Thread cx through normalization

15 files changed, 395 insertions, 347 deletions

diff --git a/dhall/src/builtins.rs b/dhall/src/builtins.rs
index f92f1c3..39cc4ef 100644
--- a/dhall/src/builtins.rs
+++ b/dhall/src/builtins.rs
@@ -11,7 +11,6 @@ use crate::syntax::{
     Const, Expr, ExprKind, InterpolatedText, InterpolatedTextContents, Label,
     NaiveDouble, NumKind, Span, UnspannedExpr, V,
 };
-use crate::Ctxt;
 
 /// Built-ins
 #[derive(Debug, Copy, Clone, PartialEq, Eq, Hash)]
@@ -90,25 +89,23 @@ impl Builtin {
 /// A partially applied builtin.
 /// Invariant: the evaluation of the given args must not be able to progress further
 #[derive(Debug, Clone)]
-pub struct BuiltinClosure {
-    env: NzEnv,
+pub struct BuiltinClosure<'cx> {
+    env: NzEnv<'cx>,
     b: Builtin,
     /// Arguments applied to the closure so far.
-    args: Vec<Nir>,
+    args: Vec<Nir<'cx>>,
 }
 
-impl BuiltinClosure {
-    pub fn new(b: Builtin, env: NzEnv) -> NirKind {
-        // TODO: thread cx
-        Ctxt::with_new(|cx| apply_builtin(cx, b, Vec::new(), env))
+impl<'cx> BuiltinClosure<'cx> {
+    pub fn new(b: Builtin, env: NzEnv<'cx>) -> NirKind<'cx> {
+        apply_builtin(b, Vec::new(), env)
     }
-    pub fn apply(&self, a: Nir) -> NirKind {
+    pub fn apply(&self, a: Nir<'cx>) -> NirKind<'cx> {
         use std::iter::once;
         let args = self.args.iter().cloned().chain(once(a)).collect();
-        // TODO: thread cx
-        Ctxt::with_new(|cx| apply_builtin(cx, self.b, args, self.env.clone()))
+        apply_builtin(self.b, args, self.env.clone())
     }
-    pub fn to_hirkind(&self, venv: VarEnv) -> HirKind {
+    pub fn to_hirkind(&self, venv: VarEnv) -> HirKind<'cx> {
         HirKind::Expr(self.args.iter().fold(
             ExprKind::Builtin(self.b),
             |acc, v| {
@@ -181,7 +178,7 @@ macro_rules! make_type {
     };
 }
 
-pub fn type_of_builtin(b: Builtin) -> Hir {
+pub fn type_of_builtin<'cx>(b: Builtin) -> Hir<'cx> {
     use Builtin::*;
     let expr = match b {
         Bool | Natural | Integer | Double | Text => make_type!(Type),
@@ -310,19 +307,19 @@ macro_rules! make_closure {
 }
 
 #[allow(clippy::cognitive_complexity)]
-fn apply_builtin(
-    cx: Ctxt<'_>,
+fn apply_builtin<'cx>(
     b: Builtin,
-    args: Vec<Nir>,
-    env: NzEnv,
-) -> NirKind {
+    args: Vec<Nir<'cx>>,
+    env: NzEnv<'cx>,
+) -> NirKind<'cx> {
+    let cx = env.cx();
     use NirKind::*;
     use NumKind::{Bool, Double, Integer, Natural};
 
     // Small helper enum
-    enum Ret {
-        NirKind(NirKind),
-        Nir(Nir),
+    enum Ret<'cx> {
+        NirKind(NirKind<'cx>),
+        Nir(Nir<'cx>),
         DoneAsIs,
     }
     let make_closure = |e| {
@@ -494,7 +491,7 @@ fn apply_builtin(
                     let mut kts = HashMap::new();
                     kts.insert(
                         "index".into(),
-                        Nir::from_builtin(Builtin::Natural),
+                        Nir::from_builtin(cx, Builtin::Natural),
                     );
                     kts.insert("value".into(), t.clone());
                     let t = Nir::from_kind(RecordType(kts));
@@ -524,7 +521,7 @@ fn apply_builtin(
             }
         }
         (Builtin::ListBuild, [t, f]) => {
-            let list_t = Nir::from_builtin(Builtin::List).app(t.clone());
+            let list_t = Nir::from_builtin(cx, Builtin::List).app(t.clone());
             Ret::Nir(
                 f.app(list_t)
                     .app(
@@ -551,7 +548,7 @@ fn apply_builtin(
             _ => Ret::DoneAsIs,
         },
         (Builtin::NaturalBuild, [f]) => Ret::Nir(
-            f.app(Nir::from_builtin(Builtin::Natural))
+            f.app(Nir::from_builtin(cx, Builtin::Natural))
                 .app(make_closure(make_closure!(
                     λ(x : Natural) ->
                     1 + var(x)
@@ -562,7 +559,7 @@ fn apply_builtin(
         (Builtin::NaturalFold, [n, t, succ, zero]) => match &*n.kind() {
             Num(Natural(0)) => Ret::Nir(zero.clone()),
             Num(Natural(n)) => {
-                let fold = Nir::from_builtin(Builtin::NaturalFold)
+                let fold = Nir::from_builtin(cx, Builtin::NaturalFold)
                     .app(Num(Natural(n - 1)).into_nir())
                     .app(t.clone())
                     .app(succ.clone())
@@ -580,12 +577,12 @@ fn apply_builtin(
     }
 }
 
-impl std::cmp::PartialEq for BuiltinClosure {
+impl<'cx> std::cmp::PartialEq for BuiltinClosure<'cx> {
     fn eq(&self, other: &Self) -> bool {
         self.b == other.b && self.args == other.args
     }
 }
-impl std::cmp::Eq for BuiltinClosure {}
+impl<'cx> std::cmp::Eq for BuiltinClosure<'cx> {}
 
 impl std::fmt::Display for Builtin {
     fn fmt(&self, f: &mut std::fmt::Formatter) -> std::fmt::Result {
diff --git a/dhall/src/ctxt.rs b/dhall/src/ctxt.rs
index 37fab35..a171ebe 100644
--- a/dhall/src/ctxt.rs
+++ b/dhall/src/ctxt.rs
@@ -23,7 +23,7 @@ pub struct StoredImport<'cx> {
 #[derive(Default)]
 pub struct CtxtS<'cx> {
     imports: FrozenVec<Box<StoredImport<'cx>>>,
-    import_results: FrozenVec<Box<Typed>>,
+    import_results: FrozenVec<Box<Typed<'cx>>>,
 }
 
 /// Context for the dhall compiler. Stores various global maps.
@@ -58,7 +58,7 @@ impl<'cx> Ctxt<'cx> {
         ImportId(id)
     }
     /// Store the result of fetching an import.
-    pub fn push_import_result(self, res: Typed) -> ImportResultId {
+    pub fn push_import_result(self, res: Typed<'cx>) -> ImportResultId {
         let id = self.0.import_results.len();
         self.0.import_results.push(Box::new(res));
         ImportResultId(id)
@@ -77,12 +77,12 @@ impl<'cx> StoredImport<'cx> {
     }
     /// Get the result of fetching this import. Returns `None` if the result has not yet been
     /// fetched.
-    pub fn get_result(&self) -> Option<&'cx Typed> {
+    pub fn get_result(&self) -> Option<&'cx Typed<'cx>> {
         let res = self.get_resultid()?;
         Some(&self.cx[res])
     }
     /// Store the result of fetching this import.
-    pub fn set_result(&self, res: Typed) -> ImportResultId {
+    pub fn set_result(&self, res: Typed<'cx>) -> ImportResultId {
         let res = self.cx.push_import_result(res);
         self.set_resultid(res);
         res
@@ -103,8 +103,8 @@ impl<'cx> std::ops::Index<ImportId> for CtxtS<'cx> {
     }
 }
 impl<'cx> std::ops::Index<ImportResultId> for CtxtS<'cx> {
-    type Output = Typed;
-    fn index(&self, id: ImportResultId) -> &Typed {
+    type Output = Typed<'cx>;
+    fn index(&self, id: ImportResultId) -> &Typed<'cx> {
         &self.import_results[id.0]
     }
 }
diff --git a/dhall/src/lib.rs b/dhall/src/lib.rs
index 661c33c..ec2b813 100644
--- a/dhall/src/lib.rs
+++ b/dhall/src/lib.rs
@@ -5,7 +5,8 @@
     clippy::needless_lifetimes,
     clippy::new_ret_no_self,
     clippy::new_without_default,
-    clippy::useless_format
+    clippy::useless_format,
+    unreachable_code
 )]
 
 pub mod builtins;
@@ -36,20 +37,20 @@ pub struct Parsed(Expr, ImportLocation);
 ///
 /// Invariant: there must be no `Import` nodes or `ImportAlt` operations left.
 #[derive(Debug, Clone)]
-pub struct Resolved(Hir);
+pub struct Resolved<'cx>(Hir<'cx>);
 
 /// A typed expression
 #[derive(Debug, Clone)]
-pub struct Typed {
-    pub hir: Hir,
-    pub ty: Type,
+pub struct Typed<'cx> {
+    pub hir: Hir<'cx>,
+    pub ty: Type<'cx>,
 }
 
 /// A normalized expression.
 ///
 /// This is actually a lie, because the expression will only get normalized on demand.
 #[derive(Debug, Clone)]
-pub struct Normalized(Nir);
+pub struct Normalized<'cx>(Nir<'cx>);
 
 /// Controls conversion from `Nir` to `Expr`
 #[derive(Copy, Clone, Default)]
@@ -76,11 +77,10 @@ impl Parsed {
         parse::parse_binary(data)
     }
 
-    pub fn resolve(self) -> Result<Resolved, Error> {
-        // TODO: thread cx
-        Ctxt::with_new(|cx| resolve::resolve(cx, self))
+    pub fn resolve<'cx>(self, cx: Ctxt<'cx>) -> Result<Resolved<'cx>, Error> {
+        resolve::resolve(cx, self)
     }
-    pub fn skip_resolve(self) -> Result<Resolved, Error> {
+    pub fn skip_resolve<'cx>(self) -> Result<Resolved<'cx>, Error> {
         resolve::skip_resolve(self)
     }
 
@@ -90,16 +90,16 @@ impl Parsed {
     }
 }
 
-impl Resolved {
-    pub fn typecheck(&self) -> Result<Typed, TypeError> {
-        // TODO: thread cx
-        Ctxt::with_new(|cx| Ok(Typed::from_tir(typecheck(cx, &self.0)?)))
+impl<'cx> Resolved<'cx> {
+    pub fn typecheck(&self, cx: Ctxt<'cx>) -> Result<Typed<'cx>, TypeError> {
+        Ok(Typed::from_tir(typecheck(cx, &self.0)?))
     }
-    pub fn typecheck_with(self, ty: &Hir) -> Result<Typed, TypeError> {
-        // TODO: thread cx
-        Ctxt::with_new(|cx| {
-            Ok(Typed::from_tir(typecheck_with(cx, &self.0, ty)?))
-        })
+    pub fn typecheck_with(
+        self,
+        cx: Ctxt<'cx>,
+        ty: &Hir<'cx>,
+    ) -> Result<Typed<'cx>, TypeError> {
+        Ok(Typed::from_tir(typecheck_with(cx, &self.0, ty)?))
     }
     /// Converts a value back to the corresponding AST expression.
     pub fn to_expr(&self) -> Expr {
@@ -107,16 +107,16 @@ impl Resolved {
     }
 }
 
-impl Typed {
-    fn from_tir(tir: Tir<'_>) -> Self {
+impl<'cx> Typed<'cx> {
+    fn from_tir(tir: Tir<'cx, '_>) -> Self {
         Typed {
             hir: tir.as_hir().clone(),
             ty: tir.ty().clone(),
         }
     }
     /// Reduce an expression to its normal form, performing beta reduction
-    pub fn normalize(&self) -> Normalized {
-        Normalized(self.hir.eval_closed_expr())
+    pub fn normalize(&self, cx: Ctxt<'cx>) -> Normalized<'cx> {
+        Normalized(self.hir.eval_closed_expr(cx))
     }
 
     /// Converts a value back to the corresponding AST expression.
@@ -124,24 +124,24 @@ impl Typed {
         self.hir.to_expr(ToExprOptions { alpha: false })
     }
 
-    pub fn ty(&self) -> &Type {
+    pub fn ty(&self) -> &Type<'cx> {
         &self.ty
     }
-    pub fn get_type(&self) -> Result<Normalized, TypeError> {
+    pub fn get_type(&self) -> Result<Normalized<'cx>, TypeError> {
         Ok(Normalized(self.ty.clone().into_nir()))
     }
 }
 
-impl Normalized {
+impl<'cx> Normalized<'cx> {
     /// Converts a value back to the corresponding AST expression.
     pub fn to_expr(&self) -> Expr {
         self.0.to_expr(ToExprOptions::default())
     }
     /// Converts a value back to the corresponding Hir expression.
-    pub fn to_hir(&self) -> Hir {
+    pub fn to_hir(&self) -> Hir<'cx> {
         self.0.to_hir_noenv()
     }
-    pub fn as_nir(&self) -> &Nir {
+    pub fn as_nir(&self) -> &Nir<'cx> {
         &self.0
     }
     /// Converts a value back to the corresponding AST expression, alpha-normalizing in the process.
@@ -178,37 +178,31 @@ impl From<Parsed> for Expr {
         other.to_expr()
     }
 }
-impl From<Normalized> for Expr {
-    fn from(other: Normalized) -> Self {
+impl<'cx> From<Normalized<'cx>> for Expr {
+    fn from(other: Normalized<'cx>) -> Self {
         other.to_expr()
     }
 }
 
-impl Display for Resolved {
+impl<'cx> Display for Resolved<'cx> {
     fn fmt(&self, f: &mut std::fmt::Formatter) -> Result<(), std::fmt::Error> {
         self.to_expr().fmt(f)
     }
 }
 
-impl Eq for Typed {}
-impl PartialEq for Typed {
-    fn eq(&self, other: &Self) -> bool {
-        self.normalize() == other.normalize()
-    }
-}
-impl Display for Typed {
+impl<'cx> Display for Typed<'cx> {
     fn fmt(&self, f: &mut std::fmt::Formatter) -> Result<(), std::fmt::Error> {
         self.to_expr().fmt(f)
     }
 }
 
-impl Eq for Normalized {}
-impl PartialEq for Normalized {
+impl<'cx> Eq for Normalized<'cx> {}
+impl<'cx> PartialEq for Normalized<'cx> {
     fn eq(&self, other: &Self) -> bool {
         self.0 == other.0
     }
 }
-impl Display for Normalized {
+impl<'cx> Display for Normalized<'cx> {
     fn fmt(&self, f: &mut std::fmt::Formatter) -> Result<(), std::fmt::Error> {
         self.to_expr().fmt(f)
     }
diff --git a/dhall/src/operations/normalization.rs b/dhall/src/operations/normalization.rs
index 28375b2..6c68e7c 100644
--- a/dhall/src/operations/normalization.rs
+++ b/dhall/src/operations/normalization.rs
@@ -8,7 +8,7 @@ use crate::semantics::{
 };
 use crate::syntax::{ExprKind, Label, NumKind};
 
-fn normalize_binop(o: BinOp, x: Nir, y: Nir) -> Ret {
+fn normalize_binop<'cx>(o: BinOp, x: Nir<'cx>, y: Nir<'cx>) -> Ret<'cx> {
     use BinOp::*;
     use NirKind::{EmptyListLit, NEListLit, Num, RecordLit, RecordType};
     use NumKind::{Bool, Natural};
@@ -119,7 +119,7 @@ fn normalize_binop(o: BinOp, x: Nir, y: Nir) -> Ret {
     }
 }
 
-fn normalize_field(v: &Nir, field: &Label) -> Ret {
+fn normalize_field<'cx>(v: &Nir<'cx>, field: &Label) -> Ret<'cx> {
     use self::BinOp::{RecursiveRecordMerge, RightBiasedRecordMerge};
     use NirKind::{Op, RecordLit, UnionConstructor, UnionType};
     use OpKind::{BinOp, Field, Projection};
@@ -187,7 +187,7 @@ fn normalize_field(v: &Nir, field: &Label) -> Ret {
     }
 }
 
-pub fn normalize_operation(opkind: OpKind<Nir>) -> Ret {
+pub fn normalize_operation<'cx>(opkind: OpKind<Nir<'cx>>) -> Ret<'cx> {
     use self::BinOp::RightBiasedRecordMerge;
     use NirKind::{
         EmptyListLit, EmptyOptionalLit, NEListLit, NEOptionalLit, Num, Op,
diff --git a/dhall/src/operations/typecheck.rs b/dhall/src/operations/typecheck.rs
index 5718114..9b19c84 100644
--- a/dhall/src/operations/typecheck.rs
+++ b/dhall/src/operations/typecheck.rs
@@ -14,8 +14,8 @@ use crate::syntax::{Const, ExprKind, Span};
 fn check_rectymerge(
     span: &Span,
     env: &TyEnv<'_>,
-    x: Nir,
-    y: Nir,
+    x: Nir<'_>,
+    y: Nir<'_>,
 ) -> Result<(), TypeError> {
     let kts_x = match x.kind() {
         NirKind::RecordType(kts) => kts,
@@ -44,13 +44,14 @@ fn check_rectymerge(
     Ok(())
 }
 
-fn typecheck_binop(
-    env: &TyEnv<'_>,
+fn typecheck_binop<'cx>(
+    env: &TyEnv<'cx>,
     span: Span,
     op: BinOp,
-    l: Tir<'_>,
-    r: Tir<'_>,
-) -> Result<Type, TypeError> {
+    l: Tir<'cx, '_>,
+    r: Tir<'cx, '_>,
+) -> Result<Type<'cx>, TypeError> {
+    let cx = env.cx();
     let span_err = |msg: &str| mk_span_err(span.clone(), msg);
     use BinOp::*;
     use NirKind::{ListType, RecordType};
@@ -124,17 +125,20 @@ fn typecheck_binop(
             Type::from_const(Const::Type)
         }
         op => {
-            let t = Type::from_builtin(match op {
-                BoolAnd | BoolOr | BoolEQ | BoolNE => Builtin::Bool,
-                NaturalPlus | NaturalTimes => Builtin::Natural,
-                TextAppend => Builtin::Text,
-                ListAppend
-                | RightBiasedRecordMerge
-                | RecursiveRecordMerge
-                | RecursiveRecordTypeMerge
-                | Equivalence => unreachable!(),
-                ImportAlt => unreachable!("ImportAlt leftover in tck"),
-            });
+            let t = Type::from_builtin(
+                cx,
+                match op {
+                    BoolAnd | BoolOr | BoolEQ | BoolNE => Builtin::Bool,
+                    NaturalPlus | NaturalTimes => Builtin::Natural,
+                    TextAppend => Builtin::Text,
+                    ListAppend
+                    | RightBiasedRecordMerge
+                    | RecursiveRecordMerge
+                    | RecursiveRecordTypeMerge
+                    | Equivalence => unreachable!(),
+                    ImportAlt => unreachable!("ImportAlt leftover in tck"),
+                },
+            );
 
             if *l.ty() != t {
                 return span_err("BinOpTypeMismatch");
@@ -149,13 +153,13 @@ fn typecheck_binop(
     })
 }
 
-fn typecheck_merge(
-    env: &TyEnv<'_>,
+fn typecheck_merge<'cx>(
+    env: &TyEnv<'cx>,
     span: Span,
-    record: &Tir<'_>,
-    scrut: &Tir<'_>,
-    type_annot: Option<&Tir<'_>>,
-) -> Result<Type, TypeError> {
+    record: &Tir<'cx, '_>,
+    scrut: &Tir<'cx, '_>,
+    type_annot: Option<&Tir<'cx, '_>>,
+) -> Result<Type<'cx>, TypeError> {
     let span_err = |msg: &str| mk_span_err(span.clone(), msg);
     use NirKind::{OptionalType, PiClosure, RecordType, UnionType};
 
@@ -287,11 +291,12 @@ fn typecheck_merge(
     })
 }
 
-pub fn typecheck_operation(
-    env: &TyEnv<'_>,
+pub fn typecheck_operation<'cx>(
+    env: &TyEnv<'cx>,
     span: Span,
-    opkind: OpKind<Tir<'_>>,
-) -> Result<Type, TypeError> {
+    opkind: OpKind<Tir<'cx, '_>>,
+) -> Result<Type<'cx>, TypeError> {
+    let cx = env.cx();
     let span_err = |msg: &str| mk_span_err(span.clone(), msg);
     use NirKind::{ListType, PiClosure, RecordType, UnionType};
     use OpKind::*;
@@ -347,7 +352,7 @@ pub fn typecheck_operation(
         }
         BinOp(o, l, r) => typecheck_binop(env, span, o, l, r)?,
         BoolIf(x, y, z) => {
-            if *x.ty().kind() != NirKind::from_builtin(Builtin::Bool) {
+            if *x.ty().kind() != NirKind::from_builtin(cx, Builtin::Bool) {
                 return span_err("InvalidPredicate");
             }
             if y.ty().ty().as_const().is_none() {
@@ -399,7 +404,7 @@ pub fn typecheck_operation(
                     return span_err(err_msg);
                 }
                 match kts.get("mapKey") {
-                    Some(t) if *t == Nir::from_builtin(Builtin::Text) => {}
+                    Some(t) if *t == Nir::from_builtin(cx, Builtin::Text) => {}
                     _ => return span_err(err_msg),
                 }
                 match kts.get("mapValue") {
@@ -418,9 +423,12 @@ pub fn typecheck_operation(
                 }
 
                 let mut kts = HashMap::new();
-                kts.insert("mapKey".into(), Nir::from_builtin(Builtin::Text));
+                kts.insert(
+                    "mapKey".into(),
+                    Nir::from_builtin(cx, Builtin::Text),
+                );
                 kts.insert("mapValue".into(), entry_type);
-                let output_type: Type = Nir::from_builtin(Builtin::List)
+                let output_type: Type = Nir::from_builtin(cx, Builtin::List)
                     .app(Nir::from_kind(RecordType(kts)))
                     .to_type(Const::Type);
                 if let Some(annot) = annot {
diff --git a/dhall/src/semantics/nze/env.rs b/dhall/src/semantics/nze/env.rs
index ec99dbe..30fa8af 100644
--- a/dhall/src/semantics/nze/env.rs
+++ b/dhall/src/semantics/nze/env.rs
@@ -1,4 +1,5 @@
 use crate::semantics::{AlphaVar, Nir, NirKind};
+use crate::Ctxt;
 
 #[derive(Debug, Clone, Copy, PartialEq, Eq)]
 pub enum NzVar {
@@ -9,19 +10,20 @@ pub enum NzVar {
 }
 
 #[derive(Debug, Clone)]
-enum EnvItem<Type> {
+enum EnvItem<'cx, T> {
     // Variable is bound with given type
-    Kept(Type),
+    Kept(T),
     // Variable has been replaced by corresponding value
-    Replaced(Nir, Type),
+    Replaced(Nir<'cx>, T),
 }
 
 #[derive(Debug, Clone)]
-pub struct ValEnv<Type> {
-    items: Vec<EnvItem<Type>>,
+pub struct ValEnv<'cx, T> {
+    cx: Ctxt<'cx>,
+    items: Vec<EnvItem<'cx, T>>,
 }
 
-pub type NzEnv = ValEnv<()>;
+pub type NzEnv<'cx> = ValEnv<'cx, ()>;
 
 impl NzVar {
     pub fn new(idx: usize) -> Self {
@@ -46,11 +48,17 @@ impl NzVar {
     }
 }
 
-impl<Type: Clone> ValEnv<Type> {
-    pub fn new() -> Self {
-        ValEnv { items: Vec::new() }
+impl<'cx, T: Clone> ValEnv<'cx, T> {
+    pub fn new(cx: Ctxt<'cx>) -> Self {
+        ValEnv {
+            cx,
+            items: Vec::new(),
+        }
+    }
+    pub fn cx(&self) -> Ctxt<'cx> {
+        self.cx
     }
-    pub fn discard_types(&self) -> ValEnv<()> {
+    pub fn discard_types(&self) -> ValEnv<'cx, ()> {
         let items = self
             .items
             .iter()
@@ -59,27 +67,27 @@ impl<Type: Clone> ValEnv<Type> {
                 EnvItem::Replaced(val, _) => EnvItem::Replaced(val.clone(), ()),
             })
             .collect();
-        ValEnv { items }
+        ValEnv { cx: self.cx, items }
     }
 
-    pub fn insert_type(&self, ty: Type) -> Self {
+    pub fn insert_type(&self, ty: T) -> Self {
         let mut env = self.clone();
         env.items.push(EnvItem::Kept(ty));
         env
     }
-    pub fn insert_value(&self, e: Nir, ty: Type) -> Self {
+    pub fn insert_value(&self, e: Nir<'cx>, ty: T) -> Self {
         let mut env = self.clone();
         env.items.push(EnvItem::Replaced(e, ty));
         env
     }
-    pub fn lookup_val(&self, var: AlphaVar) -> NirKind {
+    pub fn lookup_val(&self, var: AlphaVar) -> NirKind<'cx> {
         let idx = self.items.len() - 1 - var.idx();
         match &self.items[idx] {
             EnvItem::Kept(_) => NirKind::Var(NzVar::new(idx)),
             EnvItem::Replaced(x, _) => x.kind().clone(),
         }
     }
-    pub fn lookup_ty(&self, var: AlphaVar) -> Type {
+    pub fn lookup_ty(&self, var: AlphaVar) -> T {
         let idx = self.items.len() - 1 - var.idx();
         match &self.items[idx] {
             EnvItem::Kept(ty) | EnvItem::Replaced(_, ty) => ty.clone(),
@@ -87,8 +95,8 @@ impl<Type: Clone> ValEnv<Type> {
     }
 }
 
-impl<'a> From<&'a NzEnv> for NzEnv {
-    fn from(x: &'a NzEnv) -> Self {
+impl<'cx, 'a> From<&'a NzEnv<'cx>> for NzEnv<'cx> {
+    fn from(x: &'a NzEnv<'cx>) -> Self {
         x.clone()
     }
 }
diff --git a/dhall/src/semantics/nze/nir.rs b/dhall/src/semantics/nze/nir.rs
index 7bda836..538b8ea 100644
--- a/dhall/src/semantics/nze/nir.rs
+++ b/dhall/src/semantics/nze/nir.rs
@@ -11,7 +11,7 @@ use crate::semantics::{
 use crate::syntax::{
     Const, Expr, ExprKind, InterpolatedTextContents, Label, NumKind, Span,
 };
-use crate::ToExprOptions;
+use crate::{Ctxt, ToExprOptions};
 
 /// Stores a possibly unevaluated value. Gets (partially) normalized on-demand, sharing computation
 /// automatically. Uses a Rc<OnceCell> to share computation.
@@ -20,31 +20,31 @@ use crate::ToExprOptions;
 /// normalize as needed.
 /// Stands for "Normalized Intermediate Representation"
 #[derive(Clone)]
-pub struct Nir(Rc<lazy::Lazy<Thunk, NirKind>>);
+pub struct Nir<'cx>(Rc<lazy::Lazy<Thunk<'cx>, NirKind<'cx>>>);
 
 /// An unevaluated subexpression
 #[derive(Debug, Clone)]
-pub enum Thunk {
+pub enum Thunk<'cx> {
     /// A completely unnormalized expression.
-    Thunk { env: NzEnv, body: Hir },
+    Thunk { env: NzEnv<'cx>, body: Hir<'cx> },
     /// A partially normalized expression that may need to go through `normalize_one_layer`.
-    PartialExpr { env: NzEnv, expr: ExprKind<Nir> },
+    PartialExpr { expr: ExprKind<Nir<'cx>> },
 }
 
 /// An unevaluated subexpression that takes an argument.
 #[derive(Debug, Clone)]
-pub enum Closure {
+pub enum Closure<'cx> {
     /// Normal closure
-    Closure { env: NzEnv, body: Hir },
+    Closure { env: NzEnv<'cx>, body: Hir<'cx> },
     /// Closure that ignores the argument passed
-    ConstantClosure { body: Nir },
+    ConstantClosure { body: Nir<'cx> },
 }
 
 /// A text literal with interpolations.
 // Invariant: this must not contain interpolations that are themselves TextLits, and contiguous
 // text values must be merged.
 #[derive(Debug, Clone, PartialEq, Eq)]
-pub struct TextLit(Vec<InterpolatedTextContents<Nir>>);
+pub struct TextLit<'cx>(Vec<InterpolatedTextContents<Nir<'cx>>>);
 
 /// This represents a value in Weak Head Normal Form (WHNF). This means that the value is
 /// normalized up to the first constructor, but subexpressions may not be fully normalized.
@@ -54,67 +54,65 @@ pub struct TextLit(Vec<InterpolatedTextContents<Nir>>);
 /// In particular, this means that once we get a `NirKind`, it can be considered immutable, and
 /// we only need to recursively normalize its sub-`Nir`s to get to the NF.
 #[derive(Debug, Clone, PartialEq, Eq)]
-pub enum NirKind {
+pub enum NirKind<'cx> {
     /// Closures
     LamClosure {
         binder: Binder,
-        annot: Nir,
-        closure: Closure,
+        annot: Nir<'cx>,
+        closure: Closure<'cx>,
     },
     PiClosure {
         binder: Binder,
-        annot: Nir,
-        closure: Closure,
+        annot: Nir<'cx>,
+        closure: Closure<'cx>,
     },
-    AppliedBuiltin(BuiltinClosure),
+    AppliedBuiltin(BuiltinClosure<'cx>),
 
     Var(NzVar),
     Const(Const),
     Num(NumKind),
     // Must be a number type, Bool or Text
     BuiltinType(Builtin),
-    TextLit(TextLit),
-    EmptyOptionalLit(Nir),
-    NEOptionalLit(Nir),
-    OptionalType(Nir),
+    TextLit(TextLit<'cx>),
+    EmptyOptionalLit(Nir<'cx>),
+    NEOptionalLit(Nir<'cx>),
+    OptionalType(Nir<'cx>),
     // EmptyListLit(t) means `[] : List t`, not `[] : t`
-    EmptyListLit(Nir),
-    NEListLit(Vec<Nir>),
-    ListType(Nir),
-    RecordLit(HashMap<Label, Nir>),
-    RecordType(HashMap<Label, Nir>),
-    UnionConstructor(Label, HashMap<Label, Option<Nir>>),
-    UnionLit(Label, Nir, HashMap<Label, Option<Nir>>),
-    UnionType(HashMap<Label, Option<Nir>>),
-    Equivalence(Nir, Nir),
-    Assert(Nir),
+    EmptyListLit(Nir<'cx>),
+    NEListLit(Vec<Nir<'cx>>),
+    ListType(Nir<'cx>),
+    RecordLit(HashMap<Label, Nir<'cx>>),
+    RecordType(HashMap<Label, Nir<'cx>>),
+    UnionConstructor(Label, HashMap<Label, Option<Nir<'cx>>>),
+    UnionLit(Label, Nir<'cx>, HashMap<Label, Option<Nir<'cx>>>),
+    UnionType(HashMap<Label, Option<Nir<'cx>>>),
+    Equivalence(Nir<'cx>, Nir<'cx>),
+    Assert(Nir<'cx>),
     /// Invariant: evaluation must not be able to progress with `normalize_operation`.
     /// This is used when an operation couldn't proceed further, for example because of variables.
-    Op(OpKind<Nir>),
+    Op(OpKind<Nir<'cx>>),
 }
 
-impl Nir {
+impl<'cx> Nir<'cx> {
     /// Construct a Nir from a completely unnormalized expression.
-    pub fn new_thunk(env: NzEnv, hir: Hir) -> Nir {
+    pub fn new_thunk(env: NzEnv<'cx>, hir: Hir<'cx>) -> Self {
         Nir(Rc::new(lazy::Lazy::new(Thunk::new(env, hir))))
     }
     /// Construct a Nir from a partially normalized expression that's not in WHNF.
-    pub fn from_partial_expr(e: ExprKind<Nir>) -> Nir {
-        // TODO: env
-        let env = NzEnv::new();
-        Nir(Rc::new(lazy::Lazy::new(Thunk::from_partial_expr(env, e))))
+    pub fn from_partial_expr(e: ExprKind<Self>) -> Self {
+        Nir(Rc::new(lazy::Lazy::new(Thunk::from_partial_expr(e))))
     }
     /// Make a Nir from a NirKind
-    pub fn from_kind(v: NirKind) -> Nir {
+    pub fn from_kind(v: NirKind<'cx>) -> Self {
         Nir(Rc::new(lazy::Lazy::new_completed(v)))
     }
     pub fn from_const(c: Const) -> Self {
         Self::from_kind(NirKind::Const(c))
     }
-    pub fn from_builtin(b: Builtin) -> Self {
-        Self::from_builtin_env(b, &NzEnv::new())
+    pub fn from_builtin(cx: Ctxt<'cx>, b: Builtin) -> Self {
+        Self::from_builtin_env(b, &NzEnv::new(cx))
     }
-    pub fn from_builtin_env(b: Builtin, env: &NzEnv) -> Self {
+    pub fn from_builtin_env(b: Builtin, env: &NzEnv<'cx>) -> Self {
         Nir::from_kind(NirKind::from_builtin_env(b, env.clone()))
     }
     pub fn from_text(txt: impl ToString) -> Self {
@@ -129,51 +127,54 @@ impl Nir {
     }
 
     /// This is what you want if you want to pattern-match on the value.
-    pub fn kind(&self) -> &NirKind {
+    pub fn kind(&self) -> &NirKind<'cx> {
         &*self.0
     }
 
     /// The contents of a `Nir` are immutable and shared. If however we happen to be the sole
     /// owners, we can mutate it directly. Otherwise, this clones the internal value first.
-    pub fn kind_mut(&mut self) -> &mut NirKind {
+    pub fn kind_mut(&mut self) -> &mut NirKind<'cx> {
         Rc::make_mut(&mut self.0).get_mut()
     }
     /// If we are the sole owner of this Nir, we can avoid a clone.
-    pub fn into_kind(self) -> NirKind {
+    pub fn into_kind(self) -> NirKind<'cx> {
         match Rc::try_unwrap(self.0) {
             Ok(lazy) => lazy.into_inner(),
             Err(rc) => (**rc).clone(),
         }
     }
 
-    pub fn to_type(&self, u: impl Into<Universe>) -> Type {
+    pub fn to_type(&self, u: impl Into<Universe>) -> Type<'cx> {
         Type::new(self.clone(), u.into())
     }
     /// Converts a value back to the corresponding AST expression.
     pub fn to_expr(&self, opts: ToExprOptions) -> Expr {
         self.to_hir_noenv().to_expr(opts)
     }
-    pub fn to_expr_tyenv(&self, tyenv: &TyEnv) -> Expr {
+    pub fn to_expr_tyenv(&self, tyenv: &TyEnv<'cx>) -> Expr {
         self.to_hir(tyenv.as_varenv()).to_expr_tyenv(tyenv)
     }
 
-    pub fn app(&self, v: Nir) -> Nir {
+    pub fn app(&self, v: Self) -> Self {
         Nir::from_kind(self.app_to_kind(v))
     }
-    pub fn app_to_kind(&self, v: Nir) -> NirKind {
+    pub fn app_to_kind(&self, v: Self) -> NirKind<'cx> {
         apply_any(self, v)
     }
 
-    pub fn to_hir(&self, venv: VarEnv) -> Hir {
-        let map_uniontype = |kts: &HashMap<Label, Option<Nir>>| {
-            ExprKind::UnionType(
-                kts.iter()
-                    .map(|(k, v)| {
-                        (k.clone(), v.as_ref().map(|v| v.to_hir(venv)))
-                    })
-                    .collect(),
-            )
-        };
+    pub fn to_hir(&self, venv: VarEnv) -> Hir<'cx> {
+        let map_uniontype =
+            |kts: &HashMap<Label, Option<Nir<'cx>>>| -> ExprKind<Hir<'cx>> {
+                ExprKind::UnionType(
+                    kts.iter()
+                        .map(|(k, v)| {
+                            (k.clone(), v.as_ref().map(|v| v.to_hir(venv)))
+                        })
+                        .collect(),
+                )
+            };
+        let builtin =
+            |b| Hir::new(HirKind::Expr(ExprKind::Builtin(b)), Span::Artificial);
 
         let hir = match self.kind() {
             NirKind::Var(v) => HirKind::Var(venv.lookup(*v)),
@@ -204,21 +205,21 @@ impl Nir {
                 NirKind::BuiltinType(b) => ExprKind::Builtin(*b),
                 NirKind::Num(l) => ExprKind::Num(l.clone()),
                 NirKind::OptionalType(t) => ExprKind::Op(OpKind::App(
-                    Nir::from_builtin(Builtin::Optional).to_hir(venv),
+                    builtin(Builtin::Optional),
                     t.to_hir(venv),
                 )),
                 NirKind::EmptyOptionalLit(n) => ExprKind::Op(OpKind::App(
-                    Nir::from_builtin(Builtin::OptionalNone).to_hir(venv),
+                    builtin(Builtin::OptionalNone),
                     n.to_hir(venv),
                 )),
                 NirKind::NEOptionalLit(n) => ExprKind::SomeLit(n.to_hir(venv)),
                 NirKind::ListType(t) => ExprKind::Op(OpKind::App(
-                    Nir::from_builtin(Builtin::List).to_hir(venv),
+                    builtin(Builtin::List),
                     t.to_hir(venv),
                 )),
                 NirKind::EmptyListLit(n) => ExprKind::EmptyListLit(Hir::new(
                     HirKind::Expr(ExprKind::Op(OpKind::App(
-                        Nir::from_builtin(Builtin::List).to_hir(venv),
+                        builtin(Builtin::List),
                         n.to_hir(venv),
                     ))),
                     Span::Artificial,
@@ -276,52 +277,52 @@ impl Nir {
 
         Hir::new(hir, Span::Artificial)
     }
-    pub fn to_hir_noenv(&self) -> Hir {
+    pub fn to_hir_noenv(&self) -> Hir<'cx> {
         self.to_hir(VarEnv::new())
     }
 }
 
-impl NirKind {
-    pub fn into_nir(self) -> Nir {
+impl<'cx> NirKind<'cx> {
+    pub fn into_nir(self) -> Nir<'cx> {
         Nir::from_kind(self)
     }
 
-    pub fn from_builtin(b: Builtin) -> NirKind {
-        NirKind::from_builtin_env(b, NzEnv::new())
+    pub fn from_builtin(cx: Ctxt<'cx>, b: Builtin) -> Self {
+        NirKind::from_builtin_env(b, NzEnv::new(cx))
     }
-    pub fn from_builtin_env(b: Builtin, env: NzEnv) -> NirKind {
+    pub fn from_builtin_env(b: Builtin, env: NzEnv<'cx>) -> Self {
         BuiltinClosure::new(b, env)
     }
 }
 
-impl Thunk {
-    fn new(env: NzEnv, body: Hir) -> Self {
+impl<'cx> Thunk<'cx> {
+    fn new(env: NzEnv<'cx>, body: Hir<'cx>) -> Self {
         Thunk::Thunk { env, body }
     }
-    fn from_partial_expr(env: NzEnv, expr: ExprKind<Nir>) -> Self {
-        Thunk::PartialExpr { env, expr }
+    fn from_partial_expr(expr: ExprKind<Nir<'cx>>) -> Self {
+        Thunk::PartialExpr { expr }
     }
-    fn eval(self) -> NirKind {
+    fn eval(self) -> NirKind<'cx> {
         match self {
-            Thunk::Thunk { env, body } => normalize_hir(&env, &body),
-            Thunk::PartialExpr { env, expr } => normalize_one_layer(expr, &env),
+            Thunk::Thunk { env, body, .. } => normalize_hir(&env, &body),
+            Thunk::PartialExpr { expr } => normalize_one_layer(expr),
         }
     }
 }
 
-impl Closure {
-    pub fn new(env: &NzEnv, body: Hir) -> Self {
+impl<'cx> Closure<'cx> {
+    pub fn new(env: &NzEnv<'cx>, body: Hir<'cx>) -> Self {
         Closure::Closure {
             env: env.clone(),
             body,
         }
     }
     /// New closure that ignores its argument
-    pub fn new_constant(body: Nir) -> Self {
+    pub fn new_constant(body: Nir<'cx>) -> Self {
         Closure::ConstantClosure { body }
     }
 
-    pub fn apply(&self, val: Nir) -> Nir {
+    pub fn apply(&self, val: Nir<'cx>) -> Nir<'cx> {
         match self {
             Closure::Closure { env, body, .. } => {
                 body.eval(env.insert_value(val, ()))
@@ -329,7 +330,7 @@ impl Closure {
             Closure::ConstantClosure { body, .. } => body.clone(),
         }
     }
-    fn apply_var(&self, var: NzVar) -> Nir {
+    fn apply_var(&self, var: NzVar) -> Nir<'cx> {
         match self {
             Closure::Closure { .. } => {
                 self.apply(Nir::from_kind(NirKind::Var(var)))
@@ -339,13 +340,13 @@ impl Closure {
     }
 
     /// Convert this closure to a Hir expression
-    pub fn to_hir(&self, venv: VarEnv) -> Hir {
+    pub fn to_hir(&self, venv: VarEnv) -> Hir<'cx> {
         self.apply_var(NzVar::new(venv.size()))
             .to_hir(venv.insert())
     }
     /// If the closure variable is free in the closure, return Err. Otherwise, return the value
     /// with that free variable remove.
-    pub fn remove_binder(&self) -> Result<Nir, ()> {
+    pub fn remove_binder(&self) -> Result<Nir<'cx>, ()> {
         match self {
             Closure::Closure { .. } => {
                 let v = NzVar::fresh();
@@ -358,20 +359,20 @@ impl Closure {
     }
 }
 
-impl TextLit {
+impl<'cx> TextLit<'cx> {
     pub fn new(
-        elts: impl Iterator<Item = InterpolatedTextContents<Nir>>,
+        elts: impl Iterator<Item = InterpolatedTextContents<Nir<'cx>>>,
     ) -> Self {
         TextLit(squash_textlit(elts))
     }
-    pub fn interpolate(v: Nir) -> TextLit {
+    pub fn interpolate(v: Nir<'cx>) -> Self {
         TextLit(vec![InterpolatedTextContents::Expr(v)])
     }
-    pub fn from_text(s: String) -> TextLit {
+    pub fn from_text(s: String) -> Self {
         TextLit(vec![InterpolatedTextContents::Text(s)])
     }
 
-    pub fn concat(&self, other: &TextLit) -> TextLit {
+    pub fn concat(&self, other: &Self) -> Self {
         TextLit::new(self.iter().chain(other.iter()).cloned())
     }
     pub fn is_empty(&self) -> bool {
@@ -379,7 +380,7 @@ impl TextLit {
     }
     /// If the literal consists of only one interpolation and not text, return the interpolated
     /// value.
-    pub fn as_single_expr(&self) -> Option<&Nir> {
+    pub fn as_single_expr(&self) -> Option<&Nir<'cx>> {
         use InterpolatedTextContents::Expr;
         if let [Expr(v)] = self.0.as_slice() {
             Some(v)
@@ -398,43 +399,45 @@ impl TextLit {
             None
         }
     }
-    pub fn iter(&self) -> impl Iterator<Item = &InterpolatedTextContents<Nir>> {
+    pub fn iter(
+        &self,
+    ) -> impl Iterator<Item = &InterpolatedTextContents<Nir<'cx>>> {
         self.0.iter()
     }
 }
 
-impl lazy::Eval<NirKind> for Thunk {
-    fn eval(self) -> NirKind {
+impl<'cx> lazy::Eval<NirKind<'cx>> for Thunk<'cx> {
+    fn eval(self) -> NirKind<'cx> {
         self.eval()
     }
 }
 
 /// Compare two values for equality modulo alpha/beta-equivalence.
-impl std::cmp::PartialEq for Nir {
+impl<'cx> std::cmp::PartialEq for Nir<'cx> {
     fn eq(&self, other: &Self) -> bool {
         Rc::ptr_eq(&self.0, &other.0) || self.kind() == other.kind()
     }
 }
-impl std::cmp::Eq for Nir {}
+impl<'cx> std::cmp::Eq for Nir<'cx> {}
 
-impl std::cmp::PartialEq for Thunk {
+impl<'cx> std::cmp::PartialEq for Thunk<'cx> {
     fn eq(&self, _other: &Self) -> bool {
         unreachable!(
             "Trying to compare thunks but we should only compare WHNFs"
         )
     }
 }
-impl std::cmp::Eq for Thunk {}
+impl<'cx> std::cmp::Eq for Thunk<'cx> {}
 
-impl std::cmp::PartialEq for Closure {
+impl<'cx> std::cmp::PartialEq for Closure<'cx> {
     fn eq(&self, other: &Self) -> bool {
         let v = NzVar::fresh();
         self.apply_var(v) == other.apply_var(v)
     }
 }
-impl std::cmp::Eq for Closure {}
+impl<'cx> std::cmp::Eq for Closure<'cx> {}
 
-impl std::fmt::Debug for Nir {
+impl<'cx> std::fmt::Debug for Nir<'cx> {
     fn fmt(&self, fmt: &mut std::fmt::Formatter<'_>) -> std::fmt::Result {
         if let NirKind::Const(c) = self.kind() {
             return write!(fmt, "{:?}", c);
diff --git a/dhall/src/semantics/nze/normalize.rs b/dhall/src/semantics/nze/normalize.rs
index 62efc5f..cce421d 100644
--- a/dhall/src/semantics/nze/normalize.rs
+++ b/dhall/src/semantics/nze/normalize.rs
@@ -5,7 +5,7 @@ use crate::semantics::NzEnv;
 use crate::semantics::{Binder, Closure, Hir, HirKind, Nir, NirKind, TextLit};
 use crate::syntax::{ExprKind, InterpolatedTextContents};
 
-pub fn apply_any(f: &Nir, a: Nir) -> NirKind {
+pub fn apply_any<'cx>(f: &Nir<'cx>, a: Nir<'cx>) -> NirKind<'cx> {
     match f.kind() {
         NirKind::LamClosure { closure, .. } => closure.apply(a).kind().clone(),
         NirKind::AppliedBuiltin(closure) => closure.apply(a),
@@ -16,16 +16,16 @@ pub fn apply_any(f: &Nir, a: Nir) -> NirKind {
     }
 }
 
-pub fn squash_textlit(
-    elts: impl Iterator<Item = InterpolatedTextContents<Nir>>,
-) -> Vec<InterpolatedTextContents<Nir>> {
+pub fn squash_textlit<'cx>(
+    elts: impl Iterator<Item = InterpolatedTextContents<Nir<'cx>>>,
+) -> Vec<InterpolatedTextContents<Nir<'cx>>> {
     use std::mem::replace;
     use InterpolatedTextContents::{Expr, Text};
 
-    fn inner(
-        elts: impl Iterator<Item = InterpolatedTextContents<Nir>>,
+    fn inner<'cx>(
+        elts: impl Iterator<Item = InterpolatedTextContents<Nir<'cx>>>,
         crnt_str: &mut String,
-        ret: &mut Vec<InterpolatedTextContents<Nir>>,
+        ret: &mut Vec<InterpolatedTextContents<Nir<'cx>>>,
     ) {
         for contents in elts {
             match contents {
@@ -81,22 +81,22 @@ where
     kvs
 }
 
-pub type Ret = NirKind;
+pub type Ret<'cx> = NirKind<'cx>;
 
-pub fn ret_nir(x: Nir) -> Ret {
+pub fn ret_nir<'cx>(x: Nir<'cx>) -> Ret<'cx> {
     x.into_kind()
 }
-pub fn ret_kind(x: NirKind) -> Ret {
+pub fn ret_kind<'cx>(x: NirKind<'cx>) -> Ret<'cx> {
     x
 }
-pub fn ret_ref(x: &Nir) -> Ret {
+pub fn ret_ref<'cx>(x: &Nir<'cx>) -> Ret<'cx> {
     x.kind().clone()
 }
-pub fn ret_op(x: OpKind<Nir>) -> Ret {
+pub fn ret_op<'cx>(x: OpKind<Nir<'cx>>) -> Ret<'cx> {
     NirKind::Op(x)
 }
 
-pub fn normalize_one_layer(expr: ExprKind<Nir>, env: &NzEnv) -> NirKind {
+pub fn normalize_one_layer<'cx>(expr: ExprKind<Nir<'cx>>) -> NirKind<'cx> {
     use NirKind::{
         Assert, Const, NEListLit, NEOptionalLit, Num, RecordLit, RecordType,
         UnionType,
@@ -106,15 +106,13 @@ pub fn normalize_one_layer(expr: ExprKind<Nir>, env: &NzEnv) -> NirKind {
         ExprKind::Var(..)
         | ExprKind::Lam(..)
         | ExprKind::Pi(..)
-        | ExprKind::Let(..) => {
+        | ExprKind::Let(..)
+        | ExprKind::Builtin(..) => {
             unreachable!("This case should have been handled in normalize_hir")
         }
 
         ExprKind::Const(c) => ret_kind(Const(c)),
         ExprKind::Num(l) => ret_kind(Num(l)),
-        ExprKind::Builtin(b) => {
-            ret_kind(NirKind::from_builtin_env(b, env.clone()))
-        }
         ExprKind::TextLit(elts) => {
             let tlit = TextLit::new(elts.into_iter());
             // Simplify bare interpolation
@@ -154,7 +152,7 @@ pub fn normalize_one_layer(expr: ExprKind<Nir>, env: &NzEnv) -> NirKind {
 }
 
 /// Normalize Hir into WHNF
-pub fn normalize_hir(env: &NzEnv, hir: &Hir) -> NirKind {
+pub fn normalize_hir<'cx>(env: &NzEnv<'cx>, hir: &Hir<'cx>) -> NirKind<'cx> {
     match hir.kind() {
         HirKind::Var(var) => env.lookup_val(*var),
         HirKind::Import(hir, _) => normalize_hir(env, hir),
@@ -178,9 +176,12 @@ pub fn normalize_hir(env: &NzEnv, hir: &Hir) -> NirKind {
             let val = val.eval(env);
             body.eval(env.insert_value(val, ())).kind().clone()
         }
+        HirKind::Expr(ExprKind::Builtin(b)) => {
+            NirKind::from_builtin_env(*b, env.clone())
+        }
         HirKind::Expr(e) => {
             let e = e.map_ref(|hir| hir.eval(env));
-            normalize_one_layer(e, env)
+            normalize_one_layer(e)
         }
     }
 }
diff --git a/dhall/src/semantics/resolve/cache.rs b/dhall/src/semantics/resolve/cache.rs
index b00a2d5..59463dd 100644
--- a/dhall/src/semantics/resolve/cache.rs
+++ b/dhall/src/semantics/resolve/cache.rs
@@ -5,7 +5,7 @@ use std::path::{Path, PathBuf};
 use crate::error::{CacheError, Error};
 use crate::parse::parse_binary;
 use crate::syntax::{binary, Hash};
-use crate::Typed;
+use crate::{Ctxt, Typed};
 use std::ffi::OsStr;
 use std::fs::File;
 
@@ -52,9 +52,13 @@ impl Cache {
         self.cache_dir.join(filename_for_hash(hash))
     }
 
-    pub fn get(&self, hash: &Hash) -> Result<Typed, Error> {
+    pub fn get<'cx>(
+        &self,
+        cx: Ctxt<'cx>,
+        hash: &Hash,
+    ) -> Result<Typed<'cx>, Error> {
         let path = self.entry_path(hash);
-        let res = read_cache_file(&path, hash);
+        let res = read_cache_file(cx, &path, hash);
         if res.is_err() && path.exists() {
             // Delete cache file since it's invalid. We ignore the error.
             let _ = std::fs::remove_file(&path);
@@ -62,14 +66,22 @@ impl Cache {
         res
     }
 
-    pub fn insert(&self, hash: &Hash, expr: &Typed) -> Result<(), Error> {
+    pub fn insert<'cx>(
+        &self,
+        hash: &Hash,
+        expr: &Typed<'cx>,
+    ) -> Result<(), Error> {
         let path = self.entry_path(hash);
         write_cache_file(&path, expr)
     }
 }
 
 /// Read a file from the cache, also checking that its hash is valid.
-fn read_cache_file(path: &Path, hash: &Hash) -> Result<Typed, Error> {
+fn read_cache_file<'cx>(
+    cx: Ctxt<'cx>,
+    path: &Path,
+    hash: &Hash,
+) -> Result<Typed<'cx>, Error> {
     let data = crate::utils::read_binary_file(path)?;
 
     match hash {
@@ -81,7 +93,7 @@ fn read_cache_file(path: &Path, hash: &Hash) -> Result<Typed, Error> {
         }
     }
 
-    Ok(parse_binary(&data)?.skip_resolve()?.typecheck()?)
+    Ok(parse_binary(&data)?.skip_resolve()?.typecheck(cx)?)
 }
 
 /// Write a file to the cache.
diff --git a/dhall/src/semantics/resolve/env.rs b/dhall/src/semantics/resolve/env.rs
index 82f21e8..2b998f8 100644
--- a/dhall/src/semantics/resolve/env.rs
+++ b/dhall/src/semantics/resolve/env.rs
@@ -86,9 +86,12 @@ impl<'cx> ImportEnv<'cx> {
         Some(*self.mem_cache.get(location)?)
     }
 
-    pub fn get_from_disk_cache(&self, hash: &Option<Hash>) -> Option<Typed> {
+    pub fn get_from_disk_cache(
+        &self,
+        hash: &Option<Hash>,
+    ) -> Option<Typed<'cx>> {
         let hash = hash.as_ref()?;
-        let expr = self.disk_cache.as_ref()?.get(hash).ok()?;
+        let expr = self.disk_cache.as_ref()?.get(self.cx(), hash).ok()?;
         Some(expr)
     }
 
@@ -100,7 +103,7 @@ impl<'cx> ImportEnv<'cx> {
         self.mem_cache.insert(location, result);
     }
 
-    pub fn write_to_disk_cache(&self, hash: &Option<Hash>, expr: &Typed) {
+    pub fn write_to_disk_cache(&self, hash: &Option<Hash>, expr: &Typed<'cx>) {
         if let Some(disk_cache) = self.disk_cache.as_ref() {
             if let Some(hash) = hash {
                 let _ = disk_cache.insert(hash, &expr);
@@ -111,8 +114,8 @@ impl<'cx> ImportEnv<'cx> {
     pub fn with_cycle_detection(
         &mut self,
         location: ImportLocation,
-        do_resolve: impl FnOnce(&mut Self) -> Result<Typed, Error>,
-    ) -> Result<Typed, Error> {
+        do_resolve: impl FnOnce(&mut Self) -> Result<Typed<'cx>, Error>,
+    ) -> Result<Typed<'cx>, Error> {
         if self.stack.contains(&location) {
             return Err(
                 ImportError::ImportCycle(self.stack.clone(), location).into()
diff --git a/dhall/src/semantics/resolve/hir.rs b/dhall/src/semantics/resolve/hir.rs
index c2d1883..c67ab75 100644
--- a/dhall/src/semantics/resolve/hir.rs
+++ b/dhall/src/semantics/resolve/hir.rs
@@ -10,19 +10,19 @@ pub struct AlphaVar {
 }
 
 #[derive(Debug, Clone, PartialEq, Eq)]
-pub enum HirKind {
+pub enum HirKind<'cx> {
     /// A resolved variable (i.e. a DeBruijn index)
     Var(AlphaVar),
     /// Result of resolving an import.
-    Import(Hir, Type),
+    Import(Hir<'cx>, Type<'cx>),
     // Forbidden ExprKind variants: Var, Import, Completion
-    Expr(ExprKind<Hir>),
+    Expr(ExprKind<Hir<'cx>>),
 }
 
 // An expression with resolved variables and imports.
 #[derive(Debug, Clone)]
-pub struct Hir {
-    kind: Box<HirKind>,
+pub struct Hir<'cx> {
+    kind: Box<HirKind<'cx>>,
     span: Span,
 }
 
@@ -35,15 +35,15 @@ impl AlphaVar {
     }
 }
 
-impl Hir {
-    pub fn new(kind: HirKind, span: Span) -> Self {
+impl<'cx> Hir<'cx> {
+    pub fn new(kind: HirKind<'cx>, span: Span) -> Self {
         Hir {
             kind: Box::new(kind),
             span,
         }
     }
 
-    pub fn kind(&self) -> &HirKind {
+    pub fn kind(&self) -> &HirKind<'cx> {
         &*self.kind
     }
     pub fn span(&self) -> Span {
@@ -63,7 +63,7 @@ impl Hir {
         let opts = ToExprOptions { alpha: true };
         self.to_expr(opts)
     }
-    pub fn to_expr_tyenv(&self, env: &TyEnv) -> Expr {
+    pub fn to_expr_tyenv(&self, env: &TyEnv<'cx>) -> Expr {
         let opts = ToExprOptions { alpha: false };
         let mut env = env.as_nameenv().clone();
         hir_to_expr(self, opts, &mut env)
@@ -72,29 +72,33 @@ impl Hir {
     /// Typecheck the Hir.
     pub fn typecheck<'hir>(
         &'hir self,
-        env: &TyEnv,
-    ) -> Result<Tir<'hir>, TypeError> {
+        env: &TyEnv<'cx>,
+    ) -> Result<Tir<'cx, 'hir>, TypeError> {
         type_with(env, self, None)
     }
     pub fn typecheck_noenv<'hir>(
         &'hir self,
-        cx: Ctxt<'_>,
-    ) -> Result<Tir<'hir>, TypeError> {
+        cx: Ctxt<'cx>,
+    ) -> Result<Tir<'cx, 'hir>, TypeError> {
         self.typecheck(&TyEnv::new(cx))
     }
 
     /// Eval the Hir. It will actually get evaluated only as needed on demand.
-    pub fn eval(&self, env: impl Into<NzEnv>) -> Nir {
+    pub fn eval(&self, env: impl Into<NzEnv<'cx>>) -> Nir<'cx> {
         Nir::new_thunk(env.into(), self.clone())
     }
     /// Eval a closed Hir (i.e. without free variables). It will actually get evaluated only as
     /// needed on demand.
-    pub fn eval_closed_expr(&self) -> Nir {
-        self.eval(NzEnv::new())
+    pub fn eval_closed_expr(&self, cx: Ctxt<'cx>) -> Nir<'cx> {
+        self.eval(NzEnv::new(cx))
     }
 }
 
-fn hir_to_expr(hir: &Hir, opts: ToExprOptions, env: &mut NameEnv) -> Expr {
+fn hir_to_expr<'cx>(
+    hir: &Hir<'cx>,
+    opts: ToExprOptions,
+    env: &mut NameEnv,
+) -> Expr {
     let kind = match hir.kind() {
         HirKind::Var(v) if opts.alpha => ExprKind::Var(V("_".into(), v.idx())),
         HirKind::Var(v) => ExprKind::Var(env.label_var(*v)),
@@ -127,9 +131,9 @@ fn hir_to_expr(hir: &Hir, opts: ToExprOptions, env: &mut NameEnv) -> Expr {
     Expr::new(kind, hir.span())
 }
 
-impl std::cmp::PartialEq for Hir {
+impl<'cx> std::cmp::PartialEq for Hir<'cx> {
     fn eq(&self, other: &Self) -> bool {
         self.kind == other.kind
     }
 }
-impl std::cmp::Eq for Hir {}
+impl<'cx> std::cmp::Eq for Hir<'cx> {}
diff --git a/dhall/src/semantics/resolve/resolve.rs b/dhall/src/semantics/resolve/resolve.rs
index cf72f80..488c516 100644
--- a/dhall/src/semantics/resolve/resolve.rs
+++ b/dhall/src/semantics/resolve/resolve.rs
@@ -231,12 +231,13 @@ impl ImportLocation {
         &self,
         env: &mut ImportEnv<'cx>,
         span: Span,
-    ) -> Result<Typed, Error> {
+    ) -> Result<Typed<'cx>, Error> {
         let (hir, ty) = match self.mode {
             ImportMode::Code => {
                 let parsed = self.kind.fetch_dhall()?;
-                let typed = resolve_with_env(env, parsed)?.typecheck()?;
-                let hir = typed.normalize().to_hir();
+                let typed =
+                    resolve_with_env(env, parsed)?.typecheck(env.cx())?;
+                let hir = typed.normalize(env.cx()).to_hir();
                 (hir, typed.ty)
             }
             ImportMode::RawText => {
@@ -245,7 +246,7 @@ impl ImportLocation {
                     HirKind::Expr(ExprKind::TextLit(text.into())),
                     span,
                 );
-                (hir, Type::from_builtin(Builtin::Text))
+                (hir, Type::from_builtin(env.cx(), Builtin::Text))
             }
             ImportMode::Location => {
                 let expr = self.kind.to_location();
@@ -286,7 +287,11 @@ fn make_aslocation_uniontype() -> Expr {
     mkexpr(ExprKind::UnionType(union))
 }
 
-fn check_hash(import: &Import, typed: &Typed, span: Span) -> Result<(), Error> {
+fn check_hash<'cx>(
+    import: &Import,
+    typed: &Typed<'cx>,
+    span: Span,
+) -> Result<(), Error> {
     if let (ImportMode::Code, Some(Hash::SHA256(hash))) =
         (import.mode, &import.hash)
     {
@@ -338,11 +343,11 @@ fn desugar(expr: &Expr) -> Cow<'_, Expr> {
 
 /// Traverse the expression, handling import alternatives and passing
 /// found imports to the provided function. Also resolving names.
-fn traverse_resolve_expr(
+fn traverse_resolve_expr<'cx>(
     name_env: &mut NameEnv,
     expr: &Expr,
-    f: &mut impl FnMut(Import, Span) -> Result<Typed, Error>,
-) -> Result<Hir, Error> {
+    f: &mut impl FnMut(Import, Span) -> Result<Typed<'cx>, Error>,
+) -> Result<Hir<'cx>, Error> {
     let expr = desugar(expr);
     Ok(match expr.kind() {
         ExprKind::Var(var) => match name_env.unlabel_var(&var) {
@@ -447,7 +452,7 @@ fn fetch_import<'cx>(
 fn resolve_with_env<'cx>(
     env: &mut ImportEnv<'cx>,
     parsed: Parsed,
-) -> Result<Resolved, Error> {
+) -> Result<Resolved<'cx>, Error> {
     let Parsed(expr, base_location) = parsed;
     let resolved = traverse_resolve_expr(
         &mut NameEnv::new(),
@@ -463,17 +468,20 @@ fn resolve_with_env<'cx>(
     Ok(Resolved(resolved))
 }
 
-pub fn resolve(cx: Ctxt<'_>, parsed: Parsed) -> Result<Resolved, Error> {
+pub fn resolve<'cx>(
+    cx: Ctxt<'cx>,
+    parsed: Parsed,
+) -> Result<Resolved<'cx>, Error> {
     resolve_with_env(&mut ImportEnv::new(cx), parsed)
 }
 
-pub fn skip_resolve_expr(expr: &Expr) -> Result<Hir, Error> {
+pub fn skip_resolve_expr<'cx>(expr: &Expr) -> Result<Hir<'cx>, Error> {
     traverse_resolve_expr(&mut NameEnv::new(), expr, &mut |import, _span| {
         Err(ImportError::UnexpectedImport(import).into())
     })
 }
 
-pub fn skip_resolve(parsed: Parsed) -> Result<Resolved, Error> {
+pub fn skip_resolve<'cx>(parsed: Parsed) -> Result<Resolved<'cx>, Error> {
     let Parsed(expr, _) = parsed;
     let resolved = skip_resolve_expr(&expr)?;
     Ok(Resolved(resolved))
diff --git a/dhall/src/semantics/tck/env.rs b/dhall/src/semantics/tck/env.rs
index fc0ce9f..fdcc62d 100644
--- a/dhall/src/semantics/tck/env.rs
+++ b/dhall/src/semantics/tck/env.rs
@@ -13,7 +13,7 @@ pub struct VarEnv {
 pub struct TyEnv<'cx> {
     cx: Ctxt<'cx>,
     names: NameEnv,
-    items: ValEnv<Type>,
+    items: ValEnv<'cx, Type<'cx>>,
 }
 
 impl VarEnv {
@@ -45,7 +45,7 @@ impl<'cx> TyEnv<'cx> {
         TyEnv {
             cx,
             names: NameEnv::new(),
-            items: ValEnv::new(),
+            items: ValEnv::new(cx),
         }
     }
     pub fn cx(&self) -> Ctxt<'cx> {
@@ -54,34 +54,34 @@ impl<'cx> TyEnv<'cx> {
     pub fn as_varenv(&self) -> VarEnv {
         self.names.as_varenv()
     }
-    pub fn to_nzenv(&self) -> NzEnv {
+    pub fn to_nzenv(&self) -> NzEnv<'cx> {
         self.items.discard_types()
     }
     pub fn as_nameenv(&self) -> &NameEnv {
         &self.names
     }
 
-    pub fn insert_type(&self, x: &Label, ty: Type) -> Self {
+    pub fn insert_type(&self, x: &Label, ty: Type<'cx>) -> Self {
         TyEnv {
             cx: self.cx,
             names: self.names.insert(x),
             items: self.items.insert_type(ty),
         }
     }
-    pub fn insert_value(&self, x: &Label, e: Nir, ty: Type) -> Self {
+    pub fn insert_value(&self, x: &Label, e: Nir<'cx>, ty: Type<'cx>) -> Self {
         TyEnv {
             cx: self.cx,
             names: self.names.insert(x),
             items: self.items.insert_value(e, ty),
         }
     }
-    pub fn lookup(&self, var: AlphaVar) -> Type {
+    pub fn lookup(&self, var: AlphaVar) -> Type<'cx> {
         self.items.lookup_ty(var)
     }
 }
 
-impl<'a, 'cx> From<&'a TyEnv<'cx>> for NzEnv {
-    fn from(x: &'a TyEnv) -> Self {
+impl<'a, 'cx> From<&'a TyEnv<'cx>> for NzEnv<'cx> {
+    fn from(x: &'a TyEnv<'cx>) -> Self {
         x.to_nzenv()
     }
 }
diff --git a/dhall/src/semantics/tck/tir.rs b/dhall/src/semantics/tck/tir.rs
index f34802c..7b04f57 100644
--- a/dhall/src/semantics/tck/tir.rs
+++ b/dhall/src/semantics/tck/tir.rs
@@ -2,6 +2,7 @@ use crate::builtins::Builtin;
 use crate::error::{ErrorBuilder, TypeError};
 use crate::semantics::{mkerr, Hir, Nir, NirKind, NzEnv, TyEnv, VarEnv};
 use crate::syntax::{Const, Expr, Span};
+use crate::Ctxt;
 
 /// The type of a type. 0 is `Type`, 1 is `Kind`, etc...
 #[derive(Debug, Copy, Clone, PartialEq, Eq, PartialOrd, Ord, Default)]
@@ -9,17 +10,17 @@ pub struct Universe(u8);
 
 /// An expression representing a type
 #[derive(Debug, Clone, PartialEq, Eq)]
-pub struct Type {
-    val: Nir,
+pub struct Type<'cx> {
+    val: Nir<'cx>,
     univ: Universe,
 }
 
 /// A hir expression plus its inferred type.
 /// Stands for "Typed intermediate representation"
 #[derive(Debug, Clone)]
-pub struct Tir<'hir> {
-    hir: &'hir Hir,
-    ty: Type,
+pub struct Tir<'cx, 'hir> {
+    hir: &'hir Hir<'cx>,
+    ty: Type<'cx>,
 }
 
 impl Universe {
@@ -43,16 +44,16 @@ impl Universe {
     }
 }
 
-impl Type {
-    pub fn new(val: Nir, univ: Universe) -> Self {
+impl<'cx> Type<'cx> {
+    pub fn new(val: Nir<'cx>, univ: Universe) -> Self {
         Type { val, univ }
     }
     /// Creates a new Type and infers its universe by re-typechecking its value.
     /// TODO: ideally avoid this function altogether. Would need to store types in RecordType and
     /// PiClosure.
     pub fn new_infer_universe(
-        env: &TyEnv,
-        val: Nir,
+        env: &TyEnv<'cx>,
+        val: Nir<'cx>,
     ) -> Result<Self, TypeError> {
         let c = val.to_hir(env.as_varenv()).typecheck(env)?.ty().as_const();
         let u = match c {
@@ -67,14 +68,14 @@ impl Type {
     pub fn from_const(c: Const) -> Self {
         Self::new(Nir::from_const(c), c.to_universe().next())
     }
-    pub fn from_builtin(b: Builtin) -> Self {
+    pub fn from_builtin(cx: Ctxt<'cx>, b: Builtin) -> Self {
         use Builtin::*;
         match b {
             Bool | Natural | Integer | Double | Text => {}
             _ => unreachable!("this builtin is not a type: {}", b),
         }
 
-        Self::new(Nir::from_builtin(b), Universe::from_const(Const::Type))
+        Self::new(Nir::from_builtin(cx, b), Universe::from_const(Const::Type))
     }
 
     /// Get the type of this type
@@ -82,60 +83,60 @@ impl Type {
         self.univ
     }
 
-    pub fn to_nir(&self) -> Nir {
+    pub fn to_nir(&self) -> Nir<'cx> {
         self.val.clone()
     }
-    pub fn as_nir(&self) -> &Nir {
+    pub fn as_nir(&self) -> &Nir<'cx> {
         &self.val
     }
-    pub fn into_nir(self) -> Nir {
+    pub fn into_nir(self) -> Nir<'cx> {
         self.val
     }
     pub fn as_const(&self) -> Option<Const> {
         self.val.as_const()
     }
-    pub fn kind(&self) -> &NirKind {
+    pub fn kind(&self) -> &NirKind<'cx> {
         self.val.kind()
     }
 
-    pub fn to_hir(&self, venv: VarEnv) -> Hir {
+    pub fn to_hir(&self, venv: VarEnv) -> Hir<'cx> {
         self.val.to_hir(venv)
     }
-    pub fn to_expr_tyenv(&self, tyenv: &TyEnv) -> Expr {
+    pub fn to_expr_tyenv(&self, tyenv: &TyEnv<'cx>) -> Expr {
         self.val.to_hir(tyenv.as_varenv()).to_expr_tyenv(tyenv)
     }
 }
 
-impl<'hir> Tir<'hir> {
-    pub fn from_hir(hir: &'hir Hir, ty: Type) -> Self {
+impl<'cx, 'hir> Tir<'cx, 'hir> {
+    pub fn from_hir(hir: &'hir Hir<'cx>, ty: Type<'cx>) -> Self {
         Tir { hir, ty }
     }
 
     pub fn span(&self) -> Span {
         self.as_hir().span()
     }
-    pub fn ty(&self) -> &Type {
+    pub fn ty(&self) -> &Type<'cx> {
         &self.ty
     }
-    pub fn into_ty(self) -> Type {
+    pub fn into_ty(self) -> Type<'cx> {
         self.ty
     }
 
-    pub fn to_hir(&self) -> Hir {
+    pub fn to_hir(&self) -> Hir<'cx> {
         self.as_hir().clone()
     }
-    pub fn as_hir(&self) -> &Hir {
-        &self.hir
+    pub fn as_hir(&self) -> &'hir Hir<'cx> {
+        self.hir
     }
-    pub fn to_expr_tyenv(&self, env: &TyEnv) -> Expr {
+    pub fn to_expr_tyenv(&self, env: &TyEnv<'cx>) -> Expr {
         self.as_hir().to_expr_tyenv(env)
     }
 
     /// Eval the Tir. It will actually get evaluated only as needed on demand.
-    pub fn eval(&self, env: impl Into<NzEnv>) -> Nir {
+    pub fn eval(&self, env: impl Into<NzEnv<'cx>>) -> Nir<'cx> {
         self.as_hir().eval(env.into())
     }
-    pub fn ensure_is_type(&self, env: &TyEnv) -> Result<(), TypeError> {
+    pub fn ensure_is_type(&self, env: &TyEnv<'cx>) -> Result<(), TypeError> {
         if self.ty().as_const().is_none() {
             return mkerr(
                 ErrorBuilder::new(format!(
@@ -159,7 +160,10 @@ impl<'hir> Tir<'hir> {
         Ok(())
     }
     /// Evaluate to a Type.
-    pub fn eval_to_type(&self, env: &TyEnv) -> Result<Type, TypeError> {
+    pub fn eval_to_type(
+        &self,
+        env: &TyEnv<'cx>,
+    ) -> Result<Type<'cx>, TypeError> {
         self.ensure_is_type(env)?;
         Ok(Type::new(
             self.eval(env),
diff --git a/dhall/src/semantics/tck/typecheck.rs b/dhall/src/semantics/tck/typecheck.rs
index 7e8c0e1..8218368 100644
--- a/dhall/src/semantics/tck/typecheck.rs
+++ b/dhall/src/semantics/tck/typecheck.rs
@@ -29,11 +29,12 @@ pub fn mk_span_err<T, S: ToString>(span: Span, msg: S) -> Result<T, TypeError> {
 
 /// When all sub-expressions have been typed, check the remaining toplevel
 /// layer.
-fn type_one_layer(
-    env: &TyEnv<'_>,
-    ekind: ExprKind<Tir<'_>>,
+fn type_one_layer<'cx>(
+    env: &TyEnv<'cx>,
+    ekind: ExprKind<Tir<'cx, '_>>,
     span: Span,
-) -> Result<Type, TypeError> {
+) -> Result<Type<'cx>, TypeError> {
+    let cx = env.cx();
     let span_err = |msg: &str| mk_span_err(span.clone(), msg);
 
     Ok(match ekind {
@@ -51,18 +52,21 @@ fn type_one_layer(
 
         ExprKind::Const(Const::Type) => Type::from_const(Const::Kind),
         ExprKind::Const(Const::Kind) => Type::from_const(Const::Sort),
-        ExprKind::Num(num) => Type::from_builtin(match num {
-            NumKind::Bool(_) => Builtin::Bool,
-            NumKind::Natural(_) => Builtin::Natural,
-            NumKind::Integer(_) => Builtin::Integer,
-            NumKind::Double(_) => Builtin::Double,
-        }),
+        ExprKind::Num(num) => Type::from_builtin(
+            cx,
+            match num {
+                NumKind::Bool(_) => Builtin::Bool,
+                NumKind::Natural(_) => Builtin::Natural,
+                NumKind::Integer(_) => Builtin::Integer,
+                NumKind::Double(_) => Builtin::Double,
+            },
+        ),
         ExprKind::Builtin(b) => {
             let t_hir = type_of_builtin(b);
             typecheck(env.cx(), &t_hir)?.eval_to_type(env)?
         }
         ExprKind::TextLit(interpolated) => {
-            let text_type = Type::from_builtin(Builtin::Text);
+            let text_type = Type::from_builtin(cx, Builtin::Text);
             for contents in interpolated.iter() {
                 use InterpolatedTextContents::Expr;
                 if let Expr(x) = contents {
@@ -79,7 +83,7 @@ fn type_one_layer(
             }
 
             let t = x.ty().to_nir();
-            Nir::from_builtin(Builtin::Optional)
+            Nir::from_builtin(cx, Builtin::Optional)
                 .app(t)
                 .to_type(Const::Type)
         }
@@ -104,7 +108,9 @@ fn type_one_layer(
             }
 
             let t = x.ty().to_nir();
-            Nir::from_builtin(Builtin::List).app(t).to_type(Const::Type)
+            Nir::from_builtin(cx, Builtin::List)
+                .app(t)
+                .to_type(Const::Type)
         }
         ExprKind::RecordLit(kvs) => {
             // An empty record type has type Type
@@ -171,11 +177,11 @@ fn type_one_layer(
 /// to compare with.
 // We pass the annotation to avoid duplicating the annot checking logic. I hope one day we can use
 // it to handle the annotations in merge/toMap/etc. uniformly.
-pub fn type_with<'hir>(
-    env: &TyEnv<'_>,
-    hir: &'hir Hir,
-    annot: Option<Type>,
-) -> Result<Tir<'hir>, TypeError> {
+pub fn type_with<'cx, 'hir>(
+    env: &TyEnv<'cx>,
+    hir: &'hir Hir<'cx>,
+    annot: Option<Type<'cx>>,
+) -> Result<Tir<'cx, 'hir>, TypeError> {
     let tir = match hir.kind() {
         HirKind::Var(var) => Tir::from_hir(hir, env.lookup(*var)),
         HirKind::Import(_, ty) => Tir::from_hir(hir, ty.clone()),
@@ -268,19 +274,19 @@ pub fn type_with<'hir>(
 
 /// Typecheck an expression and return the expression annotated with its type if type-checking
 /// succeeded, or an error if type-checking failed.
-pub fn typecheck<'hir>(
-    cx: Ctxt<'_>,
-    hir: &'hir Hir,
-) -> Result<Tir<'hir>, TypeError> {
+pub fn typecheck<'cx, 'hir>(
+    cx: Ctxt<'cx>,
+    hir: &'hir Hir<'cx>,
+) -> Result<Tir<'cx, 'hir>, TypeError> {
     type_with(&TyEnv::new(cx), hir, None)
 }
 
 /// Like `typecheck`, but additionally checks that the expression's type matches the provided type.
-pub fn typecheck_with<'hir>(
-    cx: Ctxt<'_>,
-    hir: &'hir Hir,
-    ty: &Hir,
-) -> Result<Tir<'hir>, TypeError> {
+pub fn typecheck_with<'cx, 'hir>(
+    cx: Ctxt<'cx>,
+    hir: &'hir Hir<'cx>,
+    ty: &Hir<'cx>,
+) -> Result<Tir<'cx, 'hir>, TypeError> {
     let ty = typecheck(cx, ty)?.eval_to_type(&TyEnv::new(cx))?;
     type_with(&TyEnv::new(cx), hir, Some(ty))
 }