68 files changed, 1881 insertions, 2109 deletions

diff --git a/dhall/src/api/mod.rs b/dhall/src/api/mod.rs
new file mode 100644
index 0000000..0a0ef93
--- /dev/null
+++ b/dhall/src/api/mod.rs
@@ -0,0 +1,40 @@
+mod serde;
+pub(crate) mod traits;
+
+/// Deserialization of Dhall expressions into Rust
+pub mod de {
+    #[doc(hidden)]
+    pub use crate::phase::SimpleType;
+    pub use crate::traits::{Deserialize, SimpleStaticType, StaticType};
+    #[doc(hidden)]
+    pub use dhall_proc_macros::SimpleStaticType;
+
+    /// Deserialize an instance of type T from a string of Dhall text.
+    ///
+    /// This will recursively resolve all imports in the expression, and
+    /// typecheck it before deserialization. Relative imports will be resolved relative to the
+    /// provided file. More control over this process is not yet available
+    /// but will be in a coming version of this crate.
+    ///
+    /// If a type is provided, this additionally checks that the provided
+    /// expression has that type.
+    pub fn from_str<'a, T: Deserialize<'a>>(
+        s: &'a str,
+        ty: Option<&crate::phase::Type>,
+    ) -> crate::error::Result<T> {
+        T::from_str(s, ty)
+    }
+
+    /// Deserialize an instance of type T from a string of Dhall text,
+    /// additionally checking that it matches the type of T.
+    ///
+    /// This will recursively resolve all imports in the expression, and
+    /// typecheck it before deserialization. Relative imports will be resolved relative to the
+    /// provided file. More control over this process is not yet available
+    /// but will be in a coming version of this crate.
+    pub fn from_str_auto_type<'a, T: Deserialize<'a> + StaticType>(
+        s: &'a str,
+    ) -> crate::error::Result<T> {
+        from_str(s, Some(&<T as StaticType>::get_static_type()))
+    }
+}
diff --git a/dhall/src/serde.rs b/dhall/src/api/serde.rs
index 96bc765..93921ba 100644
--- a/dhall/src/serde.rs
+++ b/dhall/src/api/serde.rs
@@ -1,5 +1,5 @@
 use crate::error::{Error, Result};
-use crate::expr::{Normalized, Type};
+use crate::phase::{Normalized, Type};
 use crate::traits::Deserialize;
 use dhall_syntax::*;
 use std::borrow::Cow;
diff --git a/dhall/src/traits/deserialize.rs b/dhall/src/api/traits/deserialize.rs
index e3ff2d5..9673cf9 100644
--- a/dhall/src/traits/deserialize.rs
+++ b/dhall/src/api/traits/deserialize.rs
@@ -1,5 +1,5 @@
 use crate::error::*;
-use crate::expr::*;
+use crate::phase::*;
 
 /// A data structure that can be deserialized from a Dhall expression
 ///
diff --git a/dhall/src/traits/dynamic_type.rs b/dhall/src/api/traits/dynamic_type.rs
index 858642e..7763a28 100644
--- a/dhall/src/traits/dynamic_type.rs
+++ b/dhall/src/api/traits/dynamic_type.rs
@@ -1,9 +1,6 @@
-use crate::expr::*;
+use crate::error::TypeError;
+use crate::phase::{Normalized, Type, Typed};
 use crate::traits::StaticType;
-#[allow(unused_imports)]
-use crate::typecheck::{TypeError, TypeMessage, TypecheckContext};
-#[allow(unused_imports)]
-use dhall_syntax::{Const, ExprF};
 use std::borrow::Cow;
 
 pub trait DynamicType {
@@ -30,6 +27,6 @@ impl DynamicType for Normalized {
 
 impl DynamicType for Typed {
     fn get_type(&self) -> Result<Cow<'_, Type>, TypeError> {
-        self.0.get_type()
+        self.get_type()
     }
 }
diff --git a/dhall/src/traits/mod.rs b/dhall/src/api/traits/mod.rs
index 315e17a..315e17a 100644
--- a/dhall/src/traits/mod.rs
+++ b/dhall/src/api/traits/mod.rs
diff --git a/dhall/src/traits/static_type.rs b/dhall/src/api/traits/static_type.rs
index f90b8df..e05dfff 100644
--- a/dhall/src/traits/static_type.rs
+++ b/dhall/src/api/traits/static_type.rs
@@ -1,4 +1,4 @@
-use crate::expr::*;
+use crate::phase::*;
 use dhall_proc_macros as dhall;
 use dhall_syntax::*;
 
@@ -38,8 +38,8 @@ fn mktype(x: SubExpr<X, X>) -> SimpleType {
 
 impl<T: SimpleStaticType> StaticType for T {
     fn get_static_type() -> Type {
-        crate::expr::Normalized::from_thunk_and_type(
-            crate::normalize::Thunk::from_normalized_expr(
+        crate::phase::Normalized::from_thunk_and_type(
+            crate::core::thunk::Thunk::from_normalized_expr(
                 T::get_simple_static_type().into(),
             ),
             Type::const_type(),
diff --git a/dhall/src/core/context.rs b/dhall/src/core/context.rs
new file mode 100644
index 0000000..9b5beed
--- /dev/null
+++ b/dhall/src/core/context.rs
@@ -0,0 +1,136 @@
+use std::borrow::Cow;
+use std::rc::Rc;
+
+use dhall_syntax::context::Context;
+use dhall_syntax::{Label, V};
+
+use crate::core::thunk::Thunk;
+use crate::core::value::{AlphaVar, Value};
+use crate::phase::{Normalized, Type, Typed};
+
+#[derive(Debug, Clone)]
+enum NzEnvItem {
+    Thunk(Thunk),
+    Skip(AlphaVar),
+}
+
+#[derive(Debug, Clone)]
+pub(crate) struct NormalizationContext(Rc<Context<Label, NzEnvItem>>);
+
+#[derive(Debug, Clone)]
+pub(crate) enum TyEnvItem {
+    Type(AlphaVar, Type),
+    Value(Normalized),
+}
+
+#[derive(Debug, Clone)]
+pub(crate) struct TypecheckContext(pub(crate) Context<Label, TyEnvItem>);
+
+impl NzEnvItem {
+    pub(crate) fn shift(&self, delta: isize, var: &AlphaVar) -> Self {
+        use NzEnvItem::*;
+        match self {
+            Thunk(e) => Thunk(e.shift(delta, var)),
+            Skip(v) => Skip(v.shift(delta, var)),
+        }
+    }
+
+    pub(crate) fn subst_shift(&self, var: &AlphaVar, val: &Typed) -> Self {
+        match self {
+            NzEnvItem::Thunk(e) => NzEnvItem::Thunk(e.subst_shift(var, val)),
+            NzEnvItem::Skip(v) if v == var => NzEnvItem::Thunk(val.to_thunk()),
+            NzEnvItem::Skip(v) => NzEnvItem::Skip(v.shift(-1, var)),
+        }
+    }
+}
+
+impl NormalizationContext {
+    pub(crate) fn new() -> Self {
+        NormalizationContext(Rc::new(Context::new()))
+    }
+    pub(crate) fn skip(&self, x: &Label) -> Self {
+        NormalizationContext(Rc::new(
+            self.0
+                .map(|_, e| e.shift(1, &x.into()))
+                .insert(x.clone(), NzEnvItem::Skip(x.into())),
+        ))
+    }
+    pub(crate) fn lookup(&self, var: &V<Label>) -> Value {
+        let V(x, n) = var;
+        match self.0.lookup(x, *n) {
+            Some(NzEnvItem::Thunk(t)) => t.to_value(),
+            Some(NzEnvItem::Skip(newvar)) => Value::Var(newvar.clone()),
+            // Free variable
+            None => Value::Var(AlphaVar::from_var(var.clone())),
+        }
+    }
+    pub(crate) fn from_typecheck_ctx(tc_ctx: &TypecheckContext) -> Self {
+        use TyEnvItem::*;
+        let mut ctx = Context::new();
+        for (k, vs) in tc_ctx.0.iter_keys() {
+            for v in vs.iter() {
+                let new_item = match v {
+                    Type(var, _) => NzEnvItem::Skip(var.clone()),
+                    Value(e) => NzEnvItem::Thunk(e.to_thunk()),
+                };
+                ctx = ctx.insert(k.clone(), new_item);
+            }
+        }
+        NormalizationContext(Rc::new(ctx))
+    }
+
+    pub(crate) fn shift(&self, delta: isize, var: &AlphaVar) -> Self {
+        NormalizationContext(Rc::new(self.0.map(|_, e| e.shift(delta, var))))
+    }
+
+    pub(crate) fn subst_shift(&self, var: &AlphaVar, val: &Typed) -> Self {
+        NormalizationContext(Rc::new(
+            self.0.map(|_, e| e.subst_shift(var, val)),
+        ))
+    }
+}
+
+impl TyEnvItem {
+    fn shift(&self, delta: isize, var: &AlphaVar) -> Self {
+        use TyEnvItem::*;
+        match self {
+            Type(v, e) => Type(v.shift(delta, var), e.shift(delta, var)),
+            Value(e) => Value(e.shift(delta, var)),
+        }
+    }
+}
+
+impl TypecheckContext {
+    pub(crate) fn new() -> Self {
+        TypecheckContext(Context::new())
+    }
+    pub(crate) fn insert_type(&self, x: &Label, t: Type) -> Self {
+        TypecheckContext(self.0.map(|_, e| e.shift(1, &x.into())).insert(
+            x.clone(),
+            TyEnvItem::Type(x.into(), t.shift(1, &x.into())),
+        ))
+    }
+    pub(crate) fn insert_value(&self, x: &Label, t: Normalized) -> Self {
+        TypecheckContext(self.0.insert(x.clone(), TyEnvItem::Value(t)))
+    }
+    pub(crate) fn lookup(&self, var: &V<Label>) -> Option<Cow<'_, Type>> {
+        let V(x, n) = var;
+        match self.0.lookup(x, *n) {
+            Some(TyEnvItem::Type(_, t)) => Some(Cow::Borrowed(&t)),
+            Some(TyEnvItem::Value(t)) => Some(t.get_type()?),
+            None => None,
+        }
+    }
+    pub(crate) fn to_normalization_ctx(&self) -> NormalizationContext {
+        NormalizationContext::from_typecheck_ctx(self)
+    }
+}
+
+impl PartialEq for TypecheckContext {
+    fn eq(&self, _: &Self) -> bool {
+        // don't count contexts when comparing stuff
+        // this is dirty but needed for now
+        true
+    }
+}
+impl Eq for TypecheckContext {}
diff --git a/dhall/src/core/mod.rs b/dhall/src/core/mod.rs
new file mode 100644
index 0000000..8f5c2ca
--- /dev/null
+++ b/dhall/src/core/mod.rs
@@ -0,0 +1,3 @@
+pub(crate) mod context;
+pub(crate) mod thunk;
+pub(crate) mod value;
diff --git a/dhall/src/core/thunk.rs b/dhall/src/core/thunk.rs
new file mode 100644
index 0000000..2b013bb
--- /dev/null
+++ b/dhall/src/core/thunk.rs
@@ -0,0 +1,297 @@
+use std::cell::{Ref, RefCell};
+use std::rc::Rc;
+
+use crate::core::context::NormalizationContext;
+use crate::core::context::TypecheckContext;
+use crate::core::value::{AlphaVar, Value};
+use crate::error::TypeError;
+use crate::phase::normalize::{
+    apply_any, normalize_whnf, InputSubExpr, OutputSubExpr,
+};
+use crate::phase::typecheck::mktype;
+use crate::phase::{Type, Typed};
+
+#[derive(Debug, Clone, Copy)]
+enum Marker {
+    /// Weak Head Normal Form, i.e. subexpressions may not be normalized
+    WHNF,
+    /// Normal form, i.e. completely normalized
+    NF,
+}
+use Marker::{NF, WHNF};
+
+#[derive(Debug)]
+enum ThunkInternal {
+    /// Non-normalized value alongside a normalization context
+    Unnormalized(NormalizationContext, InputSubExpr),
+    /// Partially normalized value.
+    /// Invariant: if the marker is `NF`, the value must be fully normalized
+    Value(Marker, Value),
+}
+
+/// Stores a possibly unevaluated value. Gets (partially) normalized on-demand,
+/// sharing computation automatically.
+/// Uses a RefCell to share computation.
+#[derive(Debug, Clone)]
+pub struct Thunk(Rc<RefCell<ThunkInternal>>);
+
+/// A thunk in type position. Can optionally store a Type from the typechecking phase to preserve
+/// type information through the normalization phase.
+#[derive(Debug, Clone)]
+pub(crate) enum TypeThunk {
+    Thunk(Thunk),
+    Type(Type),
+}
+
+impl ThunkInternal {
+    fn into_thunk(self) -> Thunk {
+        Thunk(Rc::new(RefCell::new(self)))
+    }
+
+    fn normalize_whnf(&mut self) {
+        match self {
+            ThunkInternal::Unnormalized(ctx, e) => {
+                *self = ThunkInternal::Value(
+                    WHNF,
+                    normalize_whnf(ctx.clone(), e.clone()),
+                )
+            }
+            // Already at least in WHNF
+            ThunkInternal::Value(_, _) => {}
+        }
+    }
+
+    fn normalize_nf(&mut self) {
+        match self {
+            ThunkInternal::Unnormalized(_, _) => {
+                self.normalize_whnf();
+                self.normalize_nf();
+            }
+            ThunkInternal::Value(m @ WHNF, v) => {
+                v.normalize_mut();
+                *m = NF;
+            }
+            // Already in NF
+            ThunkInternal::Value(NF, _) => {}
+        }
+    }
+
+    // Always use normalize_whnf before
+    fn as_whnf(&self) -> &Value {
+        match self {
+            ThunkInternal::Unnormalized(_, _) => unreachable!(),
+            ThunkInternal::Value(_, v) => v,
+        }
+    }
+
+    // Always use normalize_nf before
+    fn as_nf(&self) -> &Value {
+        match self {
+            ThunkInternal::Unnormalized(_, _) => unreachable!(),
+            ThunkInternal::Value(WHNF, _) => unreachable!(),
+            ThunkInternal::Value(NF, v) => v,
+        }
+    }
+
+    fn shift(&self, delta: isize, var: &AlphaVar) -> Self {
+        match self {
+            ThunkInternal::Unnormalized(ctx, e) => {
+                ThunkInternal::Unnormalized(ctx.shift(delta, var), e.clone())
+            }
+            ThunkInternal::Value(m, v) => {
+                ThunkInternal::Value(*m, v.shift(delta, var))
+            }
+        }
+    }
+
+    fn subst_shift(&self, var: &AlphaVar, val: &Typed) -> Self {
+        match self {
+            ThunkInternal::Unnormalized(ctx, e) => ThunkInternal::Unnormalized(
+                ctx.subst_shift(var, val),
+                e.clone(),
+            ),
+            ThunkInternal::Value(_, v) => {
+                // The resulting value may not stay in normal form after substitution
+                ThunkInternal::Value(WHNF, v.subst_shift(var, val))
+            }
+        }
+    }
+}
+
+impl Thunk {
+    pub(crate) fn new(ctx: NormalizationContext, e: InputSubExpr) -> Thunk {
+        ThunkInternal::Unnormalized(ctx, e).into_thunk()
+    }
+
+    pub(crate) fn from_value(v: Value) -> Thunk {
+        ThunkInternal::Value(WHNF, v).into_thunk()
+    }
+
+    pub(crate) fn from_normalized_expr(e: OutputSubExpr) -> Thunk {
+        Thunk::new(NormalizationContext::new(), e.absurd())
+    }
+
+    // Normalizes contents to normal form; faster than `normalize_nf` if
+    // no one else shares this thunk
+    pub(crate) fn normalize_mut(&mut self) {
+        match Rc::get_mut(&mut self.0) {
+            // Mutate directly if sole owner
+            Some(refcell) => RefCell::get_mut(refcell).normalize_nf(),
+            // Otherwise mutate through the refcell
+            None => self.0.borrow_mut().normalize_nf(),
+        }
+    }
+
+    fn do_normalize_whnf(&self) {
+        let borrow = self.0.borrow();
+        match &*borrow {
+            ThunkInternal::Unnormalized(_, _) => {
+                drop(borrow);
+                self.0.borrow_mut().normalize_whnf();
+            }
+            // Already at least in WHNF
+            ThunkInternal::Value(_, _) => {}
+        }
+    }
+
+    fn do_normalize_nf(&self) {
+        let borrow = self.0.borrow();
+        match &*borrow {
+            ThunkInternal::Unnormalized(_, _)
+            | ThunkInternal::Value(WHNF, _) => {
+                drop(borrow);
+                self.0.borrow_mut().normalize_nf();
+            }
+            // Already in NF
+            ThunkInternal::Value(NF, _) => {}
+        }
+    }
+
+    // WARNING: avoid normalizing any thunk while holding on to this ref
+    // or you could run into BorrowMut panics
+    pub(crate) fn normalize_nf(&self) -> Ref<Value> {
+        self.do_normalize_nf();
+        Ref::map(self.0.borrow(), ThunkInternal::as_nf)
+    }
+
+    // WARNING: avoid normalizing any thunk while holding on to this ref
+    // or you could run into BorrowMut panics
+    pub(crate) fn as_value(&self) -> Ref<Value> {
+        self.do_normalize_whnf();
+        Ref::map(self.0.borrow(), ThunkInternal::as_whnf)
+    }
+
+    pub(crate) fn to_value(&self) -> Value {
+        self.as_value().clone()
+    }
+
+    pub(crate) fn normalize_to_expr(&self) -> OutputSubExpr {
+        self.normalize_to_expr_maybe_alpha(false)
+    }
+
+    pub(crate) fn normalize_to_expr_maybe_alpha(
+        &self,
+        alpha: bool,
+    ) -> OutputSubExpr {
+        self.normalize_nf().normalize_to_expr_maybe_alpha(alpha)
+    }
+
+    pub(crate) fn app_val(&self, val: Value) -> Value {
+        self.app_thunk(val.into_thunk())
+    }
+
+    pub(crate) fn app_thunk(&self, th: Thunk) -> Value {
+        apply_any(self.clone(), th)
+    }
+
+    pub(crate) fn shift(&self, delta: isize, var: &AlphaVar) -> Self {
+        self.0.borrow().shift(delta, var).into_thunk()
+    }
+
+    pub(crate) fn subst_shift(&self, var: &AlphaVar, val: &Typed) -> Self {
+        self.0.borrow().subst_shift(var, val).into_thunk()
+    }
+}
+
+impl TypeThunk {
+    pub(crate) fn from_value(v: Value) -> TypeThunk {
+        TypeThunk::from_thunk(Thunk::from_value(v))
+    }
+
+    pub(crate) fn from_thunk(th: Thunk) -> TypeThunk {
+        TypeThunk::Thunk(th)
+    }
+
+    pub(crate) fn from_type(t: Type) -> TypeThunk {
+        TypeThunk::Type(t)
+    }
+
+    pub(crate) fn normalize_mut(&mut self) {
+        match self {
+            TypeThunk::Thunk(th) => th.normalize_mut(),
+            TypeThunk::Type(_) => {}
+        }
+    }
+
+    pub(crate) fn normalize_nf(&self) -> Value {
+        match self {
+            TypeThunk::Thunk(th) => th.normalize_nf().clone(),
+            TypeThunk::Type(t) => t.to_value().normalize(),
+        }
+    }
+
+    pub(crate) fn to_value(&self) -> Value {
+        match self {
+            TypeThunk::Thunk(th) => th.to_value(),
+            TypeThunk::Type(t) => t.to_value(),
+        }
+    }
+
+    pub(crate) fn to_type(
+        &self,
+        ctx: &TypecheckContext,
+    ) -> Result<Type, TypeError> {
+        match self {
+            TypeThunk::Type(t) => Ok(t.clone()),
+            TypeThunk::Thunk(th) => {
+                // TODO: rule out statically
+                mktype(ctx, th.normalize_to_expr().absurd())
+            }
+        }
+    }
+
+    pub(crate) fn normalize_to_expr_maybe_alpha(
+        &self,
+        alpha: bool,
+    ) -> OutputSubExpr {
+        self.normalize_nf().normalize_to_expr_maybe_alpha(alpha)
+    }
+
+    pub(crate) fn shift(&self, delta: isize, var: &AlphaVar) -> Self {
+        match self {
+            TypeThunk::Thunk(th) => TypeThunk::Thunk(th.shift(delta, var)),
+            TypeThunk::Type(t) => TypeThunk::Type(t.shift(delta, var)),
+        }
+    }
+
+    pub(crate) fn subst_shift(&self, var: &AlphaVar, val: &Typed) -> Self {
+        match self {
+            TypeThunk::Thunk(th) => TypeThunk::Thunk(th.subst_shift(var, val)),
+            TypeThunk::Type(t) => TypeThunk::Type(t.subst_shift(var, val)),
+        }
+    }
+}
+
+impl std::cmp::PartialEq for Thunk {
+    fn eq(&self, other: &Self) -> bool {
+        &*self.as_value() == &*other.as_value()
+    }
+}
+impl std::cmp::Eq for Thunk {}
+
+impl std::cmp::PartialEq for TypeThunk {
+    fn eq(&self, other: &Self) -> bool {
+        self.to_value() == other.to_value()
+    }
+}
+impl std::cmp::Eq for TypeThunk {}
diff --git a/dhall/src/core/value.rs b/dhall/src/core/value.rs
new file mode 100644
index 0000000..28fcb3e
--- /dev/null
+++ b/dhall/src/core/value.rs
@@ -0,0 +1,627 @@
+use std::collections::BTreeMap;
+
+use dhall_proc_macros as dhall;
+use dhall_syntax::{
+    rc, Builtin, Const, ExprF, Integer, InterpolatedTextContents, Label,
+    Natural, V, X,
+};
+
+use crate::core::thunk::{Thunk, TypeThunk};
+use crate::phase::normalize::{
+    apply_builtin, normalize_one_layer, squash_textlit, OutputSubExpr,
+};
+use crate::phase::Typed;
+
+/// Stores a pair of variables: a normal one and if relevant one
+/// that corresponds to the alpha-normalized version of the first one.
+/// Equality is up to alpha-equivalence.
+#[derive(Debug, Clone, Eq)]
+pub(crate) struct AlphaVar {
+    normal: V<Label>,
+    alpha: Option<V<()>>,
+}
+
+// Exactly like a Label, but equality returns always true.
+// This is so that Value equality is exactly alpha-equivalence.
+#[derive(Debug, Clone, Eq)]
+pub(crate) struct AlphaLabel(Label);
+
+/// A semantic value. The invariants ensure this value represents a Weak-Head
+/// Normal Form (WHNF). This means that this first constructor is the first constructor of the
+/// final Normal Form (NF).
+/// This WHNF must be preserved by operations on `Value`s. In particular, `subst_shift` could break
+/// the invariants so need to be careful to reevaluate as needed.
+/// Subexpressions are Thunks, which are partially evaluated expressions that are normalized
+/// on-demand. When all the Thunks in a Value are at least in WHNF, and recursively so, then the
+/// Value is in NF. This is because WHNF ensures that we have the first constructor of the NF; so
+/// if we have the first constructor of the NF at all levels, we actually have the NF.
+/// Equality is up to alpha-equivalence (renaming of bound variables) and beta-equivalence
+/// (normalization). Equality will normalize only as needed.
+#[derive(Debug, Clone, PartialEq, Eq)]
+pub(crate) enum Value {
+    /// Closures
+    Lam(AlphaLabel, TypeThunk, Thunk),
+    Pi(AlphaLabel, TypeThunk, TypeThunk),
+    // Invariant: the evaluation must not be able to progress further.
+    AppliedBuiltin(Builtin, Vec<Thunk>),
+    /// `λ(x: a) -> Some x`
+    OptionalSomeClosure(TypeThunk),
+    /// `λ(x : a) -> λ(xs : List a) -> [ x ] # xs`
+    /// `λ(xs : List a) -> [ x ] # xs`
+    ListConsClosure(TypeThunk, Option<Thunk>),
+    /// `λ(x : Natural) -> x + 1`
+    NaturalSuccClosure,
+
+    Var(AlphaVar),
+    Const(Const),
+    BoolLit(bool),
+    NaturalLit(Natural),
+    IntegerLit(Integer),
+    EmptyOptionalLit(TypeThunk),
+    NEOptionalLit(Thunk),
+    EmptyListLit(TypeThunk),
+    NEListLit(Vec<Thunk>),
+    RecordLit(BTreeMap<Label, Thunk>),
+    RecordType(BTreeMap<Label, TypeThunk>),
+    UnionType(BTreeMap<Label, Option<TypeThunk>>),
+    UnionConstructor(Label, BTreeMap<Label, Option<TypeThunk>>),
+    UnionLit(Label, Thunk, BTreeMap<Label, Option<TypeThunk>>),
+    // Invariant: this must not contain interpolations that are themselves TextLits, and
+    // contiguous text values must be merged.
+    TextLit(Vec<InterpolatedTextContents<Thunk>>),
+    // Invariant: this must not contain a value captured by one of the variants above.
+    PartialExpr(ExprF<Thunk, Label, X>),
+}
+
+impl AlphaVar {
+    pub(crate) fn to_var(&self, alpha: bool) -> V<Label> {
+        match (alpha, &self.alpha) {
+            (true, Some(x)) => V("_".into(), x.1),
+            _ => self.normal.clone(),
+        }
+    }
+    pub(crate) fn from_var(normal: V<Label>) -> Self {
+        AlphaVar {
+            normal,
+            alpha: None,
+        }
+    }
+    pub(crate) fn shift(&self, delta: isize, var: &AlphaVar) -> Self {
+        AlphaVar {
+            normal: self.normal.shift(delta, &var.normal),
+            alpha: match (&self.alpha, &var.alpha) {
+                (Some(x), Some(v)) => Some(x.shift(delta, v)),
+                _ => None,
+            },
+        }
+    }
+}
+
+impl AlphaLabel {
+    fn to_label_maybe_alpha(&self, alpha: bool) -> Label {
+        if alpha {
+            "_".into()
+        } else {
+            self.to_label()
+        }
+    }
+    fn to_label(&self) -> Label {
+        self.clone().into()
+    }
+}
+
+impl Value {
+    pub(crate) fn into_thunk(self) -> Thunk {
+        Thunk::from_value(self)
+    }
+
+    /// Convert the value to a fully normalized syntactic expression
+    pub(crate) fn normalize_to_expr(&self) -> OutputSubExpr {
+        self.normalize_to_expr_maybe_alpha(false)
+    }
+    /// Convert the value to a fully normalized syntactic expression. Also alpha-normalize
+    /// if alpha is `true`
+    pub(crate) fn normalize_to_expr_maybe_alpha(
+        &self,
+        alpha: bool,
+    ) -> OutputSubExpr {
+        match self {
+            Value::Lam(x, t, e) => rc(ExprF::Lam(
+                x.to_label_maybe_alpha(alpha),
+                t.normalize_to_expr_maybe_alpha(alpha),
+                e.normalize_to_expr_maybe_alpha(alpha),
+            )),
+            Value::AppliedBuiltin(b, args) => {
+                let mut e = rc(ExprF::Builtin(*b));
+                for v in args {
+                    e = rc(ExprF::App(
+                        e,
+                        v.normalize_to_expr_maybe_alpha(alpha),
+                    ));
+                }
+                e
+            }
+            Value::OptionalSomeClosure(n) => {
+                let a = n.normalize_to_expr_maybe_alpha(alpha);
+                dhall::subexpr!(λ(x: a) -> Some x)
+            }
+            Value::ListConsClosure(a, None) => {
+                // Avoid accidental capture of the new `x` variable
+                let a1 = a.shift(1, &Label::from("x").into());
+                let a1 = a1.normalize_to_expr_maybe_alpha(alpha);
+                let a = a.normalize_to_expr_maybe_alpha(alpha);
+                dhall::subexpr!(λ(x : a) -> λ(xs : List a1) -> [ x ] # xs)
+            }
+            Value::ListConsClosure(n, Some(v)) => {
+                // Avoid accidental capture of the new `xs` variable
+                let v = v.shift(1, &Label::from("xs").into());
+                let v = v.normalize_to_expr_maybe_alpha(alpha);
+                let a = n.normalize_to_expr_maybe_alpha(alpha);
+                dhall::subexpr!(λ(xs : List a) -> [ v ] # xs)
+            }
+            Value::NaturalSuccClosure => {
+                dhall::subexpr!(λ(x : Natural) -> x + 1)
+            }
+            Value::Pi(x, t, e) => rc(ExprF::Pi(
+                x.to_label_maybe_alpha(alpha),
+                t.normalize_to_expr_maybe_alpha(alpha),
+                e.normalize_to_expr_maybe_alpha(alpha),
+            )),
+            Value::Var(v) => rc(ExprF::Var(v.to_var(alpha))),
+            Value::Const(c) => rc(ExprF::Const(*c)),
+            Value::BoolLit(b) => rc(ExprF::BoolLit(*b)),
+            Value::NaturalLit(n) => rc(ExprF::NaturalLit(*n)),
+            Value::IntegerLit(n) => rc(ExprF::IntegerLit(*n)),
+            Value::EmptyOptionalLit(n) => rc(ExprF::App(
+                rc(ExprF::Builtin(Builtin::OptionalNone)),
+                n.normalize_to_expr_maybe_alpha(alpha),
+            )),
+            Value::NEOptionalLit(n) => {
+                rc(ExprF::SomeLit(n.normalize_to_expr_maybe_alpha(alpha)))
+            }
+            Value::EmptyListLit(n) => {
+                rc(ExprF::EmptyListLit(n.normalize_to_expr_maybe_alpha(alpha)))
+            }
+            Value::NEListLit(elts) => rc(ExprF::NEListLit(
+                elts.into_iter()
+                    .map(|n| n.normalize_to_expr_maybe_alpha(alpha))
+                    .collect(),
+            )),
+            Value::RecordLit(kvs) => rc(ExprF::RecordLit(
+                kvs.iter()
+                    .map(|(k, v)| {
+                        (k.clone(), v.normalize_to_expr_maybe_alpha(alpha))
+                    })
+                    .collect(),
+            )),
+            Value::RecordType(kts) => rc(ExprF::RecordType(
+                kts.iter()
+                    .map(|(k, v)| {
+                        (k.clone(), v.normalize_to_expr_maybe_alpha(alpha))
+                    })
+                    .collect(),
+            )),
+            Value::UnionType(kts) => rc(ExprF::UnionType(
+                kts.iter()
+                    .map(|(k, v)| {
+                        (
+                            k.clone(),
+                            v.as_ref().map(|v| {
+                                v.normalize_to_expr_maybe_alpha(alpha)
+                            }),
+                        )
+                    })
+                    .collect(),
+            )),
+            Value::UnionConstructor(l, kts) => {
+                let kts = kts
+                    .iter()
+                    .map(|(k, v)| {
+                        (
+                            k.clone(),
+                            v.as_ref().map(|v| {
+                                v.normalize_to_expr_maybe_alpha(alpha)
+                            }),
+                        )
+                    })
+                    .collect();
+                rc(ExprF::Field(rc(ExprF::UnionType(kts)), l.clone()))
+            }
+            Value::UnionLit(l, v, kts) => rc(ExprF::UnionLit(
+                l.clone(),
+                v.normalize_to_expr_maybe_alpha(alpha),
+                kts.iter()
+                    .map(|(k, v)| {
+                        (
+                            k.clone(),
+                            v.as_ref().map(|v| {
+                                v.normalize_to_expr_maybe_alpha(alpha)
+                            }),
+                        )
+                    })
+                    .collect(),
+            )),
+            Value::TextLit(elts) => {
+                use InterpolatedTextContents::{Expr, Text};
+                rc(ExprF::TextLit(
+                    elts.iter()
+                        .map(|contents| match contents {
+                            Expr(e) => {
+                                Expr(e.normalize_to_expr_maybe_alpha(alpha))
+                            }
+                            Text(s) => Text(s.clone()),
+                        })
+                        .collect(),
+                ))
+            }
+            Value::PartialExpr(e) => {
+                rc(e.map_ref_simple(|v| v.normalize_to_expr_maybe_alpha(alpha)))
+            }
+        }
+    }
+
+    // Deprecated
+    pub(crate) fn normalize(&self) -> Value {
+        let mut v = self.clone();
+        v.normalize_mut();
+        v
+    }
+
+    pub(crate) fn normalize_mut(&mut self) {
+        match self {
+            Value::NaturalSuccClosure
+            | Value::Var(_)
+            | Value::Const(_)
+            | Value::BoolLit(_)
+            | Value::NaturalLit(_)
+            | Value::IntegerLit(_) => {}
+
+            Value::EmptyOptionalLit(tth)
+            | Value::OptionalSomeClosure(tth)
+            | Value::EmptyListLit(tth) => {
+                tth.normalize_mut();
+            }
+
+            Value::NEOptionalLit(th) => {
+                th.normalize_mut();
+            }
+            Value::Lam(_, t, e) => {
+                t.normalize_mut();
+                e.normalize_mut();
+            }
+            Value::Pi(_, t, e) => {
+                t.normalize_mut();
+                e.normalize_mut();
+            }
+            Value::AppliedBuiltin(_, args) => {
+                for x in args.iter_mut() {
+                    x.normalize_mut();
+                }
+            }
+            Value::ListConsClosure(t, v) => {
+                t.normalize_mut();
+                for x in v.iter_mut() {
+                    x.normalize_mut();
+                }
+            }
+            Value::NEListLit(elts) => {
+                for x in elts.iter_mut() {
+                    x.normalize_mut();
+                }
+            }
+            Value::RecordLit(kvs) => {
+                for x in kvs.values_mut() {
+                    x.normalize_mut();
+                }
+            }
+            Value::RecordType(kvs) => {
+                for x in kvs.values_mut() {
+                    x.normalize_mut();
+                }
+            }
+            Value::UnionType(kts) | Value::UnionConstructor(_, kts) => {
+                for x in kts.values_mut().flat_map(|opt| opt) {
+                    x.normalize_mut();
+                }
+            }
+            Value::UnionLit(_, v, kts) => {
+                v.normalize_mut();
+                for x in kts.values_mut().flat_map(|opt| opt) {
+                    x.normalize_mut();
+                }
+            }
+            Value::TextLit(elts) => {
+                for x in elts.iter_mut() {
+                    use InterpolatedTextContents::{Expr, Text};
+                    match x {
+                        Expr(n) => n.normalize_mut(),
+                        Text(_) => {}
+                    }
+                }
+            }
+            Value::PartialExpr(e) => {
+                // TODO: need map_mut_simple
+                e.map_ref_simple(|v| {
+                    v.normalize_nf();
+                });
+            }
+        }
+    }
+
+    /// Apply to a value
+    pub(crate) fn app(self, val: Value) -> Value {
+        self.app_val(val)
+    }
+
+    /// Apply to a value
+    pub(crate) fn app_val(self, val: Value) -> Value {
+        self.app_thunk(val.into_thunk())
+    }
+
+    /// Apply to a thunk
+    pub(crate) fn app_thunk(self, th: Thunk) -> Value {
+        Thunk::from_value(self).app_thunk(th)
+    }
+
+    pub(crate) fn from_builtin(b: Builtin) -> Value {
+        Value::AppliedBuiltin(b, vec![])
+    }
+
+    pub(crate) fn shift(&self, delta: isize, var: &AlphaVar) -> Self {
+        match self {
+            Value::Lam(x, t, e) => Value::Lam(
+                x.clone(),
+                t.shift(delta, var),
+                e.shift(delta, &var.shift(1, &x.into())),
+            ),
+            Value::AppliedBuiltin(b, args) => Value::AppliedBuiltin(
+                *b,
+                args.iter().map(|v| v.shift(delta, var)).collect(),
+            ),
+            Value::NaturalSuccClosure => Value::NaturalSuccClosure,
+            Value::OptionalSomeClosure(tth) => {
+                Value::OptionalSomeClosure(tth.shift(delta, var))
+            }
+            Value::ListConsClosure(t, v) => Value::ListConsClosure(
+                t.shift(delta, var),
+                v.as_ref().map(|v| v.shift(delta, var)),
+            ),
+            Value::Pi(x, t, e) => Value::Pi(
+                x.clone(),
+                t.shift(delta, var),
+                e.shift(delta, &var.shift(1, &x.into())),
+            ),
+            Value::Var(v) => Value::Var(v.shift(delta, var)),
+            Value::Const(c) => Value::Const(*c),
+            Value::BoolLit(b) => Value::BoolLit(*b),
+            Value::NaturalLit(n) => Value::NaturalLit(*n),
+            Value::IntegerLit(n) => Value::IntegerLit(*n),
+            Value::EmptyOptionalLit(tth) => {
+                Value::EmptyOptionalLit(tth.shift(delta, var))
+            }
+            Value::NEOptionalLit(th) => {
+                Value::NEOptionalLit(th.shift(delta, var))
+            }
+            Value::EmptyListLit(tth) => {
+                Value::EmptyListLit(tth.shift(delta, var))
+            }
+            Value::NEListLit(elts) => Value::NEListLit(
+                elts.iter().map(|v| v.shift(delta, var)).collect(),
+            ),
+            Value::RecordLit(kvs) => Value::RecordLit(
+                kvs.iter()
+                    .map(|(k, v)| (k.clone(), v.shift(delta, var)))
+                    .collect(),
+            ),
+            Value::RecordType(kvs) => Value::RecordType(
+                kvs.iter()
+                    .map(|(k, v)| (k.clone(), v.shift(delta, var)))
+                    .collect(),
+            ),
+            Value::UnionType(kts) => Value::UnionType(
+                kts.iter()
+                    .map(|(k, v)| {
+                        (k.clone(), v.as_ref().map(|v| v.shift(delta, var)))
+                    })
+                    .collect(),
+            ),
+            Value::UnionConstructor(x, kts) => Value::UnionConstructor(
+                x.clone(),
+                kts.iter()
+                    .map(|(k, v)| {
+                        (k.clone(), v.as_ref().map(|v| v.shift(delta, var)))
+                    })
+                    .collect(),
+            ),
+            Value::UnionLit(x, v, kts) => Value::UnionLit(
+                x.clone(),
+                v.shift(delta, var),
+                kts.iter()
+                    .map(|(k, v)| {
+                        (k.clone(), v.as_ref().map(|v| v.shift(delta, var)))
+                    })
+                    .collect(),
+            ),
+            Value::TextLit(elts) => Value::TextLit(
+                elts.iter()
+                    .map(|contents| {
+                        use InterpolatedTextContents::{Expr, Text};
+                        match contents {
+                            Expr(th) => Expr(th.shift(delta, var)),
+                            Text(s) => Text(s.clone()),
+                        }
+                    })
+                    .collect(),
+            ),
+            Value::PartialExpr(e) => {
+                Value::PartialExpr(e.map_ref_with_special_handling_of_binders(
+                    |v| v.shift(delta, var),
+                    |x, v| v.shift(delta, &var.shift(1, &x.into())),
+                    X::clone,
+                    Label::clone,
+                ))
+            }
+        }
+    }
+
+    pub(crate) fn subst_shift(&self, var: &AlphaVar, val: &Typed) -> Self {
+        match self {
+            // Retry normalizing since substituting may allow progress
+            Value::AppliedBuiltin(b, args) => apply_builtin(
+                *b,
+                args.iter().map(|v| v.subst_shift(var, val)).collect(),
+            ),
+            // Retry normalizing since substituting may allow progress
+            Value::PartialExpr(e) => {
+                normalize_one_layer(e.map_ref_with_special_handling_of_binders(
+                    |v| v.subst_shift(var, val),
+                    |x, v| {
+                        v.subst_shift(
+                            &var.shift(1, &x.into()),
+                            &val.shift(1, &x.into()),
+                        )
+                    },
+                    X::clone,
+                    Label::clone,
+                ))
+            }
+            // Retry normalizing since substituting may allow progress
+            Value::TextLit(elts) => {
+                Value::TextLit(squash_textlit(elts.iter().map(|contents| {
+                    use InterpolatedTextContents::{Expr, Text};
+                    match contents {
+                        Expr(th) => Expr(th.subst_shift(var, val)),
+                        Text(s) => Text(s.clone()),
+                    }
+                })))
+            }
+            Value::Lam(x, t, e) => Value::Lam(
+                x.clone(),
+                t.subst_shift(var, val),
+                e.subst_shift(
+                    &var.shift(1, &x.into()),
+                    &val.shift(1, &x.into()),
+                ),
+            ),
+            Value::NaturalSuccClosure => Value::NaturalSuccClosure,
+            Value::OptionalSomeClosure(tth) => {
+                Value::OptionalSomeClosure(tth.subst_shift(var, val))
+            }
+            Value::ListConsClosure(t, v) => Value::ListConsClosure(
+                t.subst_shift(var, val),
+                v.as_ref().map(|v| v.subst_shift(var, val)),
+            ),
+            Value::Pi(x, t, e) => Value::Pi(
+                x.clone(),
+                t.subst_shift(var, val),
+                e.subst_shift(
+                    &var.shift(1, &x.into()),
+                    &val.shift(1, &x.into()),
+                ),
+            ),
+            Value::Var(v) if v == var => val.to_value().clone(),
+            Value::Var(v) => Value::Var(v.shift(-1, var)),
+            Value::Const(c) => Value::Const(*c),
+            Value::BoolLit(b) => Value::BoolLit(*b),
+            Value::NaturalLit(n) => Value::NaturalLit(*n),
+            Value::IntegerLit(n) => Value::IntegerLit(*n),
+            Value::EmptyOptionalLit(tth) => {
+                Value::EmptyOptionalLit(tth.subst_shift(var, val))
+            }
+            Value::NEOptionalLit(th) => {
+                Value::NEOptionalLit(th.subst_shift(var, val))
+            }
+            Value::EmptyListLit(tth) => {
+                Value::EmptyListLit(tth.subst_shift(var, val))
+            }
+            Value::NEListLit(elts) => Value::NEListLit(
+                elts.iter().map(|v| v.subst_shift(var, val)).collect(),
+            ),
+            Value::RecordLit(kvs) => Value::RecordLit(
+                kvs.iter()
+                    .map(|(k, v)| (k.clone(), v.subst_shift(var, val)))
+                    .collect(),
+            ),
+            Value::RecordType(kvs) => Value::RecordType(
+                kvs.iter()
+                    .map(|(k, v)| (k.clone(), v.subst_shift(var, val)))
+                    .collect(),
+            ),
+            Value::UnionType(kts) => Value::UnionType(
+                kts.iter()
+                    .map(|(k, v)| {
+                        (k.clone(), v.as_ref().map(|v| v.subst_shift(var, val)))
+                    })
+                    .collect(),
+            ),
+            Value::UnionConstructor(x, kts) => Value::UnionConstructor(
+                x.clone(),
+                kts.iter()
+                    .map(|(k, v)| {
+                        (k.clone(), v.as_ref().map(|v| v.subst_shift(var, val)))
+                    })
+                    .collect(),
+            ),
+            Value::UnionLit(x, v, kts) => Value::UnionLit(
+                x.clone(),
+                v.subst_shift(var, val),
+                kts.iter()
+                    .map(|(k, v)| {
+                        (k.clone(), v.as_ref().map(|v| v.subst_shift(var, val)))
+                    })
+                    .collect(),
+            ),
+        }
+    }
+}
+
+impl std::cmp::PartialEq for AlphaVar {
+    fn eq(&self, other: &Self) -> bool {
+        match (&self.alpha, &other.alpha) {
+            (Some(x), Some(y)) => x == y,
+            (None, None) => self.normal == other.normal,
+            _ => false,
+        }
+    }
+}
+impl std::cmp::PartialEq for AlphaLabel {
+    fn eq(&self, _other: &Self) -> bool {
+        true
+    }
+}
+
+impl From<Label> for AlphaVar {
+    fn from(x: Label) -> AlphaVar {
+        AlphaVar {
+            normal: V(x, 0),
+            alpha: Some(V((), 0)),
+        }
+    }
+}
+impl<'a> From<&'a Label> for AlphaVar {
+    fn from(x: &'a Label) -> AlphaVar {
+        x.clone().into()
+    }
+}
+impl From<AlphaLabel> for AlphaVar {
+    fn from(x: AlphaLabel) -> AlphaVar {
+        let l: Label = x.into();
+        l.into()
+    }
+}
+impl<'a> From<&'a AlphaLabel> for AlphaVar {
+    fn from(x: &'a AlphaLabel) -> AlphaVar {
+        x.clone().into()
+    }
+}
+
+impl From<Label> for AlphaLabel {
+    fn from(x: Label) -> AlphaLabel {
+        AlphaLabel(x)
+    }
+}
+impl From<AlphaLabel> for Label {
+    fn from(x: AlphaLabel) -> Label {
+        x.0
+    }
+}
diff --git a/dhall/src/error.rs b/dhall/src/error.rs
deleted file mode 100644
index 6ed0bfb..0000000
--- a/dhall/src/error.rs
+++ /dev/null
@@ -1,52 +0,0 @@
-pub type Result<T> = std::result::Result<T, Error>;
-
-#[derive(Debug)]
-#[non_exhaustive]
-pub enum Error {
-    IO(std::io::Error),
-    Parse(dhall_syntax::ParseError),
-    Decode(crate::binary::DecodeError),
-    Resolve(crate::imports::ImportError),
-    Typecheck(crate::typecheck::TypeError),
-    Deserialize(String),
-}
-
-impl std::fmt::Display for Error {
-    fn fmt(&self, f: &mut std::fmt::Formatter) -> std::fmt::Result {
-        match self {
-            Error::IO(err) => write!(f, "{}", err),
-            Error::Parse(err) => write!(f, "{}", err),
-            Error::Decode(err) => write!(f, "{:?}", err),
-            Error::Resolve(err) => write!(f, "{:?}", err),
-            Error::Typecheck(err) => write!(f, "{:?}", err),
-            Error::Deserialize(err) => write!(f, "{}", err),
-        }
-    }
-}
-
-impl std::error::Error for Error {}
-impl From<std::io::Error> for Error {
-    fn from(err: std::io::Error) -> Error {
-        Error::IO(err)
-    }
-}
-impl From<dhall_syntax::ParseError> for Error {
-    fn from(err: dhall_syntax::ParseError) -> Error {
-        Error::Parse(err)
-    }
-}
-impl From<crate::binary::DecodeError> for Error {
-    fn from(err: crate::binary::DecodeError) -> Error {
-        Error::Decode(err)
-    }
-}
-impl From<crate::imports::ImportError> for Error {
-    fn from(err: crate::imports::ImportError) -> Error {
-        Error::Resolve(err)
-    }
-}
-impl From<crate::typecheck::TypeError> for Error {
-    fn from(err: crate::typecheck::TypeError) -> Error {
-        Error::Typecheck(err)
-    }
-}
diff --git a/dhall/src/error/mod.rs b/dhall/src/error/mod.rs
new file mode 100644
index 0000000..f84d078
--- /dev/null
+++ b/dhall/src/error/mod.rs
@@ -0,0 +1,169 @@
+use std::io::Error as IOError;
+
+use dhall_syntax::{BinOp, Import, Label, ParseError, V};
+
+use crate::core::context::TypecheckContext;
+use crate::phase::resolve::ImportStack;
+use crate::phase::{Normalized, Type, Typed};
+
+pub type Result<T> = std::result::Result<T, Error>;
+
+#[derive(Debug)]
+#[non_exhaustive]
+pub enum Error {
+    IO(IOError),
+    Parse(ParseError),
+    Decode(DecodeError),
+    Resolve(ImportError),
+    Typecheck(TypeError),
+    Deserialize(String),
+}
+
+#[derive(Debug)]
+pub enum ImportError {
+    Recursive(Import, Box<Error>),
+    UnexpectedImport(Import),
+    ImportCycle(ImportStack, Import),
+}
+
+#[derive(Debug)]
+pub enum DecodeError {
+    CBORError(serde_cbor::error::Error),
+    WrongFormatError(String),
+}
+
+/// A structured type error that includes context
+#[derive(Debug)]
+pub struct TypeError {
+    type_message: TypeMessage,
+    context: TypecheckContext,
+}
+
+/// The specific type error
+#[derive(Debug)]
+pub(crate) enum TypeMessage {
+    UnboundVariable(V<Label>),
+    InvalidInputType(Normalized),
+    InvalidOutputType(Normalized),
+    NotAFunction(Typed),
+    TypeMismatch(Typed, Normalized, Typed),
+    AnnotMismatch(Typed, Normalized),
+    Untyped,
+    InvalidListElement(usize, Normalized, Typed),
+    InvalidListType(Normalized),
+    InvalidOptionalType(Normalized),
+    InvalidPredicate(Typed),
+    IfBranchMismatch(Typed, Typed),
+    IfBranchMustBeTerm(bool, Typed),
+    InvalidFieldType(Label, Type),
+    NotARecord(Label, Normalized),
+    MissingRecordField(Label, Typed),
+    MissingUnionField(Label, Normalized),
+    BinOpTypeMismatch(BinOp, Typed),
+    NoDependentTypes(Normalized, Normalized),
+    InvalidTextInterpolation(Typed),
+    Sort,
+    Unimplemented,
+}
+
+impl TypeError {
+    pub(crate) fn new(
+        context: &TypecheckContext,
+        type_message: TypeMessage,
+    ) -> Self {
+        TypeError {
+            context: context.clone(),
+            type_message,
+        }
+    }
+}
+
+impl From<TypeError> for std::option::NoneError {
+    fn from(_: TypeError) -> std::option::NoneError {
+        std::option::NoneError
+    }
+}
+
+impl std::error::Error for TypeMessage {
+    fn description(&self) -> &str {
+        use TypeMessage::*;
+        match *self {
+            // UnboundVariable => "Unbound variable",
+            InvalidInputType(_) => "Invalid function input",
+            InvalidOutputType(_) => "Invalid function output",
+            NotAFunction(_) => "Not a function",
+            TypeMismatch(_, _, _) => "Wrong type of function argument",
+            _ => "Unhandled error",
+        }
+    }
+}
+
+impl std::fmt::Display for TypeMessage {
+    fn fmt(&self, f: &mut std::fmt::Formatter) -> std::fmt::Result {
+        match self {
+            // UnboundVariable(_) => {
+            //     f.write_str(include_str!("errors/UnboundVariable.txt"))
+            // }
+            // TypeMismatch(e0, e1, e2) => {
+            //     let template = include_str!("errors/TypeMismatch.txt");
+            //     let s = template
+            //         .replace("$txt0", &format!("{}", e0.as_expr()))
+            //         .replace("$txt1", &format!("{}", e1.as_expr()))
+            //         .replace("$txt2", &format!("{}", e2.as_expr()))
+            //         .replace(
+            //             "$txt3",
+            //             &format!(
+            //                 "{}",
+            //                 e2.get_type()
+            //                     .unwrap()
+            //                     .as_normalized()
+            //                     .unwrap()
+            //                     .as_expr()
+            //             ),
+            //         );
+            //     f.write_str(&s)
+            // }
+            _ => f.write_str("Unhandled error message"),
+        }
+    }
+}
+
+impl std::fmt::Display for Error {
+    fn fmt(&self, f: &mut std::fmt::Formatter) -> std::fmt::Result {
+        match self {
+            Error::IO(err) => write!(f, "{}", err),
+            Error::Parse(err) => write!(f, "{}", err),
+            Error::Decode(err) => write!(f, "{:?}", err),
+            Error::Resolve(err) => write!(f, "{:?}", err),
+            Error::Typecheck(err) => write!(f, "{:?}", err),
+            Error::Deserialize(err) => write!(f, "{}", err),
+        }
+    }
+}
+
+impl std::error::Error for Error {}
+impl From<IOError> for Error {
+    fn from(err: IOError) -> Error {
+        Error::IO(err)
+    }
+}
+impl From<ParseError> for Error {
+    fn from(err: ParseError) -> Error {
+        Error::Parse(err)
+    }
+}
+impl From<DecodeError> for Error {
+    fn from(err: DecodeError) -> Error {
+        Error::Decode(err)
+    }
+}
+impl From<ImportError> for Error {
+    fn from(err: ImportError) -> Error {
+        Error::Resolve(err)
+    }
+}
+impl From<TypeError> for Error {
+    fn from(err: TypeError) -> Error {
+        Error::Typecheck(err)
+    }
+}
diff --git a/dhall/src/errors/AnnotMismatch.txt b/dhall/src/error/text/AnnotMismatch.txt
index 4904bf8..4904bf8 100644
--- a/dhall/src/errors/AnnotMismatch.txt
+++ b/dhall/src/error/text/AnnotMismatch.txt
diff --git a/dhall/src/errors/CantTextAppend.txt b/dhall/src/error/text/CantTextAppend.txt
index 26b9ceb..26b9ceb 100644
--- a/dhall/src/errors/CantTextAppend.txt
+++ b/dhall/src/error/text/CantTextAppend.txt
diff --git a/dhall/src/errors/DuplicateAlternative.txt b/dhall/src/error/text/DuplicateAlternative.txt
index 077f8aa..077f8aa 100644
--- a/dhall/src/errors/DuplicateAlternative.txt
+++ b/dhall/src/error/text/DuplicateAlternative.txt
diff --git a/dhall/src/errors/FieldCollision.txt b/dhall/src/error/text/FieldCollision.txt
index 2b2d260..2b2d260 100644
--- a/dhall/src/errors/FieldCollision.txt
+++ b/dhall/src/error/text/FieldCollision.txt
diff --git a/dhall/src/errors/HandlerInputTypeMismatch.txt b/dhall/src/error/text/HandlerInputTypeMismatch.txt
index 7d3525b..7d3525b 100644
--- a/dhall/src/errors/HandlerInputTypeMismatch.txt
+++ b/dhall/src/error/text/HandlerInputTypeMismatch.txt
diff --git a/dhall/src/errors/HandlerNotAFunction.txt b/dhall/src/error/text/HandlerNotAFunction.txt
index ff87443..ff87443 100644
--- a/dhall/src/errors/HandlerNotAFunction.txt
+++ b/dhall/src/error/text/HandlerNotAFunction.txt
diff --git a/dhall/src/errors/HandlerOutputTypeMismatch.txt b/dhall/src/error/text/HandlerOutputTypeMismatch.txt
index f359459..f359459 100644
--- a/dhall/src/errors/HandlerOutputTypeMismatch.txt
+++ b/dhall/src/error/text/HandlerOutputTypeMismatch.txt
diff --git a/dhall/src/errors/IfBranchMismatch.txt b/dhall/src/error/text/IfBranchMismatch.txt
index a95b130..a95b130 100644
--- a/dhall/src/errors/IfBranchMismatch.txt
+++ b/dhall/src/error/text/IfBranchMismatch.txt
diff --git a/dhall/src/errors/IfBranchMustBeTerm.txt b/dhall/src/error/text/IfBranchMustBeTerm.txt
index 4c15881..4c15881 100644
--- a/dhall/src/errors/IfBranchMustBeTerm.txt
+++ b/dhall/src/error/text/IfBranchMustBeTerm.txt
diff --git a/dhall/src/errors/InvalidAlterantive.txt b/dhall/src/error/text/InvalidAlterantive.txt
index 391fc3a..391fc3a 100644
--- a/dhall/src/errors/InvalidAlterantive.txt
+++ b/dhall/src/error/text/InvalidAlterantive.txt
diff --git a/dhall/src/errors/InvalidAlterantiveType.txt b/dhall/src/error/text/InvalidAlterantiveType.txt
index f5dadef..f5dadef 100644
--- a/dhall/src/errors/InvalidAlterantiveType.txt
+++ b/dhall/src/error/text/InvalidAlterantiveType.txt
diff --git a/dhall/src/errors/InvalidField.txt b/dhall/src/error/text/InvalidField.txt
index bfbf106..bfbf106 100644
--- a/dhall/src/errors/InvalidField.txt
+++ b/dhall/src/error/text/InvalidField.txt
diff --git a/dhall/src/errors/InvalidFieldType.txt b/dhall/src/error/text/InvalidFieldType.txt
index 4f76a64..4f76a64 100644
--- a/dhall/src/errors/InvalidFieldType.txt
+++ b/dhall/src/error/text/InvalidFieldType.txt
diff --git a/dhall/src/errors/InvalidInputType.txt b/dhall/src/error/text/InvalidInputType.txt
index eabafa4..eabafa4 100644
--- a/dhall/src/errors/InvalidInputType.txt
+++ b/dhall/src/error/text/InvalidInputType.txt
diff --git a/dhall/src/errors/InvalidListElement.txt b/dhall/src/error/text/InvalidListElement.txt
index 59db7b7..59db7b7 100644
--- a/dhall/src/errors/InvalidListElement.txt
+++ b/dhall/src/error/text/InvalidListElement.txt
diff --git a/dhall/src/errors/InvalidListType.txt b/dhall/src/error/text/InvalidListType.txt
index 676647e..676647e 100644
--- a/dhall/src/errors/InvalidListType.txt
+++ b/dhall/src/error/text/InvalidListType.txt
diff --git a/dhall/src/errors/InvalidOptionType.txt b/dhall/src/error/text/InvalidOptionType.txt
index 3bc81de..3bc81de 100644
--- a/dhall/src/errors/InvalidOptionType.txt
+++ b/dhall/src/error/text/InvalidOptionType.txt
diff --git a/dhall/src/errors/InvalidOptionalElement.txt b/dhall/src/error/text/InvalidOptionalElement.txt
index 0254220..0254220 100644
--- a/dhall/src/errors/InvalidOptionalElement.txt
+++ b/dhall/src/error/text/InvalidOptionalElement.txt
diff --git a/dhall/src/errors/InvalidOptionalLiteral.txt b/dhall/src/error/text/InvalidOptionalLiteral.txt
index 41c0fdc..41c0fdc 100644
--- a/dhall/src/errors/InvalidOptionalLiteral.txt
+++ b/dhall/src/error/text/InvalidOptionalLiteral.txt
diff --git a/dhall/src/errors/InvalidOutputType.txt b/dhall/src/error/text/InvalidOutputType.txt
index dd2695d..dd2695d 100644
--- a/dhall/src/errors/InvalidOutputType.txt
+++ b/dhall/src/error/text/InvalidOutputType.txt
diff --git a/dhall/src/errors/InvalidPredicate.txt b/dhall/src/error/text/InvalidPredicate.txt
index 4c15881..4c15881 100644
--- a/dhall/src/errors/InvalidPredicate.txt
+++ b/dhall/src/error/text/InvalidPredicate.txt
diff --git a/dhall/src/errors/MissingField.txt b/dhall/src/error/text/MissingField.txt
index de14a33..de14a33 100644
--- a/dhall/src/errors/MissingField.txt
+++ b/dhall/src/error/text/MissingField.txt
diff --git a/dhall/src/errors/MissingHandler.txt b/dhall/src/error/text/MissingHandler.txt
index 433445e..433445e 100644
--- a/dhall/src/errors/MissingHandler.txt
+++ b/dhall/src/error/text/MissingHandler.txt
diff --git a/dhall/src/errors/MustCombineARecord.txt b/dhall/src/error/text/MustCombineARecord.txt
index 141b969..141b969 100644
--- a/dhall/src/errors/MustCombineARecord.txt
+++ b/dhall/src/error/text/MustCombineARecord.txt
diff --git a/dhall/src/errors/MustMergeARecord.txt b/dhall/src/error/text/MustMergeARecord.txt
index 79094bd..79094bd 100644
--- a/dhall/src/errors/MustMergeARecord.txt
+++ b/dhall/src/error/text/MustMergeARecord.txt
diff --git a/dhall/src/errors/MustMergeUnion.txt b/dhall/src/error/text/MustMergeUnion.txt
index 68df70c..68df70c 100644
--- a/dhall/src/errors/MustMergeUnion.txt
+++ b/dhall/src/error/text/MustMergeUnion.txt
diff --git a/dhall/src/errors/NoDependentLet.txt b/dhall/src/error/text/NoDependentLet.txt
index fdc65b4..fdc65b4 100644
--- a/dhall/src/errors/NoDependentLet.txt
+++ b/dhall/src/error/text/NoDependentLet.txt
diff --git a/dhall/src/errors/NoDependentTypes.txt b/dhall/src/error/text/NoDependentTypes.txt
index 435bdcb..435bdcb 100644
--- a/dhall/src/errors/NoDependentTypes.txt
+++ b/dhall/src/error/text/NoDependentTypes.txt
diff --git a/dhall/src/errors/NotAFunction.txt b/dhall/src/error/text/NotAFunction.txt
index dd2695d..dd2695d 100644
--- a/dhall/src/errors/NotAFunction.txt
+++ b/dhall/src/error/text/NotAFunction.txt
diff --git a/dhall/src/errors/NotARecord.txt b/dhall/src/error/text/NotARecord.txt
index e0eebc8..e0eebc8 100644
--- a/dhall/src/errors/NotARecord.txt
+++ b/dhall/src/error/text/NotARecord.txt
diff --git a/dhall/src/errors/TypeMismatch.txt b/dhall/src/error/text/TypeMismatch.txt
index 4904bf8..4904bf8 100644
--- a/dhall/src/errors/TypeMismatch.txt
+++ b/dhall/src/error/text/TypeMismatch.txt
diff --git a/dhall/src/errors/UnboundVariable.txt b/dhall/src/error/text/UnboundVariable.txt
index bd7d483..bd7d483 100644
--- a/dhall/src/errors/UnboundVariable.txt
+++ b/dhall/src/error/text/UnboundVariable.txt
diff --git a/dhall/src/errors/Untyped.txt b/dhall/src/error/text/Untyped.txt
index 4904bf8..4904bf8 100644
--- a/dhall/src/errors/Untyped.txt
+++ b/dhall/src/error/text/Untyped.txt
diff --git a/dhall/src/errors/UnusedHandler.txt b/dhall/src/error/text/UnusedHandler.txt
index 2e46a12..2e46a12 100644
--- a/dhall/src/errors/UnusedHandler.txt
+++ b/dhall/src/error/text/UnusedHandler.txt
diff --git a/dhall/src/expr.rs b/dhall/src/expr.rs
deleted file mode 100644
index 7dbbf1c..0000000
--- a/dhall/src/expr.rs
+++ /dev/null
@@ -1,244 +0,0 @@
-use crate::imports::ImportRoot;
-use crate::normalize::{Thunk, Value};
-use dhall_syntax::*;
-
-macro_rules! derive_other_traits {
-    ($ty:ident) => {
-        impl std::cmp::PartialEq for $ty {
-            fn eq(&self, other: &Self) -> bool {
-                self.0 == other.0
-            }
-        }
-
-        impl std::cmp::Eq for $ty {}
-
-        impl std::fmt::Display for $ty {
-            fn fmt(
-                &self,
-                f: &mut std::fmt::Formatter,
-            ) -> Result<(), std::fmt::Error> {
-                self.0.fmt(f)
-            }
-        }
-    };
-}
-
-#[derive(Debug, Clone)]
-pub(crate) struct Parsed(
-    pub(crate) SubExpr<Span, Import>,
-    pub(crate) ImportRoot,
-);
-derive_other_traits!(Parsed);
-
-#[derive(Debug, Clone)]
-pub(crate) struct Resolved(pub(crate) SubExpr<Span, Normalized>);
-derive_other_traits!(Resolved);
-
-pub(crate) use self::typed::TypedInternal;
-
-#[derive(Debug, Clone)]
-pub(crate) struct Typed(pub(crate) TypedInternal);
-
-#[derive(Debug, Clone)]
-pub(crate) struct Normalized(pub(crate) TypedInternal);
-
-impl std::cmp::PartialEq for Normalized {
-    fn eq(&self, other: &Self) -> bool {
-        self.0 == other.0
-    }
-}
-
-impl std::cmp::Eq for Normalized {}
-
-impl std::fmt::Display for Normalized {
-    fn fmt(&self, f: &mut std::fmt::Formatter) -> Result<(), std::fmt::Error> {
-        self.to_expr().fmt(f)
-    }
-}
-
-mod typed {
-    use super::{Type, Typed};
-    use crate::normalize::{AlphaVar, Thunk, Value};
-    use crate::typecheck::{
-        TypeError, TypeInternal, TypeMessage, TypecheckContext,
-    };
-    use dhall_syntax::{Const, SubExpr, X};
-    use std::borrow::Cow;
-
-    #[derive(Debug, Clone)]
-    pub(crate) enum TypedInternal {
-        // The `Sort` higher-kinded type doesn't have a type
-        Sort,
-        // Any other value, along with its type
-        Value(Thunk, Option<Type>),
-    }
-
-    impl TypedInternal {
-        pub(crate) fn from_thunk_and_type(th: Thunk, t: Type) -> Self {
-            TypedInternal::Value(th, Some(t))
-        }
-
-        pub(crate) fn from_thunk_untyped(th: Thunk) -> Self {
-            TypedInternal::Value(th, None)
-        }
-
-        // TODO: Avoid cloning if possible
-        pub(crate) fn to_value(&self) -> Value {
-            match self {
-                TypedInternal::Value(th, _) => th.to_value(),
-                TypedInternal::Sort => Value::Const(Const::Sort),
-            }
-        }
-
-        pub(crate) fn to_expr(&self) -> SubExpr<X, X> {
-            self.to_value().normalize_to_expr()
-        }
-
-        pub(crate) fn to_expr_alpha(&self) -> SubExpr<X, X> {
-            self.to_value().normalize_to_expr_maybe_alpha(true)
-        }
-
-        pub(crate) fn to_thunk(&self) -> Thunk {
-            match self {
-                TypedInternal::Value(th, _) => th.clone(),
-                TypedInternal::Sort => {
-                    Thunk::from_value(Value::Const(Const::Sort))
-                }
-            }
-        }
-
-        pub(crate) fn to_type(&self) -> Type {
-            match self {
-                TypedInternal::Sort => Type(TypeInternal::Const(Const::Sort)),
-                TypedInternal::Value(th, _) => match &*th.as_value() {
-                    Value::Const(c) => Type(TypeInternal::Const(*c)),
-                    _ => {
-                        Type(TypeInternal::Typed(Box::new(Typed(self.clone()))))
-                    }
-                },
-            }
-        }
-
-        pub(crate) fn get_type(&self) -> Result<Cow<'_, Type>, TypeError> {
-            match self {
-                TypedInternal::Value(_, Some(t)) => Ok(Cow::Borrowed(t)),
-                TypedInternal::Value(_, None) => Err(TypeError::new(
-                    &TypecheckContext::new(),
-                    TypeMessage::Untyped,
-                )),
-                TypedInternal::Sort => Err(TypeError::new(
-                    &TypecheckContext::new(),
-                    TypeMessage::Sort,
-                )),
-            }
-        }
-
-        pub(crate) fn shift(&self, delta: isize, var: &AlphaVar) -> Self {
-            match self {
-                TypedInternal::Value(th, t) => TypedInternal::Value(
-                    th.shift(delta, var),
-                    t.as_ref().map(|x| x.shift(delta, var)),
-                ),
-                TypedInternal::Sort => TypedInternal::Sort,
-            }
-        }
-
-        pub(crate) fn subst_shift(&self, var: &AlphaVar, val: &Typed) -> Self {
-            match self {
-                TypedInternal::Value(th, t) => TypedInternal::Value(
-                    th.subst_shift(var, val),
-                    t.as_ref().map(|x| x.subst_shift(var, val)),
-                ),
-                TypedInternal::Sort => TypedInternal::Sort,
-            }
-        }
-    }
-
-    impl std::cmp::PartialEq for TypedInternal {
-        fn eq(&self, other: &Self) -> bool {
-            self.to_value() == other.to_value()
-        }
-    }
-
-    impl std::cmp::Eq for TypedInternal {}
-}
-
-/// A Dhall expression representing a simple type.
-///
-/// This captures what is usually simply called a "type", like
-/// `Bool`, `{ x: Integer }` or `Natural -> Text`.
-///
-/// For a more general notion of "type", see [Type].
-#[derive(Debug, Clone)]
-pub struct SimpleType(pub(crate) SubExpr<X, X>);
-derive_other_traits!(SimpleType);
-
-pub(crate) use crate::typecheck::TypeInternal;
-
-/// A Dhall expression representing a (possibly higher-kinded) type.
-///
-/// This includes [SimpleType]s but also higher-kinded expressions like
-/// `Type`, `Kind` and `{ x: Type }`.
-#[derive(Debug, Clone, PartialEq, Eq)]
-pub struct Type(pub(crate) TypeInternal);
-
-impl std::fmt::Display for Type {
-    fn fmt(&self, f: &mut std::fmt::Formatter) -> Result<(), std::fmt::Error> {
-        self.to_normalized().fmt(f)
-    }
-}
-
-// Exposed for the macros
-#[doc(hidden)]
-impl From<SimpleType> for SubExpr<X, X> {
-    fn from(x: SimpleType) -> SubExpr<X, X> {
-        x.0
-    }
-}
-
-// Exposed for the macros
-#[doc(hidden)]
-impl From<SubExpr<X, X>> for SimpleType {
-    fn from(x: SubExpr<X, X>) -> SimpleType {
-        SimpleType(x)
-    }
-}
-
-// Exposed for the macros
-#[doc(hidden)]
-impl From<Normalized> for Typed {
-    fn from(x: Normalized) -> Typed {
-        Typed(x.0)
-    }
-}
-
-impl Normalized {
-    pub(crate) fn from_thunk_and_type(th: Thunk, t: Type) -> Self {
-        Normalized(TypedInternal::from_thunk_and_type(th, t))
-    }
-    pub(crate) fn to_expr(&self) -> SubExpr<X, X> {
-        self.0.to_expr()
-    }
-    #[allow(dead_code)]
-    pub(crate) fn to_expr_alpha(&self) -> SubExpr<X, X> {
-        self.0.to_expr_alpha()
-    }
-    pub(crate) fn to_value(&self) -> Value {
-        self.0.to_value()
-    }
-    pub(crate) fn to_thunk(&self) -> Thunk {
-        self.0.to_thunk()
-    }
-}
-
-impl Typed {
-    pub(crate) fn from_thunk_and_type(th: Thunk, t: Type) -> Self {
-        Typed(TypedInternal::from_thunk_and_type(th, t))
-    }
-    pub(crate) fn from_thunk_untyped(th: Thunk) -> Self {
-        Typed(TypedInternal::from_thunk_untyped(th))
-    }
-    pub(crate) fn const_sort() -> Self {
-        Typed(TypedInternal::Sort)
-    }
-}
diff --git a/dhall/src/lib.rs b/dhall/src/lib.rs
index a531f64..8d1496a 100644
--- a/dhall/src/lib.rs
+++ b/dhall/src/lib.rs
@@ -123,51 +123,10 @@
 #[macro_use]
 mod tests;
 
-#[cfg(test)]
-mod parser;
-
-mod binary;
-/// When manipulating Dhall expressions goes wrong.
+pub(crate) mod api;
+pub(crate) mod core;
 pub mod error;
-pub mod expr;
-mod imports;
-mod normalize;
-mod serde;
-mod traits;
-mod typecheck;
-
-/// Deserialization of Dhall expressions into Rust
-pub mod de {
-    pub use crate::traits::{Deserialize, SimpleStaticType, StaticType};
-    #[doc(hidden)]
-    pub use dhall_proc_macros::SimpleStaticType;
-
-    /// Deserialize an instance of type T from a string of Dhall text.
-    ///
-    /// This will recursively resolve all imports in the expression, and
-    /// typecheck it before deserialization. Relative imports will be resolved relative to the
-    /// provided file. More control over this process is not yet available
-    /// but will be in a coming version of this crate.
-    ///
-    /// If a type is provided, this additionally checks that the provided
-    /// expression has that type.
-    pub fn from_str<'a, T: Deserialize<'a>>(
-        s: &'a str,
-        ty: Option<&crate::expr::Type>,
-    ) -> crate::error::Result<T> {
-        T::from_str(s, ty)
-    }
+pub(crate) mod phase;
+pub(crate) use api::traits;
 
-    /// Deserialize an instance of type T from a string of Dhall text,
-    /// additionally checking that it matches the type of T.
-    ///
-    /// This will recursively resolve all imports in the expression, and
-    /// typecheck it before deserialization. Relative imports will be resolved relative to the
-    /// provided file. More control over this process is not yet available
-    /// but will be in a coming version of this crate.
-    pub fn from_str_auto_type<'a, T: Deserialize<'a> + StaticType>(
-        s: &'a str,
-    ) -> crate::error::Result<T> {
-        from_str(s, Some(&<T as StaticType>::get_static_type()))
-    }
-}
+pub use api::de;
diff --git a/dhall/src/main.rs b/dhall/src/main.rs
deleted file mode 100644
index e25a535..0000000
--- a/dhall/src/main.rs
+++ /dev/null
@@ -1,93 +0,0 @@
-// use std::error::Error;
-// use std::io::{self, Read};
-// use term_painter::ToStyle;
-
-// const ERROR_STYLE: term_painter::Color = term_painter::Color::Red;
-// const BOLD: term_painter::Attr = term_painter::Attr::Bold;
-
-// fn print_error(message: &str, source: &str, start: usize, end: usize) {
-//     let line_number = bytecount::count(source[..start].as_bytes(), b'\n');
-//     let line_start = source[..start].rfind('\n').map(|i| i + 1).unwrap_or(0);
-//     let line_end = source[end..].find('\n').unwrap_or(0) + end;
-//     let context_prefix = &source[line_start..start];
-//     let context_highlighted = &source[start..end];
-//     let context_suffix = &source[end..line_end];
-
-//     let line_number_str = line_number.to_string();
-//     let line_number_width = line_number_str.len();
-
-//     BOLD.with(|| {
-//         ERROR_STYLE.with(|| {
-//             print!("error: ");
-//         });
-//         println!("{}", message);
-//     });
-//     BOLD.with(|| {
-//         print!("  -->");
-//     });
-//     println!(" (stdin):{}:0", line_number);
-//     BOLD.with(|| {
-//         println!("{:w$} |", "", w = line_number_width);
-//         print!("{} |", line_number_str);
-//     });
-//     print!(" {}", context_prefix);
-//     BOLD.with(|| {
-//         ERROR_STYLE.with(|| {
-//             print!("{}", context_highlighted);
-//         });
-//     });
-//     println!("{}", context_suffix);
-//     BOLD.with(|| {
-//         print!("{:w$} |", "", w = line_number_width);
-//         ERROR_STYLE.with(|| {
-//             println!(
-//                 " {:so$}{:^>ew$}",
-//                 "",
-//                 "",
-//                 so = source[line_start..start].chars().count(),
-//                 ew = ::std::cmp::max(1, source[start..end].chars().count())
-//             );
-//         });
-//     });
-// }
-
-fn main() {
-    // let mut buffer = String::new();
-    // io::stdin().read_to_string(&mut buffer).unwrap();
-
-    // TODO: public API is too restricted for this
-    // let expr = match dhall::expr::Parsed::parse_str(&buffer) {
-    //     Ok(expr) => expr,
-    //     Err(e) => {
-    //         print_error(&format!("Parse error {}", e), &buffer, 0, 0);
-    //         return;
-    //     }
-    // };
-
-    // let expr = expr.resolve().unwrap();
-
-    // let expr = match expr.typecheck() {
-    //     Ok(expr) => expr,
-    //     Err(e) => {
-    //         // TODO: implement pretty type error printing
-    //         // let explain = ::std::env::args().any(|s| s == "--explain");
-    //         // if !explain {
-    //         //     term_painter::Color::BrightBlack.with(|| {
-    //         //         println!("Use \"dhall --explain\" for detailed errors");
-    //         //     });
-    //         // }
-    //         // ERROR_STYLE.with(|| print!("Error: "));
-    //         // println!("{}", e.type_message.description());
-    //         // if explain {
-    //         //     println!("{}", e.type_message);
-    //         // }
-    //         // println!("{}", e.current);
-    //         // // FIXME Print source position
-    //         return;
-    //     }
-    // };
-
-    // let expr = expr.normalize();
-
-    // println!("{}", expr);
-}
diff --git a/dhall/src/parser.rs b/dhall/src/parser.rs
deleted file mode 100644
index 3648c4f..0000000
--- a/dhall/src/parser.rs
+++ /dev/null
@@ -1,6 +0,0 @@
-#[cfg(test)]
-mod spec_tests {
-    #![rustfmt::skip]
-    // See ../build.rs
-    include!(concat!(env!("OUT_DIR"), "/parser_tests.rs"));
-}
diff --git a/dhall/src/binary.rs b/dhall/src/phase/binary.rs
index 9c31d4c..30aa7a0 100644
--- a/dhall/src/binary.rs
+++ b/dhall/src/phase/binary.rs
@@ -1,14 +1,15 @@
-use dhall_syntax::*;
-use itertools::*;
+use itertools::Itertools;
 use serde_cbor::value::value as cbor;
 
-type ParsedExpr = SubExpr<X, Import>;
+use dhall_syntax::{
+    rc, ExprF, FilePrefix, Hash, Import, ImportHashed, ImportLocation,
+    ImportMode, Integer, InterpolatedText, Label, Natural, Scheme, SubExpr,
+    URL, V, X,
+};
 
-#[derive(Debug)]
-pub enum DecodeError {
-    CBORError(serde_cbor::error::Error),
-    WrongFormatError(String),
-}
+use crate::error::DecodeError;
+
+type ParsedExpr = SubExpr<X, Import>;
 
 pub fn decode(data: &[u8]) -> Result<ParsedExpr, DecodeError> {
     match serde_cbor::de::from_slice(data) {
diff --git a/dhall/src/phase/mod.rs b/dhall/src/phase/mod.rs
new file mode 100644
index 0000000..c8a8ffd
--- /dev/null
+++ b/dhall/src/phase/mod.rs
@@ -0,0 +1,334 @@
+use std::borrow::Cow;
+use std::fmt::Display;
+use std::path::Path;
+
+use dhall_syntax::{Const, Import, Span, SubExpr, X};
+
+use crate::core::context::TypecheckContext;
+use crate::core::thunk::Thunk;
+use crate::core::value::{AlphaVar, Value};
+use crate::error::{Error, ImportError, TypeError, TypeMessage};
+
+use resolve::ImportRoot;
+use typecheck::type_of_const;
+
+pub(crate) mod binary;
+pub(crate) mod normalize;
+pub(crate) mod parse;
+pub(crate) mod resolve;
+pub(crate) mod typecheck;
+
+pub(crate) type ParsedSubExpr = SubExpr<Span, Import>;
+pub(crate) type ResolvedSubExpr = SubExpr<Span, Normalized>;
+pub(crate) type NormalizedSubExpr = SubExpr<X, X>;
+
+#[derive(Debug, Clone)]
+pub(crate) struct Parsed(pub(crate) ParsedSubExpr, pub(crate) ImportRoot);
+
+/// An expression where all imports have been resolved
+#[derive(Debug, Clone)]
+pub(crate) struct Resolved(pub(crate) ResolvedSubExpr);
+
+/// A typed expression
+#[derive(Debug, Clone)]
+pub(crate) enum Typed {
+    // Any value, along with (optionally) its type
+    Value(Thunk, Option<Type>),
+    // One of the base higher-kinded typed.
+    // Used to avoid storing the same tower ot Type->Kind->Sort
+    // over and over again. Also enables having Sort as a type
+    // even though it doesn't itself have a type.
+    Const(Const),
+}
+
+/// A normalized expression.
+///
+/// Invariant: the contained Typed expression must be in normal form,
+#[derive(Debug, Clone)]
+pub(crate) struct Normalized(pub(crate) Typed);
+
+/// A Dhall expression representing a simple type.
+///
+/// This captures what is usually simply called a "type", like
+/// `Bool`, `{ x: Integer }` or `Natural -> Text`.
+///
+/// For a more general notion of "type", see [Type].
+#[derive(Debug, Clone)]
+pub struct SimpleType(pub(crate) NormalizedSubExpr);
+
+/// A Dhall expression representing a (possibly higher-kinded) type.
+///
+/// This includes [SimpleType]s but also higher-kinded expressions like
+/// `Type`, `Kind` and `{ x: Type }`.
+#[derive(Debug, Clone, PartialEq, Eq)]
+pub struct Type(pub(crate) Box<Typed>);
+
+impl Parsed {
+    pub fn parse_file(f: &Path) -> Result<Parsed, Error> {
+        parse::parse_file(f)
+    }
+
+    pub fn parse_str(s: &str) -> Result<Parsed, Error> {
+        parse::parse_str(s)
+    }
+
+    #[allow(dead_code)]
+    pub fn parse_binary_file(f: &Path) -> Result<Parsed, Error> {
+        parse::parse_binary_file(f)
+    }
+
+    pub fn resolve(self) -> Result<Resolved, ImportError> {
+        resolve::resolve(self)
+    }
+
+    #[allow(dead_code)]
+    pub fn skip_resolve(self) -> Result<Resolved, ImportError> {
+        resolve::skip_resolve_expr(self)
+    }
+}
+
+impl Resolved {
+    pub fn typecheck(self) -> Result<Typed, TypeError> {
+        typecheck::typecheck(self)
+    }
+    pub fn typecheck_with(self, ty: &Type) -> Result<Typed, TypeError> {
+        typecheck::typecheck_with(self, ty)
+    }
+    /// Pretends this expression has been typechecked. Use with care.
+    #[allow(dead_code)]
+    pub fn skip_typecheck(self) -> Typed {
+        typecheck::skip_typecheck(self)
+    }
+}
+
+impl Typed {
+    /// Reduce an expression to its normal form, performing beta reduction
+    ///
+    /// `normalize` does not type-check the expression.  You may want to type-check
+    /// expressions before normalizing them since normalization can convert an
+    /// ill-typed expression into a well-typed expression.
+    ///
+    /// However, `normalize` will not fail if the expression is ill-typed and will
+    /// leave ill-typed sub-expressions unevaluated.
+    pub fn normalize(self) -> Normalized {
+        match &self {
+            Typed::Const(_) => {}
+            Typed::Value(thunk, _) => {
+                thunk.normalize_nf();
+            }
+        }
+        Normalized(self)
+    }
+
+    pub(crate) fn from_thunk_and_type(th: Thunk, t: Type) -> Self {
+        Typed::Value(th, Some(t))
+    }
+    pub(crate) fn from_thunk_untyped(th: Thunk) -> Self {
+        Typed::Value(th, None)
+    }
+    pub(crate) fn from_const(c: Const) -> Self {
+        Typed::Const(c)
+    }
+
+    // TODO: Avoid cloning if possible
+    pub(crate) fn to_value(&self) -> Value {
+        match self {
+            Typed::Value(th, _) => th.to_value(),
+            Typed::Const(c) => Value::Const(*c),
+        }
+    }
+    pub(crate) fn to_expr(&self) -> NormalizedSubExpr {
+        self.to_value().normalize_to_expr()
+    }
+    pub(crate) fn to_expr_alpha(&self) -> NormalizedSubExpr {
+        self.to_value().normalize_to_expr_maybe_alpha(true)
+    }
+    pub(crate) fn to_thunk(&self) -> Thunk {
+        match self {
+            Typed::Value(th, _) => th.clone(),
+            Typed::Const(c) => Thunk::from_value(Value::Const(*c)),
+        }
+    }
+    // Deprecated
+    pub(crate) fn to_type(&self) -> Type {
+        self.clone().into_type()
+    }
+    pub(crate) fn into_type(self) -> Type {
+        Type(Box::new(self))
+    }
+
+    pub(crate) fn get_type(&self) -> Result<Cow<'_, Type>, TypeError> {
+        match self {
+            Typed::Value(_, Some(t)) => Ok(Cow::Borrowed(t)),
+            Typed::Value(_, None) => Err(TypeError::new(
+                &TypecheckContext::new(),
+                TypeMessage::Untyped,
+            )),
+            Typed::Const(c) => Ok(Cow::Owned(type_of_const(*c)?)),
+        }
+    }
+
+    pub(crate) fn shift(&self, delta: isize, var: &AlphaVar) -> Self {
+        match self {
+            Typed::Value(th, t) => Typed::Value(
+                th.shift(delta, var),
+                t.as_ref().map(|x| x.shift(delta, var)),
+            ),
+            Typed::Const(c) => Typed::Const(*c),
+        }
+    }
+
+    pub(crate) fn subst_shift(&self, var: &AlphaVar, val: &Typed) -> Self {
+        match self {
+            Typed::Value(th, t) => Typed::Value(
+                th.subst_shift(var, val),
+                t.as_ref().map(|x| x.subst_shift(var, val)),
+            ),
+            Typed::Const(c) => Typed::Const(*c),
+        }
+    }
+}
+
+impl Type {
+    pub(crate) fn to_normalized(&self) -> Normalized {
+        self.0.clone().normalize()
+    }
+    pub(crate) fn to_expr(&self) -> NormalizedSubExpr {
+        self.0.to_expr()
+    }
+    pub(crate) fn to_value(&self) -> Value {
+        self.0.to_value()
+    }
+    pub(crate) fn as_const(&self) -> Option<Const> {
+        // TODO: avoid clone
+        match &self.to_value() {
+            Value::Const(c) => Some(*c),
+            _ => None,
+        }
+    }
+    pub(crate) fn internal_whnf(&self) -> Option<Value> {
+        Some(self.to_value())
+    }
+    pub(crate) fn get_type(&self) -> Result<Cow<'_, Type>, TypeError> {
+        self.0.get_type()
+    }
+
+    pub(crate) fn const_sort() -> Self {
+        Type::from_const(Const::Sort)
+    }
+    pub(crate) fn const_kind() -> Self {
+        Type::from_const(Const::Kind)
+    }
+    pub(crate) fn const_type() -> Self {
+        Type::from_const(Const::Type)
+    }
+    pub(crate) fn from_const(c: Const) -> Self {
+        Type(Box::new(Typed::from_const(c)))
+    }
+
+    pub(crate) fn shift(&self, delta: isize, var: &AlphaVar) -> Self {
+        Type(Box::new(self.0.shift(delta, var)))
+    }
+    pub(crate) fn subst_shift(&self, var: &AlphaVar, val: &Typed) -> Self {
+        Type(Box::new(self.0.subst_shift(var, val)))
+    }
+}
+
+impl Normalized {
+    pub(crate) fn from_thunk_and_type(th: Thunk, t: Type) -> Self {
+        Normalized(Typed::from_thunk_and_type(th, t))
+    }
+
+    pub(crate) fn to_expr(&self) -> NormalizedSubExpr {
+        self.0.to_expr()
+    }
+    #[allow(dead_code)]
+    pub(crate) fn to_expr_alpha(&self) -> NormalizedSubExpr {
+        self.0.to_expr_alpha()
+    }
+    pub(crate) fn to_value(&self) -> Value {
+        self.0.to_value()
+    }
+    pub(crate) fn to_thunk(&self) -> Thunk {
+        self.0.to_thunk()
+    }
+    pub(crate) fn to_type(self) -> Type {
+        self.0.to_type()
+    }
+    pub(crate) fn get_type(&self) -> Result<Cow<'_, Type>, TypeError> {
+        self.0.get_type()
+    }
+
+    pub(crate) fn shift(&self, delta: isize, var: &AlphaVar) -> Self {
+        Normalized(self.0.shift(delta, var))
+    }
+}
+
+macro_rules! derive_traits_for_wrapper_struct {
+    ($ty:ident) => {
+        impl std::cmp::PartialEq for $ty {
+            fn eq(&self, other: &Self) -> bool {
+                self.0 == other.0
+            }
+        }
+
+        impl std::cmp::Eq for $ty {}
+
+        impl std::fmt::Display for $ty {
+            fn fmt(
+                &self,
+                f: &mut std::fmt::Formatter,
+            ) -> Result<(), std::fmt::Error> {
+                self.0.fmt(f)
+            }
+        }
+    };
+}
+
+derive_traits_for_wrapper_struct!(Parsed);
+derive_traits_for_wrapper_struct!(Resolved);
+derive_traits_for_wrapper_struct!(Normalized);
+derive_traits_for_wrapper_struct!(SimpleType);
+
+impl Eq for Typed {}
+impl PartialEq for Typed {
+    fn eq(&self, other: &Self) -> bool {
+        self.to_value() == other.to_value()
+    }
+}
+
+impl Display for Typed {
+    fn fmt(&self, f: &mut std::fmt::Formatter) -> Result<(), std::fmt::Error> {
+        self.to_expr().fmt(f)
+    }
+}
+
+impl Display for Type {
+    fn fmt(&self, f: &mut std::fmt::Formatter) -> Result<(), std::fmt::Error> {
+        self.to_normalized().fmt(f)
+    }
+}
+
+// Exposed for the macros
+#[doc(hidden)]
+impl From<SimpleType> for NormalizedSubExpr {
+    fn from(x: SimpleType) -> NormalizedSubExpr {
+        x.0
+    }
+}
+
+// Exposed for the macros
+#[doc(hidden)]
+impl From<NormalizedSubExpr> for SimpleType {
+    fn from(x: NormalizedSubExpr) -> SimpleType {
+        SimpleType(x)
+    }
+}
+
+// Exposed for the macros
+#[doc(hidden)]
+impl From<Normalized> for Typed {
+    fn from(x: Normalized) -> Typed {
+        x.0
+    }
+}
diff --git a/dhall/src/normalize.rs b/dhall/src/phase/normalize.rs
index 35ab45d..5dfcfb6 100644
--- a/dhall/src/normalize.rs
+++ b/dhall/src/phase/normalize.rs
@@ -1,1025 +1,16 @@
-#![allow(non_snake_case)]
 use std::collections::BTreeMap;
-use std::rc::Rc;
 
-use dhall_proc_macros as dhall;
-use dhall_syntax::context::Context;
-use dhall_syntax::{
-    rc, BinOp, Builtin, Const, ExprF, Integer, InterpolatedTextContents, Label,
-    Natural, Span, SubExpr, V, X,
-};
+use dhall_syntax::{BinOp, Builtin, ExprF, InterpolatedTextContents, Label, X};
 
-use crate::expr::{Normalized, Type, Typed, TypedInternal};
+use crate::core::context::NormalizationContext;
+use crate::core::thunk::{Thunk, TypeThunk};
+use crate::core::value::Value;
+use crate::phase::{NormalizedSubExpr, ResolvedSubExpr, Typed};
 
-type InputSubExpr = SubExpr<Span, Normalized>;
-type OutputSubExpr = SubExpr<X, X>;
+pub(crate) type InputSubExpr = ResolvedSubExpr;
+pub(crate) type OutputSubExpr = NormalizedSubExpr;
 
-impl Typed {
-    /// Reduce an expression to its normal form, performing beta reduction
-    ///
-    /// `normalize` does not type-check the expression.  You may want to type-check
-    /// expressions before normalizing them since normalization can convert an
-    /// ill-typed expression into a well-typed expression.
-    ///
-    /// However, `normalize` will not fail if the expression is ill-typed and will
-    /// leave ill-typed sub-expressions unevaluated.
-    ///
-    pub fn normalize(self) -> Normalized {
-        match &self.0 {
-            TypedInternal::Sort => {}
-            TypedInternal::Value(thunk, _) => {
-                thunk.normalize_nf();
-            }
-        }
-        Normalized(self.0)
-    }
-
-    pub(crate) fn shift(&self, delta: isize, var: &AlphaVar) -> Self {
-        Typed(self.0.shift(delta, var))
-    }
-
-    pub(crate) fn subst_shift(&self, var: &AlphaVar, val: &Typed) -> Self {
-        Typed(self.0.subst_shift(var, val))
-    }
-
-    pub(crate) fn to_value(&self) -> Value {
-        self.0.to_value()
-    }
-
-    pub(crate) fn to_thunk(&self) -> Thunk {
-        self.0.to_thunk()
-    }
-}
-
-/// Stores a pair of variables: a normal one and if relevant one
-/// that corresponds to the alpha-normalized version of the first one.
-#[derive(Debug, Clone, Eq)]
-pub(crate) struct AlphaVar {
-    normal: V<Label>,
-    alpha: Option<V<()>>,
-}
-
-impl AlphaVar {
-    pub(crate) fn to_var(&self, alpha: bool) -> V<Label> {
-        match (alpha, &self.alpha) {
-            (true, Some(x)) => V("_".into(), x.1),
-            _ => self.normal.clone(),
-        }
-    }
-    pub(crate) fn from_var(normal: V<Label>) -> Self {
-        AlphaVar {
-            normal,
-            alpha: None,
-        }
-    }
-    pub(crate) fn shift(&self, delta: isize, var: &AlphaVar) -> Self {
-        AlphaVar {
-            normal: self.normal.shift(delta, &var.normal),
-            alpha: match (&self.alpha, &var.alpha) {
-                (Some(x), Some(v)) => Some(x.shift(delta, v)),
-                _ => None,
-            },
-        }
-    }
-}
-
-/// Equality is up to alpha-equivalence.
-impl std::cmp::PartialEq for AlphaVar {
-    fn eq(&self, other: &Self) -> bool {
-        match (&self.alpha, &other.alpha) {
-            (Some(x), Some(y)) => x == y,
-            (None, None) => self.normal == other.normal,
-            _ => false,
-        }
-    }
-}
-
-impl From<Label> for AlphaVar {
-    fn from(x: Label) -> AlphaVar {
-        AlphaVar {
-            normal: V(x, 0),
-            alpha: Some(V((), 0)),
-        }
-    }
-}
-impl<'a> From<&'a Label> for AlphaVar {
-    fn from(x: &'a Label) -> AlphaVar {
-        x.clone().into()
-    }
-}
-impl From<AlphaLabel> for AlphaVar {
-    fn from(x: AlphaLabel) -> AlphaVar {
-        let l: Label = x.into();
-        l.into()
-    }
-}
-impl<'a> From<&'a AlphaLabel> for AlphaVar {
-    fn from(x: &'a AlphaLabel) -> AlphaVar {
-        x.clone().into()
-    }
-}
-
-// Exactly like a Label, but equality returns always true.
-// This is so that Value equality is exactly alpha-equivalence.
-#[derive(Debug, Clone, Eq)]
-pub(crate) struct AlphaLabel(Label);
-
-impl AlphaLabel {
-    fn to_label_maybe_alpha(&self, alpha: bool) -> Label {
-        if alpha {
-            "_".into()
-        } else {
-            self.to_label()
-        }
-    }
-    fn to_label(&self) -> Label {
-        self.clone().into()
-    }
-}
-
-impl std::cmp::PartialEq for AlphaLabel {
-    fn eq(&self, _other: &Self) -> bool {
-        true
-    }
-}
-
-impl From<Label> for AlphaLabel {
-    fn from(x: Label) -> AlphaLabel {
-        AlphaLabel(x)
-    }
-}
-impl From<AlphaLabel> for Label {
-    fn from(x: AlphaLabel) -> Label {
-        x.0
-    }
-}
-
-#[derive(Debug, Clone)]
-enum EnvItem {
-    Thunk(Thunk),
-    Skip(AlphaVar),
-}
-
-impl EnvItem {
-    fn shift(&self, delta: isize, var: &AlphaVar) -> Self {
-        use EnvItem::*;
-        match self {
-            Thunk(e) => Thunk(e.shift(delta, var)),
-            Skip(v) => Skip(v.shift(delta, var)),
-        }
-    }
-
-    pub(crate) fn subst_shift(&self, var: &AlphaVar, val: &Typed) -> Self {
-        match self {
-            EnvItem::Thunk(e) => EnvItem::Thunk(e.subst_shift(var, val)),
-            EnvItem::Skip(v) if v == var => EnvItem::Thunk(val.to_thunk()),
-            EnvItem::Skip(v) => EnvItem::Skip(v.shift(-1, var)),
-        }
-    }
-}
-
-#[derive(Debug, Clone)]
-pub(crate) struct NormalizationContext(Rc<Context<Label, EnvItem>>);
-
-impl NormalizationContext {
-    pub(crate) fn new() -> Self {
-        NormalizationContext(Rc::new(Context::new()))
-    }
-    fn skip(&self, x: &Label) -> Self {
-        NormalizationContext(Rc::new(
-            self.0
-                .map(|_, e| e.shift(1, &x.into()))
-                .insert(x.clone(), EnvItem::Skip(x.into())),
-        ))
-    }
-    fn lookup(&self, var: &V<Label>) -> Value {
-        let V(x, n) = var;
-        match self.0.lookup(x, *n) {
-            Some(EnvItem::Thunk(t)) => t.to_value(),
-            Some(EnvItem::Skip(newvar)) => Value::Var(newvar.clone()),
-            // Free variable
-            None => Value::Var(AlphaVar::from_var(var.clone())),
-        }
-    }
-    pub(crate) fn from_typecheck_ctx(
-        tc_ctx: &crate::typecheck::TypecheckContext,
-    ) -> Self {
-        use crate::typecheck::EnvItem::*;
-        let mut ctx = Context::new();
-        for (k, vs) in tc_ctx.0.iter_keys() {
-            for v in vs.iter() {
-                let new_item = match v {
-                    Type(var, _) => EnvItem::Skip(var.clone()),
-                    Value(e) => EnvItem::Thunk(e.to_thunk()),
-                };
-                ctx = ctx.insert(k.clone(), new_item);
-            }
-        }
-        NormalizationContext(Rc::new(ctx))
-    }
-
-    fn shift(&self, delta: isize, var: &AlphaVar) -> Self {
-        NormalizationContext(Rc::new(self.0.map(|_, e| e.shift(delta, var))))
-    }
-
-    fn subst_shift(&self, var: &AlphaVar, val: &Typed) -> Self {
-        NormalizationContext(Rc::new(
-            self.0.map(|_, e| e.subst_shift(var, val)),
-        ))
-    }
-}
-
-/// A semantic value.
-/// Equality is up to alpha-equivalence (renaming of bound variables).
-#[derive(Debug, Clone, PartialEq, Eq)]
-pub(crate) enum Value {
-    /// Closures
-    Lam(AlphaLabel, Thunk, Thunk),
-    AppliedBuiltin(Builtin, Vec<Thunk>),
-    /// `λ(x: a) -> Some x`
-    OptionalSomeClosure(TypeThunk),
-    /// `λ(x : a) -> λ(xs : List a) -> [ x ] # xs`
-    /// `λ(xs : List a) -> [ x ] # xs`
-    ListConsClosure(TypeThunk, Option<Thunk>),
-    /// `λ(x : Natural) -> x + 1`
-    NaturalSuccClosure,
-    Pi(AlphaLabel, TypeThunk, TypeThunk),
-
-    Var(AlphaVar),
-    Const(Const),
-    BoolLit(bool),
-    NaturalLit(Natural),
-    IntegerLit(Integer),
-    EmptyOptionalLit(TypeThunk),
-    NEOptionalLit(Thunk),
-    EmptyListLit(TypeThunk),
-    NEListLit(Vec<Thunk>),
-    RecordLit(BTreeMap<Label, Thunk>),
-    RecordType(BTreeMap<Label, TypeThunk>),
-    UnionType(BTreeMap<Label, Option<TypeThunk>>),
-    UnionConstructor(Label, BTreeMap<Label, Option<TypeThunk>>),
-    UnionLit(Label, Thunk, BTreeMap<Label, Option<TypeThunk>>),
-    TextLit(Vec<InterpolatedTextContents<Thunk>>),
-    /// Invariant: This must not contain a value captured by one of the variants above.
-    PartialExpr(ExprF<Thunk, Label, X>),
-}
-
-impl Value {
-    pub(crate) fn into_thunk(self) -> Thunk {
-        Thunk::from_value(self)
-    }
-
-    /// Convert the value to a fully normalized syntactic expression
-    pub(crate) fn normalize_to_expr(&self) -> OutputSubExpr {
-        self.normalize_to_expr_maybe_alpha(false)
-    }
-    /// Convert the value to a fully normalized syntactic expression. Also alpha-normalize
-    /// if alpha is `true`
-    pub(crate) fn normalize_to_expr_maybe_alpha(
-        &self,
-        alpha: bool,
-    ) -> OutputSubExpr {
-        match self {
-            Value::Lam(x, t, e) => rc(ExprF::Lam(
-                x.to_label_maybe_alpha(alpha),
-                t.normalize_to_expr_maybe_alpha(alpha),
-                e.normalize_to_expr_maybe_alpha(alpha),
-            )),
-            Value::AppliedBuiltin(b, args) => {
-                let mut e = rc(ExprF::Builtin(*b));
-                for v in args {
-                    e = rc(ExprF::App(
-                        e,
-                        v.normalize_to_expr_maybe_alpha(alpha),
-                    ));
-                }
-                e
-            }
-            Value::OptionalSomeClosure(n) => {
-                let a = n.normalize_to_expr_maybe_alpha(alpha);
-                dhall::subexpr!(λ(x: a) -> Some x)
-            }
-            Value::ListConsClosure(a, None) => {
-                // Avoid accidental capture of the new `x` variable
-                let a1 = a.shift(1, &Label::from("x").into());
-                let a1 = a1.normalize_to_expr_maybe_alpha(alpha);
-                let a = a.normalize_to_expr_maybe_alpha(alpha);
-                dhall::subexpr!(λ(x : a) -> λ(xs : List a1) -> [ x ] # xs)
-            }
-            Value::ListConsClosure(n, Some(v)) => {
-                // Avoid accidental capture of the new `xs` variable
-                let v = v.shift(1, &Label::from("xs").into());
-                let v = v.normalize_to_expr_maybe_alpha(alpha);
-                let a = n.normalize_to_expr_maybe_alpha(alpha);
-                dhall::subexpr!(λ(xs : List a) -> [ v ] # xs)
-            }
-            Value::NaturalSuccClosure => {
-                dhall::subexpr!(λ(x : Natural) -> x + 1)
-            }
-            Value::Pi(x, t, e) => rc(ExprF::Pi(
-                x.to_label_maybe_alpha(alpha),
-                t.normalize_to_expr_maybe_alpha(alpha),
-                e.normalize_to_expr_maybe_alpha(alpha),
-            )),
-            Value::Var(v) => rc(ExprF::Var(v.to_var(alpha))),
-            Value::Const(c) => rc(ExprF::Const(*c)),
-            Value::BoolLit(b) => rc(ExprF::BoolLit(*b)),
-            Value::NaturalLit(n) => rc(ExprF::NaturalLit(*n)),
-            Value::IntegerLit(n) => rc(ExprF::IntegerLit(*n)),
-            Value::EmptyOptionalLit(n) => rc(ExprF::App(
-                rc(ExprF::Builtin(Builtin::OptionalNone)),
-                n.normalize_to_expr_maybe_alpha(alpha),
-            )),
-            Value::NEOptionalLit(n) => {
-                rc(ExprF::SomeLit(n.normalize_to_expr_maybe_alpha(alpha)))
-            }
-            Value::EmptyListLit(n) => {
-                rc(ExprF::EmptyListLit(n.normalize_to_expr_maybe_alpha(alpha)))
-            }
-            Value::NEListLit(elts) => rc(ExprF::NEListLit(
-                elts.into_iter()
-                    .map(|n| n.normalize_to_expr_maybe_alpha(alpha))
-                    .collect(),
-            )),
-            Value::RecordLit(kvs) => rc(ExprF::RecordLit(
-                kvs.iter()
-                    .map(|(k, v)| {
-                        (k.clone(), v.normalize_to_expr_maybe_alpha(alpha))
-                    })
-                    .collect(),
-            )),
-            Value::RecordType(kts) => rc(ExprF::RecordType(
-                kts.iter()
-                    .map(|(k, v)| {
-                        (k.clone(), v.normalize_to_expr_maybe_alpha(alpha))
-                    })
-                    .collect(),
-            )),
-            Value::UnionType(kts) => rc(ExprF::UnionType(
-                kts.iter()
-                    .map(|(k, v)| {
-                        (
-                            k.clone(),
-                            v.as_ref().map(|v| {
-                                v.normalize_to_expr_maybe_alpha(alpha)
-                            }),
-                        )
-                    })
-                    .collect(),
-            )),
-            Value::UnionConstructor(l, kts) => {
-                let kts = kts
-                    .iter()
-                    .map(|(k, v)| {
-                        (
-                            k.clone(),
-                            v.as_ref().map(|v| {
-                                v.normalize_to_expr_maybe_alpha(alpha)
-                            }),
-                        )
-                    })
-                    .collect();
-                rc(ExprF::Field(rc(ExprF::UnionType(kts)), l.clone()))
-            }
-            Value::UnionLit(l, v, kts) => rc(ExprF::UnionLit(
-                l.clone(),
-                v.normalize_to_expr_maybe_alpha(alpha),
-                kts.iter()
-                    .map(|(k, v)| {
-                        (
-                            k.clone(),
-                            v.as_ref().map(|v| {
-                                v.normalize_to_expr_maybe_alpha(alpha)
-                            }),
-                        )
-                    })
-                    .collect(),
-            )),
-            Value::TextLit(elts) => {
-                use InterpolatedTextContents::{Expr, Text};
-                rc(ExprF::TextLit(
-                    elts.iter()
-                        .map(|contents| match contents {
-                            Expr(e) => {
-                                Expr(e.normalize_to_expr_maybe_alpha(alpha))
-                            }
-                            Text(s) => Text(s.clone()),
-                        })
-                        .collect(),
-                ))
-            }
-            Value::PartialExpr(e) => {
-                rc(e.map_ref_simple(|v| v.normalize_to_expr_maybe_alpha(alpha)))
-            }
-        }
-    }
-
-    // Deprecated
-    fn normalize(&self) -> Value {
-        let mut v = self.clone();
-        v.normalize_mut();
-        v
-    }
-
-    pub(crate) fn normalize_mut(&mut self) {
-        match self {
-            Value::NaturalSuccClosure
-            | Value::Var(_)
-            | Value::Const(_)
-            | Value::BoolLit(_)
-            | Value::NaturalLit(_)
-            | Value::IntegerLit(_) => {}
-
-            Value::EmptyOptionalLit(tth)
-            | Value::OptionalSomeClosure(tth)
-            | Value::EmptyListLit(tth) => {
-                tth.normalize_mut();
-            }
-
-            Value::NEOptionalLit(th) => {
-                th.normalize_mut();
-            }
-            Value::Lam(_, t, e) => {
-                t.normalize_mut();
-                e.normalize_mut();
-            }
-            Value::Pi(_, t, e) => {
-                t.normalize_mut();
-                e.normalize_mut();
-            }
-            Value::AppliedBuiltin(_, args) => {
-                for x in args.iter_mut() {
-                    x.normalize_mut();
-                }
-            }
-            Value::ListConsClosure(t, v) => {
-                t.normalize_mut();
-                for x in v.iter_mut() {
-                    x.normalize_mut();
-                }
-            }
-            Value::NEListLit(elts) => {
-                for x in elts.iter_mut() {
-                    x.normalize_mut();
-                }
-            }
-            Value::RecordLit(kvs) => {
-                for x in kvs.values_mut() {
-                    x.normalize_mut();
-                }
-            }
-            Value::RecordType(kvs) => {
-                for x in kvs.values_mut() {
-                    x.normalize_mut();
-                }
-            }
-            Value::UnionType(kts) | Value::UnionConstructor(_, kts) => {
-                for x in kts.values_mut().flat_map(|opt| opt) {
-                    x.normalize_mut();
-                }
-            }
-            Value::UnionLit(_, v, kts) => {
-                v.normalize_mut();
-                for x in kts.values_mut().flat_map(|opt| opt) {
-                    x.normalize_mut();
-                }
-            }
-            Value::TextLit(elts) => {
-                for x in elts.iter_mut() {
-                    use InterpolatedTextContents::{Expr, Text};
-                    match x {
-                        Expr(n) => n.normalize_mut(),
-                        Text(_) => {}
-                    }
-                }
-            }
-            Value::PartialExpr(e) => {
-                // TODO: need map_mut_simple
-                e.map_ref_simple(|v| {
-                    v.normalize_nf();
-                });
-            }
-        }
-    }
-
-    /// Apply to a value
-    pub(crate) fn app(self, val: Value) -> Value {
-        self.app_val(val)
-    }
-
-    /// Apply to a value
-    pub(crate) fn app_val(self, val: Value) -> Value {
-        self.app_thunk(val.into_thunk())
-    }
-
-    /// Apply to a thunk
-    pub(crate) fn app_thunk(self, th: Thunk) -> Value {
-        Thunk::from_value(self).app_thunk(th)
-    }
-
-    pub(crate) fn from_builtin(b: Builtin) -> Value {
-        Value::AppliedBuiltin(b, vec![])
-    }
-
-    fn shift(&self, delta: isize, var: &AlphaVar) -> Self {
-        match self {
-            Value::Lam(x, t, e) => Value::Lam(
-                x.clone(),
-                t.shift(delta, var),
-                e.shift(delta, &var.shift(1, &x.into())),
-            ),
-            Value::AppliedBuiltin(b, args) => Value::AppliedBuiltin(
-                *b,
-                args.iter().map(|v| v.shift(delta, var)).collect(),
-            ),
-            Value::NaturalSuccClosure => Value::NaturalSuccClosure,
-            Value::OptionalSomeClosure(tth) => {
-                Value::OptionalSomeClosure(tth.shift(delta, var))
-            }
-            Value::ListConsClosure(t, v) => Value::ListConsClosure(
-                t.shift(delta, var),
-                v.as_ref().map(|v| v.shift(delta, var)),
-            ),
-            Value::Pi(x, t, e) => Value::Pi(
-                x.clone(),
-                t.shift(delta, var),
-                e.shift(delta, &var.shift(1, &x.into())),
-            ),
-            Value::Var(v) => Value::Var(v.shift(delta, var)),
-            Value::Const(c) => Value::Const(*c),
-            Value::BoolLit(b) => Value::BoolLit(*b),
-            Value::NaturalLit(n) => Value::NaturalLit(*n),
-            Value::IntegerLit(n) => Value::IntegerLit(*n),
-            Value::EmptyOptionalLit(tth) => {
-                Value::EmptyOptionalLit(tth.shift(delta, var))
-            }
-            Value::NEOptionalLit(th) => {
-                Value::NEOptionalLit(th.shift(delta, var))
-            }
-            Value::EmptyListLit(tth) => {
-                Value::EmptyListLit(tth.shift(delta, var))
-            }
-            Value::NEListLit(elts) => Value::NEListLit(
-                elts.iter().map(|v| v.shift(delta, var)).collect(),
-            ),
-            Value::RecordLit(kvs) => Value::RecordLit(
-                kvs.iter()
-                    .map(|(k, v)| (k.clone(), v.shift(delta, var)))
-                    .collect(),
-            ),
-            Value::RecordType(kvs) => Value::RecordType(
-                kvs.iter()
-                    .map(|(k, v)| (k.clone(), v.shift(delta, var)))
-                    .collect(),
-            ),
-            Value::UnionType(kts) => Value::UnionType(
-                kts.iter()
-                    .map(|(k, v)| {
-                        (k.clone(), v.as_ref().map(|v| v.shift(delta, var)))
-                    })
-                    .collect(),
-            ),
-            Value::UnionConstructor(x, kts) => Value::UnionConstructor(
-                x.clone(),
-                kts.iter()
-                    .map(|(k, v)| {
-                        (k.clone(), v.as_ref().map(|v| v.shift(delta, var)))
-                    })
-                    .collect(),
-            ),
-            Value::UnionLit(x, v, kts) => Value::UnionLit(
-                x.clone(),
-                v.shift(delta, var),
-                kts.iter()
-                    .map(|(k, v)| {
-                        (k.clone(), v.as_ref().map(|v| v.shift(delta, var)))
-                    })
-                    .collect(),
-            ),
-            Value::TextLit(elts) => Value::TextLit(
-                elts.iter()
-                    .map(|contents| {
-                        use InterpolatedTextContents::{Expr, Text};
-                        match contents {
-                            Expr(th) => Expr(th.shift(delta, var)),
-                            Text(s) => Text(s.clone()),
-                        }
-                    })
-                    .collect(),
-            ),
-            Value::PartialExpr(e) => {
-                Value::PartialExpr(e.map_ref_with_special_handling_of_binders(
-                    |v| v.shift(delta, var),
-                    |x, v| v.shift(delta, &var.shift(1, &x.into())),
-                    X::clone,
-                    Label::clone,
-                ))
-            }
-        }
-    }
-
-    pub(crate) fn subst_shift(&self, var: &AlphaVar, val: &Typed) -> Self {
-        match self {
-            // Retry normalizing since substituting may allow progress
-            Value::AppliedBuiltin(b, args) => apply_builtin(
-                *b,
-                args.iter().map(|v| v.subst_shift(var, val)).collect(),
-            ),
-            // Retry normalizing since substituting may allow progress
-            Value::PartialExpr(e) => {
-                normalize_one_layer(e.map_ref_with_special_handling_of_binders(
-                    |v| v.subst_shift(var, val),
-                    |x, v| {
-                        v.subst_shift(
-                            &var.shift(1, &x.into()),
-                            &val.shift(1, &x.into()),
-                        )
-                    },
-                    X::clone,
-                    Label::clone,
-                ))
-            }
-            // Retry normalizing since substituting may allow progress
-            Value::TextLit(elts) => {
-                Value::TextLit(squash_textlit(elts.iter().map(|contents| {
-                    use InterpolatedTextContents::{Expr, Text};
-                    match contents {
-                        Expr(th) => Expr(th.subst_shift(var, val)),
-                        Text(s) => Text(s.clone()),
-                    }
-                })))
-            }
-            Value::Lam(x, t, e) => Value::Lam(
-                x.clone(),
-                t.subst_shift(var, val),
-                e.subst_shift(
-                    &var.shift(1, &x.into()),
-                    &val.shift(1, &x.into()),
-                ),
-            ),
-            Value::NaturalSuccClosure => Value::NaturalSuccClosure,
-            Value::OptionalSomeClosure(tth) => {
-                Value::OptionalSomeClosure(tth.subst_shift(var, val))
-            }
-            Value::ListConsClosure(t, v) => Value::ListConsClosure(
-                t.subst_shift(var, val),
-                v.as_ref().map(|v| v.subst_shift(var, val)),
-            ),
-            Value::Pi(x, t, e) => Value::Pi(
-                x.clone(),
-                t.subst_shift(var, val),
-                e.subst_shift(
-                    &var.shift(1, &x.into()),
-                    &val.shift(1, &x.into()),
-                ),
-            ),
-            Value::Var(v) if v == var => val.to_value().clone(),
-            Value::Var(v) => Value::Var(v.shift(-1, var)),
-            Value::Const(c) => Value::Const(*c),
-            Value::BoolLit(b) => Value::BoolLit(*b),
-            Value::NaturalLit(n) => Value::NaturalLit(*n),
-            Value::IntegerLit(n) => Value::IntegerLit(*n),
-            Value::EmptyOptionalLit(tth) => {
-                Value::EmptyOptionalLit(tth.subst_shift(var, val))
-            }
-            Value::NEOptionalLit(th) => {
-                Value::NEOptionalLit(th.subst_shift(var, val))
-            }
-            Value::EmptyListLit(tth) => {
-                Value::EmptyListLit(tth.subst_shift(var, val))
-            }
-            Value::NEListLit(elts) => Value::NEListLit(
-                elts.iter().map(|v| v.subst_shift(var, val)).collect(),
-            ),
-            Value::RecordLit(kvs) => Value::RecordLit(
-                kvs.iter()
-                    .map(|(k, v)| (k.clone(), v.subst_shift(var, val)))
-                    .collect(),
-            ),
-            Value::RecordType(kvs) => Value::RecordType(
-                kvs.iter()
-                    .map(|(k, v)| (k.clone(), v.subst_shift(var, val)))
-                    .collect(),
-            ),
-            Value::UnionType(kts) => Value::UnionType(
-                kts.iter()
-                    .map(|(k, v)| {
-                        (k.clone(), v.as_ref().map(|v| v.subst_shift(var, val)))
-                    })
-                    .collect(),
-            ),
-            Value::UnionConstructor(x, kts) => Value::UnionConstructor(
-                x.clone(),
-                kts.iter()
-                    .map(|(k, v)| {
-                        (k.clone(), v.as_ref().map(|v| v.subst_shift(var, val)))
-                    })
-                    .collect(),
-            ),
-            Value::UnionLit(x, v, kts) => Value::UnionLit(
-                x.clone(),
-                v.subst_shift(var, val),
-                kts.iter()
-                    .map(|(k, v)| {
-                        (k.clone(), v.as_ref().map(|v| v.subst_shift(var, val)))
-                    })
-                    .collect(),
-            ),
-        }
-    }
-}
-
-mod thunk {
-    use super::{
-        apply_any, normalize_whnf, AlphaVar, InputSubExpr,
-        NormalizationContext, OutputSubExpr, Value,
-    };
-    use crate::expr::Typed;
-    use std::cell::{Ref, RefCell};
-    use std::rc::Rc;
-
-    #[derive(Debug, Clone, Copy)]
-    enum Marker {
-        /// Weak Head Normal Form, i.e. subexpressions may not be normalized
-        WHNF,
-        /// Normal form, i.e. completely normalized
-        NF,
-    }
-    use Marker::{NF, WHNF};
-
-    #[derive(Debug)]
-    enum ThunkInternal {
-        /// Non-normalized value alongside a normalization context
-        Unnormalized(NormalizationContext, InputSubExpr),
-        /// Partially normalized value.
-        /// Invariant: if the marker is `NF`, the value must be fully normalized
-        Value(Marker, Value),
-    }
-
-    /// Stores a possibl unevaluated value. Uses RefCell to ensure that
-    /// the value gets normalized at most once.
-    #[derive(Debug, Clone)]
-    pub struct Thunk(Rc<RefCell<ThunkInternal>>);
-
-    impl ThunkInternal {
-        fn into_thunk(self) -> Thunk {
-            Thunk(Rc::new(RefCell::new(self)))
-        }
-
-        fn normalize_whnf(&mut self) {
-            match self {
-                ThunkInternal::Unnormalized(ctx, e) => {
-                    *self = ThunkInternal::Value(
-                        WHNF,
-                        normalize_whnf(ctx.clone(), e.clone()),
-                    )
-                }
-                // Already at least in WHNF
-                ThunkInternal::Value(_, _) => {}
-            }
-        }
-
-        fn normalize_nf(&mut self) {
-            match self {
-                ThunkInternal::Unnormalized(_, _) => {
-                    self.normalize_whnf();
-                    self.normalize_nf();
-                }
-                ThunkInternal::Value(m @ WHNF, v) => {
-                    v.normalize_mut();
-                    *m = NF;
-                }
-                // Already in NF
-                ThunkInternal::Value(NF, _) => {}
-            }
-        }
-
-        // Always use normalize_whnf before
-        fn as_whnf(&self) -> &Value {
-            match self {
-                ThunkInternal::Unnormalized(_, _) => unreachable!(),
-                ThunkInternal::Value(_, v) => v,
-            }
-        }
-
-        // Always use normalize_nf before
-        fn as_nf(&self) -> &Value {
-            match self {
-                ThunkInternal::Unnormalized(_, _) => unreachable!(),
-                ThunkInternal::Value(WHNF, _) => unreachable!(),
-                ThunkInternal::Value(NF, v) => v,
-            }
-        }
-
-        fn shift(&self, delta: isize, var: &AlphaVar) -> Self {
-            match self {
-                ThunkInternal::Unnormalized(ctx, e) => {
-                    ThunkInternal::Unnormalized(
-                        ctx.shift(delta, var),
-                        e.clone(),
-                    )
-                }
-                ThunkInternal::Value(m, v) => {
-                    ThunkInternal::Value(*m, v.shift(delta, var))
-                }
-            }
-        }
-
-        fn subst_shift(&self, var: &AlphaVar, val: &Typed) -> Self {
-            match self {
-                ThunkInternal::Unnormalized(ctx, e) => {
-                    ThunkInternal::Unnormalized(
-                        ctx.subst_shift(var, val),
-                        e.clone(),
-                    )
-                }
-                ThunkInternal::Value(_, v) => {
-                    // The resulting value may not stay in normal form after substitution
-                    ThunkInternal::Value(WHNF, v.subst_shift(var, val))
-                }
-            }
-        }
-    }
-
-    impl Thunk {
-        pub(crate) fn new(ctx: NormalizationContext, e: InputSubExpr) -> Thunk {
-            ThunkInternal::Unnormalized(ctx, e).into_thunk()
-        }
-
-        pub(crate) fn from_value(v: Value) -> Thunk {
-            ThunkInternal::Value(WHNF, v).into_thunk()
-        }
-
-        pub(crate) fn from_normalized_expr(e: OutputSubExpr) -> Thunk {
-            Thunk::new(
-                NormalizationContext::new(),
-                e.embed_absurd().note_absurd(),
-            )
-        }
-
-        // Normalizes contents to normal form; faster than `normalize_nf` if
-        // no one else shares this thunk
-        pub(crate) fn normalize_mut(&mut self) {
-            match Rc::get_mut(&mut self.0) {
-                // Mutate directly if sole owner
-                Some(refcell) => RefCell::get_mut(refcell).normalize_nf(),
-                // Otherwise mutate through the refcell
-                None => self.0.borrow_mut().normalize_nf(),
-            }
-        }
-
-        fn do_normalize_whnf(&self) {
-            let borrow = self.0.borrow();
-            match &*borrow {
-                ThunkInternal::Unnormalized(_, _) => {
-                    drop(borrow);
-                    self.0.borrow_mut().normalize_whnf();
-                }
-                // Already at least in WHNF
-                ThunkInternal::Value(_, _) => {}
-            }
-        }
-
-        fn do_normalize_nf(&self) {
-            let borrow = self.0.borrow();
-            match &*borrow {
-                ThunkInternal::Unnormalized(_, _)
-                | ThunkInternal::Value(WHNF, _) => {
-                    drop(borrow);
-                    self.0.borrow_mut().normalize_nf();
-                }
-                // Already in NF
-                ThunkInternal::Value(NF, _) => {}
-            }
-        }
-
-        // WARNING: avoid normalizing any thunk while holding on to this ref
-        // or you could run into BorrowMut panics
-        pub(crate) fn normalize_nf(&self) -> Ref<Value> {
-            self.do_normalize_nf();
-            Ref::map(self.0.borrow(), ThunkInternal::as_nf)
-        }
-
-        // WARNING: avoid normalizing any thunk while holding on to this ref
-        // or you could run into BorrowMut panics
-        pub(crate) fn as_value(&self) -> Ref<Value> {
-            self.do_normalize_whnf();
-            Ref::map(self.0.borrow(), ThunkInternal::as_whnf)
-        }
-
-        pub(crate) fn to_value(&self) -> Value {
-            self.as_value().clone()
-        }
-
-        pub(crate) fn normalize_to_expr(&self) -> OutputSubExpr {
-            self.normalize_to_expr_maybe_alpha(false)
-        }
-
-        pub(crate) fn normalize_to_expr_maybe_alpha(
-            &self,
-            alpha: bool,
-        ) -> OutputSubExpr {
-            self.normalize_nf().normalize_to_expr_maybe_alpha(alpha)
-        }
-
-        pub(crate) fn app_val(&self, val: Value) -> Value {
-            self.app_thunk(val.into_thunk())
-        }
-
-        pub(crate) fn app_thunk(&self, th: Thunk) -> Value {
-            apply_any(self.clone(), th)
-        }
-
-        pub(crate) fn shift(&self, delta: isize, var: &AlphaVar) -> Self {
-            self.0.borrow().shift(delta, var).into_thunk()
-        }
-
-        pub(crate) fn subst_shift(&self, var: &AlphaVar, val: &Typed) -> Self {
-            self.0.borrow().subst_shift(var, val).into_thunk()
-        }
-    }
-
-    impl std::cmp::PartialEq for Thunk {
-        fn eq(&self, other: &Self) -> bool {
-            &*self.as_value() == &*other.as_value()
-        }
-    }
-    impl std::cmp::Eq for Thunk {}
-}
-
-pub(crate) use thunk::Thunk;
-
-/// A thunk in type position.
-#[derive(Debug, Clone)]
-pub(crate) enum TypeThunk {
-    Thunk(Thunk),
-    Type(Type),
-}
-
-impl TypeThunk {
-    fn from_value(v: Value) -> TypeThunk {
-        TypeThunk::from_thunk(Thunk::from_value(v))
-    }
-
-    fn from_thunk(th: Thunk) -> TypeThunk {
-        TypeThunk::Thunk(th)
-    }
-
-    pub(crate) fn from_type(t: Type) -> TypeThunk {
-        TypeThunk::Type(t)
-    }
-
-    fn normalize_mut(&mut self) {
-        match self {
-            TypeThunk::Thunk(th) => th.normalize_mut(),
-            TypeThunk::Type(_) => {}
-        }
-    }
-
-    pub(crate) fn normalize_nf(&self) -> Value {
-        match self {
-            TypeThunk::Thunk(th) => th.normalize_nf().clone(),
-            TypeThunk::Type(t) => t.to_value().normalize(),
-        }
-    }
-
-    pub(crate) fn to_value(&self) -> Value {
-        match self {
-            TypeThunk::Thunk(th) => th.to_value(),
-            TypeThunk::Type(t) => t.to_value(),
-        }
-    }
-
-    pub(crate) fn normalize_to_expr_maybe_alpha(
-        &self,
-        alpha: bool,
-    ) -> OutputSubExpr {
-        self.normalize_nf().normalize_to_expr_maybe_alpha(alpha)
-    }
-
-    fn shift(&self, delta: isize, var: &AlphaVar) -> Self {
-        match self {
-            TypeThunk::Thunk(th) => TypeThunk::Thunk(th.shift(delta, var)),
-            TypeThunk::Type(t) => TypeThunk::Type(t.shift(delta, var)),
-        }
-    }
-
-    pub(crate) fn subst_shift(&self, var: &AlphaVar, val: &Typed) -> Self {
-        match self {
-            TypeThunk::Thunk(th) => TypeThunk::Thunk(th.subst_shift(var, val)),
-            TypeThunk::Type(t) => TypeThunk::Type(t.subst_shift(var, val)),
-        }
-    }
-}
-
-impl std::cmp::PartialEq for TypeThunk {
-    fn eq(&self, other: &Self) -> bool {
-        self.to_value() == other.to_value()
-    }
-}
-impl std::cmp::Eq for TypeThunk {}
-
-fn apply_builtin(b: Builtin, args: Vec<Thunk>) -> Value {
+pub(crate) fn apply_builtin(b: Builtin, args: Vec<Thunk>) -> Value {
     use dhall_syntax::Builtin::*;
     use Value::*;
 
@@ -1207,7 +198,7 @@ fn apply_builtin(b: Builtin, args: Vec<Thunk>) -> Value {
     }
 }
 
-fn apply_any(f: Thunk, a: Thunk) -> Value {
+pub(crate) fn apply_any(f: Thunk, a: Thunk) -> Value {
     let fallback = |f: Thunk, a: Thunk| Value::PartialExpr(ExprF::App(f, a));
 
     let f_borrow = f.as_value();
@@ -1263,7 +254,7 @@ fn apply_any(f: Thunk, a: Thunk) -> Value {
     }
 }
 
-fn squash_textlit(
+pub(crate) fn squash_textlit(
     elts: impl Iterator<Item = InterpolatedTextContents<Thunk>>,
 ) -> Vec<InterpolatedTextContents<Thunk>> {
     use std::mem::replace;
@@ -1306,7 +297,10 @@ fn squash_textlit(
 }
 
 /// Reduces the imput expression to a Value. Evaluates as little as possible.
-fn normalize_whnf(ctx: NormalizationContext, expr: InputSubExpr) -> Value {
+pub(crate) fn normalize_whnf(
+    ctx: NormalizationContext,
+    expr: InputSubExpr,
+) -> Value {
     match expr.as_ref() {
         ExprF::Embed(e) => return e.to_value(),
         ExprF::Var(v) => return ctx.lookup(v),
@@ -1325,7 +319,7 @@ fn normalize_whnf(ctx: NormalizationContext, expr: InputSubExpr) -> Value {
     normalize_one_layer(expr)
 }
 
-fn normalize_one_layer(expr: ExprF<Thunk, Label, X>) -> Value {
+pub(crate) fn normalize_one_layer(expr: ExprF<Thunk, Label, X>) -> Value {
     use Value::{
         BoolLit, EmptyListLit, EmptyOptionalLit, IntegerLit, Lam, NEListLit,
         NEOptionalLit, NaturalLit, Pi, RecordLit, RecordType, TextLit,
@@ -1345,7 +339,9 @@ fn normalize_one_layer(expr: ExprF<Thunk, Label, X>) -> Value {
         ExprF::Embed(_) => unreachable!(),
         ExprF::Var(_) => unreachable!(),
         ExprF::Annot(x, _) => RetThunk(x),
-        ExprF::Lam(x, t, e) => RetValue(Lam(x.into(), t, e)),
+        ExprF::Lam(x, t, e) => {
+            RetValue(Lam(x.into(), TypeThunk::from_thunk(t), e))
+        }
         ExprF::Pi(x, t, e) => RetValue(Pi(
             x.into(),
             TypeThunk::from_thunk(t),
diff --git a/dhall/src/phase/parse.rs b/dhall/src/phase/parse.rs
new file mode 100644
index 0000000..6b426af
--- /dev/null
+++ b/dhall/src/phase/parse.rs
@@ -0,0 +1,38 @@
+use std::fs::File;
+use std::io::Read;
+use std::path::Path;
+
+use dhall_syntax::parse_expr;
+
+use crate::error::Error;
+use crate::phase::resolve::ImportRoot;
+use crate::phase::Parsed;
+
+pub(crate) fn parse_file(f: &Path) -> Result<Parsed, Error> {
+    let mut buffer = String::new();
+    File::open(f)?.read_to_string(&mut buffer)?;
+    let expr = parse_expr(&*buffer)?;
+    let root = ImportRoot::LocalDir(f.parent().unwrap().to_owned());
+    Ok(Parsed(expr, root))
+}
+
+pub(crate) fn parse_str(s: &str) -> Result<Parsed, Error> {
+    let expr = parse_expr(s)?;
+    let root = ImportRoot::LocalDir(std::env::current_dir()?);
+    Ok(Parsed(expr, root))
+}
+
+pub(crate) fn parse_binary_file(f: &Path) -> Result<Parsed, Error> {
+    let mut buffer = Vec::new();
+    File::open(f)?.read_to_end(&mut buffer)?;
+    let expr = crate::phase::binary::decode(&buffer)?;
+    let root = ImportRoot::LocalDir(f.parent().unwrap().to_owned());
+    Ok(Parsed(expr.note_absurd(), root))
+}
+
+#[cfg(test)]
+mod spec_tests {
+    #![rustfmt::skip]
+    // See build.rs
+    include!(concat!(env!("OUT_DIR"), "/parser_tests.rs"));
+}
diff --git a/dhall/src/imports.rs b/dhall/src/phase/resolve.rs
index 87642a2..5ab03ac 100644
--- a/dhall/src/imports.rs
+++ b/dhall/src/phase/resolve.rs
@@ -1,18 +1,10 @@
-use crate::error::Error;
-use crate::expr::*;
-use dhall_syntax::*;
 use std::collections::HashMap;
-use std::fs::File;
-use std::io::Read;
-use std::path::Path;
-use std::path::PathBuf;
-
-#[derive(Debug)]
-pub enum ImportError {
-    Recursive(Import, Box<Error>),
-    UnexpectedImport(Import),
-    ImportCycle(ImportStack, Import),
-}
+use std::path::{Path, PathBuf};
+
+use dhall_syntax::Import;
+
+use crate::error::{Error, ImportError};
+use crate::phase::{Normalized, Parsed, Resolved};
 
 /// A root from which to resolve relative imports.
 #[derive(Debug, Clone, PartialEq, Eq)]
@@ -22,7 +14,7 @@ pub enum ImportRoot {
 
 type ImportCache = HashMap<Import, Normalized>;
 
-type ImportStack = Vec<Import>;
+pub(crate) type ImportStack = Vec<Import>;
 
 fn resolve_import(
     import: &Import,
@@ -97,7 +89,11 @@ fn do_resolve_expr(
     Ok(Resolved(expr))
 }
 
-fn skip_resolve_expr(
+pub(crate) fn resolve(e: Parsed) -> Result<Resolved, ImportError> {
+    do_resolve_expr(e, &mut HashMap::new(), &Vec::new())
+}
+
+pub(crate) fn skip_resolve_expr(
     Parsed(expr, _root): Parsed,
 ) -> Result<Resolved, ImportError> {
     let resolve = |import: &Import| -> Result<Normalized, ImportError> {
@@ -107,40 +103,6 @@ fn skip_resolve_expr(
     Ok(Resolved(expr))
 }
 
-impl Parsed {
-    pub fn parse_file(f: &Path) -> Result<Parsed, Error> {
-        let mut buffer = String::new();
-        File::open(f)?.read_to_string(&mut buffer)?;
-        let expr = parse_expr(&*buffer)?;
-        let root = ImportRoot::LocalDir(f.parent().unwrap().to_owned());
-        Ok(Parsed(expr.unnote().note_absurd(), root))
-    }
-
-    pub fn parse_str(s: &str) -> Result<Parsed, Error> {
-        let expr = parse_expr(s)?;
-        let root = ImportRoot::LocalDir(std::env::current_dir()?);
-        Ok(Parsed(expr, root))
-    }
-
-    #[allow(dead_code)]
-    pub fn parse_binary_file(f: &Path) -> Result<Parsed, Error> {
-        let mut buffer = Vec::new();
-        File::open(f)?.read_to_end(&mut buffer)?;
-        let expr = crate::binary::decode(&buffer)?;
-        let root = ImportRoot::LocalDir(f.parent().unwrap().to_owned());
-        Ok(Parsed(expr.note_absurd(), root))
-    }
-
-    pub fn resolve(self) -> Result<Resolved, ImportError> {
-        crate::imports::do_resolve_expr(self, &mut HashMap::new(), &Vec::new())
-    }
-
-    #[allow(dead_code)]
-    pub fn skip_resolve(self) -> Result<Resolved, ImportError> {
-        crate::imports::skip_resolve_expr(self)
-    }
-}
-
 #[cfg(test)]
 mod spec_tests {
     #![rustfmt::skip]
diff --git a/dhall/src/typecheck.rs b/dhall/src/phase/typecheck.rs
index 8d6b6eb..32c1531 100644
--- a/dhall/src/typecheck.rs
+++ b/dhall/src/phase/typecheck.rs
@@ -1,361 +1,18 @@
 #![allow(non_snake_case)]
 use std::borrow::Borrow;
-use std::borrow::Cow;
 use std::collections::BTreeMap;
-use std::fmt;
 
-use crate::expr::*;
-use crate::normalize::{
-    AlphaVar, NormalizationContext, Thunk, TypeThunk, Value,
-};
-use crate::traits::DynamicType;
 use dhall_proc_macros as dhall;
-use dhall_syntax;
-use dhall_syntax::context::Context;
-use dhall_syntax::*;
-
-use self::TypeMessage::*;
-
-impl Resolved {
-    pub fn typecheck(self) -> Result<Typed, TypeError> {
-        type_of(self.0)
-    }
-    pub fn typecheck_with(self, ty: &Type) -> Result<Typed, TypeError> {
-        let expr: SubExpr<_, _> = self.0;
-        let ty: SubExpr<_, _> = ty.to_expr().embed_absurd().note_absurd();
-        type_of(expr.rewrap(ExprF::Annot(expr.clone(), ty)))
-    }
-    /// Pretends this expression has been typechecked. Use with care.
-    #[allow(dead_code)]
-    pub fn skip_typecheck(self) -> Typed {
-        Typed::from_thunk_untyped(Thunk::new(
-            NormalizationContext::new(),
-            self.0,
-        ))
-    }
-}
-
-impl Typed {
-    fn to_type(&self) -> Type {
-        match &self.to_value() {
-            Value::Const(c) => Type(TypeInternal::Const(*c)),
-            _ => Type(TypeInternal::Typed(Box::new(self.clone()))),
-        }
-    }
-}
-
-impl Normalized {
-    fn shift(&self, delta: isize, var: &AlphaVar) -> Self {
-        Normalized(self.0.shift(delta, var))
-    }
-    pub(crate) fn to_type(self) -> Type {
-        self.0.to_type()
-    }
-}
-
-impl Type {
-    pub(crate) fn to_normalized(&self) -> Normalized {
-        self.0.to_normalized()
-    }
-    pub(crate) fn to_expr(&self) -> SubExpr<X, X> {
-        self.0.to_expr()
-    }
-    pub(crate) fn to_value(&self) -> Value {
-        self.0.to_value()
-    }
-    pub(crate) fn get_type(&self) -> Result<Cow<'_, Type>, TypeError> {
-        self.0.get_type()
-    }
-    fn as_const(&self) -> Option<Const> {
-        self.0.as_const()
-    }
-    fn internal_whnf(&self) -> Option<Value> {
-        self.0.whnf()
-    }
-    pub(crate) fn shift(&self, delta: isize, var: &AlphaVar) -> Self {
-        Type(self.0.shift(delta, var))
-    }
-    pub(crate) fn subst_shift(&self, var: &AlphaVar, val: &Typed) -> Self {
-        Type(self.0.subst_shift(var, val))
-    }
-
-    fn const_sort() -> Self {
-        Type(TypeInternal::Const(Const::Sort))
-    }
-    fn const_kind() -> Self {
-        Type(TypeInternal::Const(Const::Kind))
-    }
-    pub(crate) fn const_type() -> Self {
-        Type(TypeInternal::Const(Const::Type))
-    }
-}
-
-impl TypeThunk {
-    fn to_type(&self, ctx: &TypecheckContext) -> Result<Type, TypeError> {
-        match self {
-            TypeThunk::Type(t) => Ok(t.clone()),
-            TypeThunk::Thunk(th) => {
-                // TODO: rule out statically
-                mktype(ctx, th.normalize_to_expr().embed_absurd().note_absurd())
-            }
-        }
-    }
-}
-
-/// A semantic type. This is partially redundant with `dhall_syntax::Expr`, on purpose. `TypeInternal` should
-/// be limited to syntactic expressions: either written by the user or meant to be printed.
-/// The rule is the following: we must _not_ construct values of type `Expr` while typechecking,
-/// but only construct `TypeInternal`s.
-#[derive(Debug, Clone)]
-pub(crate) enum TypeInternal {
-    Const(Const),
-    /// This must not contain a Const value.
-    Typed(Box<Typed>),
-}
-
-impl TypeInternal {
-    fn to_typed(&self) -> Typed {
-        match self {
-            TypeInternal::Typed(e) => e.as_ref().clone(),
-            TypeInternal::Const(c) => const_to_typed(*c),
-        }
-    }
-    fn to_normalized(&self) -> Normalized {
-        self.to_typed().normalize()
-    }
-    fn to_expr(&self) -> SubExpr<X, X> {
-        self.to_normalized().to_expr()
-    }
-    fn to_value(&self) -> Value {
-        self.to_typed().to_value()
-    }
-    pub(crate) fn get_type(&self) -> Result<Cow<'_, Type>, TypeError> {
-        Ok(match self {
-            TypeInternal::Typed(e) => e.get_type()?,
-            TypeInternal::Const(c) => Cow::Owned(type_of_const(*c)?),
-        })
-    }
-    fn as_const(&self) -> Option<Const> {
-        match self {
-            TypeInternal::Const(c) => Some(*c),
-            _ => None,
-        }
-    }
-    fn whnf(&self) -> Option<Value> {
-        match self {
-            TypeInternal::Typed(e) => Some(e.to_value()),
-            _ => None,
-        }
-    }
-    fn shift(&self, delta: isize, var: &AlphaVar) -> Self {
-        use TypeInternal::*;
-        match self {
-            Typed(e) => Typed(Box::new(e.shift(delta, var))),
-            Const(c) => Const(*c),
-        }
-    }
-    fn subst_shift(&self, var: &AlphaVar, val: &Typed) -> Self {
-        use TypeInternal::*;
-        match self {
-            Typed(e) => Typed(Box::new(e.subst_shift(var, val))),
-            Const(c) => Const(*c),
-        }
-    }
-}
-
-impl Eq for TypeInternal {}
-impl PartialEq for TypeInternal {
-    fn eq(&self, other: &Self) -> bool {
-        self.to_normalized() == other.to_normalized()
-    }
-}
-
-#[derive(Debug, Clone)]
-pub(crate) enum EnvItem {
-    Type(AlphaVar, Type),
-    Value(Normalized),
-}
-
-impl EnvItem {
-    fn shift(&self, delta: isize, var: &AlphaVar) -> Self {
-        use EnvItem::*;
-        match self {
-            Type(v, e) => Type(v.shift(delta, var), e.shift(delta, var)),
-            Value(e) => Value(e.shift(delta, var)),
-        }
-    }
-}
-
-#[derive(Debug, Clone)]
-pub(crate) struct TypecheckContext(pub(crate) Context<Label, EnvItem>);
-
-impl TypecheckContext {
-    pub(crate) fn new() -> Self {
-        TypecheckContext(Context::new())
-    }
-    pub(crate) fn insert_type(&self, x: &Label, t: Type) -> Self {
-        TypecheckContext(
-            self.0.map(|_, e| e.shift(1, &x.into())).insert(
-                x.clone(),
-                EnvItem::Type(x.into(), t.shift(1, &x.into())),
-            ),
-        )
-    }
-    pub(crate) fn insert_value(&self, x: &Label, t: Normalized) -> Self {
-        TypecheckContext(self.0.insert(x.clone(), EnvItem::Value(t)))
-    }
-    pub(crate) fn lookup(&self, var: &V<Label>) -> Option<Cow<'_, Type>> {
-        let V(x, n) = var;
-        match self.0.lookup(x, *n) {
-            Some(EnvItem::Type(_, t)) => Some(Cow::Borrowed(&t)),
-            Some(EnvItem::Value(t)) => Some(t.get_type()?),
-            None => None,
-        }
-    }
-    fn to_normalization_ctx(&self) -> NormalizationContext {
-        NormalizationContext::from_typecheck_ctx(self)
-    }
-}
-
-impl PartialEq for TypecheckContext {
-    fn eq(&self, _: &Self) -> bool {
-        // don't count contexts when comparing stuff
-        // this is dirty but needed for now
-        true
-    }
-}
-impl Eq for TypecheckContext {}
-
-fn function_check(a: Const, b: Const) -> Result<Const, ()> {
-    use dhall_syntax::Const::*;
-    match (a, b) {
-        (_, Type) => Ok(Type),
-        (Kind, Kind) => Ok(Kind),
-        (Sort, Sort) => Ok(Sort),
-        (Sort, Kind) => Ok(Sort),
-        _ => Err(()),
-    }
-}
-
-// Equality up to alpha-equivalence (renaming of bound variables)
-fn prop_equal<T, U>(eL0: T, eR0: U) -> bool
-where
-    T: Borrow<Type>,
-    U: Borrow<Type>,
-{
-    eL0.borrow().to_value() == eR0.borrow().to_value()
-}
-
-fn const_to_typed(c: Const) -> Typed {
-    match c {
-        Const::Sort => Typed::const_sort(),
-        _ => Typed::from_thunk_and_type(
-            Value::Const(c).into_thunk(),
-            type_of_const(c).unwrap(),
-        ),
-    }
-}
-
-fn const_to_type(c: Const) -> Type {
-    Type(TypeInternal::Const(c))
-}
-
-fn type_of_const(c: Const) -> Result<Type, TypeError> {
-    match c {
-        Const::Type => Ok(Type::const_kind()),
-        Const::Kind => Ok(Type::const_sort()),
-        Const::Sort => {
-            return Err(TypeError::new(
-                &TypecheckContext::new(),
-                TypeMessage::Sort,
-            ))
-        }
-    }
-}
-
-fn type_of_builtin<E>(b: Builtin) -> Expr<X, E> {
-    use dhall_syntax::Builtin::*;
-    match b {
-        Bool | Natural | Integer | Double | Text => dhall::expr!(Type),
-        List | Optional => dhall::expr!(
-            Type -> Type
-        ),
-
-        NaturalFold => dhall::expr!(
-            Natural ->
-            forall (natural: Type) ->
-            forall (succ: natural -> natural) ->
-            forall (zero: natural) ->
-            natural
-        ),
-        NaturalBuild => dhall::expr!(
-            (forall (natural: Type) ->
-                forall (succ: natural -> natural) ->
-                forall (zero: natural) ->
-                natural) ->
-            Natural
-        ),
-        NaturalIsZero | NaturalEven | NaturalOdd => dhall::expr!(
-            Natural -> Bool
-        ),
-        NaturalToInteger => dhall::expr!(Natural -> Integer),
-        NaturalShow => dhall::expr!(Natural -> Text),
-
-        IntegerToDouble => dhall::expr!(Integer -> Double),
-        IntegerShow => dhall::expr!(Integer -> Text),
-        DoubleShow => dhall::expr!(Double -> Text),
-        TextShow => dhall::expr!(Text -> Text),
-
-        ListBuild => dhall::expr!(
-            forall (a: Type) ->
-            (forall (list: Type) ->
-                forall (cons: a -> list -> list) ->
-                forall (nil: list) ->
-                list) ->
-            List a
-        ),
-        ListFold => dhall::expr!(
-            forall (a: Type) ->
-            List a ->
-            forall (list: Type) ->
-            forall (cons: a -> list -> list) ->
-            forall (nil: list) ->
-            list
-        ),
-        ListLength => dhall::expr!(forall (a: Type) -> List a -> Natural),
-        ListHead | ListLast => {
-            dhall::expr!(forall (a: Type) -> List a -> Optional a)
-        }
-        ListIndexed => dhall::expr!(
-            forall (a: Type) ->
-            List a ->
-            List { index: Natural, value: a }
-        ),
-        ListReverse => dhall::expr!(
-            forall (a: Type) -> List a -> List a
-        ),
+use dhall_syntax::{
+    rc, Builtin, Const, Expr, ExprF, InterpolatedTextContents, Label, Span,
+    SubExpr, X,
+};
 
-        OptionalBuild => dhall::expr!(
-            forall (a: Type) ->
-            (forall (optional: Type) ->
-                forall (just: a -> optional) ->
-                forall (nothing: optional) ->
-                optional) ->
-            Optional a
-        ),
-        OptionalFold => dhall::expr!(
-            forall (a: Type) ->
-            Optional a ->
-            forall (optional: Type) ->
-            forall (just: a -> optional) ->
-            forall (nothing: optional) ->
-            optional
-        ),
-        OptionalNone => dhall::expr!(
-            forall (a: Type) -> Optional a
-        ),
-    }
-}
+use crate::core::context::{NormalizationContext, TypecheckContext};
+use crate::core::thunk::{Thunk, TypeThunk};
+use crate::core::value::Value;
+use crate::error::{TypeError, TypeMessage};
+use crate::phase::{Normalized, Resolved, Type, Typed};
 
 macro_rules! ensure_equal {
     ($x:expr, $y:expr, $err:expr $(,)*) => {
@@ -386,6 +43,7 @@ pub(crate) enum TypeIntermediate {
 
 impl TypeIntermediate {
     fn typecheck(self) -> Result<Typed, TypeError> {
+        use crate::error::TypeMessage::*;
         let mkerr = |ctx, msg| TypeError::new(ctx, msg);
         Ok(match &self {
             TypeIntermediate::Pi(ctx, x, ta, tb) => {
@@ -439,7 +97,7 @@ impl TypeIntermediate {
                         TypeThunk::from_type(tb.clone()),
                     )
                     .into_thunk(),
-                    const_to_type(k),
+                    Type::from_const(k),
                 )
             }
             TypeIntermediate::RecordType(ctx, kts) => {
@@ -469,7 +127,7 @@ impl TypeIntermediate {
                             .collect(),
                     )
                     .into_thunk(),
-                    const_to_type(k),
+                    Type::from_const(k),
                 )
             }
             TypeIntermediate::UnionType(ctx, kts) => {
@@ -508,7 +166,7 @@ impl TypeIntermediate {
                             .collect(),
                     )
                     .into_thunk(),
-                    const_to_type(k),
+                    Type::from_const(k),
                 )
             }
             TypeIntermediate::ListType(ctx, t) => {
@@ -520,7 +178,7 @@ impl TypeIntermediate {
                     Value::from_builtin(Builtin::List)
                         .app(t.to_value())
                         .into_thunk(),
-                    const_to_type(Const::Type),
+                    Type::from_const(Const::Type),
                 )
             }
             TypeIntermediate::OptionalType(ctx, t) => {
@@ -532,23 +190,140 @@ impl TypeIntermediate {
                     Value::from_builtin(Builtin::Optional)
                         .app(t.to_value())
                         .into_thunk(),
-                    const_to_type(Const::Type),
+                    Type::from_const(Const::Type),
                 )
             }
         })
     }
 }
 
+fn function_check(a: Const, b: Const) -> Result<Const, ()> {
+    use dhall_syntax::Const::*;
+    match (a, b) {
+        (_, Type) => Ok(Type),
+        (Kind, Kind) => Ok(Kind),
+        (Sort, Sort) => Ok(Sort),
+        (Sort, Kind) => Ok(Sort),
+        _ => Err(()),
+    }
+}
+
+// Equality up to alpha-equivalence (renaming of bound variables)
+fn prop_equal<T, U>(eL0: T, eR0: U) -> bool
+where
+    T: Borrow<Type>,
+    U: Borrow<Type>,
+{
+    eL0.borrow().to_value() == eR0.borrow().to_value()
+}
+
+pub(crate) fn type_of_const(c: Const) -> Result<Type, TypeError> {
+    match c {
+        Const::Type => Ok(Type::const_kind()),
+        Const::Kind => Ok(Type::const_sort()),
+        Const::Sort => {
+            return Err(TypeError::new(
+                &TypecheckContext::new(),
+                TypeMessage::Sort,
+            ))
+        }
+    }
+}
+
+fn type_of_builtin(b: Builtin) -> Expr<X, X> {
+    use dhall_syntax::Builtin::*;
+    match b {
+        Bool | Natural | Integer | Double | Text => dhall::expr!(Type),
+        List | Optional => dhall::expr!(
+            Type -> Type
+        ),
+
+        NaturalFold => dhall::expr!(
+            Natural ->
+            forall (natural: Type) ->
+            forall (succ: natural -> natural) ->
+            forall (zero: natural) ->
+            natural
+        ),
+        NaturalBuild => dhall::expr!(
+            (forall (natural: Type) ->
+                forall (succ: natural -> natural) ->
+                forall (zero: natural) ->
+                natural) ->
+            Natural
+        ),
+        NaturalIsZero | NaturalEven | NaturalOdd => dhall::expr!(
+            Natural -> Bool
+        ),
+        NaturalToInteger => dhall::expr!(Natural -> Integer),
+        NaturalShow => dhall::expr!(Natural -> Text),
+
+        IntegerToDouble => dhall::expr!(Integer -> Double),
+        IntegerShow => dhall::expr!(Integer -> Text),
+        DoubleShow => dhall::expr!(Double -> Text),
+        TextShow => dhall::expr!(Text -> Text),
+
+        ListBuild => dhall::expr!(
+            forall (a: Type) ->
+            (forall (list: Type) ->
+                forall (cons: a -> list -> list) ->
+                forall (nil: list) ->
+                list) ->
+            List a
+        ),
+        ListFold => dhall::expr!(
+            forall (a: Type) ->
+            List a ->
+            forall (list: Type) ->
+            forall (cons: a -> list -> list) ->
+            forall (nil: list) ->
+            list
+        ),
+        ListLength => dhall::expr!(forall (a: Type) -> List a -> Natural),
+        ListHead | ListLast => {
+            dhall::expr!(forall (a: Type) -> List a -> Optional a)
+        }
+        ListIndexed => dhall::expr!(
+            forall (a: Type) ->
+            List a ->
+            List { index: Natural, value: a }
+        ),
+        ListReverse => dhall::expr!(
+            forall (a: Type) -> List a -> List a
+        ),
+
+        OptionalBuild => dhall::expr!(
+            forall (a: Type) ->
+            (forall (optional: Type) ->
+                forall (just: a -> optional) ->
+                forall (nothing: optional) ->
+                optional) ->
+            Optional a
+        ),
+        OptionalFold => dhall::expr!(
+            forall (a: Type) ->
+            Optional a ->
+            forall (optional: Type) ->
+            forall (just: a -> optional) ->
+            forall (nothing: optional) ->
+            optional
+        ),
+        OptionalNone => dhall::expr!(
+            forall (a: Type) -> Optional a
+        ),
+    }
+}
+
 /// Takes an expression that is meant to contain a Type
 /// and turn it into a type, typechecking it along the way.
-fn mktype(
+pub(crate) fn mktype(
     ctx: &TypecheckContext,
     e: SubExpr<Span, Normalized>,
 ) -> Result<Type, TypeError> {
     Ok(type_with(ctx, e)?.to_type())
 }
 
-fn builtin_to_type(b: Builtin) -> Result<Type, TypeError> {
+pub(crate) fn builtin_to_type(b: Builtin) -> Result<Type, TypeError> {
     mktype(
         &TypecheckContext::new(),
         SubExpr::from_expr_no_note(ExprF::Builtin(b)),
@@ -645,6 +420,7 @@ fn type_last_layer(
     ctx: &TypecheckContext,
     e: ExprF<Typed, Label, Normalized>,
 ) -> Result<Ret, TypeError> {
+    use crate::error::TypeMessage::*;
     use dhall_syntax::BinOp::*;
     use dhall_syntax::Builtin::*;
     use dhall_syntax::ExprF::*;
@@ -857,9 +633,9 @@ fn type_last_layer(
                 // ))),
             }
         }
-        Const(c) => Ok(RetTyped(const_to_typed(c))),
+        Const(c) => Ok(RetTyped(Typed::from_const(c))),
         Builtin(b) => {
-            Ok(RetType(mktype(ctx, rc(type_of_builtin(b)).note_absurd())?))
+            Ok(RetType(mktype(ctx, rc(type_of_builtin(b)).absurd())?))
         }
         BoolLit(_) => Ok(RetType(builtin_to_type(Bool)?)),
         NaturalLit(_) => Ok(RetType(builtin_to_type(Natural)?)),
@@ -927,99 +703,20 @@ fn type_of(e: SubExpr<Span, Normalized>) -> Result<Typed, TypeError> {
     Ok(e)
 }
 
-/// The specific type error
-#[derive(Debug)]
-pub(crate) enum TypeMessage {
-    UnboundVariable(V<Label>),
-    InvalidInputType(Normalized),
-    InvalidOutputType(Normalized),
-    NotAFunction(Typed),
-    TypeMismatch(Typed, Normalized, Typed),
-    AnnotMismatch(Typed, Normalized),
-    Untyped,
-    InvalidListElement(usize, Normalized, Typed),
-    InvalidListType(Normalized),
-    InvalidOptionalType(Normalized),
-    InvalidPredicate(Typed),
-    IfBranchMismatch(Typed, Typed),
-    IfBranchMustBeTerm(bool, Typed),
-    InvalidFieldType(Label, Type),
-    NotARecord(Label, Normalized),
-    MissingRecordField(Label, Typed),
-    MissingUnionField(Label, Normalized),
-    BinOpTypeMismatch(BinOp, Typed),
-    NoDependentTypes(Normalized, Normalized),
-    InvalidTextInterpolation(Typed),
-    Sort,
-    Unimplemented,
-}
-
-/// A structured type error that includes context
-#[derive(Debug)]
-pub struct TypeError {
-    type_message: TypeMessage,
-    context: TypecheckContext,
-}
-
-impl TypeError {
-    pub(crate) fn new(
-        context: &TypecheckContext,
-        type_message: TypeMessage,
-    ) -> Self {
-        TypeError {
-            context: context.clone(),
-            type_message,
-        }
-    }
-}
-
-impl From<TypeError> for std::option::NoneError {
-    fn from(_: TypeError) -> std::option::NoneError {
-        std::option::NoneError
-    }
+pub(crate) fn typecheck(e: Resolved) -> Result<Typed, TypeError> {
+    type_of(e.0)
 }
 
-impl ::std::error::Error for TypeMessage {
-    fn description(&self) -> &str {
-        match *self {
-            // UnboundVariable => "Unbound variable",
-            InvalidInputType(_) => "Invalid function input",
-            InvalidOutputType(_) => "Invalid function output",
-            NotAFunction(_) => "Not a function",
-            TypeMismatch(_, _, _) => "Wrong type of function argument",
-            _ => "Unhandled error",
-        }
-    }
+pub(crate) fn typecheck_with(
+    e: Resolved,
+    ty: &Type,
+) -> Result<Typed, TypeError> {
+    let expr: SubExpr<_, _> = e.0;
+    let ty: SubExpr<_, _> = ty.to_expr().absurd();
+    type_of(expr.rewrap(ExprF::Annot(expr.clone(), ty)))
 }
-
-impl fmt::Display for TypeMessage {
-    fn fmt(&self, f: &mut fmt::Formatter) -> Result<(), fmt::Error> {
-        match self {
-            // UnboundVariable(_) => {
-            //     f.write_str(include_str!("errors/UnboundVariable.txt"))
-            // }
-            // TypeMismatch(e0, e1, e2) => {
-            //     let template = include_str!("errors/TypeMismatch.txt");
-            //     let s = template
-            //         .replace("$txt0", &format!("{}", e0.as_expr()))
-            //         .replace("$txt1", &format!("{}", e1.as_expr()))
-            //         .replace("$txt2", &format!("{}", e2.as_expr()))
-            //         .replace(
-            //             "$txt3",
-            //             &format!(
-            //                 "{}",
-            //                 e2.get_type()
-            //                     .unwrap()
-            //                     .as_normalized()
-            //                     .unwrap()
-            //                     .as_expr()
-            //             ),
-            //         );
-            //     f.write_str(&s)
-            // }
-            _ => f.write_str("Unhandled error message"),
-        }
-    }
+pub(crate) fn skip_typecheck(e: Resolved) -> Typed {
+    Typed::from_thunk_untyped(Thunk::new(NormalizationContext::new(), e.0))
 }
 
 #[cfg(test)]
diff --git a/dhall/src/tests.rs b/dhall/src/tests.rs
index 6b2ab60..4fa1cf5 100644
--- a/dhall/src/tests.rs
+++ b/dhall/src/tests.rs
@@ -34,8 +34,7 @@ macro_rules! make_spec_test {
 }
 
 use crate::error::{Error, Result};
-use crate::expr::Parsed;
-use crate::traits::DynamicType;
+use crate::phase::Parsed;
 use std::path::PathBuf;
 
 #[derive(Copy, Clone)]
diff --git a/dhall/tests/traits.rs b/dhall/tests/traits.rs
index 6604c06..65220dc 100644
--- a/dhall/tests/traits.rs
+++ b/dhall/tests/traits.rs
@@ -5,7 +5,7 @@ use dhall_syntax::{SubExpr, X};
 
 #[test]
 fn test_static_type() {
-    fn mktype(x: SubExpr<X, X>) -> dhall::expr::SimpleType {
+    fn mktype(x: SubExpr<X, X>) -> dhall::de::SimpleType {
         x.into()
     }
 
diff --git a/dhall_proc_macros/src/derive.rs b/dhall_proc_macros/src/derive.rs
index 1ccb28b..a5f0925 100644
--- a/dhall_proc_macros/src/derive.rs
+++ b/dhall_proc_macros/src/derive.rs
@@ -169,9 +169,9 @@ pub fn derive_simple_static_type_inner(
                 for #ident #ty_generics
                 #where_clause {
             fn get_simple_static_type() ->
-                    ::dhall::expr::SimpleType {
+                    ::dhall::de::SimpleType {
                 #(#assertions)*
-                ::dhall::expr::SimpleType::from(#get_type)
+                ::dhall::de::SimpleType::from(#get_type)
             }
         }
     };
diff --git a/dhall_proc_macros/src/quote.rs b/dhall_proc_macros/src/quote.rs
index eaf4946..77ed5de 100644
--- a/dhall_proc_macros/src/quote.rs
+++ b/dhall_proc_macros/src/quote.rs
@@ -7,7 +7,7 @@ use std::collections::BTreeMap;
 
 pub fn expr(input: proc_macro::TokenStream) -> proc_macro::TokenStream {
     let input_str = input.to_string();
-    let expr: SubExpr<_, Import> = parse_expr(&input_str).unwrap().unnote();
+    let expr: SubExpr<_, Import> = parse_expr(&input_str).unwrap();
     let no_import =
         |_: &Import| -> X { panic!("Don't use import in dhall::expr!()") };
     let expr = expr.map_embed(no_import);
@@ -17,7 +17,7 @@ pub fn expr(input: proc_macro::TokenStream) -> proc_macro::TokenStream {
 
 pub fn subexpr(input: proc_macro::TokenStream) -> proc_macro::TokenStream {
     let input_str = input.to_string();
-    let expr: SubExpr<_, Import> = parse_expr(&input_str).unwrap().unnote();
+    let expr: SubExpr<_, Import> = parse_expr(&input_str).unwrap();
     let no_import =
         |_: &Import| -> X { panic!("Don't use import in dhall::subexpr!()") };
     let expr = expr.map_embed(no_import);
@@ -94,8 +94,8 @@ where
 
 // Returns an expression of type SubExpr<_, _>. Expects interpolated variables
 // to be of type SubExpr<_, _>.
-fn quote_subexpr(
-    expr: &SubExpr<X, X>,
+fn quote_subexpr<N>(
+    expr: &SubExpr<N, X>,
     ctx: &Context<Label, ()>,
 ) -> TokenStream {
     use dhall_syntax::ExprF::*;
@@ -131,7 +131,7 @@ fn quote_subexpr(
 
 // Returns an expression of type Expr<_, _>. Expects interpolated variables
 // to be of type SubExpr<_, _>.
-fn quote_expr(expr: &Expr<X, X>, ctx: &Context<Label, ()>) -> TokenStream {
+fn quote_expr<N>(expr: &Expr<N, X>, ctx: &Context<Label, ()>) -> TokenStream {
     use dhall_syntax::ExprF::*;
     match expr.map_ref_with_special_handling_of_binders(
         |e| quote_subexpr(e, ctx),
diff --git a/dhall_syntax/src/context.rs b/dhall_syntax/src/core/context.rs
index 55bfff5..55bfff5 100644
--- a/dhall_syntax/src/context.rs
+++ b/dhall_syntax/src/core/context.rs
diff --git a/dhall_syntax/src/core.rs b/dhall_syntax/src/core/expr.rs
index 7cdda64..2b76b9a 100644
--- a/dhall_syntax/src/core.rs
+++ b/dhall_syntax/src/core/expr.rs
@@ -343,15 +343,11 @@ impl<N, E> Expr<N, E> {
     {
         trivial_result(self.traverse_embed(|x| Ok(map_embed(x))))
     }
+}
 
-    pub fn squash_embed<E2>(
-        &self,
-        f: impl FnMut(&E) -> SubExpr<N, E2>,
-    ) -> SubExpr<N, E2>
-    where
-        N: Clone,
-    {
-        trivial_result(self.visit(&mut visitor::SquashEmbedVisitor(f)))
+impl Expr<X, X> {
+    pub fn absurd<N, E>(&self) -> Expr<N, E> {
+        self.visit(&mut visitor::AbsurdVisitor)
     }
 }
 
@@ -361,12 +357,6 @@ impl<E: Clone> Expr<X, E> {
     }
 }
 
-impl<N: Clone> Expr<N, X> {
-    pub fn embed_absurd<E>(&self) -> Expr<N, E> {
-        self.visit(&mut visitor::EmbedAbsurdVisitor)
-    }
-}
-
 impl<N, E> SubExpr<N, E> {
     pub fn as_ref(&self) -> &Expr<N, E> {
         &self.0.as_ref().0
@@ -380,17 +370,6 @@ impl<N, E> SubExpr<N, E> {
         SubExpr(Rc::new((x, None)))
     }
 
-    pub fn unnote(&self) -> SubExpr<X, E>
-    where
-        E: Clone,
-    {
-        SubExpr::from_expr_no_note(
-            self.as_ref().visit(&mut visitor::UnNoteVisitor),
-        )
-    }
-}
-
-impl<N: Clone, E> SubExpr<N, E> {
     pub fn rewrap<E2>(&self, x: Expr<N, E2>) -> SubExpr<N, E2>
     where
         N: Clone,
@@ -422,7 +401,10 @@ impl<N: Clone, E> SubExpr<N, E> {
         &'a self,
         map_expr: impl FnMut(&'a Self) -> Self,
         map_under_binder: impl FnMut(&'a Label, &'a Self) -> Self,
-    ) -> Self {
+    ) -> Self
+    where
+        N: Clone,
+    {
         match self.as_ref() {
             ExprF::Embed(_) => SubExpr::clone(self),
             // This calls ExprF::map_ref
@@ -436,9 +418,9 @@ impl<N: Clone, E> SubExpr<N, E> {
     }
 }
 
-impl<N: Clone> SubExpr<N, X> {
-    pub fn embed_absurd<T>(&self) -> SubExpr<N, T> {
-        self.rewrap(self.as_ref().embed_absurd())
+impl SubExpr<X, X> {
+    pub fn absurd<N: Clone, T>(&self) -> SubExpr<N, T> {
+        SubExpr::from_expr_no_note(self.as_ref().absurd())
     }
 }
 
diff --git a/dhall_syntax/src/import.rs b/dhall_syntax/src/core/import.rs
index 00f293c..00f293c 100644
--- a/dhall_syntax/src/import.rs
+++ b/dhall_syntax/src/core/import.rs
diff --git a/dhall_syntax/src/label.rs b/dhall_syntax/src/core/label.rs
index 43c3f53..43c3f53 100644
--- a/dhall_syntax/src/label.rs
+++ b/dhall_syntax/src/core/label.rs
diff --git a/dhall_syntax/src/core/mod.rs b/dhall_syntax/src/core/mod.rs
new file mode 100644
index 0000000..7762479
--- /dev/null
+++ b/dhall_syntax/src/core/mod.rs
@@ -0,0 +1,10 @@
+mod expr;
+pub use expr::*;
+mod import;
+pub use import::*;
+mod label;
+pub use label::*;
+mod text;
+pub use text::*;
+pub mod context;
+pub mod visitor;
diff --git a/dhall_syntax/src/text.rs b/dhall_syntax/src/core/text.rs
index 83643d9..83643d9 100644
--- a/dhall_syntax/src/text.rs
+++ b/dhall_syntax/src/core/text.rs
diff --git a/dhall_syntax/src/visitor.rs b/dhall_syntax/src/core/visitor.rs
index 7fdf217..20bfc72 100644
--- a/dhall_syntax/src/visitor.rs
+++ b/dhall_syntax/src/core/visitor.rs
@@ -421,78 +421,6 @@ where
     }
 }
 
-pub struct SquashEmbedVisitor<F1>(pub F1);
-
-impl<'a, 'b, N, E1, E2, F1>
-    ExprFVeryGenericVisitor<'a, SubExpr<N, E2>, SubExpr<N, E1>, Label, E1>
-    for &'b mut SquashEmbedVisitor<F1>
-where
-    N: Clone + 'a,
-    F1: FnMut(&E1) -> SubExpr<N, E2>,
-{
-    type Error = X;
-    type SE2 = SubExpr<N, E2>;
-    type L2 = Label;
-    type E2 = E2;
-
-    fn visit_subexpr(
-        &mut self,
-        subexpr: &'a SubExpr<N, E1>,
-    ) -> Result<Self::SE2, Self::Error> {
-        Ok(subexpr.as_ref().visit(&mut **self)?)
-    }
-
-    fn visit_label(
-        &mut self,
-        label: &'a Label,
-    ) -> Result<Self::L2, Self::Error> {
-        Ok(Label::clone(label))
-    }
-
-    fn visit_binder(
-        mut self,
-        label: &'a Label,
-        subexpr: &'a SubExpr<N, E1>,
-    ) -> Result<(Self::L2, Self::SE2), Self::Error> {
-        Ok((self.visit_label(label)?, self.visit_subexpr(subexpr)?))
-    }
-
-    fn visit_embed_squash(
-        self,
-        embed: &'a E1,
-    ) -> Result<SubExpr<N, E2>, Self::Error> {
-        Ok((self.0)(embed))
-    }
-
-    // Called with the result of the map, in the non-embed case.
-    // Useful to change the result type, and/or avoid some loss of info
-    fn visit_resulting_exprf(
-        result: ExprF<Self::SE2, Self::L2, Self::E2>,
-    ) -> Result<SubExpr<N, E2>, Self::Error> {
-        // TODO: don't lose note
-        Ok(SubExpr::from_expr_no_note(result))
-    }
-}
-
-pub struct UnNoteVisitor;
-
-impl<'a, 'b, N, E>
-    ExprFInFallibleVisitor<'a, SubExpr<N, E>, SubExpr<X, E>, Label, Label, E, E>
-    for &'b mut UnNoteVisitor
-where
-    E: Clone + 'a,
-{
-    fn visit_subexpr(&mut self, subexpr: &'a SubExpr<N, E>) -> SubExpr<X, E> {
-        SubExpr::from_expr_no_note(subexpr.as_ref().visit(&mut **self))
-    }
-    fn visit_embed(self, embed: &'a E) -> E {
-        E::clone(embed)
-    }
-    fn visit_label(&mut self, label: &'a Label) -> Label {
-        Label::clone(label)
-    }
-}
-
 pub struct NoteAbsurdVisitor;
 
 impl<'a, 'b, N, E>
@@ -512,16 +440,14 @@ where
     }
 }
 
-pub struct EmbedAbsurdVisitor;
+pub struct AbsurdVisitor;
 
 impl<'a, 'b, N, E>
-    ExprFInFallibleVisitor<'a, SubExpr<N, X>, SubExpr<N, E>, Label, Label, X, E>
-    for &'b mut EmbedAbsurdVisitor
-where
-    N: Clone + 'a,
+    ExprFInFallibleVisitor<'a, SubExpr<X, X>, SubExpr<N, E>, Label, Label, X, E>
+    for &'b mut AbsurdVisitor
 {
-    fn visit_subexpr(&mut self, subexpr: &'a SubExpr<N, X>) -> SubExpr<N, E> {
-        subexpr.rewrap(subexpr.as_ref().visit(&mut **self))
+    fn visit_subexpr(&mut self, subexpr: &'a SubExpr<X, X>) -> SubExpr<N, E> {
+        SubExpr::from_expr_no_note(subexpr.as_ref().visit(&mut **self))
     }
     fn visit_embed(self, embed: &'a X) -> E {
         match *embed {}
diff --git a/dhall_syntax/src/lib.rs b/dhall_syntax/src/lib.rs
index 3db8222..193c6ea 100644
--- a/dhall_syntax/src/lib.rs
+++ b/dhall_syntax/src/lib.rs
@@ -13,16 +13,10 @@
 //! [dhall-rust]: https://github.com/Nadrieril/dhall-rust
 
 mod core;
+pub use crate::core::context;
+pub use crate::core::visitor;
 pub use crate::core::*;
-mod import;
-pub use crate::import::*;
-mod label;
-pub use crate::label::*;
-mod text;
-pub use crate::text::*;
 mod printer;
 pub use crate::printer::*;
 mod parser;
 pub use crate::parser::*;
-pub mod context;
-pub mod visitor;