]
    And(Metadata, Moo<Expression>),

    /// Ensures that `a->b` (material implication).
    #[compatible(JsonInput, SMT)]
    Imply(Metadata, Moo<Expression>, Moo<Expression>),

    /// `iff(a, b)` a <-> b
    #[compatible(JsonInput, SMT)]
    Iff(Metadata, Moo<Expression>, Moo<Expression>),

    #[compatible(JsonInput)]
    Union(Metadata, Moo<Expression>, Moo<Expression>),

    #[compatible(JsonInput)]
    In(Metadata, Moo<Expression>, Moo<Expression>),

    #[compatible(JsonInput)]
    Intersect(Metadata, Moo<Expression>, Moo<Expression>),

    #[compatible(JsonInput)]
    Supset(Metadata, Moo<Expression>, Moo<Expression>),

    #[compatible(JsonInput)]
    SupsetEq(Metadata, Moo<Expression>, Moo<Expression>),

    #[compatible(JsonInput)]
    Subset(Metadata, Moo<Expression>, Moo<Expression>),

    #[compatible(JsonInput)]
    SubsetEq(Metadata, Moo<Expression>, Moo<Expression>),

    #[compatible(JsonInput, SMT)]
    Eq(Metadata, Moo<Expression>, Moo<Expression>),

    #[compatible(JsonInput, SMT)]
    Neq(Metadata, Moo<Expression>, Moo<Expression>),

    #[compatible(JsonInput, SMT)]
    Geq(Metadata, Moo<Expression>, Moo<Expression>),

    #[compatible(JsonInput, SMT)]
    Leq(Metadata, Moo<Expression>, Moo<Expression>),

    #[compatible(JsonInput, SMT)]
    Gt(Metadata, Moo<Expression>, Moo<Expression>),

    #[compatible(JsonInput, SMT)]
    Lt(Metadata, Moo<Expression>, Moo<Expression>),

    /// Division after preventing division by zero, usually with a bubble
    #[compatible(SMT)]
    SafeDiv(Metadata, Moo<Expression>, Moo<Expression>),

    /// Division with a possibly undefined value (division by 0)
    #[compatible(JsonInput)]
    UnsafeDiv(Metadata, Moo<Expression>, Moo<Expression>),

    /// Modulo after preventing mod 0, usually with a bubble
    #[compatible(SMT)]
    SafeMod(Metadata, Moo<Expression>, Moo<Expression>),

    /// Modulo with a possibly undefined value (mod 0)
    #[compatible(JsonInput)]
    UnsafeMod(Metadata, Moo<Expression>, Moo<Expression>),

    /// Negation: `-x`
    #[compatible(JsonInput, SMT)]
    Neg(Metadata, Moo<Expression>),

    /// Set of domain values function is defined for
    #[compatible(JsonInput)]
    Defined(Metadata, Moo<Expression>),

    /// Set of codomain values function is defined for
    #[compatible(JsonInput)]
    Range(Metadata, Moo<Expression>),

    /// Unsafe power`x**y` (possibly undefined)
    ///
    /// Defined when (X!=0 \\/ Y!=0) /\ Y>=0
    #[compatible(JsonInput)]
    UnsafePow(Metadata, Moo<Expression>, Moo<Expression>),

    /// `UnsafePow` after preventing undefinedness
    SafePow(Metadata, Moo<Expression>, Moo<Expression>),

    /// Flatten matrix operator
    /// `flatten(M)` or `flatten(n, M)`
    /// where M is a matrix and n is an optional integer argument indicating depth of flattening
    Flatten(Metadata, Option<Moo<Expression>>, Moo<Expression>),

    /// `allDiff(<vec_expr>)`
    #[compatible(JsonInput)]
    AllDiff(Metadata, Moo<Expression>),

    /// Binary subtraction operator
    ///
    /// This is a parser-level construct, and is immediately normalised to `Sum([a,-b])`.
    /// TODO: make this compatible with Set Difference calculations - need to change return type and domain for this expression and write a set comprehension rule.
    /// have already edited minus_to_sum to prevent this from applying to sets
    #[compatible(JsonInput)]
    Minus(Metadata, Moo<Expression>, Moo<Expression>),

    /// Ensures that x=|y| i.e. x is the absolute value of y.
    ///
    /// Low-level Minion constraint.
    ///
    /// # See also
    ///
    /// + [Minion documentation](https://minion-solver.readthedocs.io/en/stable/usage/constraints.html#abs)
    #[compatible(Minion)]
    FlatAbsEq(Metadata, Moo<Atom>, Moo<Atom>),

    /// Ensures that `alldiff([a,b,...])`.
    ///
    /// Low-level Minion constraint.
    ///
    /// # See also
    ///
    /// + [Minion documentation](https://minion-solver.readthedocs.io/en/stable/usage/constraints.html#alldiff)
    #[compatible(Minion)]
    FlatAllDiff(Metadata, Vec<Atom>),

    /// Ensures that sum(vec) >= x.
    ///
    /// Low-level Minion constraint.
    ///
    /// # See also
    ///
    /// + [Minion documentation](https://minion-solver.readthedocs.io/en/stable/usage/constraints.html#sumgeq)
    #[compatible(Minion)]
    FlatSumGeq(Metadata, Vec<Atom>, Atom),

    /// Ensures that sum(vec) <= x.
    ///
    /// Low-level Minion constraint.
    ///
    /// # See also
    ///
    /// + [Minion documentation](https://minion-solver.readthedocs.io/en/stable/usage/constraints.html#sumleq)
    #[compatible(Minion)]
    FlatSumLeq(Metadata, Vec<Atom>, Atom),

    /// `ineq(x,y,k)` ensures that x <= y + k.
    ///
    /// Low-level Minion constraint.
    ///
    /// # See also
    ///
    /// + [Minion documentation](https://minion-solver.readthedocs.io/en/stable/usage/constraints.html#ineq)
    #[compatible(Minion)]
    FlatIneq(Metadata, Moo<Atom>, Moo<Atom>, Box<Literal>),

    /// `w-literal(x,k)` ensures that x == k, where x is a variable and k a constant.
    ///
    /// Low-level Minion constraint.
    ///
    /// This is a low-level Minion constraint and you should probably use Eq instead. The main use
    /// of w-literal is to convert boolean variables to constraints so that they can be used inside
    /// watched-and and watched-or.
    ///
    /// # See also
    ///
    /// + [Minion documentation](https://minion-solver.readthedocs.io/en/stable/usage/constraints.html#minuseq)
    /// + `rules::minion::boolean_literal_to_wliteral`.
    #[compatible(Minion)]
    #[polyquine_skip]
    FlatWatchedLiteral(Metadata, Reference, Literal),

    /// `weightedsumleq(cs,xs,total)` ensures that cs.xs <= total, where cs.xs is the scalar dot
    /// product of cs and xs.
    ///
    /// Low-level Minion constraint.
    ///
    /// Represents a weighted sum of the form `ax + by + cz + ...`
    ///
    /// # See also
    ///
    /// + [Minion
    /// documentation](https://minion-solver.readthedocs.io/en/stable/usage/constraints.html#weightedsumleq)
    FlatWeightedSumLeq(Metadata, Vec<Literal>, Vec<Atom>, Moo<Atom>),

    /// `weightedsumgeq(cs,xs,total)` ensures that cs.xs >= total, where cs.xs is the scalar dot
    /// product of cs and xs.
    ///
    /// Low-level Minion constraint.
    ///
    /// Represents a weighted sum of the form `ax + by + cz + ...`
    ///
    /// # See also
    ///
    /// + [Minion
    /// documentation](https://minion-solver.readthedocs.io/en/stable/usage/constraints.html#weightedsumleq)
    FlatWeightedSumGeq(Metadata, Vec<Literal>, Vec<Atom>, Moo<Atom>),

    /// Ensures that x =-y, where x and y are atoms.
    ///
    /// Low-level Minion constraint.
    ///
    /// # See also
    ///
    /// + [Minion documentation](https://minion-solver.readthedocs.io/en/stable/usage/constraints.html#minuseq)
    #[compatible(Minion)]
    FlatMinusEq(Metadata, Moo<Atom>, Moo<Atom>),

    /// Ensures that x*y=z.
    ///
    /// Low-level Minion constraint.
    ///
    /// # See also
    ///
    /// + [Minion documentation](https://minion-solver.readthedocs.io/en/stable/usage/constraints.html#product)
    #[compatible(Minion)]
    FlatProductEq(Metadata, Moo<Atom>, Moo<Atom>, Moo<Atom>),

    /// Ensures that floor(x/y)=z. Always true when y=0.
    ///
    /// Low-level Minion constraint.
    ///
    /// # See also
    ///
    /// + [Minion documentation](https://minion-solver.readthedocs.io/en/stable/usage/constraints.html#div_undefzero)
    #[compatible(Minion)]
    MinionDivEqUndefZero(Metadata, Moo<Atom>, Moo<Atom>, Moo<Atom>),

    /// Ensures that x%y=z. Always true when y=0.
    ///
    /// Low-level Minion constraint.
    ///
    /// # See also
    ///
    /// + [Minion documentation](https://minion-solver.readthedocs.io/en/stable/usage/constraints.html#mod_undefzero)
    #[compatible(Minion)]
    MinionModuloEqUndefZero(Metadata, Moo<Atom>, Moo<Atom>, Moo<Atom>),

    /// Ensures that `x**y = z`.
    ///
    /// Low-level Minion constraint.
    ///
    /// This constraint is false when `y<0` except for `1**y=1` and `(-1)**y=z` (where z is 1 if y
    /// is odd and z is -1 if y is even).
    ///
    /// # See also
    ///
    /// + [Github comment about `pow` semantics](https://github.com/minion/minion/issues/40#issuecomment-2595914891)
    /// + [Minion documentation](https://minion-solver.readthedocs.io/en/stable/usage/constraints.html#pow)
    MinionPow(Metadata, Moo<Atom>, Moo<Atom>, Moo<Atom>),

    /// `reify(constraint,r)` ensures that r=1 iff `constraint` is satisfied, where r is a 0/1
    /// variable.
    ///
    /// Low-level Minion constraint.
    ///
    /// # See also
    ///
    ///  + [Minion documentation](https://minion-solver.readthedocs.io/en/stable/usage/constraints.html#reify)
    #[compatible(Minion)]
    MinionReify(Metadata, Moo<Expression>, Atom),

    /// `reifyimply(constraint,r)` ensures that `r->constraint`, where r is a 0/1 variable.
    /// variable.
    ///
    /// Low-level Minion constraint.
    ///
    /// # See also
    ///
    ///  + [Minion documentation](https://minion-solver.readthedocs.io/en/stable/usage/constraints.html#reifyimply)
    #[compatible(Minion)]
    MinionReifyImply(Metadata, Moo<Expression>, Atom),

    /// `w-inintervalset(x, [a1,a2, b1,b2, … ])` ensures that the value of x belongs to one of the
    /// intervals {a1,…,a2}, {b1,…,b2} etc.
    ///
    /// The list of intervals must be given in numerical order.
    ///
    /// Low-level Minion constraint.
    ///
    /// # See also
    ///>
    ///  + [Minion documentation](https://minion-solver.readthedocs.io/en/stable/usage/constraints.html#w-inintervalset)
    #[compatible(Minion)]
    MinionWInIntervalSet(Metadata, Atom, Vec<i32>),

    /// `w-inset(x, [v1, v2, … ])` ensures that the value of `x` is one of the explicitly given values `v1`, `v2`, etc.
    ///
    /// This constraint enforces membership in a specific set of discrete values rather than intervals.
    ///
    /// The list of values must be given in numerical order.
    ///
    /// Low-level Minion constraint.
    ///
    /// # See also
    ///
    ///  + [Minion documentation](https://minion-solver.readthedocs.io/en/stable/usage/constraints.html#w-inset)
    #[compatible(Minion)]
    MinionWInSet(Metadata, Atom, Vec<i32>),

    /// `element_one(vec, i, e)` specifies that `vec[i] = e`. This implies that i is
    /// in the range `[1..len(vec)]`.
    ///
    /// Low-level Minion constraint.
    ///
    /// # See also
    ///
    ///  + [Minion documentation](https://minion-solver.readthedocs.io/en/stable/usage/constraints.html#element_one)
    #[compatible(Minion)]
    MinionElementOne(Metadata, Vec<Atom>, Moo<Atom>, Moo<Atom>),

    /// Declaration of an auxiliary variable.
    ///
    /// As with Savile Row, we semantically distinguish this from `Eq`.
    #[compatible(Minion)]
    #[polyquine_skip]
    AuxDeclaration(Metadata, Reference, Moo<Expression>),

    /// This expression is for encoding ints for the SAT solver, it stores the encoding type, the vector of booleans and the min/max for the int.
    #[compatible(SAT)]
    SATInt(Metadata, SATIntEncoding, Moo<Expression>, (i32, i32)),

    /// Addition over a pair of expressions (i.e. a + b) rather than a vec-expr like Expression::Sum.
    /// This is for compatibility with backends that do not support addition over vectors.
    #[compatible(SMT)]
    PairwiseSum(Metadata, Moo<Expression>, Moo<Expression>),

    /// Multiplication over a pair of expressions (i.e. a * b) rather than a vec-expr like Expression::Product.
    /// This is for compatibility with backends that do not support multiplication over vectors.
    #[compatible(SMT)]
    PairwiseProduct(Metadata, Moo<Expression>, Moo<Expression>),

    #[compatible(JsonInput)]
    Image(Metadata, Moo<Expression>, Moo<Expression>),

    #[compatible(JsonInput)]
    ImageSet(Metadata, Moo<Expression>, Moo<Expression>),

    #[compatible(JsonInput)]
    PreImage(Metadata, Moo<Expression>, Moo<Expression>),

    #[compatible(JsonInput)]
    Inverse(Metadata, Moo<Expression>, Moo<Expression>),

    #[compatible(JsonInput)]
    Restrict(Metadata, Moo<Expression>, Moo<Expression>),

    /// Lexicographical < between two matrices.
    ///
    /// A <lex B iff: A[i] < B[i] for some i /\ (A[j] > B[j] for some j -> i < j)
    /// I.e. A must be less than B at some index i, and if it is greater than B at another index j,
    /// then j comes after i.
    /// I.e. A must be greater than B at the first index where they differ.
    ///
    /// E.g. [1, 1] <lex [2, 1] and [1, 1] <lex [1, 2]
    LexLt(Metadata, Moo<Expression>, Moo<Expression>),

    /// Lexicographical <= between two matrices
    LexLeq(Metadata, Moo<Expression>, Moo<Expression>),

    /// Lexicographical > between two matrices
    /// This is a parser-level construct, and is immediately normalised to LexLt(b, a)
    LexGt(Metadata, Moo<Expression>, Moo<Expression>),

    /// Lexicographical >= between two matrices
    /// This is a parser-level construct, and is immediately normalised to LexLeq(b, a)
    LexGeq(Metadata, Moo<Expression>, Moo<Expression>),

    /// Low-level minion constraint. See Expression::LexLt
    FlatLexLt(Metadata, Vec<Atom>, Vec<Atom>),

    /// Low-level minion constraint. See Expression::LexLeq
    FlatLexLeq(Metadata, Vec<Atom>, Vec<Atom>),
}

// for the given matrix literal, return a bounded domain from the min to max of applying op to each
// child expression.
//
// Op must be monotonic.
//
// Returns none if unbounded
fn bounded_i32_domain_for_matrix_literal_monotonic(
    e: &Expression,
    op: fn(i32, i32) -> Option<i32>,
) -> Option<DomainPtr> {
    // only care about the elements, not the indices
    let (mut exprs, _) = e.clone().unwrap_matrix_unchecked()?;

    // fold each element's domain into one using op.
    //
    // here, I assume that op is monotone. This means that the bounds of op([a1,a2],[b1,b2])  for
    // the ranges [a1,a2], [b1,b2] will be
    // [min(op(a1,b1),op(a2,b1),op(a1,b2),op(a2,b2)),max(op(a1,b1),op(a2,b1),op(a1,b2),op(a2,b2))].
    //
    // We used to not assume this, and work out the bounds by applying op on the Cartesian product
    // of A and B; however, this caused a combinatorial explosion and my computer to run out of
    // memory (on the hakank_eprime_xkcd test)...
    //Int
    // For example, to find the bounds of the intervals [1,4], [1,5] combined using op, we used to do
    //  [min(op(1,1), op(1,2),op(1,3),op(1,4),op(1,5),op(2,1)..
    //
    // +,-,/,* are all monotone, so this assumption should be fine for now...

    let expr = exprs.pop()?;
    let dom = expr.domain_of()?;
    let Some(GroundDomain::Int(ranges)) = dom.as_ground() else {
        return None;
    };

    let (mut current_min, mut current_max) = range_vec_bounds_i32(ranges)?;

    for expr in exprs {
        let dom = expr.domain_of()?;
        let Some(GroundDomain::Int(ranges)) = dom.as_ground() else {
            return None;
        };

        let (min, max) = range_vec_bounds_i32(ranges)?;

        // all the possible new values for current_min / current_max
        let minmax = op(min, current_max)?;
        let minmin = op(min, current_min)?;
        let maxmin = op(max, current_min)?;
        let maxmax = op(max, current_max)?;
        let vals = [minmax, minmin, maxmin, maxmax];

        current_min = *vals
            .iter()
            .min()
            .expect("vals iterator should not be empty, and should have a minimum.");
        current_max = *vals
            .iter()
            .max()
            .expect("vals iterator should not be empty, and should have a maximum.");
    }

    if current_min == current_max {
        Some(Domain::int(vec![Range::Single(current_min)]))
    } else {
        Some(Domain::int(vec![Range::Bounded(current_min, current_max)]))
    }
}

// Returns none if unbounded
fn range_vec_bounds_i32(ranges: &Vec<Range<i32>>) -> Option<(i32, i32)> {
    let mut min = i32::MAX;
    let mut max = i32::MIN;
    for r in ranges {
        match r {
            Range::Single(i) => {
                if *i < min {
                    min = *i;
                }
                if *i > max {
                    max = *i;
                }
            }
            Range::Bounded(i, j) => {
                if *i < min {
                    min = *i;
                }
                if *j > max {
                    max = *j;
                }
            }
            Range::UnboundedR(_) | Range::UnboundedL(_) | Range::Unbounded => return None,
        }
    }
    Some((min, max))
}

impl Expression {
    /// Returns the possible values of the expression, recursing to leaf expressions
    pub fn domain_of(&self) -> Option<DomainPtr> {
        //println!("domain_of {self}");
        let ret = match self {
            Expression::Union(_, a, b) => Some(Domain::set(
                SetAttr::<IntVal>::default(),
                a.domain_of()?.union(&b.domain_of()?).ok()?,
            )),
            Expression::Intersect(_, a, b) => Some(Domain::set(
                SetAttr::<IntVal>::default(),
                a.domain_of()?.intersect(&b.domain_of()?).ok()?,
            )),
            Expression::In(_, _, _) => Some(Domain::bool()),
            Expression::Supset(_, _, _) => Some(Domain::bool()),
            Expression::SupsetEq(_, _, _) => Some(Domain::bool()),
            Expression::Subset(_, _, _) => Some(Domain::bool()),
            Expression::SubsetEq(_, _, _) => Some(Domain::bool()),
            Expression::AbstractLiteral(_, abslit) => abslit.domain_of(),
            Expression::DominanceRelation(_, _) => Some(Domain::bool()),
            Expression::FromSolution(_, expr) => Some(expr.domain_of()),
            Expression::Metavar(_, _) => None,
            Expression::Comprehension(_, comprehension) => comprehension.domain_of(),
            Expression::AbstractComprehension(_, comprehension) => comprehension.domain_of(),
            Expression::UnsafeIndex(_, matrix, _) | Expression::SafeIndex(_, matrix, _) => {
                let dom = matrix.domain_of()?;
                if let Some((elem_domain, _)) = dom.as_matrix() {
                    return Some(elem_domain);
                }

                // may actually use the value in the future
                #[allow(clippy::redundant_pattern_matching)]
                if let Some(_) = dom.as_tuple() {
                    // TODO: We can implement proper indexing for tuples
                    return None;
                }

                // may actually use the value in the future
                #[allow(clippy::redundant_pattern_matching)]
                if let Some(_) = dom.as_record() {
                    // TODO: We can implement proper indexing for records
                    return None;
                }

                bug!("subject of an index operation should support indexing")
            }
            Expression::UnsafeSlice(_, matrix, indices)
            | Expression::SafeSlice(_, matrix, indices) => {
                let sliced_dimension = indices.iter().position(Option::is_none);

                let dom = matrix.domain_of()?;
                let Some((elem_domain, index_domains)) = dom.as_matrix() else {
                    bug!("subject of an index operation should be a matrix");
                };

                match sliced_dimension {
                    Some(dimension) => Some(Domain::matrix(
                        elem_domain,
                        vec![index_domains[dimension].clone()],
                    )),

                    // same as index
                    None => Some(elem_domain),
                }
            }
            Expression::InDomain(_, _, _) => Some(Domain::bool()),
            Expression::Atomic(_, atom) => Some(atom.domain_of()),
            Expression::Scope(_, _) => Some(Domain::bool()),
            Expression::Sum(_, e) => {
                bounded_i32_domain_for_matrix_literal_monotonic(e, |x, y| Some(x + y))
            }
            Expression::Product(_, e) => {
                bounded_i32_domain_for_matrix_literal_monotonic(e, |x, y| Some(x * y))
            }
            Expression::Min(_, e) => bounded_i32_domain_for_matrix_literal_monotonic(e, |x, y| {
                Some(if x < y { x } else { y })
            }),
            Expression::Max(_, e) => bounded_i32_domain_for_matrix_literal_monotonic(e, |x, y| {
                Some(if x > y { x } else { y })
            }),
            Expression::UnsafeDiv(_, a, b) => a
                .domain_of()?
                .resolve()?
                .apply_i32(
                    // rust integer division is truncating; however, we want to always round down,
                    // including for negative numbers.
                    |x, y| {
                        if y != 0 {
                            Some((x as f32 / y as f32).floor() as i32)
                        } else {
                            None
                        }
                    },
                    b.domain_of()?.resolve()?.as_ref(),
                )
                .map(DomainPtr::from)
                .ok(),
            Expression::SafeDiv(_, a, b) => {
                // rust integer division is truncating; however, we want to always round down
                // including for negative numbers.
                let domain = a
                    .domain_of()?
                    .resolve()?
                    .apply_i32(
                        |x, y| {
                            if y != 0 {
                                Some((x as f32 / y as f32).floor() as i32)
                            } else {
                                None
                            }
                        },
                        b.domain_of()?.resolve()?.as_ref(),
                    )
                    .unwrap_or_else(|err| bug!("Got {err} when computing domain of {self}"));

                if let GroundDomain::Int(ranges) = domain {
                    let mut ranges = ranges;
                    ranges.push(Range::Single(0));
                    return Some(Domain::int(ranges));
                } else {
                    bug!("Domain of {self} was not integer")
                }
            }
            Expression::UnsafeMod(_, a, b) => a
                .domain_of()?
                .resolve()?
                .apply_i32(
                    |x, y| if y != 0 { Some(x % y) } else { None },
                    b.domain_of()?.resolve()?.as_ref(),
                )
                .map(DomainPtr::from)
                .ok(),
            Expression::SafeMod(_, a, b) => {
                let domain = a
                    .domain_of()?
                    .resolve()?
                    .apply_i32(
                        |x, y| if y != 0 { Some(x % y) } else { None },
                        b.domain_of()?.resolve()?.as_ref(),
                    )
                    .unwrap_or_else(|err| bug!("Got {err} when computing domain of {self}"));

                if let GroundDomain::Int(ranges) = domain {
                    let mut ranges = ranges;
                    ranges.push(Range::Single(0));
                    return Some(Domain::int(ranges));
                } else {
                    bug!("Domain of {self} was not integer")
                }
            }
            Expression::SafePow(_, a, b) | Expression::UnsafePow(_, a, b) => a
                .domain_of()?
                .resolve()?
                .apply_i32(
                    |x, y| {
                        if (x != 0 || y != 0) && y >= 0 {
                            Some(x.pow(y as u32))
                        } else {
                            None
                        }
                    },
                    b.domain_of()?.resolve()?.as_ref(),
                )
                .map(DomainPtr::from)
                .ok(),
            Expression::Root(_, _) => None,
            Expression::Bubble(_, inner, _) => inner.domain_of(),
            Expression::AuxDeclaration(_, _, _) => Some(Domain::bool()),
            Expression::And(_, _) => Some(Domain::bool()),
            Expression::Not(_, _) => Some(Domain::bool()),
            Expression::Or(_, _) => Some(Domain::bool()),
            Expression::Imply(_, _, _) => Some(Domain::bool()),
            Expression::Iff(_, _, _) => Some(Domain::bool()),
            Expression::Eq(_, _, _) => Some(Domain::bool()),
            Expression::Neq(_, _, _) => Some(Domain::bool()),
            Expression::Geq(_, _, _) => Some(Domain::bool()),
            Expression::Leq(_, _, _) => Some(Domain::bool()),
            Expression::Gt(_, _, _) => Some(Domain::bool()),
            Expression::Lt(_, _, _) => Some(Domain::bool()),
            Expression::FlatAbsEq(_, _, _) => Some(Domain::bool()),
            Expression::FlatSumGeq(_, _, _) => Some(Domain::bool()),
            Expression::FlatSumLeq(_, _, _) => Some(Domain::bool()),
            Expression::MinionDivEqUndefZero(_, _, _, _) => Some(Domain::bool()),
            Expression::MinionModuloEqUndefZero(_, _, _, _) => Some(Domain::bool()),
            Expression::FlatIneq(_, _, _, _) => Some(Domain::bool()),
            Expression::Flatten(_, n, m) => {
                if let Some(expr) = n {
                    if expr.return_type() == ReturnType::Int {
                        // TODO: handle flatten with depth argument
                        return None;
                    }
                } else {
                    // TODO: currently only works for matrices
                    let dom = m.domain_of()?.resolve()?;
                    let (val_dom, idx_doms) = match dom.as_ref() {
                        GroundDomain::Matrix(val, idx) => (val, idx),
                        _ => return None,
                    };
                    let num_elems = matrix::num_elements(idx_doms).ok()? as i32;

                    let new_index_domain = Domain::int(vec![Range::Bounded(1, num_elems)]);
                    return Some(Domain::matrix(
                        val_dom.clone().into(),
                        vec![new_index_domain],
                    ));
                }
                None
            }
            Expression::AllDiff(_, _) => Some(Domain::bool()),
            Expression::FlatWatchedLiteral(_, _, _) => Some(Domain::bool()),
            Expression::MinionReify(_, _, _) => Some(Domain::bool()),
            Expression::MinionReifyImply(_, _, _) => Some(Domain::bool()),
            Expression::MinionWInIntervalSet(_, _, _) => Some(Domain::bool()),
            Expression::MinionWInSet(_, _, _) => Some(Domain::bool()),
            Expression::MinionElementOne(_, _, _, _) => Some(Domain::bool()),
            Expression::Neg(_, x) => {
                let dom = x.domain_of()?;
                let mut ranges = dom.as_int()?;

                ranges = ranges
                    .into_iter()
                    .map(|r| match r {
                        Range::Single(x) => Range::Single(-x),
                        Range::Bounded(x, y) => Range::Bounded(-y, -x),
                        Range::UnboundedR(i) => Range::UnboundedL(-i),
                        Range::UnboundedL(i) => Range::UnboundedR(-i),
                        Range::Unbounded => Range::Unbounded,
                    })
                    .collect();

                Some(Domain::int(ranges))
            }
            Expression::Minus(_, a, b) => a
                .domain_of()?
                .resolve()?
                .apply_i32(|x, y| Some(x - y), b.domain_of()?.resolve()?.as_ref())
                .map(DomainPtr::from)
                .ok(),
            Expression::FlatAllDiff(_, _) => Some(Domain::bool()),
            Expression::FlatMinusEq(_, _, _) => Some(Domain::bool()),
            Expression::FlatProductEq(_, _, _, _) => Some(Domain::bool()),
            Expression::FlatWeightedSumLeq(_, _, _, _) => Some(Domain::bool()),
            Expression::FlatWeightedSumGeq(_, _, _, _) => Some(Domain::bool()),
            Expression::Abs(_, a) => a
                .domain_of()?
                .resolve()?
                .apply_i32(|a, _| Some(a.abs()), a.domain_of()?.resolve()?.as_ref())
                .map(DomainPtr::from)
                .ok(),
            Expression::MinionPow(_, _, _, _) => Some(Domain::bool()),
            Expression::ToInt(_, _) => Some(Domain::int(vec![Range::Bounded(0, 1)])),
            Expression::SATInt(_, _, _, (low, high)) => {
                Some(Domain::int_ground(vec![Range::Bounded(*low, *high)]))
            }
            Expression::PairwiseSum(_, a, b) => a
                .domain_of()?
                .resolve()?
                .apply_i32(|a, b| Some(a + b), b.domain_of()?.resolve()?.as_ref())
                .map(DomainPtr::from)
                .ok(),
            Expression::PairwiseProduct(_, a, b) => a
                .domain_of()?
                .resolve()?
                .apply_i32(|a, b| Some(a * b), b.domain_of()?.resolve()?.as_ref())
                .map(DomainPtr::from)
                .ok(),
            Expression::Defined(_, function) => get_function_domain(function),
            Expression::Range(_, function) => get_function_codomain(function),
            Expression::Image(_, function, _) => get_function_codomain(function),
            Expression::ImageSet(_, function, _) => get_function_codomain(function),
            Expression::PreImage(_, function, _) => get_function_domain(function),
            Expression::Restrict(_, function, new_domain) => {
                let (attrs, _, codom) = function.domain_of()?.as_function()?;
                let new_dom = new_domain.domain_of()?;
                Some(Domain::function(attrs, new_dom, codom))
            }
            Expression::Inverse(..) => Some(Domain::bool()),
            Expression::LexLt(..) => Some(Domain::bool()),
            Expression::LexLeq(..) => Some(Domain::bool()),
            Expression::LexGt(..) => Some(Domain::bool()),
            Expression::LexGeq(..) => Some(Domain::bool()),
            Expression::FlatLexLt(..) => Some(Domain::bool()),
            Expression::FlatLexLeq(..) => Some(Domain::bool()),
        };
        if let Some(dom) = &ret
            && let Some(ranges) = dom.as_int_ground()
            && ranges.len() > 1
        {
            // TODO: (flm8) the Minion bindings currently only support single ranges for domains, so we use the min/max bounds
            // Once they support a full domain as we define it, we can remove this conversion
            let (min, max) = range_vec_bounds_i32(ranges)?;
            return Some(Domain::int(vec![Range::Bounded(min, max)]));
        }
        ret
    }

    pub fn get_meta(&self) -> Metadata {
        let metas: VecDeque<Metadata> = self.children_bi();
        metas[0].clone()
    }

    pub fn set_meta(&self, meta: Metadata) {
        self.transform_bi(&|_| meta.clone());
    }

    /// Checks whether this expression is safe.
    ///
    /// An expression is unsafe if can be undefined, or if any of its children can be undefined.
    ///
    /// Unsafe expressions are (typically) prefixed with Unsafe in our AST, and can be made
    /// safe through the use of bubble rules.
    pub fn is_safe(&self) -> bool {
        // TODO: memoise in Metadata
        for expr in self.universe() {
            match expr {
                Expression::UnsafeDiv(_, _, _)
                | Expression::UnsafeMod(_, _, _)
                | Expression::UnsafePow(_, _, _)
                | Expression::UnsafeIndex(_, _, _)
                | Expression::Bubble(_, _, _)
                | Expression::UnsafeSlice(_, _, _) => {
                    return false;
                }
                _ => {}
            }
        }
        true
    }

    pub fn is_clean(&self) -> bool {
        let metadata = self.get_meta();
        metadata.clean
    }

    pub fn set_clean(&mut self, bool_value: bool) {
        let mut metadata = self.get_meta();
        metadata.clean = bool_value;
        self.set_meta(metadata);
    }

    /// True if the expression is an associative and commutative operator
    pub fn is_associative_commutative_operator(&self) -> bool {
        TryInto::<ACOperatorKind>::try_into(self).is_ok()
    }

    /// True if the expression is a matrix literal.
    ///
    /// This is true for both forms of matrix literals: those with elements of type [`Literal`] and
    /// [`Expression`].
    pub fn is_matrix_literal(&self) -> bool {
        matches!(
            self,
            Expression::AbstractLiteral(_, AbstractLiteral::Matrix(_, _))
                | Expression::Atomic(
                    _,
                    Atom::Literal(Literal::AbstractLiteral(AbstractLiteral::Matrix(_, _))),
                )
        )
    }

    /// True iff self and other are both atomic and identical.
    ///
    /// This method is useful to cheaply check equivalence. Assuming CSE is enabled, any unifiable
    /// expressions will be rewritten to a common variable. This is much cheaper than checking the
    /// entire subtrees of `self` and `other`.
    pub fn identical_atom_to(&self, other: &Expression) -> bool {
        let atom1: Result<&Atom, _> = self.try_into();
        let atom2: Result<&Atom, _> = other.try_into();

        if let (Ok(atom1), Ok(atom2)) = (atom1, atom2) {
            atom2 == atom1
        } else {
            false
        }
    }

    /// If the expression is a list, returns a *copied* vector of the inner expressions.
    ///
    /// A list is any a matrix with the domain `int(1..)`. This includes matrix literals without
    /// any explicitly specified domain.
    pub fn unwrap_list(&self) -> Option<Vec<Expression>> {
        match self {
            Expression::AbstractLiteral(_, matrix @ AbstractLiteral::Matrix(_, _)) => {
                matrix.unwrap_list().cloned()
            }
            Expression::Atomic(
                _,
                Atom::Literal(Literal::AbstractLiteral(matrix @ AbstractLiteral::Matrix(_, _))),
            ) => matrix.unwrap_list().map(|elems| {
                elems
                    .clone()
                    .into_iter()
                    .map(|x: Literal| Expression::Atomic(Metadata::new(), Atom::Literal(x)))
                    .collect_vec()
            }),
            _ => None,
        }
    }

    /// If the expression is a matrix, gets it elements and index domain.
    ///
    /// **Consider using the safer [`Expression::unwrap_list`] instead.**
    ///
    /// It is generally undefined to edit the length of a matrix unless it is a list (as defined by
    /// [`Expression::unwrap_list`]). Users of this function should ensure that, if the matrix is
    /// reconstructed, the index domain and the number of elements in the matrix remain the same.
    pub fn unwrap_matrix_unchecked(self) -> Option<(Vec<Expression>, DomainPtr)> {
        match self {
            Expression::AbstractLiteral(_, AbstractLiteral::Matrix(elems, domain)) => {
                Some((elems, domain))
            }
            Expression::Atomic(
                _,
                Atom::Literal(Literal::AbstractLiteral(AbstractLiteral::Matrix(elems, domain))),
            ) => Some((
                elems
                    .into_iter()
                    .map(|x: Literal| Expression::Atomic(Metadata::new(), Atom::Literal(x)))
                    .collect_vec(),
                domain.into(),
            )),

            _ => None,
        }
    }

    /// For a Root expression, extends the inner vec with the given vec.
    ///
    /// # Panics
    /// Panics if the expression is not Root.
    pub fn extend_root(self, exprs: Vec<Expression>) -> Expression {
        match self {
            Expression::Root(meta, mut children) => {
                children.extend(exprs);
                Expression::Root(meta, children)
            }
            _ => panic!("extend_root called on a non-Root expression"),
        }
    }

    /// Converts the expression to a literal, if possible.
    pub fn into_literal(self) -> Option<Literal> {
        match self {
            Expression::Atomic(_, Atom::Literal(lit)) => Some(lit),
            Expression::AbstractLiteral(_, abslit) => {
                Some(Literal::AbstractLiteral(abslit.into_literals()?))
            }
            Expression::Neg(_, e) => {
                let Literal::Int(i) = Moo::unwrap_or_clone(e).into_literal()? else {
                    bug!("negated literal should be an int");
                };

                Some(Literal::Int(-i))
            }

            _ => None,
        }
    }

    /// If this expression is an associative-commutative operator, return its [ACOperatorKind].
    pub fn to_ac_operator_kind(&self) -> Option<ACOperatorKind> {
        TryFrom::try_from(self).ok()
    }

    /// Returns the categories of all sub-expressions of self.
    pub fn universe_categories(&self) -> HashSet<Category> {
        self.universe()
            .into_iter()
            .map(|x| x.category_of())
            .collect()
    }
}

pub fn get_function_domain(function: &Moo<Expression>) -> Option<DomainPtr> {
    let function_domain = function.domain_of()?;
    match function_domain.resolve().as_ref() {
        Some(d) => {
            match d.as_ref() {
                GroundDomain::Function(_, domain, _) => Some(domain.clone().into()),
                // Not defined for anything other than a function
                _ => None,
            }
        }
        None => {
            match function_domain.as_unresolved()? {
                UnresolvedDomain::Function(_, domain, _) => Some(domain.clone()),
                // Not defined for anything other than a function
                _ => None,
            }
        }
    }
}

pub fn get_function_codomain(function: &Moo<Expression>) -> Option<DomainPtr> {
    let function_domain = function.domain_of()?;
    match function_domain.resolve().as_ref() {
        Some(d) => {
            match d.as_ref() {
                GroundDomain::Function(_, _, codomain) => Some(codomain.clone().into()),
                // Not defined for anything other than a function
                _ => None,
            }
        }
        None => {
            match function_domain.as_unresolved()? {
                UnresolvedDomain::Function(_, _, codomain) => Some(codomain.clone()),
                // Not defined for anything other than a function
                _ => None,
            }
        }
    }
}

impl TryFrom<&Expression> for i32 {
    type Error = ();

    fn try_from(value: &Expression) -> Result<Self, Self::Error> {
        let Expression::Atomic(_, atom) = value else {
            return Err(());
        };

        let Atom::Literal(lit) = atom else {
            return Err(());
        };

        let Literal::Int(i) = lit else {
            return Err(());
        };

        Ok(*i)
    }
}

impl TryFrom<Expression> for i32 {
    type Error = ();

    fn try_from(value: Expression) -> Result<Self, Self::Error> {
        TryFrom::<&Expression>::try_from(&value)
    }
}
impl From<i32> for Expression {
    fn from(i: i32) -> Self {
        Expression::Atomic(Metadata::new(), Atom::Literal(Literal::Int(i)))
    }
}

impl From<bool> for Expression {
    fn from(b: bool) -> Self {
        Expression::Atomic(Metadata::new(), Atom::Literal(Literal::Bool(b)))
    }
}

impl From<Atom> for Expression {
    fn from(value: Atom) -> Self {
        Expression::Atomic(Metadata::new(), value)
    }
}

impl From<Literal> for Expression {
    fn from(value: Literal) -> Self {
        Expression::Atomic(Metadata::new(), value.into())
    }
}

impl From<Moo<Expression>> for Expression {
    fn from(val: Moo<Expression>) -> Self {
        val.as_ref().clone()
    }
}

impl CategoryOf for Expression {
    fn category_of(&self) -> Category {
        // take highest category of all the expressions children
        let category = self.cata(&move |x,children| {

            if let Some(max_category) = children.iter().max() {
                // if this expression contains subexpressions, return the maximum category of the
                // subexpressions
                *max_category
            } else {
                // this expression has no children
                let mut max_category = Category::Bottom;

                // calculate the category by looking at all atoms, submodels, comprehensions, and
                // declarationptrs inside this expression

                // this should generically cover all leaf types we currently have in oxide.

                // if x contains submodels (including comprehensions)
                if !Biplate::<SubModel>::universe_bi(&x).is_empty() {
                    // assume that the category is decision
                    return Category::Decision;
                }

                // if x contains atoms
                if let Some(max_atom_category) = Biplate::<Atom>::universe_bi(&x).iter().map(|x| x.category_of()).max()
                // and those atoms have a higher category than we already know about
                && max_atom_category > max_category{
                    // update category 
                    max_category = max_atom_category;
                }

                // if x contains declarationPtrs
                if let Some(max_declaration_category) = Biplate::<DeclarationPtr>::universe_bi(&x).iter().map(|x| x.category_of()).max()
                // and those pointers have a higher category than we already know about
                && max_declaration_category > max_category{
                    // update category 
                    max_category = max_declaration_category;
                }
                max_category

            }
        });

        if cfg!(debug_assertions) {
            trace!(
                category= %category,
                expression= %self,
                "Called Expression::category_of()"
            );
        };
        category
    }
}

impl Display for Expression {
    fn fmt(&self, f: &mut Formatter<'_>) -> std::fmt::Result {
        match &self {
            Expression::Union(_, box1, box2) => {
                write!(f, "({} union {})", box1.clone(), box2.clone())
            }
            Expression::In(_, e1, e2) => {
                write!(f, "{e1} in {e2}")
            }
            Expression::Intersect(_, box1, box2) => {
                write!(f, "({} intersect {})", box1.clone(), box2.clone())
            }
            Expression::Supset(_, box1, box2) => {
                write!(f, "({} supset {})", box1.clone(), box2.clone())
            }
            Expression::SupsetEq(_, box1, box2) => {
                write!(f, "({} supsetEq {})", box1.clone(), box2.clone())
            }
            Expression::Subset(_, box1, box2) => {
                write!(f, "({} subset {})", box1.clone(), box2.clone())
            }
            Expression::SubsetEq(_, box1, box2) => {
                write!(f, "({} subsetEq {})", box1.clone(), box2.clone())
            }

            Expression::AbstractLiteral(_, l) => l.fmt(f),
            Expression::Comprehension(_, c) => c.fmt(f),
            Expression::AbstractComprehension(_, c) => c.fmt(f),
            Expression::UnsafeIndex(_, e1, e2) | Expression::SafeIndex(_, e1, e2) => {
                write!(f, "{e1}{}", pretty_vec(e2))
            }
            Expression::UnsafeSlice(_, e1, es) | Expression::SafeSlice(_, e1, es) => {
                let args = es
                    .iter()
                    .map(|x| match x {
                        Some(x) => format!("{x}"),
                        None => "..".into(),
                    })
                    .join(",");

                write!(f, "{e1}[{args}]")
            }
            Expression::InDomain(_, e, domain) => {
                write!(f, "__inDomain({e},{domain})")
            }
            Expression::Root(_, exprs) => {
                write!(f, "{}", pretty_expressions_as_top_level(exprs))
            }
            Expression::DominanceRelation(_, expr) => write!(f, "DominanceRelation({expr})"),
            Expression::FromSolution(_, expr) => write!(f, "FromSolution({expr})"),
            Expression::Metavar(_, name) => write!(f, "&{name}"),
            Expression::Atomic(_, atom) => atom.fmt(f),
            Expression::Scope(_, submodel) => write!(f, "{{\n{submodel}\n}}"),
            Expression::Abs(_, a) => write!(f, "|{a}|"),
            Expression::Sum(_, e) => {
                write!(f, "sum({e})")
            }
            Expression::Product(_, e) => {
                write!(f, "product({e})")
            }
            Expression::Min(_, e) => {
                write!(f, "min({e})")
            }
            Expression::Max(_, e) => {
                write!(f, "max({e})")
            }
            Expression::Not(_, expr_box) => {
                write!(f, "!({})", expr_box.clone())
            }
            Expression::Or(_, e) => {
                write!(f, "or({e})")
            }
            Expression::And(_, e) => {
                write!(f, "and({e})")
            }
            Expression::Imply(_, box1, box2) => {
                write!(f, "({box1}) -> ({box2})")
            }
            Expression::Iff(_, box1, box2) => {
                write!(f, "({box1}) <-> ({box2})")
            }
            Expression::Eq(_, box1, box2) => {
                write!(f, "({} = {})", box1.clone(), box2.clone())
            }
            Expression::Neq(_, box1, box2) => {
                write!(f, "({} != {})", box1.clone(), box2.clone())
            }
            Expression::Geq(_, box1, box2) => {
                write!(f, "({} >= {})", box1.clone(), box2.clone())
            }
            Expression::Leq(_, box1, box2) => {
                write!(f, "({} <= {})", box1.clone(), box2.clone())
            }
            Expression::Gt(_, box1, box2) => {
                write!(f, "({} > {})", box1.clone(), box2.clone())
            }
            Expression::Lt(_, box1, box2) => {
                write!(f, "({} < {})", box1.clone(), box2.clone())
            }
            Expression::FlatSumGeq(_, box1, box2) => {
                write!(f, "SumGeq({}, {})", pretty_vec(box1), box2.clone())
            }
            Expression::FlatSumLeq(_, box1, box2) => {
                write!(f, "SumLeq({}, {})", pretty_vec(box1), box2.clone())
            }
            Expression::FlatIneq(_, box1, box2, box3) => write!(
                f,
                "Ineq({}, {}, {})",
                box1.clone(),
                box2.clone(),
                box3.clone()
            ),
            Expression::Flatten(_, n, m) => {
                if let Some(n) = n {
                    write!(f, "flatten({n}, {m})")
                } else {
                    write!(f, "flatten({m})")
                }
            }
            Expression::AllDiff(_, e) => {
                write!(f, "allDiff({e})")
            }
            Expression::Bubble(_, box1, box2) => {
                write!(f, "{{{} @ {}}}", box1.clone(), box2.clone())
            }
            Expression::SafeDiv(_, box1, box2) => {
                write!(f, "SafeDiv({}, {})", box1.clone(), box2.clone())
            }
            Expression::UnsafeDiv(_, box1, box2) => {
                write!(f, "UnsafeDiv({}, {})", box1.clone(), box2.clone())
            }
            Expression::UnsafePow(_, box1, box2) => {
                write!(f, "UnsafePow({}, {})", box1.clone(), box2.clone())
            }
            Expression::SafePow(_, box1, box2) => {
                write!(f, "SafePow({}, {})", box1.clone(), box2.clone())
            }
            Expression::MinionDivEqUndefZero(_, box1, box2, box3) => {
                write!(
                    f,
                    "DivEq({}, {}, {})",
                    box1.clone(),
                    box2.clone(),
                    box3.clone()
                )
            }
            Expression::MinionModuloEqUndefZero(_, box1, box2, box3) => {
                write!(
                    f,
                    "ModEq({}, {}, {})",
                    box1.clone(),
                    box2.clone(),
                    box3.clone()
                )
            }
            Expression::FlatWatchedLiteral(_, x, l) => {
                write!(f, "WatchedLiteral({x},{l})")
            }
            Expression::MinionReify(_, box1, box2) => {
                write!(f, "Reify({}, {})", box1.clone(), box2.clone())
            }
            Expression::MinionReifyImply(_, box1, box2) => {
                write!(f, "ReifyImply({}, {})", box1.clone(), box2.clone())
            }
            Expression::MinionWInIntervalSet(_, atom, intervals) => {
                let intervals = intervals.iter().join(",");
                write!(f, "__minion_w_inintervalset({atom},[{intervals}])")
            }
            Expression::MinionWInSet(_, atom, values) => {
                let values = values.iter().join(",");
                write!(f, "__minion_w_inset({atom},{values})")
            }
            Expression::AuxDeclaration(_, reference, e) => {
                write!(f, "{} =aux {}", reference, e.clone())
            }
            Expression::UnsafeMod(_, a, b) => {
                write!(f, "{} % {}", a.clone(), b.clone())
            }
            Expression::SafeMod(_, a, b) => {
                write!(f, "SafeMod({},{})", a.clone(), b.clone())
            }
            Expression::Neg(_, a) => {
                write!(f, "-({})", a.clone())
            }
            Expression::Minus(_, a, b) => {
                write!(f, "({} - {})", a.clone(), b.clone())
            }
            Expression::FlatAllDiff(_, es) => {
                write!(f, "__flat_alldiff({})", pretty_vec(es))
            }
            Expression::FlatAbsEq(_, a, b) => {
                write!(f, "AbsEq({},{})", a.clone(), b.clone())
            }
            Expression::FlatMinusEq(_, a, b) => {
                write!(f, "MinusEq({},{})", a.clone(), b.clone())
            }
            Expression::FlatProductEq(_, a, b, c) => {
                write!(
                    f,
                    "FlatProductEq({},{},{})",
                    a.clone(),
                    b.clone(),
                    c.clone()
                )
            }
            Expression::FlatWeightedSumLeq(_, cs, vs, total) => {
                write!(
                    f,
                    "FlatWeightedSumLeq({},{},{})",
                    pretty_vec(cs),
                    pretty_vec(vs),
                    total.clone()
                )
            }
            Expression::FlatWeightedSumGeq(_, cs, vs, total) => {
                write!(
                    f,
                    "FlatWeightedSumGeq({},{},{})",
                    pretty_vec(cs),
                    pretty_vec(vs),
                    total.clone()
                )
            }
            Expression::MinionPow(_, atom, atom1, atom2) => {
                write!(f, "MinionPow({atom},{atom1},{atom2})")
            }
            Expression::MinionElementOne(_, atoms, atom, atom1) => {
                let atoms = atoms.iter().join(",");
                write!(f, "__minion_element_one([{atoms}],{atom},{atom1})")
            }

            Expression::ToInt(_, expr) => {
                write!(f, "toInt({expr})")
            }

            Expression::SATInt(_, encoding, bits, (min, max)) => {
                write!(f, "SATInt({encoding:?}, {bits} [{min}, {max}])")
            }

            Expression::PairwiseSum(_, a, b) => write!(f, "PairwiseSum({a}, {b})"),
            Expression::PairwiseProduct(_, a, b) => write!(f, "PairwiseProduct({a}, {b})"),

            Expression::Defined(_, function) => write!(f, "defined({function})"),
            Expression::Range(_, function) => write!(f, "range({function})"),
            Expression::Image(_, function, elems) => write!(f, "image({function},{elems})"),
            Expression::ImageSet(_, function, elems) => write!(f, "imageSet({function},{elems})"),
            Expression::PreImage(_, function, elems) => write!(f, "preImage({function},{elems})"),
            Expression::Inverse(_, a, b) => write!(f, "inverse({a},{b})"),
            Expression::Restrict(_, function, domain) => write!(f, "restrict({function},{domain})"),

            Expression::LexLt(_, a, b) => write!(f, "({a} <lex {b})"),
            Expression::LexLeq(_, a, b) => write!(f, "({a} <=lex {b})"),
            Expression::LexGt(_, a, b) => write!(f, "({a} >lex {b})"),
            Expression::LexGeq(_, a, b) => write!(f, "({a} >=lex {b})"),
            Expression::FlatLexLt(_, a, b) => {
                write!(f, "FlatLexLt({}, {})", pretty_vec(a), pretty_vec(b))
            }
            Expression::FlatLexLeq(_, a, b) => {
                write!(f, "FlatLexLeq({}, {})", pretty_vec(a), pretty_vec(b))
            }
        }
    }
}

impl Typeable for Expression {
    fn return_type(&self) -> ReturnType {
        match self {
            Expression::Union(_, subject, _) => ReturnType::Set(Box::new(subject.return_type())),
            Expression::Intersect(_, subject, _) => {
                ReturnType::Set(Box::new(subject.return_type()))
            }
            Expression::In(_, _, _) => ReturnType::Bool,
            Expression::Supset(_, _, _) => ReturnType::Bool,
            Expression::SupsetEq(_, _, _) => ReturnType::Bool,
            Expression::Subset(_, _, _) => ReturnType::Bool,
            Expression::SubsetEq(_, _, _) => ReturnType::Bool,
            Expression::AbstractLiteral(_, lit) => lit.return_type(),
            Expression::UnsafeIndex(_, subject, idx) | Expression::SafeIndex(_, subject, idx) => {
                let subject_ty = subject.return_type();
                match subject_ty {
                    ReturnType::Matrix(_) => {
                        // For n-dimensional matrices, unwrap the element type until
                        // we either get to the innermost element type or the last index
                        let mut elem_typ = subject_ty;
                        let mut idx_len = idx.len();
                        while idx_len > 0
                            && let ReturnType::Matrix(new_elem_typ) = &elem_typ
                        {
                            elem_typ = *new_elem_typ.clone();
                            idx_len -= 1;
                        }
                        elem_typ
                    }
                    // TODO: We can implement indexing for these eventually
                    ReturnType::Record(_) | ReturnType::Tuple(_) => ReturnType::Unknown,
                    _ => bug!(
                        "Invalid indexing operation: expected the operand to be a collection, got {self}: {subject_ty}"
                    ),
                }
            }
            Expression::UnsafeSlice(_, subject, _) | Expression::SafeSlice(_, subject, _) => {
                ReturnType::Matrix(Box::new(subject.return_type()))
            }
            Expression::InDomain(_, _, _) => ReturnType::Bool,
            Expression::Comprehension(_, comp) => comp.return_type(),
            Expression::AbstractComprehension(_, comp) => comp.return_type(),
            Expression::Root(_, _) => ReturnType::Bool,
            Expression::DominanceRelation(_, _) => ReturnType::Bool,
            Expression::FromSolution(_, expr) => expr.return_type(),
            Expression::Metavar(_, _) => ReturnType::Unknown,
            Expression::Atomic(_, atom) => atom.return_type(),
            Expression::Scope(_, scope) => scope.return_type(),
            Expression::Abs(_, _) => ReturnType::Int,
            Expression::Sum(_, _) => ReturnType::Int,
            Expression::Product(_, _) => ReturnType::Int,
            Expression::Min(_, _) => ReturnType::Int,
            Expression::Max(_, _) => ReturnType::Int,
            Expression::Not(_, _) => ReturnType::Bool,
            Expression::Or(_, _) => ReturnType::Bool,
            Expression::Imply(_, _, _) => ReturnType::Bool,
            Expression::Iff(_, _, _) => ReturnType::Bool,
            Expression::And(_, _) => ReturnType::Bool,
            Expression::Eq(_, _, _) => ReturnType::Bool,
            Expression::Neq(_, _, _) => ReturnType::Bool,
            Expression::Geq(_, _, _) => ReturnType::Bool,
            Expression::Leq(_, _, _) => ReturnType::Bool,
            Expression::Gt(_, _, _) => ReturnType::Bool,
            Expression::Lt(_, _, _) => ReturnType::Bool,
            Expression::SafeDiv(_, _, _) => ReturnType::Int,
            Expression::UnsafeDiv(_, _, _) => ReturnType::Int,
            Expression::FlatAllDiff(_, _) => ReturnType::Bool,
            Expression::FlatSumGeq(_, _, _) => ReturnType::Bool,
            Expression::FlatSumLeq(_, _, _) => ReturnType::Bool,
            Expression::MinionDivEqUndefZero(_, _, _, _) => ReturnType::Bool,
            Expression::FlatIneq(_, _, _, _) => ReturnType::Bool,
            Expression::Flatten(_, _, matrix) => {
                let matrix_type = matrix.return_type();
                match matrix_type {
                    ReturnType::Matrix(_) => {
                        // unwrap until we get to innermost element
                        let mut elem_type = matrix_type;
                        while let ReturnType::Matrix(new_elem_type) = &elem_type {
                            elem_type = *new_elem_type.clone();
                        }
                        ReturnType::Matrix(Box::new(elem_type))
                    }
                    _ => bug!(
                        "Invalid indexing operation: expected the operand to be a collection, got {self}: {matrix_type}"
                    ),
                }
            }
            Expression::AllDiff(_, _) => ReturnType::Bool,
            Expression::Bubble(_, inner, _) => inner.return_type(),
            Expression::FlatWatchedLiteral(_, _, _) => ReturnType::Bool,
            Expression::MinionReify(_, _, _) => ReturnType::Bool,
            Expression::MinionReifyImply(_, _, _) => ReturnType::Bool,
            Expression::MinionWInIntervalSet(_, _, _) => ReturnType::Bool,
            Expression::MinionWInSet(_, _, _) => ReturnType::Bool,
            Expression::MinionElementOne(_, _, _, _) => ReturnType::Bool,
            Expression::AuxDeclaration(_, _, _) => ReturnType::Bool,
            Expression::UnsafeMod(_, _, _) => ReturnType::Int,
            Expression::SafeMod(_, _, _) => ReturnType::Int,
            Expression::MinionModuloEqUndefZero(_, _, _, _) => ReturnType::Bool,
            Expression::Neg(_, _) => ReturnType::Int,
            Expression::UnsafePow(_, _, _) => ReturnType::Int,
            Expression::SafePow(_, _, _) => ReturnType::Int,
            Expression::Minus(_, _, _) => ReturnType::Int,
            Expression::FlatAbsEq(_, _, _) => ReturnType::Bool,
            Expression::FlatMinusEq(_, _, _) => ReturnType::Bool,
            Expression::FlatProductEq(_, _, _, _) => ReturnType::Bool,
            Expression::FlatWeightedSumLeq(_, _, _, _) => ReturnType::Bool,
            Expression::FlatWeightedSumGeq(_, _, _, _) => ReturnType::Bool,
            Expression::MinionPow(_, _, _, _) => ReturnType::Bool,
            Expression::ToInt(_, _) => ReturnType::Int,
            Expression::SATInt(..) => ReturnType::Int,
            Expression::PairwiseSum(_, _, _) => ReturnType::Int,
            Expression::PairwiseProduct(_, _, _) => ReturnType::Int,
            Expression::Defined(_, function) => {
                let subject = function.return_type();
                match subject {
                    ReturnType::Function(domain, _) => *domain,
                    _ => bug!(
                        "Invalid defined operation: expected the operand to be a function, got {self}: {subject}"
                    ),
                }
            }
            Expression::Range(_, function) => {
                let subject = function.return_type();
                match subject {
                    ReturnType::Function(_, codomain) => *codomain,
                    _ => bug!(
                        "Invalid range operation: expected the operand to be a function, got {self}: {subject}"
                    ),
                }
            }
            Expression::Image(_, function, _) => {
                let subject = function.return_type();
                match subject {
                    ReturnType::Function(_, codomain) => *codomain,
                    _ => bug!(
                        "Invalid image operation: expected the operand to be a function, got {self}: {subject}"
                    ),
                }
            }
            Expression::ImageSet(_, function, _) => {
                let subject = function.return_type();
                match subject {
                    ReturnType::Function(_, codomain) => *codomain,
                    _ => bug!(
                        "Invalid imageSet operation: expected the operand to be a function, got {self}: {subject}"
                    ),
                }
            }
            Expression::PreImage(_, function, _) => {
                let subject = function.return_type();
                match subject {
                    ReturnType::Function(domain, _) => *domain,
                    _ => bug!(
                        "Invalid preImage operation: expected the operand to be a function, got {self}: {subject}"
                    ),
                }
            }
            Expression::Restrict(_, function, new_domain) => {
                let subject = function.return_type();
                match subject {
                    ReturnType::Function(_, codomain) => {
                        ReturnType::Function(Box::new(new_domain.return_type()), codomain)
                    }
                    _ => bug!(
                        "Invalid preImage operation: expected the operand to be a function, got {self}: {subject}"
                    ),
                }
            }
            Expression::Inverse(..) => ReturnType::Bool,
            Expression::LexLt(..) => ReturnType::Bool,
            Expression::LexGt(..) => ReturnType::Bool,
            Expression::LexLeq(..) => ReturnType::Bool,
            Expression::LexGeq(..) => ReturnType::Bool,
            Expression::FlatLexLt(..) => ReturnType::Bool,
            Expression::FlatLexLeq(..) => ReturnType::Bool,
        }
    }
}

#[cfg(test)]
mod tests {

    use crate::matrix_expr;

    use super::*;

    #[test]
    fn test_domain_of_constant_sum() {
        let c1 = Expression::Atomic(Metadata::new(), Atom::Literal(Literal::Int(1)));
        let c2 = Expression::Atomic(Metadata::new(), Atom::Literal(Literal::Int(2)));
        let sum = Expression::Sum(Metadata::new(), Moo::new(matrix_expr![c1, c2]));
        assert_eq!(sum.domain_of(), Some(Domain::int(vec![Range::Single(3)])));
    }

    #[test]
    fn test_domain_of_constant_invalid_type() {
        let c1 = Expression::Atomic(Metadata::new(), Atom::Literal(Literal::Int(1)));
        let c2 = Expression::Atomic(Metadata::new(), Atom::Literal(Literal::Bool(true)));
        let sum = Expression::Sum(Metadata::new(), Moo::new(matrix_expr![c1, c2]));
        assert_eq!(sum.domain_of(), None);
    }

    #[test]
    fn test_domain_of_empty_sum() {
        let sum = Expression::Sum(Metadata::new(), Moo::new(matrix_expr![]));
        assert_eq!(sum.domain_of(), None);
    }
}