diff --git a/Cargo.lock b/Cargo.lock
index 00e8991..a9af070 100644
--- a/Cargo.lock
+++ b/Cargo.lock
@@ -730,6 +730,7 @@ version = "0.1.0"
 dependencies = [
  "ariadne",
  "datatest-stable",
+ "indexmap",
  "kerolox-ir",
  "lsp-types",
  "ropey",
diff --git a/Cargo.toml b/Cargo.toml
index 66e1774..c37feac 100644
--- a/Cargo.toml
+++ b/Cargo.toml
@@ -16,6 +16,7 @@ ariadne = { version = "0.5", features = ["auto-color"] }
 datatest-stable = "0.3"
 derive-where = "1.6"
 futures-util = { version = "0.3", default-features = false }
+indexmap = "2"
 lsp-types = "0.94"
 ordered-float = { version = "4", features = ["serde"] }
 ropey = "1.6"
diff --git a/crates/frontend/Cargo.toml b/crates/frontend/Cargo.toml
index ef85680..0846b25 100644
--- a/crates/frontend/Cargo.toml
+++ b/crates/frontend/Cargo.toml
@@ -9,6 +9,7 @@ rust-version.workspace = true
 
 [dependencies]
 ariadne.workspace = true
+indexmap.workspace = true
 kerolox-ir = { workspace = true, features = ["salsa"] }
 lsp-types.workspace = true
 ropey.workspace = true
diff --git a/crates/frontend/src/resolve.rs b/crates/frontend/src/resolve.rs
index c3300c5..b5bd367 100644
--- a/crates/frontend/src/resolve.rs
+++ b/crates/frontend/src/resolve.rs
@@ -19,8 +19,9 @@
 //! The "resolve" stage of the frontend: match up names of objects with the
 //! semantic objects they refer to.
 
-use std::collections::BTreeMap;
+use std::{collections::BTreeMap, convert::Infallible, marker::PhantomData, sync::Arc};
 
+use indexmap::IndexSet;
 use salsa::Update;
 
 use crate::prelude::*;
@@ -64,3 +65,248 @@ impl<'db> NamespaceItem<'db> {
         }
     }
 }
+
+/// Resolves all references in an [ast::Rule].
+#[salsa::tracked]
+pub fn rule<'db>(db: &'db dyn Database, ast: ast::Rule<'db>) -> Rule<'db> {
+    // resolve the body
+    let body = match ast.body(db) {
+        // if a body is present, resolve separately
+        Some(body) => rule_body(db, body),
+
+        // if a body is absent, create an explicit rule body by hand
+        None => RuleBody {
+            meta: ast.ast(db),
+            vars: Default::default(),
+            loaded: Default::default(),
+            body: Expr {
+                meta: ast.ast(db),
+                kind: ir::ExprKind::Extra(Arc::new(ExprExtra::Implicit)),
+            },
+        },
+    };
+
+    // the head is empty for now because it is untyped
+    let head = Default::default();
+
+    // resolve the name of the target relation
+    let relation = relation_name(db, ast.relation(db));
+
+    // assemble the finished rule
+    Rule {
+        meta: ast,
+        relation,
+        head,
+        body,
+    }
+}
+
+/// Resolves all references in an [ast::Assumption].
+#[salsa::tracked]
+pub fn assumption<'db>(db: &'db dyn Database, ast: ast::Assumption<'db>) -> Assumption<'db> {
+    todo!()
+}
+
+/// Resolves all references in an [ast::RuleBody].
+#[salsa::tracked]
+pub fn rule_body<'db>(db: &'db dyn Database, ast: ast::RuleBody<'db>) -> RuleBody<'db> {
+    // initialize conversion tables
+    let mut vars = IndexSet::new();
+    let mut loaded = IndexSet::new();
+
+    // convert AST clauses to resolved clauses
+    let clauses = ast
+        .clauses(db)
+        .into_iter()
+        .map(|ast| expr(db, &mut vars, &mut loaded, &ast));
+
+    // reduce each clause to a single "and" operation
+    let body = clauses.reduce(|lhs, rhs| Expr {
+        meta: ast.ast(db),
+        kind: ir::ExprKind::BinaryOp {
+            op: ir::BinaryOpKind::And.into(),
+            lhs: Arc::new(lhs),
+            rhs: Arc::new(rhs),
+        },
+    });
+
+    // if the body has no clauses at all, mark it specially
+    let body = body.unwrap_or(Expr {
+        meta: ast.ast(db),
+        kind: ir::ExprKind::Extra(Arc::new(ExprExtra::Implicit)),
+    });
+
+    // assemble completed rule body
+    RuleBody {
+        loaded: loaded.into_iter().collect(),
+        vars: vars.into_iter().collect(),
+        meta: ast.ast(db),
+        body,
+    }
+}
+
+/// Internal conversion tool to resolved expressions, with side-effects.
+pub fn expr<'db>(
+    db: &'db dyn Database,
+    vars: &mut IndexSet<VariableMeta>,
+    loaded: &mut IndexSet<RelationLabel<'db>>,
+    expr: &ast::Expr,
+) -> Expr<'db> {
+    // alias recursive call with curried side-effects
+    let mut resolve = |ast| crate::resolve::expr(db, vars, loaded, ast);
+
+    // convert inner expression variant
+    use ir::ExprKind::*;
+    let kind = match &expr.kind {
+        // directly translate existing value definitions
+        // TODO: symbols are unresolved, handle unreachability better?
+        Value(value) => Value(value.clone()),
+
+        // recursively descend into unary operations
+        UnaryOp { op, term } => UnaryOp {
+            op: *op,
+            term: Arc::new(resolve(term.as_ref())),
+        },
+
+        // recursively descend into binary operations
+        BinaryOp { op, lhs, rhs } => BinaryOp {
+            op: *op,
+            lhs: Arc::new(resolve(lhs.as_ref())),
+            rhs: Arc::new(resolve(rhs.as_ref())),
+        },
+
+        // do deeper conversion for AST-specific expression variants
+        Extra(extra) => match extra.as_ref() {
+            // insert a fresh variable identified by this expression's AST node
+            ast::ExprExtra::Hole => Variable(vars.insert_full(VariableMeta::Hole(expr.meta)).0),
+
+            // recursively convert elements of tuples
+            ast::ExprExtra::Tuple(exprs) => Extra(Arc::new(ExprExtra::Tuple(
+                exprs.iter().map(resolve).collect(),
+            ))),
+
+            ast::ExprExtra::SymbolName(name) => todo!(),
+
+            // resolve common variable name to index
+            ast::ExprExtra::VariableName(name) => {
+                Variable(vars.insert_full(VariableMeta::Named(name.clone())).0)
+            }
+
+            ast::ExprExtra::Apply(apply) => todo!(),
+
+            ast::ExprExtra::Aggregate(aggregate) => todo!(),
+        },
+
+        // TODO: handle unreachability better?
+        Variable(idx) => Variable(*idx),
+
+        // TODO: handle unreachability better?
+        Load { relation, query } => Load {
+            relation: *relation,
+            query: query.clone(),
+        },
+    };
+
+    // construct converted expression
+    Expr {
+        meta: expr.meta,
+        kind,
+    }
+}
+
+/// Resolve a reference to a relation by name.
+// TODO: track incrementally?
+pub fn relation_name<'db>(db: &'db dyn Database, name: ast::Name) -> RelationLabel<'db> {
+    todo!()
+}
+
+/// A type alias for a resolve stage [ir::Rule].
+pub type Rule<'db> = ir::Rule<ProgramInfo<'db>>;
+
+/// A type alias for a resolve stage [ir::Assumption].
+pub type Assumption<'db> = ir::Assumption<ProgramInfo<'db>>;
+
+/// A type alias for a resolve stage [ir::RuleBody].
+pub type RuleBody<'db> = ir::RuleBody<ProgramInfo<'db>>;
+
+/// A type alias for a resolve stage [ir::Expr].
+pub type Expr<'db> = ir::Expr<ProgramInfo<'db>>;
+
+/// Resolve stage-specific extensions to [ir::ProgramInfo].
+pub struct ProgramInfo<'db>(PhantomData<&'db ()>);
+
+impl<'db> ir::ProgramInfo for ProgramInfo<'db> {
+    type SymbolMeta = Infallible;
+
+    /// [RelationLabel] fallibly identifies relations after the resolution stage.
+    type RelationLabel = RelationLabel<'db>;
+
+    type AssumptionMeta = Infallible;
+
+    type RuleMeta = ast::Rule<'db>;
+
+    /// Resolved rule bodies point only to their AST origins.
+    ///
+    /// Rule bodies may be implicit, so there is not always an associated
+    /// [ast::RuleBody]. In this case, the AST node is the rule, not its body.
+    type RuleBodyMeta = AstNode;
+
+    type VariableMeta = VariableMeta;
+
+    /// Information about the source location is preserved from the AST stage.
+    type ExprMeta = AstNode;
+
+    type BinaryOp = ast::BinaryOpKind;
+
+    type UnaryOp = ir::UnaryOpKind;
+
+    type ExprExtra = Arc<ExprExtra<'db>>;
+}
+
+/// Extra [ExprKind] variants in the resolve stage.
+#[derive(Clone, PartialEq, Eq, Hash)]
+pub enum ExprExtra<'db> {
+    /// If a rule body has no clauses, this is its body's expression variant.
+    Implicit,
+
+    /// A structured tuple of sub-expressions.
+    Tuple(Vec<Expr<'db>>),
+
+    /// A resolved symbol.
+    ///
+    /// Not yet aggregated globally, so no index as [ir::Value::Symbol] yet.
+    Symbol(WithAst<ast::Name>),
+
+    /// A resolved application expression.
+    Apply(Apply<'db>),
+}
+
+/// Identifiers for relations in the resolve stage.
+#[derive(Clone, PartialEq, Eq, Hash)]
+pub enum RelationLabel<'db> {
+    /// The relation has been resolved to a concrete relation object.
+    Relation(ast::Relation<'db>),
+
+    /// The relation could not be resolved.
+    Unknown(ast::Name),
+}
+
+/// Resolved identification of a variable within a rule body.
+#[derive(Clone, PartialEq, Eq, Hash)]
+pub enum VariableMeta {
+    /// The variable has a name.
+    Named(String),
+
+    /// The variable is unnamed (a hole) but is unique to its AST node.
+    Hole(AstNode),
+}
+
+/// A high-level application operation.
+#[derive(Clone, PartialEq, Eq, Hash)]
+pub struct Apply<'db> {
+    /// The source relation's index in the parent [RuleBody].
+    pub relation: usize,
+
+    /// The parameters to the function or query.
+    pub body: Expr<'db>,
+}