Merge branch 'reorganize'

6 files changed, 559 insertions, 1531 deletions

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)]