Merge remote-tracking branch 'origin/master' into fintan/canonicalize

7 files changed, 984 insertions, 1244 deletions

diff --git a/dhall/src/phase/.resolve.rs.swp b/dhall/src/phase/.resolve.rs.swp
new file mode 100644
index 0000000..5314300
--- /dev/null
+++ b/dhall/src/phase/.resolve.rs.swp
diff --git a/dhall/src/phase/binary.rs b/dhall/src/phase/binary.rs
index 89b6db2..16e7ce9 100644
--- a/dhall/src/phase/binary.rs
+++ b/dhall/src/phase/binary.rs
@@ -5,30 +5,26 @@ use std::vec;
 
 use dhall_syntax::map::DupTreeMap;
 use dhall_syntax::{
-    rc, ExprF, FilePrefix, Hash, Import, ImportHashed, ImportLocation,
-    ImportMode, Integer, InterpolatedText, Label, Natural, Scheme, SubExpr,
-    URL, V, File,
+    rc, Expr, ExprF, FilePrefix, Hash, Import, ImportLocation, ImportMode,
+    Integer, InterpolatedText, Label, Natural, Scheme, URL, V, File
 };
 
 use crate::error::{DecodeError, EncodeError};
-use crate::phase::{DecodedSubExpr, ParsedSubExpr};
+use crate::phase::DecodedExpr;
 
-pub fn decode(data: &[u8]) -> Result<DecodedSubExpr, DecodeError> {
+pub(crate) fn decode(data: &[u8]) -> Result<DecodedExpr, DecodeError> {
     match serde_cbor::de::from_slice(data) {
         Ok(v) => cbor_value_to_dhall(&v),
         Err(e) => Err(DecodeError::CBORError(e)),
     }
 }
 
-//TODO: encode normalized expression too
-pub fn encode(expr: &ParsedSubExpr) -> Result<Vec<u8>, EncodeError> {
+pub(crate) fn encode<E>(expr: &Expr<E>) -> Result<Vec<u8>, EncodeError> {
     serde_cbor::ser::to_vec(&Serialize::Expr(expr))
         .map_err(|e| EncodeError::CBORError(e))
 }
 
-fn cbor_value_to_dhall(
-    data: &cbor::Value,
-) -> Result<DecodedSubExpr, DecodeError> {
+fn cbor_value_to_dhall(data: &cbor::Value) -> Result<DecodedExpr, DecodeError> {
     use cbor::Value::*;
     use dhall_syntax::{BinOp, Builtin, Const};
     use ExprF::*;
@@ -262,20 +258,12 @@ fn cbor_value_to_dhall(
                         };
                         let headers = match rest.next() {
                             Some(Null) => None,
-                            // TODO
-                            // Some(x) => {
-                            //     match cbor_value_to_dhall(&x)?.as_ref() {
-                            //         Embed(import) => Some(Box::new(
-                            //             import.location_hashed.clone(),
-                            //         )),
-                            //         _ => Err(DecodeError::WrongFormatError(
-                            //             "import/remote/headers".to_owned(),
-                            //         ))?,
-                            //     }
-                            // }
+                            Some(x) => {
+                                let x = cbor_value_to_dhall(&x)?;
+                                Some(x)
+                            }
                             _ => Err(DecodeError::WrongFormatError(
-                                "import/remote/headers is unimplemented"
-                                    .to_owned(),
+                                "import/remote/headers".to_owned(),
                             ))?,
                         };
                         let authority = match rest.next() {
@@ -343,9 +331,10 @@ fn cbor_value_to_dhall(
                         "import/type".to_owned(),
                     ))?,
                 };
-                Embed(Import {
+                Import(dhall_syntax::Import {
                     mode,
-                    location_hashed: ImportHashed { hash, location },
+                    hash,
+                    location,
                 })
             }
             [U64(25), bindings..] => {
@@ -380,6 +369,15 @@ fn cbor_value_to_dhall(
                 let y = cbor_value_to_dhall(&y)?;
                 Annot(x, y)
             }
+            [U64(27), x] => {
+                let x = cbor_value_to_dhall(&x)?;
+                ToMap(x, None)
+            }
+            [U64(27), x, y] => {
+                let x = cbor_value_to_dhall(&x)?;
+                let y = cbor_value_to_dhall(&y)?;
+                ToMap(x, Some(y))
+            }
             [U64(28), x] => {
                 let x = cbor_value_to_dhall(&x)?;
                 EmptyListLit(x)
@@ -394,7 +392,7 @@ fn cbor_map_to_dhall_map<'a, T>(
     map: impl IntoIterator<Item = (&'a cbor::ObjectKey, &'a cbor::Value)>,
 ) -> Result<T, DecodeError>
 where
-    T: FromIterator<(Label, DecodedSubExpr)>,
+    T: FromIterator<(Label, DecodedExpr)>,
 {
     map.into_iter()
         .map(|(k, v)| -> Result<(_, _), _> {
@@ -411,7 +409,7 @@ fn cbor_map_to_dhall_opt_map<'a, T>(
     map: impl IntoIterator<Item = (&'a cbor::ObjectKey, &'a cbor::Value)>,
 ) -> Result<T, DecodeError>
 where
-    T: FromIterator<(Label, Option<DecodedSubExpr>)>,
+    T: FromIterator<(Label, Option<DecodedExpr>)>,
 {
     map.into_iter()
         .map(|(k, v)| -> Result<(_, _), _> {
@@ -427,11 +425,11 @@ where
         .collect::<Result<_, _>>()
 }
 
-enum Serialize<'a> {
-    Expr(&'a ParsedSubExpr),
+enum Serialize<'a, E> {
+    Expr(&'a Expr<E>),
     CBOR(cbor::Value),
-    RecordMap(&'a DupTreeMap<Label, ParsedSubExpr>),
-    UnionMap(&'a DupTreeMap<Label, Option<ParsedSubExpr>>),
+    RecordMap(&'a DupTreeMap<Label, Expr<E>>),
+    UnionMap(&'a DupTreeMap<Label, Option<Expr<E>>>),
 }
 
 macro_rules! count {
@@ -451,7 +449,7 @@ macro_rules! ser_seq {
     }};
 }
 
-fn serialize_subexpr<S>(ser: S, e: &ParsedSubExpr) -> Result<S::Ok, S::Error>
+fn serialize_subexpr<S, E>(ser: S, e: &Expr<E>) -> Result<S::Ok, S::Error>
 where
     S: serde::ser::Serializer,
 {
@@ -461,21 +459,14 @@ where
     use std::iter::once;
 
     use self::Serialize::{RecordMap, UnionMap};
-    fn expr(x: &ParsedSubExpr) -> self::Serialize<'_> {
+    fn expr<E>(x: &Expr<E>) -> self::Serialize<'_, E> {
         self::Serialize::Expr(x)
     }
-    fn cbor<'a>(v: cbor::Value) -> self::Serialize<'a> {
-        self::Serialize::CBOR(v)
-    }
-    fn tag<'a>(x: u64) -> self::Serialize<'a> {
-        cbor(U64(x))
-    }
-    fn null<'a>() -> self::Serialize<'a> {
-        cbor(cbor::Value::Null)
-    }
-    fn label<'a>(l: &Label) -> self::Serialize<'a> {
-        cbor(cbor::Value::String(l.into()))
-    }
+    let cbor =
+        |v: cbor::Value| -> self::Serialize<'_, E> { self::Serialize::CBOR(v) };
+    let tag = |x: u64| cbor(U64(x));
+    let null = || cbor(cbor::Value::Null);
+    let label = |l: &Label| cbor(cbor::Value::String(l.into()));
 
     match e.as_ref() {
         Const(c) => ser.serialize_str(&c.to_string()),
@@ -571,25 +562,33 @@ where
         Merge(x, y, Some(z)) => {
             ser_seq!(ser; tag(6), expr(x), expr(y), expr(z))
         }
+        ToMap(x, None) => ser_seq!(ser; tag(27), expr(x)),
+        ToMap(x, Some(y)) => ser_seq!(ser; tag(27), expr(x), expr(y)),
         Projection(x, ls) => ser.collect_seq(
             once(tag(10))
                 .chain(once(expr(x)))
                 .chain(ls.iter().map(label)),
         ),
-        Embed(import) => serialize_import(ser, import),
+        Import(import) => serialize_import(ser, import),
+        Embed(_) => unimplemented!(
+            "An expression with resolved imports cannot be binary-encoded"
+        ),
     }
 }
 
-fn serialize_import<S>(ser: S, import: &Import) -> Result<S::Ok, S::Error>
+fn serialize_import<S, E>(
+    ser: S,
+    import: &Import<Expr<E>>,
+) -> Result<S::Ok, S::Error>
 where
     S: serde::ser::Serializer,
 {
     use cbor::Value::{Bytes, Null, U64};
     use serde::ser::SerializeSeq;
 
-    let count = 4 + match &import.location_hashed.location {
-        ImportLocation::Remote(url) => 3 + url.path.clone().into_iter().len(),
-        ImportLocation::Local(_, path) => path.clone().into_iter().len(),
+    let count = 4 + match &import.location {
+        ImportLocation::Remote(url) => 3 + url.path.file_path.len(),
+        ImportLocation::Local(_, path) => path.file_path.len(),
         ImportLocation::Env(_) => 1,
         ImportLocation::Missing => 0,
     };
@@ -597,7 +596,7 @@ where
 
     ser_seq.serialize_element(&U64(24))?;
 
-    let hash = match &import.location_hashed.hash {
+    let hash = match &import.hash {
         None => Null,
         Some(Hash::SHA256(h)) => {
             let mut bytes = vec![18, 32];
@@ -614,7 +613,7 @@ where
     };
     ser_seq.serialize_element(&U64(mode))?;
 
-    let scheme = match &import.location_hashed.location {
+    let scheme = match &import.location {
         ImportLocation::Remote(url) => match url.scheme {
             Scheme::HTTP => 0,
             Scheme::HTTPS => 1,
@@ -630,21 +629,16 @@ where
     };
     ser_seq.serialize_element(&U64(scheme))?;
 
-    match &import.location_hashed.location {
+    match &import.location {
         ImportLocation::Remote(url) => {
             match &url.headers {
                 None => ser_seq.serialize_element(&Null)?,
-                Some(location_hashed) => {
-                    ser_seq.serialize_element(&self::Serialize::Expr(
-                        &SubExpr::from_expr_no_note(ExprF::Embed(Import {
-                            mode: ImportMode::Code,
-                            location_hashed: location_hashed.as_ref().clone(),
-                        })),
-                    ))?
+                Some(e) => {
+                    ser_seq.serialize_element(&self::Serialize::Expr(e))?
                 }
             };
             ser_seq.serialize_element(&url.authority)?;
-            for p in url.path.clone().into_iter() {
+            for p in url.path.file_path.iter() {
                 ser_seq.serialize_element(&p)?;
             }
             match &url.query {
@@ -653,7 +647,7 @@ where
             };
         }
         ImportLocation::Local(_, path) => {
-            for p in path.clone().into_iter() {
+            for p in path.file_path.iter() {
                 ser_seq.serialize_element(&p)?;
             }
         }
@@ -666,7 +660,7 @@ where
     ser_seq.end()
 }
 
-impl<'a> serde::ser::Serialize for Serialize<'a> {
+impl<'a, E> serde::ser::Serialize for Serialize<'a, E> {
     fn serialize<S>(&self, ser: S) -> Result<S::Ok, S::Error>
     where
         S: serde::ser::Serializer,
@@ -692,13 +686,10 @@ impl<'a> serde::ser::Serialize for Serialize<'a> {
     }
 }
 
-fn collect_nested_applications<'a, N, E>(
-    e: &'a SubExpr<N, E>,
-) -> (&'a SubExpr<N, E>, Vec<&'a SubExpr<N, E>>) {
-    fn go<'a, N, E>(
-        e: &'a SubExpr<N, E>,
-        vec: &mut Vec<&'a SubExpr<N, E>>,
-    ) -> &'a SubExpr<N, E> {
+fn collect_nested_applications<'a, E>(
+    e: &'a Expr<E>,
+) -> (&'a Expr<E>, Vec<&'a Expr<E>>) {
+    fn go<'a, E>(e: &'a Expr<E>, vec: &mut Vec<&'a Expr<E>>) -> &'a Expr<E> {
         match e.as_ref() {
             ExprF::App(f, a) => {
                 vec.push(a);
@@ -712,16 +703,15 @@ fn collect_nested_applications<'a, N, E>(
     (e, vec)
 }
 
-type LetBinding<'a, N, E> =
-    (&'a Label, &'a Option<SubExpr<N, E>>, &'a SubExpr<N, E>);
+type LetBinding<'a, E> = (&'a Label, &'a Option<Expr<E>>, &'a Expr<E>);
 
-fn collect_nested_lets<'a, N, E>(
-    e: &'a SubExpr<N, E>,
-) -> (&'a SubExpr<N, E>, Vec<LetBinding<'a, N, E>>) {
-    fn go<'a, N, E>(
-        e: &'a SubExpr<N, E>,
-        vec: &mut Vec<LetBinding<'a, N, E>>,
-    ) -> &'a SubExpr<N, E> {
+fn collect_nested_lets<'a, E>(
+    e: &'a Expr<E>,
+) -> (&'a Expr<E>, Vec<LetBinding<'a, E>>) {
+    fn go<'a, E>(
+        e: &'a Expr<E>,
+        vec: &mut Vec<LetBinding<'a, E>>,
+    ) -> &'a Expr<E> {
         match e.as_ref() {
             ExprF::Let(l, t, v, e) => {
                 vec.push((l, t, v));
diff --git a/dhall/src/phase/mod.rs b/dhall/src/phase/mod.rs
index ccedff2..2c5505c 100644
--- a/dhall/src/phase/mod.rs
+++ b/dhall/src/phase/mod.rs
@@ -1,17 +1,14 @@
-use std::borrow::Cow;
 use std::fmt::Display;
 use std::path::Path;
 
-use dhall_syntax::{Const, Import, Span, SubExpr, X};
+use dhall_syntax::{Builtin, Const, Expr};
 
-use crate::core::context::TypecheckContext;
-use crate::core::thunk::Thunk;
-use crate::core::value::Value;
+use crate::core::value::{ToExprOptions, Value};
+use crate::core::valuef::ValueF;
 use crate::core::var::{AlphaVar, Shift, Subst};
-use crate::error::{EncodeError, Error, ImportError, TypeError, TypeMessage};
+use crate::error::{EncodeError, Error, ImportError, TypeError};
 
 use resolve::ImportRoot;
-use typecheck::type_of_const;
 
 pub(crate) mod binary;
 pub(crate) mod normalize;
@@ -19,30 +16,23 @@ pub(crate) mod parse;
 pub(crate) mod resolve;
 pub(crate) mod typecheck;
 
-pub type ParsedSubExpr = SubExpr<Span, Import>;
-pub type DecodedSubExpr = SubExpr<X, Import>;
-pub type ResolvedSubExpr = SubExpr<Span, Normalized>;
-pub type NormalizedSubExpr = SubExpr<X, X>;
+pub type ParsedExpr = Expr<!>;
+pub type DecodedExpr = Expr<!>;
+pub type ResolvedExpr = Expr<Normalized>;
+pub type NormalizedExpr = Expr<Normalized>;
 
 #[derive(Debug, Clone)]
-pub struct Parsed(ParsedSubExpr, ImportRoot);
+pub struct Parsed(ParsedExpr, ImportRoot);
 
 /// An expression where all imports have been resolved
+///
+/// Invariant: there must be no `Import` nodes or `ImportAlt` operations left.
 #[derive(Debug, Clone)]
-pub struct Resolved(ResolvedSubExpr);
+pub struct Resolved(ResolvedExpr);
 
 /// A typed expression
 #[derive(Debug, Clone)]
-pub enum Typed {
-    // Any value, along with (optionally) its type
-    Untyped(Thunk),
-    Typed(Thunk, Box<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),
-}
+pub struct Typed(Value);
 
 /// A normalized expression.
 ///
@@ -50,8 +40,6 @@ pub enum Typed {
 #[derive(Debug, Clone)]
 pub struct Normalized(Typed);
 
-pub type Type = Typed;
-
 impl Parsed {
     pub fn parse_file(f: &Path) -> Result<Parsed, Error> {
         parse::parse_file(f)
@@ -59,11 +47,9 @@ impl Parsed {
     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)
     }
-    #[allow(dead_code)]
     pub fn parse_binary(data: &[u8]) -> Result<Parsed, Error> {
         parse::parse_binary(data)
     }
@@ -71,12 +57,10 @@ impl Parsed {
     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)
     }
 
-    #[allow(dead_code)]
     pub fn encode(&self) -> Result<Vec<u8>, EncodeError> {
         crate::phase::binary::encode(&self.0)
     }
@@ -84,15 +68,11 @@ impl Parsed {
 
 impl Resolved {
     pub fn typecheck(self) -> Result<Typed, TypeError> {
-        typecheck::typecheck(self)
+        Ok(typecheck::typecheck(self.0)?.into_typed())
     }
-    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)
+    pub fn typecheck_with(self, ty: &Typed) -> Result<Typed, TypeError> {
+        Ok(typecheck::typecheck_with(self.0, ty.normalize_to_expr())?
+            .into_typed())
     }
 }
 
@@ -105,117 +85,110 @@ impl Typed {
     ///
     /// 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::Untyped(thunk) | Typed::Typed(thunk, _) => {
-                thunk.normalize_nf();
-            }
-        }
+    pub fn normalize(mut self) -> Normalized {
+        self.normalize_mut();
         Normalized(self)
     }
 
-    pub fn from_thunk_and_type(th: Thunk, t: Type) -> Self {
-        Typed::Typed(th, Box::new(t))
+    pub(crate) fn from_const(c: Const) -> Self {
+        Typed(Value::from_const(c))
     }
-    pub fn from_thunk_untyped(th: Thunk) -> Self {
-        Typed::Untyped(th)
+    pub(crate) fn from_valuef_and_type(v: ValueF, t: Typed) -> Self {
+        Typed(Value::from_valuef_and_type(v, t.into_value()))
     }
-    pub fn from_const(c: Const) -> Self {
-        Typed::Const(c)
+    pub(crate) fn from_value(th: Value) -> Self {
+        Typed(th)
     }
-    pub fn from_value_untyped(v: Value) -> Self {
-        Typed::from_thunk_untyped(Thunk::from_value(v))
+    pub(crate) fn const_type() -> Self {
+        Typed::from_const(Const::Type)
     }
 
-    // TODO: Avoid cloning if possible
-    pub fn to_value(&self) -> Value {
-        match self {
-            Typed::Untyped(th) | Typed::Typed(th, _) => th.to_value(),
-            Typed::Const(c) => Value::Const(*c),
-        }
-    }
-    pub fn to_expr(&self) -> NormalizedSubExpr {
-        self.to_value().normalize_to_expr()
-    }
-    pub fn to_expr_alpha(&self) -> NormalizedSubExpr {
-        self.to_value().normalize_to_expr_maybe_alpha(true)
+    pub(crate) fn to_expr(&self) -> NormalizedExpr {
+        self.0.to_expr(ToExprOptions {
+            alpha: false,
+            normalize: false,
+        })
     }
-    pub fn to_thunk(&self) -> Thunk {
-        match self {
-            Typed::Untyped(th) | Typed::Typed(th, _) => th.clone(),
-            Typed::Const(c) => Thunk::from_value(Value::Const(*c)),
-        }
+    pub fn normalize_to_expr(&self) -> NormalizedExpr {
+        self.0.to_expr(ToExprOptions {
+            alpha: false,
+            normalize: true,
+        })
     }
-    // Deprecated
-    pub fn to_type(&self) -> Type {
-        self.clone().into_type()
+    pub(crate) fn normalize_to_expr_alpha(&self) -> NormalizedExpr {
+        self.0.to_expr(ToExprOptions {
+            alpha: true,
+            normalize: true,
+        })
     }
-    // Deprecated
-    pub fn into_type(self) -> Type {
-        self
+    pub(crate) fn to_value(&self) -> Value {
+        self.0.clone()
     }
-    pub fn to_normalized(&self) -> Normalized {
-        self.clone().normalize()
+    pub(crate) fn into_value(self) -> Value {
+        self.0
     }
-    pub fn as_const(&self) -> Option<Const> {
-        // TODO: avoid clone
-        match &self.to_value() {
-            Value::Const(c) => Some(*c),
-            _ => None,
-        }
+
+    pub(crate) fn normalize_mut(&mut self) {
+        self.0.normalize_mut()
     }
 
-    pub fn normalize_mut(&mut self) {
-        match self {
-            Typed::Untyped(th) | Typed::Typed(th, _) => th.normalize_mut(),
-            Typed::Const(_) => {}
-        }
+    pub(crate) fn get_type(&self) -> Result<Typed, TypeError> {
+        Ok(self.0.get_type()?.into_typed())
     }
 
-    pub fn get_type(&self) -> Result<Cow<'_, Type>, TypeError> {
-        match self {
-            Typed::Untyped(_) => Err(TypeError::new(
-                &TypecheckContext::new(),
-                TypeMessage::Untyped,
-            )),
-            Typed::Typed(_, t) => Ok(Cow::Borrowed(t)),
-            Typed::Const(c) => Ok(Cow::Owned(type_of_const(*c)?)),
-        }
+    pub fn make_builtin_type(b: Builtin) -> Self {
+        Typed::from_value(Value::from_builtin(b))
+    }
+    pub fn make_optional_type(t: Typed) -> Self {
+        Typed::from_value(
+            Value::from_builtin(Builtin::Optional).app(t.to_value()),
+        )
+    }
+    pub fn make_list_type(t: Typed) -> Self {
+        Typed::from_value(Value::from_builtin(Builtin::List).app(t.to_value()))
+    }
+    pub fn make_record_type(
+        kts: impl Iterator<Item = (String, Typed)>,
+    ) -> Self {
+        Typed::from_valuef_and_type(
+            ValueF::RecordType(
+                kts.map(|(k, t)| (k.into(), t.into_value())).collect(),
+            ),
+            Typed::const_type(),
+        )
+    }
+    pub fn make_union_type(
+        kts: impl Iterator<Item = (String, Option<Typed>)>,
+    ) -> Self {
+        Typed::from_valuef_and_type(
+            ValueF::UnionType(
+                kts.map(|(k, t)| (k.into(), t.map(|t| t.into_value())))
+                    .collect(),
+            ),
+            Typed::const_type(),
+        )
     }
 }
 
 impl Normalized {
-    #[allow(dead_code)]
-    pub fn to_expr(&self) -> NormalizedSubExpr {
-        self.0.to_expr()
-    }
-    #[allow(dead_code)]
-    pub fn to_expr_alpha(&self) -> NormalizedSubExpr {
-        self.0.to_expr_alpha()
+    pub fn encode(&self) -> Result<Vec<u8>, EncodeError> {
+        crate::phase::binary::encode(&self.to_expr())
     }
-    #[allow(dead_code)]
-    pub fn to_type(&self) -> Type {
-        self.0.to_type()
+
+    pub(crate) fn to_expr(&self) -> NormalizedExpr {
+        self.0.normalize_to_expr()
     }
-    pub fn to_value(&self) -> Value {
-        self.0.to_value()
+    pub(crate) fn to_expr_alpha(&self) -> NormalizedExpr {
+        self.0.normalize_to_expr_alpha()
     }
-    pub fn into_typed(self) -> Typed {
+    pub(crate) fn into_typed(self) -> Typed {
         self.0
     }
 }
 
 impl Shift for Typed {
     fn shift(&self, delta: isize, var: &AlphaVar) -> Option<Self> {
-        Some(match self {
-            Typed::Untyped(th) => Typed::Untyped(th.shift(delta, var)?),
-            Typed::Typed(th, t) => Typed::Typed(
-                th.shift(delta, var)?,
-                Box::new(t.shift(delta, var)?),
-            ),
-            Typed::Const(c) => Typed::Const(*c),
-        })
+        Some(Typed(self.0.shift(delta, var)?))
     }
 }
 
@@ -225,16 +198,9 @@ impl Shift for Normalized {
     }
 }
 
-impl Subst<Typed> for Typed {
-    fn subst_shift(&self, var: &AlphaVar, val: &Typed) -> Self {
-        match self {
-            Typed::Untyped(th) => Typed::Untyped(th.subst_shift(var, val)),
-            Typed::Typed(th, t) => Typed::Typed(
-                th.subst_shift(var, val),
-                Box::new(t.subst_shift(var, val)),
-            ),
-            Typed::Const(c) => Typed::Const(*c),
-        }
+impl Subst<Value> for Typed {
+    fn subst_shift(&self, var: &AlphaVar, val: &Value) -> Self {
+        Typed(self.0.subst_shift(var, val))
     }
 }
 
@@ -263,10 +229,21 @@ derive_traits_for_wrapper_struct!(Parsed);
 derive_traits_for_wrapper_struct!(Resolved);
 derive_traits_for_wrapper_struct!(Normalized);
 
+impl std::hash::Hash for Normalized {
+    fn hash<H>(&self, state: &mut H)
+    where
+        H: std::hash::Hasher,
+    {
+        if let Ok(vec) = self.encode() {
+            vec.hash(state)
+        }
+    }
+}
+
 impl Eq for Typed {}
 impl PartialEq for Typed {
     fn eq(&self, other: &Self) -> bool {
-        self.to_value() == other.to_value()
+        self.0 == other.0
     }
 }
 
diff --git a/dhall/src/phase/normalize.rs b/dhall/src/phase/normalize.rs
index 405677a..3f6e99c 100644
--- a/dhall/src/phase/normalize.rs
+++ b/dhall/src/phase/normalize.rs
@@ -1,348 +1,431 @@
 use std::collections::HashMap;
 
+use dhall_syntax::Const::Type;
 use dhall_syntax::{
-    BinOp, Builtin, ExprF, InterpolatedText, InterpolatedTextContents,
-    NaiveDouble, X,
+    BinOp, Builtin, ExprF, InterpolatedText, InterpolatedTextContents, Label,
+    NaiveDouble,
 };
 
-use crate::core::context::NormalizationContext;
-use crate::core::thunk::{Thunk, TypeThunk};
 use crate::core::value::Value;
-use crate::core::var::Subst;
-use crate::phase::{NormalizedSubExpr, ResolvedSubExpr, Typed};
-
-pub type InputSubExpr = ResolvedSubExpr;
-pub type OutputSubExpr = NormalizedSubExpr;
+use crate::core::valuef::ValueF;
+use crate::core::var::{AlphaLabel, Shift, Subst};
+use crate::phase::Normalized;
+
+// Ad-hoc macro to help construct closures
+macro_rules! make_closure {
+    (#$var:ident) => { $var.clone() };
+    (var($var:ident, $n:expr, $($ty:tt)*)) => {{
+        let var = crate::core::var::AlphaVar::from_var_and_alpha(
+            Label::from(stringify!($var)).into(),
+            $n
+        );
+        ValueF::Var(var)
+            .into_value_with_type(make_closure!($($ty)*))
+    }};
+    // Warning: assumes that $ty, as a dhall value, has type `Type`
+    (λ($var:ident : $($ty:tt)*) -> $($body:tt)*) => {{
+        let var: AlphaLabel = Label::from(stringify!($var)).into();
+        let ty = make_closure!($($ty)*);
+        let body = make_closure!($($body)*);
+        let body_ty = body.get_type_not_sort();
+        let lam_ty = ValueF::Pi(var.clone(), ty.clone(), body_ty)
+            .into_value_with_type(Value::from_const(Type));
+        ValueF::Lam(var, ty, body).into_value_with_type(lam_ty)
+    }};
+    (Natural) => {
+        Value::from_builtin(Builtin::Natural)
+    };
+    (List $($rest:tt)*) => {
+        Value::from_builtin(Builtin::List)
+            .app(make_closure!($($rest)*))
+    };
+    (Some($($rest:tt)*)) => {{
+        let v = make_closure!($($rest)*);
+        let v_type = v.get_type_not_sort();
+        let opt_v_type = Value::from_builtin(Builtin::Optional).app(v_type);
+        ValueF::NEOptionalLit(v).into_value_with_type(opt_v_type)
+    }};
+    (1 + $($rest:tt)*) => {
+        ValueF::PartialExpr(ExprF::BinOp(
+            dhall_syntax::BinOp::NaturalPlus,
+            make_closure!($($rest)*),
+            Value::from_valuef_and_type(
+                ValueF::NaturalLit(1),
+                make_closure!(Natural)
+            ),
+        )).into_value_with_type(
+            make_closure!(Natural)
+        )
+    };
+    ([ $($head:tt)* ] # $($tail:tt)*) => {{
+        let head = make_closure!($($head)*);
+        let tail = make_closure!($($tail)*);
+        let list_type = tail.get_type_not_sort();
+        ValueF::PartialExpr(ExprF::BinOp(
+            dhall_syntax::BinOp::ListAppend,
+            ValueF::NEListLit(vec![head])
+                .into_value_with_type(list_type.clone()),
+            tail,
+        )).into_value_with_type(list_type)
+    }};
+}
 
 #[allow(clippy::cognitive_complexity)]
-pub fn apply_builtin(b: Builtin, args: Vec<Thunk>) -> Value {
+pub(crate) fn apply_builtin(
+    b: Builtin,
+    args: Vec<Value>,
+    ty: &Value,
+) -> ValueF {
     use dhall_syntax::Builtin::*;
-    use Value::*;
+    use ValueF::*;
+
+    // Small helper enum
+    enum Ret<'a> {
+        ValueF(ValueF),
+        Value(Value),
+        // For applications that can return a function, it's important to keep the remaining
+        // arguments to apply them to the resulting function.
+        ValueWithRemainingArgs(&'a [Value], Value),
+        DoneAsIs,
+    }
 
-    // Return Ok((unconsumed args, returned value)), or Err(()) if value could not be produced.
     let ret = match (b, args.as_slice()) {
-        (OptionalNone, [t, r..]) => {
-            Ok((r, EmptyOptionalLit(TypeThunk::from_thunk(t.clone()))))
-        }
-        (NaturalIsZero, [n, r..]) => match &*n.as_value() {
-            NaturalLit(n) => Ok((r, BoolLit(*n == 0))),
-            _ => Err(()),
+        (OptionalNone, [t]) => Ret::ValueF(EmptyOptionalLit(t.clone())),
+        (NaturalIsZero, [n]) => match &*n.as_whnf() {
+            NaturalLit(n) => Ret::ValueF(BoolLit(*n == 0)),
+            _ => Ret::DoneAsIs,
         },
-        (NaturalEven, [n, r..]) => match &*n.as_value() {
-            NaturalLit(n) => Ok((r, BoolLit(*n % 2 == 0))),
-            _ => Err(()),
+        (NaturalEven, [n]) => match &*n.as_whnf() {
+            NaturalLit(n) => Ret::ValueF(BoolLit(*n % 2 == 0)),
+            _ => Ret::DoneAsIs,
         },
-        (NaturalOdd, [n, r..]) => match &*n.as_value() {
-            NaturalLit(n) => Ok((r, BoolLit(*n % 2 != 0))),
-            _ => Err(()),
+        (NaturalOdd, [n]) => match &*n.as_whnf() {
+            NaturalLit(n) => Ret::ValueF(BoolLit(*n % 2 != 0)),
+            _ => Ret::DoneAsIs,
         },
-        (NaturalToInteger, [n, r..]) => match &*n.as_value() {
-            NaturalLit(n) => Ok((r, IntegerLit(*n as isize))),
-            _ => Err(()),
+        (NaturalToInteger, [n]) => match &*n.as_whnf() {
+            NaturalLit(n) => Ret::ValueF(IntegerLit(*n as isize)),
+            _ => Ret::DoneAsIs,
         },
-        (NaturalShow, [n, r..]) => match &*n.as_value() {
-            NaturalLit(n) => Ok((
-                r,
-                TextLit(vec![InterpolatedTextContents::Text(n.to_string())]),
-            )),
-            _ => Err(()),
+        (NaturalShow, [n]) => match &*n.as_whnf() {
+            NaturalLit(n) => {
+                Ret::ValueF(TextLit(vec![InterpolatedTextContents::Text(
+                    n.to_string(),
+                )]))
+            }
+            _ => Ret::DoneAsIs,
         },
-        (NaturalSubtract, [a, b, r..]) => {
-            match (&*a.as_value(), &*b.as_value()) {
-                (NaturalLit(a), NaturalLit(b)) => {
-                    Ok((r, NaturalLit(if b > a { b - a } else { 0 })))
-                }
-                (NaturalLit(0), b) => Ok((r, b.clone())),
-                (_, NaturalLit(0)) => Ok((r, NaturalLit(0))),
-                _ if a == b => Ok((r, NaturalLit(0))),
-                _ => Err(()),
+        (NaturalSubtract, [a, b]) => match (&*a.as_whnf(), &*b.as_whnf()) {
+            (NaturalLit(a), NaturalLit(b)) => {
+                Ret::ValueF(NaturalLit(if b > a { b - a } else { 0 }))
             }
-        }
-        (IntegerShow, [n, r..]) => match &*n.as_value() {
+            (NaturalLit(0), _) => Ret::Value(b.clone()),
+            (_, NaturalLit(0)) => Ret::ValueF(NaturalLit(0)),
+            _ if a == b => Ret::ValueF(NaturalLit(0)),
+            _ => Ret::DoneAsIs,
+        },
+        (IntegerShow, [n]) => match &*n.as_whnf() {
             IntegerLit(n) => {
                 let s = if *n < 0 {
                     n.to_string()
                 } else {
                     format!("+{}", n)
                 };
-                Ok((r, TextLit(vec![InterpolatedTextContents::Text(s)])))
+                Ret::ValueF(TextLit(vec![InterpolatedTextContents::Text(s)]))
             }
-            _ => Err(()),
+            _ => Ret::DoneAsIs,
         },
-        (IntegerToDouble, [n, r..]) => match &*n.as_value() {
-            IntegerLit(n) => Ok((r, DoubleLit(NaiveDouble::from(*n as f64)))),
-            _ => Err(()),
+        (IntegerToDouble, [n]) => match &*n.as_whnf() {
+            IntegerLit(n) => {
+                Ret::ValueF(DoubleLit(NaiveDouble::from(*n as f64)))
+            }
+            _ => Ret::DoneAsIs,
         },
-        (DoubleShow, [n, r..]) => match &*n.as_value() {
-            DoubleLit(n) => Ok((
-                r,
-                TextLit(vec![InterpolatedTextContents::Text(n.to_string())]),
-            )),
-            _ => Err(()),
+        (DoubleShow, [n]) => match &*n.as_whnf() {
+            DoubleLit(n) => {
+                Ret::ValueF(TextLit(vec![InterpolatedTextContents::Text(
+                    n.to_string(),
+                )]))
+            }
+            _ => Ret::DoneAsIs,
         },
-        (TextShow, [v, r..]) => match &*v.as_value() {
+        (TextShow, [v]) => match &*v.as_whnf() {
             TextLit(elts) => {
                 match elts.as_slice() {
                     // Empty string literal.
                     [] => {
                         // Printing InterpolatedText takes care of all the escaping
-                        let txt: InterpolatedText<X> =
+                        let txt: InterpolatedText<Normalized> =
                             std::iter::empty().collect();
                         let s = txt.to_string();
-                        Ok((
-                            r,
-                            TextLit(vec![InterpolatedTextContents::Text(s)]),
-                        ))
+                        Ret::ValueF(TextLit(vec![
+                            InterpolatedTextContents::Text(s),
+                        ]))
                     }
                     // If there are no interpolations (invariants ensure that when there are no
                     // interpolations, there is a single Text item) in the literal.
                     [InterpolatedTextContents::Text(s)] => {
                         // Printing InterpolatedText takes care of all the escaping
-                        let txt: InterpolatedText<X> = std::iter::once(
-                            InterpolatedTextContents::Text(s.clone()),
-                        )
-                        .collect();
+                        let txt: InterpolatedText<Normalized> =
+                            std::iter::once(InterpolatedTextContents::Text(
+                                s.clone(),
+                            ))
+                            .collect();
                         let s = txt.to_string();
-                        Ok((
-                            r,
-                            TextLit(vec![InterpolatedTextContents::Text(s)]),
-                        ))
+                        Ret::ValueF(TextLit(vec![
+                            InterpolatedTextContents::Text(s),
+                        ]))
                     }
-                    _ => Err(()),
+                    _ => Ret::DoneAsIs,
                 }
             }
-            _ => Err(()),
+            _ => Ret::DoneAsIs,
         },
-        (ListLength, [_, l, r..]) => match &*l.as_value() {
-            EmptyListLit(_) => Ok((r, NaturalLit(0))),
-            NEListLit(xs) => Ok((r, NaturalLit(xs.len()))),
-            _ => Err(()),
+        (ListLength, [_, l]) => match &*l.as_whnf() {
+            EmptyListLit(_) => Ret::ValueF(NaturalLit(0)),
+            NEListLit(xs) => Ret::ValueF(NaturalLit(xs.len())),
+            _ => Ret::DoneAsIs,
         },
-        (ListHead, [_, l, r..]) => match &*l.as_value() {
-            EmptyListLit(n) => Ok((r, EmptyOptionalLit(n.clone()))),
+        (ListHead, [_, l]) => match &*l.as_whnf() {
+            EmptyListLit(n) => Ret::ValueF(EmptyOptionalLit(n.clone())),
             NEListLit(xs) => {
-                Ok((r, NEOptionalLit(xs.iter().next().unwrap().clone())))
+                Ret::ValueF(NEOptionalLit(xs.iter().next().unwrap().clone()))
             }
-            _ => Err(()),
+            _ => Ret::DoneAsIs,
         },
-        (ListLast, [_, l, r..]) => match &*l.as_value() {
-            EmptyListLit(n) => Ok((r, EmptyOptionalLit(n.clone()))),
-            NEListLit(xs) => {
-                Ok((r, NEOptionalLit(xs.iter().rev().next().unwrap().clone())))
-            }
-            _ => Err(()),
+        (ListLast, [_, l]) => match &*l.as_whnf() {
+            EmptyListLit(n) => Ret::ValueF(EmptyOptionalLit(n.clone())),
+            NEListLit(xs) => Ret::ValueF(NEOptionalLit(
+                xs.iter().rev().next().unwrap().clone(),
+            )),
+            _ => Ret::DoneAsIs,
         },
-        (ListReverse, [_, l, r..]) => match &*l.as_value() {
-            EmptyListLit(n) => Ok((r, EmptyListLit(n.clone()))),
+        (ListReverse, [_, l]) => match &*l.as_whnf() {
+            EmptyListLit(n) => Ret::ValueF(EmptyListLit(n.clone())),
             NEListLit(xs) => {
-                Ok((r, NEListLit(xs.iter().rev().cloned().collect())))
+                Ret::ValueF(NEListLit(xs.iter().rev().cloned().collect()))
             }
-            _ => Err(()),
+            _ => Ret::DoneAsIs,
         },
-        (ListIndexed, [_, l, r..]) => match &*l.as_value() {
-            EmptyListLit(t) => {
-                let mut kts = HashMap::new();
-                kts.insert(
-                    "index".into(),
-                    TypeThunk::from_value(Value::from_builtin(Natural)),
-                );
-                kts.insert("value".into(), t.clone());
-                Ok((r, EmptyListLit(TypeThunk::from_value(RecordType(kts)))))
-            }
-            NEListLit(xs) => {
-                let xs = xs
-                    .iter()
-                    .enumerate()
-                    .map(|(i, e)| {
-                        let i = NaturalLit(i);
-                        let mut kvs = HashMap::new();
-                        kvs.insert("index".into(), Thunk::from_value(i));
-                        kvs.insert("value".into(), e.clone());
-                        Thunk::from_value(RecordLit(kvs))
-                    })
-                    .collect();
-                Ok((r, NEListLit(xs)))
+        (ListIndexed, [_, l]) => {
+            let l_whnf = l.as_whnf();
+            match &*l_whnf {
+                EmptyListLit(_) | NEListLit(_) => {
+                    // Extract the type of the list elements
+                    let t = match &*l_whnf {
+                        EmptyListLit(t) => t.clone(),
+                        NEListLit(xs) => xs[0].get_type_not_sort(),
+                        _ => unreachable!(),
+                    };
+
+                    // Construct the returned record type: { index: Natural, value: t }
+                    let mut kts = HashMap::new();
+                    kts.insert("index".into(), Value::from_builtin(Natural));
+                    kts.insert("value".into(), t.clone());
+                    let t = Value::from_valuef_and_type(
+                        RecordType(kts),
+                        Value::from_const(Type),
+                    );
+
+                    // Construct the new list, with added indices
+                    let list = match &*l_whnf {
+                        EmptyListLit(_) => EmptyListLit(t),
+                        NEListLit(xs) => NEListLit(
+                            xs.iter()
+                                .enumerate()
+                                .map(|(i, e)| {
+                                    let mut kvs = HashMap::new();
+                                    kvs.insert(
+                                        "index".into(),
+                                        Value::from_valuef_and_type(
+                                            NaturalLit(i),
+                                            Value::from_builtin(
+                                                Builtin::Natural,
+                                            ),
+                                        ),
+                                    );
+                                    kvs.insert("value".into(), e.clone());
+                                    Value::from_valuef_and_type(
+                                        RecordLit(kvs),
+                                        t.clone(),
+                                    )
+                                })
+                                .collect(),
+                        ),
+                        _ => unreachable!(),
+                    };
+                    Ret::ValueF(list)
+                }
+                _ => Ret::DoneAsIs,
             }
-            _ => Err(()),
-        },
-        (ListBuild, [t, f, r..]) => match &*f.as_value() {
+        }
+        (ListBuild, [t, f]) => match &*f.as_whnf() {
             // fold/build fusion
-            Value::AppliedBuiltin(ListFold, args) => {
+            ValueF::AppliedBuiltin(ListFold, args) => {
                 if args.len() >= 2 {
-                    Ok((r, args[1].to_value()))
+                    Ret::Value(args[1].clone())
                 } else {
                     // Do we really need to handle this case ?
                     unimplemented!()
                 }
             }
-            _ => Ok((
-                r,
-                f.app_val(Value::from_builtin(List).app_thunk(t.clone()))
-                    .app_val(ListConsClosure(
-                        TypeThunk::from_thunk(t.clone()),
-                        None,
-                    ))
-                    .app_val(EmptyListLit(TypeThunk::from_thunk(t.clone()))),
-            )),
+            _ => {
+                let list_t = Value::from_builtin(List).app(t.clone());
+                Ret::Value(
+                    f.app(list_t.clone())
+                        .app({
+                            // Move `t` under new variables
+                            let t1 = t.under_binder(Label::from("x"));
+                            let t2 = t1.under_binder(Label::from("xs"));
+                            make_closure!(
+                                λ(x : #t) ->
+                                λ(xs : List #t1) ->
+                                [ var(x, 1, #t2) ] # var(xs, 0, List #t2)
+                            )
+                        })
+                        .app(
+                            EmptyListLit(t.clone())
+                                .into_value_with_type(list_t),
+                        ),
+                )
+            }
         },
-        (ListFold, [_, l, _, cons, nil, r..]) => match &*l.as_value() {
-            EmptyListLit(_) => Ok((r, nil.to_value())),
+        (ListFold, [_, l, _, cons, nil, r..]) => match &*l.as_whnf() {
+            EmptyListLit(_) => Ret::ValueWithRemainingArgs(r, nil.clone()),
             NEListLit(xs) => {
                 let mut v = nil.clone();
-                for x in xs.iter().rev() {
-                    v = cons
-                        .clone()
-                        .app_thunk(x.clone())
-                        .app_thunk(v)
-                        .into_thunk();
+                for x in xs.iter().cloned().rev() {
+                    v = cons.app(x).app(v);
                 }
-                Ok((r, v.to_value()))
+                Ret::ValueWithRemainingArgs(r, v)
             }
-            _ => Err(()),
+            _ => Ret::DoneAsIs,
         },
-        (OptionalBuild, [t, f, r..]) => match &*f.as_value() {
+        (OptionalBuild, [t, f]) => match &*f.as_whnf() {
             // fold/build fusion
-            Value::AppliedBuiltin(OptionalFold, args) => {
+            ValueF::AppliedBuiltin(OptionalFold, args) => {
                 if args.len() >= 2 {
-                    Ok((r, args[1].to_value()))
+                    Ret::Value(args[1].clone())
                 } else {
                     // Do we really need to handle this case ?
                     unimplemented!()
                 }
             }
-            _ => Ok((
-                r,
-                f.app_val(Value::from_builtin(Optional).app_thunk(t.clone()))
-                    .app_val(OptionalSomeClosure(TypeThunk::from_thunk(
-                        t.clone(),
-                    )))
-                    .app_val(EmptyOptionalLit(TypeThunk::from_thunk(
-                        t.clone(),
-                    ))),
-            )),
+            _ => {
+                let optional_t = Value::from_builtin(Optional).app(t.clone());
+                Ret::Value(
+                    f.app(optional_t.clone())
+                        .app({
+                            let t1 = t.under_binder(Label::from("x"));
+                            make_closure!(λ(x: #t) -> Some(var(x, 0, #t1)))
+                        })
+                        .app(
+                            EmptyOptionalLit(t.clone())
+                                .into_value_with_type(optional_t),
+                        ),
+                )
+            }
         },
-        (OptionalFold, [_, v, _, just, nothing, r..]) => match &*v.as_value() {
-            EmptyOptionalLit(_) => Ok((r, nothing.to_value())),
-            NEOptionalLit(x) => Ok((r, just.app_thunk(x.clone()))),
-            _ => Err(()),
+        (OptionalFold, [_, v, _, just, nothing, r..]) => match &*v.as_whnf() {
+            EmptyOptionalLit(_) => {
+                Ret::ValueWithRemainingArgs(r, nothing.clone())
+            }
+            NEOptionalLit(x) => {
+                Ret::ValueWithRemainingArgs(r, just.app(x.clone()))
+            }
+            _ => Ret::DoneAsIs,
         },
-        (NaturalBuild, [f, r..]) => match &*f.as_value() {
+        (NaturalBuild, [f]) => match &*f.as_whnf() {
             // fold/build fusion
-            Value::AppliedBuiltin(NaturalFold, args) => {
+            ValueF::AppliedBuiltin(NaturalFold, args) => {
                 if !args.is_empty() {
-                    Ok((r, args[0].to_value()))
+                    Ret::Value(args[0].clone())
                 } else {
                     // Do we really need to handle this case ?
                     unimplemented!()
                 }
             }
-            _ => Ok((
-                r,
-                f.app_val(Value::from_builtin(Natural))
-                    .app_val(NaturalSuccClosure)
-                    .app_val(NaturalLit(0)),
-            )),
+            _ => Ret::Value(
+                f.app(Value::from_builtin(Natural))
+                    .app(make_closure!(
+                        λ(x : Natural) -> 1 + var(x, 0, Natural)
+                    ))
+                    .app(
+                        NaturalLit(0)
+                            .into_value_with_type(Value::from_builtin(Natural)),
+                    ),
+            ),
         },
-        (NaturalFold, [n, t, succ, zero, r..]) => match &*n.as_value() {
-            NaturalLit(0) => Ok((r, zero.to_value())),
+        (NaturalFold, [n, t, succ, zero, r..]) => match &*n.as_whnf() {
+            NaturalLit(0) => Ret::ValueWithRemainingArgs(r, zero.clone()),
             NaturalLit(n) => {
                 let fold = Value::from_builtin(NaturalFold)
-                    .app(NaturalLit(n - 1))
-                    .app_thunk(t.clone())
-                    .app_thunk(succ.clone())
-                    .app_thunk(zero.clone());
-                Ok((r, succ.app_val(fold)))
+                    .app(
+                        NaturalLit(n - 1)
+                            .into_value_with_type(Value::from_builtin(Natural)),
+                    )
+                    .app(t.clone())
+                    .app(succ.clone())
+                    .app(zero.clone());
+                Ret::ValueWithRemainingArgs(r, succ.app(fold))
             }
-            _ => Err(()),
+            _ => Ret::DoneAsIs,
         },
-        _ => Err(()),
+        _ => Ret::DoneAsIs,
     };
     match ret {
-        Ok((unconsumed_args, mut v)) => {
+        Ret::ValueF(v) => v,
+        Ret::Value(v) => v.to_whnf_check_type(ty),
+        Ret::ValueWithRemainingArgs(unconsumed_args, mut v) => {
             let n_consumed_args = args.len() - unconsumed_args.len();
             for x in args.into_iter().skip(n_consumed_args) {
-                v = v.app_thunk(x);
+                v = v.app(x);
             }
-            v
+            v.to_whnf_check_type(ty)
         }
-        Err(()) => AppliedBuiltin(b, args),
+        Ret::DoneAsIs => AppliedBuiltin(b, args),
     }
 }
 
-pub 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();
+pub(crate) fn apply_any(f: Value, a: Value, ty: &Value) -> ValueF {
+    let f_borrow = f.as_whnf();
     match &*f_borrow {
-        Value::Lam(x, _, e) => {
-            let val = Typed::from_thunk_untyped(a);
-            e.subst_shift(&x.into(), &val).to_value()
+        ValueF::Lam(x, _, e) => {
+            e.subst_shift(&x.into(), &a).to_whnf_check_type(ty)
         }
-        Value::AppliedBuiltin(b, args) => {
+        ValueF::AppliedBuiltin(b, args) => {
             use std::iter::once;
             let args = args.iter().cloned().chain(once(a.clone())).collect();
-            apply_builtin(*b, args)
-        }
-        Value::OptionalSomeClosure(_) => Value::NEOptionalLit(a),
-        Value::ListConsClosure(t, None) => {
-            Value::ListConsClosure(t.clone(), Some(a))
+            apply_builtin(*b, args, ty)
         }
-        Value::ListConsClosure(_, Some(x)) => {
-            let a_borrow = a.as_value();
-            match &*a_borrow {
-                Value::EmptyListLit(_) => Value::NEListLit(vec![x.clone()]),
-                Value::NEListLit(xs) => {
-                    use std::iter::once;
-                    let xs =
-                        once(x.clone()).chain(xs.iter().cloned()).collect();
-                    Value::NEListLit(xs)
-                }
-                _ => {
-                    drop(f_borrow);
-                    drop(a_borrow);
-                    fallback(f, a)
-                }
-            }
-        }
-        Value::NaturalSuccClosure => {
-            let a_borrow = a.as_value();
-            match &*a_borrow {
-                Value::NaturalLit(n) => Value::NaturalLit(n + 1),
-                _ => {
-                    drop(f_borrow);
-                    drop(a_borrow);
-                    fallback(f, a)
-                }
-            }
-        }
-        Value::UnionConstructor(l, kts) => {
-            Value::UnionLit(l.clone(), a, kts.clone())
+        ValueF::UnionConstructor(l, kts) => {
+            ValueF::UnionLit(l.clone(), a, kts.clone())
         }
         _ => {
             drop(f_borrow);
-            fallback(f, a)
+            ValueF::PartialExpr(ExprF::App(f, a))
         }
     }
 }
 
-pub fn squash_textlit(
-    elts: impl Iterator<Item = InterpolatedTextContents<Thunk>>,
-) -> Vec<InterpolatedTextContents<Thunk>> {
+pub(crate) fn squash_textlit(
+    elts: impl Iterator<Item = InterpolatedTextContents<Value>>,
+) -> Vec<InterpolatedTextContents<Value>> {
     use std::mem::replace;
     use InterpolatedTextContents::{Expr, Text};
 
     fn inner(
-        elts: impl Iterator<Item = InterpolatedTextContents<Thunk>>,
+        elts: impl Iterator<Item = InterpolatedTextContents<Value>>,
         crnt_str: &mut String,
-        ret: &mut Vec<InterpolatedTextContents<Thunk>>,
+        ret: &mut Vec<InterpolatedTextContents<Value>>,
     ) {
         for contents in elts {
             match contents {
                 Text(s) => crnt_str.push_str(&s),
                 Expr(e) => {
-                    let e_borrow = e.as_value();
+                    let e_borrow = e.as_whnf();
                     match &*e_borrow {
-                        Value::TextLit(elts2) => {
+                        ValueF::TextLit(elts2) => {
                             inner(elts2.iter().cloned(), crnt_str, ret)
                         }
                         _ => {
@@ -367,134 +450,20 @@ pub fn squash_textlit(
     ret
 }
 
-/// Reduces the imput expression to a Value. Evaluates as little as possible.
-pub 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),
-        _ => {}
-    }
-
-    // Thunk subexpressions
-    let expr: ExprF<Thunk, X> =
-        expr.as_ref().map_ref_with_special_handling_of_binders(
-            |e| Thunk::new(ctx.clone(), e.clone()),
-            |x, e| Thunk::new(ctx.skip(x), e.clone()),
-            |_| unreachable!(),
-        );
-
-    normalize_one_layer(expr)
-}
-
-// Small helper enum to avoid repetition
-enum Ret<'a> {
-    Value(Value),
-    Thunk(Thunk),
-    ThunkRef(&'a Thunk),
-    Expr(ExprF<Thunk, X>),
-}
-
-/// Performs an intersection of two HashMaps.
-///
-/// # Arguments
-///
-/// * `f` - Will compute the final value from the intersecting
-///         key and the values from both maps.
-///
-/// # Description
-///
-/// If the key is present in both maps then the final value for
-/// that key is computed via the `f` function.
-///
-/// The final map will contain the shared keys from the
-/// two input maps with the final computed value from `f`.
-pub(crate) fn intersection_with_key<K, T, U, V>(
-    mut f: impl FnMut(&K, &T, &U) -> V,
-    map1: &HashMap<K, T>,
-    map2: &HashMap<K, U>,
-) -> HashMap<K, V>
-where
-    K: std::hash::Hash + Eq + Clone,
-{
-    let mut kvs = HashMap::new();
-
-    for (k, t) in map1 {
-        // Only insert in the final map if the key exists in both
-        if let Some(u) = map2.get(k) {
-            kvs.insert(k.clone(), f(k, t, u));
-        }
-    }
-
-    kvs
-}
-
-/// Performs an outer join of two HashMaps.
-///
-/// # Arguments
-///
-/// * `ft` - Will convert the values of the first map
-///          into the target value.
-///
-/// * `fu` - Will convert the values of the second map
-///          into the target value.
-///
-/// * `fktu` - Will convert the key and values from both maps
-///           into the target type.
-///
-/// # Description
-///
-/// If the key is present in both maps then the final value for
-/// that key is computed via the `fktu` function. Otherwise, the
-/// final value will be calculated by either the `ft` or `fu` value
-/// depending on which map the key is present in.
-///
-/// The final map will contain all keys from the two input maps with
-/// also values computed as per above.
-pub(crate) fn outer_join<K, T, U, V>(
-    mut ft: impl FnMut(&T) -> V,
-    mut fu: impl FnMut(&U) -> V,
-    mut fktu: impl FnMut(&K, &T, &U) -> V,
-    map1: &HashMap<K, T>,
-    map2: &HashMap<K, U>,
-) -> HashMap<K, V>
-where
-    K: std::hash::Hash + Eq + Clone,
-{
-    let mut kvs = HashMap::new();
-
-    for (k1, t) in map1 {
-        let v = if let Some(u) = map2.get(k1) {
-            // The key exists in both maps
-            // so use all values for computation
-            fktu(k1, t, u)
-        } else {
-            // Key only exists in map1
-            ft(t)
-        };
-        kvs.insert(k1.clone(), v);
-    }
-
-    for (k1, u) in map2 {
-        // Insert if key was missing in map1
-        kvs.entry(k1.clone()).or_insert(fu(u));
-    }
-
-    kvs
-}
-
-pub(crate) fn merge_maps<K, V>(
+pub(crate) fn merge_maps<K, V, F, Err>(
     map1: &HashMap<K, V>,
     map2: &HashMap<K, V>,
-    mut f: impl FnMut(&V, &V) -> V,
-) -> HashMap<K, V>
+    mut f: F,
+) -> Result<HashMap<K, V>, Err>
 where
+    F: FnMut(&K, &V, &V) -> Result<V, Err>,
     K: std::hash::Hash + Eq + Clone,
     V: Clone,
 {
     let mut kvs = HashMap::new();
     for (x, v2) in map2 {
         let newv = if let Some(v1) = map1.get(x) {
-            f(v1, v2)
+            f(x, v1, v2)?
         } else {
             v2.clone()
         };
@@ -504,85 +473,98 @@ where
         // Insert only if key not already present
         kvs.entry(x.clone()).or_insert_with(|| v1.clone());
     }
-    kvs
+    Ok(kvs)
 }
 
-fn apply_binop<'a>(o: BinOp, x: &'a Thunk, y: &'a Thunk) -> Option<Ret<'a>> {
+// Small helper enum to avoid repetition
+enum Ret<'a> {
+    ValueF(ValueF),
+    Value(Value),
+    ValueRef(&'a Value),
+    Expr(ExprF<Value, Normalized>),
+}
+
+fn apply_binop<'a>(
+    o: BinOp,
+    x: &'a Value,
+    y: &'a Value,
+    ty: &Value,
+) -> Option<Ret<'a>> {
     use BinOp::{
         BoolAnd, BoolEQ, BoolNE, BoolOr, Equivalence, ListAppend, NaturalPlus,
         NaturalTimes, RecursiveRecordMerge, RecursiveRecordTypeMerge,
         RightBiasedRecordMerge, TextAppend,
     };
-    use Value::{
+    use ValueF::{
         BoolLit, EmptyListLit, NEListLit, NaturalLit, RecordLit, RecordType,
         TextLit,
     };
-    let x_borrow = x.as_value();
-    let y_borrow = y.as_value();
+    let x_borrow = x.as_whnf();
+    let y_borrow = y.as_whnf();
     Some(match (o, &*x_borrow, &*y_borrow) {
-        (BoolAnd, BoolLit(true), _) => Ret::ThunkRef(y),
-        (BoolAnd, _, BoolLit(true)) => Ret::ThunkRef(x),
-        (BoolAnd, BoolLit(false), _) => Ret::Value(BoolLit(false)),
-        (BoolAnd, _, BoolLit(false)) => Ret::Value(BoolLit(false)),
-        (BoolAnd, _, _) if x == y => Ret::ThunkRef(x),
-        (BoolOr, BoolLit(true), _) => Ret::Value(BoolLit(true)),
-        (BoolOr, _, BoolLit(true)) => Ret::Value(BoolLit(true)),
-        (BoolOr, BoolLit(false), _) => Ret::ThunkRef(y),
-        (BoolOr, _, BoolLit(false)) => Ret::ThunkRef(x),
-        (BoolOr, _, _) if x == y => Ret::ThunkRef(x),
-        (BoolEQ, BoolLit(true), _) => Ret::ThunkRef(y),
-        (BoolEQ, _, BoolLit(true)) => Ret::ThunkRef(x),
-        (BoolEQ, BoolLit(x), BoolLit(y)) => Ret::Value(BoolLit(x == y)),
-        (BoolEQ, _, _) if x == y => Ret::Value(BoolLit(true)),
-        (BoolNE, BoolLit(false), _) => Ret::ThunkRef(y),
-        (BoolNE, _, BoolLit(false)) => Ret::ThunkRef(x),
-        (BoolNE, BoolLit(x), BoolLit(y)) => Ret::Value(BoolLit(x != y)),
-        (BoolNE, _, _) if x == y => Ret::Value(BoolLit(false)),
-
-        (NaturalPlus, NaturalLit(0), _) => Ret::ThunkRef(y),
-        (NaturalPlus, _, NaturalLit(0)) => Ret::ThunkRef(x),
+        (BoolAnd, BoolLit(true), _) => Ret::ValueRef(y),
+        (BoolAnd, _, BoolLit(true)) => Ret::ValueRef(x),
+        (BoolAnd, BoolLit(false), _) => Ret::ValueF(BoolLit(false)),
+        (BoolAnd, _, BoolLit(false)) => Ret::ValueF(BoolLit(false)),
+        (BoolAnd, _, _) if x == y => Ret::ValueRef(x),
+        (BoolOr, BoolLit(true), _) => Ret::ValueF(BoolLit(true)),
+        (BoolOr, _, BoolLit(true)) => Ret::ValueF(BoolLit(true)),
+        (BoolOr, BoolLit(false), _) => Ret::ValueRef(y),
+        (BoolOr, _, BoolLit(false)) => Ret::ValueRef(x),
+        (BoolOr, _, _) if x == y => Ret::ValueRef(x),
+        (BoolEQ, BoolLit(true), _) => Ret::ValueRef(y),
+        (BoolEQ, _, BoolLit(true)) => Ret::ValueRef(x),
+        (BoolEQ, BoolLit(x), BoolLit(y)) => Ret::ValueF(BoolLit(x == y)),
+        (BoolEQ, _, _) if x == y => Ret::ValueF(BoolLit(true)),
+        (BoolNE, BoolLit(false), _) => Ret::ValueRef(y),
+        (BoolNE, _, BoolLit(false)) => Ret::ValueRef(x),
+        (BoolNE, BoolLit(x), BoolLit(y)) => Ret::ValueF(BoolLit(x != y)),
+        (BoolNE, _, _) if x == y => Ret::ValueF(BoolLit(false)),
+
+        (NaturalPlus, NaturalLit(0), _) => Ret::ValueRef(y),
+        (NaturalPlus, _, NaturalLit(0)) => Ret::ValueRef(x),
         (NaturalPlus, NaturalLit(x), NaturalLit(y)) => {
-            Ret::Value(NaturalLit(x + y))
+            Ret::ValueF(NaturalLit(x + y))
         }
-        (NaturalTimes, NaturalLit(0), _) => Ret::Value(NaturalLit(0)),
-        (NaturalTimes, _, NaturalLit(0)) => Ret::Value(NaturalLit(0)),
-        (NaturalTimes, NaturalLit(1), _) => Ret::ThunkRef(y),
-        (NaturalTimes, _, NaturalLit(1)) => Ret::ThunkRef(x),
+        (NaturalTimes, NaturalLit(0), _) => Ret::ValueF(NaturalLit(0)),
+        (NaturalTimes, _, NaturalLit(0)) => Ret::ValueF(NaturalLit(0)),
+        (NaturalTimes, NaturalLit(1), _) => Ret::ValueRef(y),
+        (NaturalTimes, _, NaturalLit(1)) => Ret::ValueRef(x),
         (NaturalTimes, NaturalLit(x), NaturalLit(y)) => {
-            Ret::Value(NaturalLit(x * y))
+            Ret::ValueF(NaturalLit(x * y))
         }
 
-        (ListAppend, EmptyListLit(_), _) => Ret::ThunkRef(y),
-        (ListAppend, _, EmptyListLit(_)) => Ret::ThunkRef(x),
-        (ListAppend, NEListLit(xs), NEListLit(ys)) => {
-            Ret::Value(NEListLit(xs.iter().chain(ys.iter()).cloned().collect()))
-        }
+        (ListAppend, EmptyListLit(_), _) => Ret::ValueRef(y),
+        (ListAppend, _, EmptyListLit(_)) => Ret::ValueRef(x),
+        (ListAppend, NEListLit(xs), NEListLit(ys)) => Ret::ValueF(NEListLit(
+            xs.iter().chain(ys.iter()).cloned().collect(),
+        )),
 
-        (TextAppend, TextLit(x), _) if x.is_empty() => Ret::ThunkRef(y),
-        (TextAppend, _, TextLit(y)) if y.is_empty() => Ret::ThunkRef(x),
-        (TextAppend, TextLit(x), TextLit(y)) => Ret::Value(TextLit(
+        (TextAppend, TextLit(x), _) if x.is_empty() => Ret::ValueRef(y),
+        (TextAppend, _, TextLit(y)) if y.is_empty() => Ret::ValueRef(x),
+        (TextAppend, TextLit(x), TextLit(y)) => Ret::ValueF(TextLit(
             squash_textlit(x.iter().chain(y.iter()).cloned()),
         )),
         (TextAppend, TextLit(x), _) => {
             use std::iter::once;
             let y = InterpolatedTextContents::Expr(y.clone());
-            Ret::Value(TextLit(squash_textlit(
+            Ret::ValueF(TextLit(squash_textlit(
                 x.iter().cloned().chain(once(y)),
             )))
         }
         (TextAppend, _, TextLit(y)) => {
             use std::iter::once;
             let x = InterpolatedTextContents::Expr(x.clone());
-            Ret::Value(TextLit(squash_textlit(
+            Ret::ValueF(TextLit(squash_textlit(
                 once(x).chain(y.iter().cloned()),
             )))
         }
 
         (RightBiasedRecordMerge, _, RecordLit(kvs)) if kvs.is_empty() => {
-            Ret::ThunkRef(x)
+            Ret::ValueRef(x)
         }
         (RightBiasedRecordMerge, RecordLit(kvs), _) if kvs.is_empty() => {
-            Ret::ThunkRef(y)
+            Ret::ValueRef(y)
         }
         (RightBiasedRecordMerge, RecordLit(kvs1), RecordLit(kvs2)) => {
             let mut kvs = kvs2.clone();
@@ -590,92 +572,83 @@ fn apply_binop<'a>(o: BinOp, x: &'a Thunk, y: &'a Thunk) -> Option<Ret<'a>> {
                 // Insert only if key not already present
                 kvs.entry(x.clone()).or_insert_with(|| v.clone());
             }
-            Ret::Value(RecordLit(kvs))
+            Ret::ValueF(RecordLit(kvs))
         }
 
         (RecursiveRecordMerge, _, RecordLit(kvs)) if kvs.is_empty() => {
-            Ret::ThunkRef(x)
+            Ret::ValueRef(x)
         }
         (RecursiveRecordMerge, RecordLit(kvs), _) if kvs.is_empty() => {
-            Ret::ThunkRef(y)
+            Ret::ValueRef(y)
         }
         (RecursiveRecordMerge, RecordLit(kvs1), RecordLit(kvs2)) => {
-            let kvs = merge_maps(kvs1, kvs2, |v1, v2| {
-                Thunk::from_partial_expr(ExprF::BinOp(
-                    RecursiveRecordMerge,
-                    v1.clone(),
-                    v2.clone(),
+            let ty_borrow = ty.as_whnf();
+            let kts = match &*ty_borrow {
+                RecordType(kts) => kts,
+                _ => unreachable!("Internal type error"),
+            };
+            let kvs = merge_maps::<_, _, _, !>(kvs1, kvs2, |k, v1, v2| {
+                Ok(Value::from_valuef_and_type(
+                    ValueF::PartialExpr(ExprF::BinOp(
+                        RecursiveRecordMerge,
+                        v1.clone(),
+                        v2.clone(),
+                    )),
+                    kts.get(k).expect("Internal type error").clone(),
                 ))
-            });
-            Ret::Value(RecordLit(kvs))
+            })?;
+            Ret::ValueF(RecordLit(kvs))
         }
 
-        (RecursiveRecordTypeMerge, _, RecordType(kvs)) if kvs.is_empty() => {
-            Ret::ThunkRef(x)
-        }
-        (RecursiveRecordTypeMerge, RecordType(kvs), _) if kvs.is_empty() => {
-            Ret::ThunkRef(y)
+        (RecursiveRecordTypeMerge, _, _) | (Equivalence, _, _) => {
+            unreachable!("This case should have been handled in typecheck")
         }
-        (RecursiveRecordTypeMerge, RecordType(kvs1), RecordType(kvs2)) => {
-            let kvs = merge_maps(kvs1, kvs2, |v1, v2| {
-                TypeThunk::from_thunk(Thunk::from_partial_expr(ExprF::BinOp(
-                    RecursiveRecordTypeMerge,
-                    v1.to_thunk(),
-                    v2.to_thunk(),
-                )))
-            });
-            Ret::Value(RecordType(kvs))
-        }
-
-        (Equivalence, _, _) => Ret::Value(Value::Equivalence(
-            TypeThunk::from_thunk(x.clone()),
-            TypeThunk::from_thunk(y.clone()),
-        )),
 
         _ => return None,
     })
 }
 
-pub fn normalize_one_layer(expr: ExprF<Thunk, X>) -> Value {
-    use Value::{
-        AppliedBuiltin, BoolLit, DoubleLit, EmptyListLit, IntegerLit, Lam,
-        NEListLit, NEOptionalLit, NaturalLit, Pi, RecordLit, RecordType,
-        TextLit, UnionConstructor, UnionLit, UnionType,
+pub(crate) fn normalize_one_layer(
+    expr: ExprF<Value, Normalized>,
+    ty: &Value,
+) -> ValueF {
+    use ValueF::{
+        AppliedBuiltin, BoolLit, DoubleLit, EmptyListLit, IntegerLit,
+        NEListLit, NEOptionalLit, NaturalLit, RecordLit, TextLit,
+        UnionConstructor, UnionLit, UnionType,
     };
 
     let ret = match expr {
-        ExprF::Embed(_) => unreachable!(),
-        ExprF::Var(_) => unreachable!(),
-        ExprF::Annot(x, _) => Ret::Thunk(x),
-        ExprF::Assert(_) => Ret::Expr(expr),
-        ExprF::Lam(x, t, e) => {
-            Ret::Value(Lam(x.into(), TypeThunk::from_thunk(t), e))
+        ExprF::Import(_) => unreachable!(
+            "There should remain no imports in a resolved expression"
+        ),
+        // Those cases have already been completely handled in the typechecking phase (using
+        // `RetWhole`), so they won't appear here.
+        ExprF::Lam(_, _, _)
+        | ExprF::Pi(_, _, _)
+        | ExprF::Let(_, _, _, _)
+        | ExprF::Embed(_)
+        | ExprF::Const(_)
+        | ExprF::Builtin(_)
+        | ExprF::Var(_)
+        | ExprF::Annot(_, _)
+        | ExprF::RecordType(_)
+        | ExprF::UnionType(_) => {
+            unreachable!("This case should have been handled in typecheck")
         }
-        ExprF::Pi(x, t, e) => Ret::Value(Pi(
-            x.into(),
-            TypeThunk::from_thunk(t),
-            TypeThunk::from_thunk(e),
-        )),
-        ExprF::Let(x, _, v, b) => {
-            let v = Typed::from_thunk_untyped(v);
-            Ret::Thunk(b.subst_shift(&x.into(), &v))
-        }
-        ExprF::App(v, a) => Ret::Value(v.app_thunk(a)),
-        ExprF::Builtin(b) => Ret::Value(Value::from_builtin(b)),
-        ExprF::Const(c) => Ret::Value(Value::Const(c)),
-        ExprF::BoolLit(b) => Ret::Value(BoolLit(b)),
-        ExprF::NaturalLit(n) => Ret::Value(NaturalLit(n)),
-        ExprF::IntegerLit(n) => Ret::Value(IntegerLit(n)),
-        ExprF::DoubleLit(n) => Ret::Value(DoubleLit(n)),
-        ExprF::SomeLit(e) => Ret::Value(NEOptionalLit(e)),
+        ExprF::Assert(_) => Ret::Expr(expr),
+        ExprF::App(v, a) => Ret::Value(v.app(a)),
+        ExprF::BoolLit(b) => Ret::ValueF(BoolLit(b)),
+        ExprF::NaturalLit(n) => Ret::ValueF(NaturalLit(n)),
+        ExprF::IntegerLit(n) => Ret::ValueF(IntegerLit(n)),
+        ExprF::DoubleLit(n) => Ret::ValueF(DoubleLit(n)),
+        ExprF::SomeLit(e) => Ret::ValueF(NEOptionalLit(e)),
         ExprF::EmptyListLit(ref t) => {
             // Check if the type is of the form `List x`
-            let t_borrow = t.as_value();
+            let t_borrow = t.as_whnf();
             match &*t_borrow {
                 AppliedBuiltin(Builtin::List, args) if args.len() == 1 => {
-                    Ret::Value(EmptyListLit(TypeThunk::from_thunk(
-                        args[0].clone(),
-                    )))
+                    Ret::ValueF(EmptyListLit(args[0].clone()))
                 }
                 _ => {
                     drop(t_borrow);
@@ -684,43 +657,33 @@ pub fn normalize_one_layer(expr: ExprF<Thunk, X>) -> Value {
             }
         }
         ExprF::NEListLit(elts) => {
-            Ret::Value(NEListLit(elts.into_iter().collect()))
+            Ret::ValueF(NEListLit(elts.into_iter().collect()))
         }
         ExprF::RecordLit(kvs) => {
-            Ret::Value(RecordLit(kvs.into_iter().collect()))
+            Ret::ValueF(RecordLit(kvs.into_iter().collect()))
         }
-        ExprF::RecordType(kts) => Ret::Value(RecordType(
-            kts.into_iter()
-                .map(|(k, t)| (k, TypeThunk::from_thunk(t)))
-                .collect(),
-        )),
-        ExprF::UnionType(kts) => Ret::Value(UnionType(
-            kts.into_iter()
-                .map(|(k, t)| (k, t.map(|t| TypeThunk::from_thunk(t))))
-                .collect(),
-        )),
         ExprF::TextLit(elts) => {
             use InterpolatedTextContents::Expr;
             let elts: Vec<_> = squash_textlit(elts.into_iter());
             // Simplify bare interpolation
             if let [Expr(th)] = elts.as_slice() {
-                Ret::Thunk(th.clone())
+                Ret::Value(th.clone())
             } else {
-                Ret::Value(TextLit(elts))
+                Ret::ValueF(TextLit(elts))
             }
         }
         ExprF::BoolIf(ref b, ref e1, ref e2) => {
-            let b_borrow = b.as_value();
+            let b_borrow = b.as_whnf();
             match &*b_borrow {
-                BoolLit(true) => Ret::ThunkRef(e1),
-                BoolLit(false) => Ret::ThunkRef(e2),
+                BoolLit(true) => Ret::ValueRef(e1),
+                BoolLit(false) => Ret::ValueRef(e2),
                 _ => {
-                    let e1_borrow = e1.as_value();
-                    let e2_borrow = e2.as_value();
+                    let e1_borrow = e1.as_whnf();
+                    let e2_borrow = e2.as_whnf();
                     match (&*e1_borrow, &*e2_borrow) {
                         // Simplify `if b then True else False`
-                        (BoolLit(true), BoolLit(false)) => Ret::ThunkRef(b),
-                        _ if e1 == e2 => Ret::ThunkRef(e1),
+                        (BoolLit(true), BoolLit(false)) => Ret::ValueRef(b),
+                        _ if e1 == e2 => Ret::ValueRef(e1),
                         _ => {
                             drop(b_borrow);
                             drop(e1_borrow);
@@ -731,18 +694,18 @@ pub fn normalize_one_layer(expr: ExprF<Thunk, X>) -> Value {
                 }
             }
         }
-        ExprF::BinOp(o, ref x, ref y) => match apply_binop(o, x, y) {
+        ExprF::BinOp(o, ref x, ref y) => match apply_binop(o, x, y, ty) {
             Some(ret) => ret,
             None => Ret::Expr(expr),
         },
 
-        ExprF::Projection(_, ls) if ls.is_empty() => {
-            Ret::Value(RecordLit(HashMap::new()))
+        ExprF::Projection(_, ref ls) if ls.is_empty() => {
+            Ret::ValueF(RecordLit(HashMap::new()))
         }
         ExprF::Projection(ref v, ref ls) => {
-            let v_borrow = v.as_value();
+            let v_borrow = v.as_whnf();
             match &*v_borrow {
-                RecordLit(kvs) => Ret::Value(RecordLit(
+                RecordLit(kvs) => Ret::ValueF(RecordLit(
                     ls.iter()
                         .filter_map(|l| {
                             kvs.get(l).map(|x| (l.clone(), x.clone()))
@@ -756,17 +719,17 @@ pub fn normalize_one_layer(expr: ExprF<Thunk, X>) -> Value {
             }
         }
         ExprF::Field(ref v, ref l) => {
-            let v_borrow = v.as_value();
+            let v_borrow = v.as_whnf();
             match &*v_borrow {
                 RecordLit(kvs) => match kvs.get(l) {
-                    Some(r) => Ret::Thunk(r.clone()),
+                    Some(r) => Ret::Value(r.clone()),
                     None => {
                         drop(v_borrow);
                         Ret::Expr(expr)
                     }
                 },
                 UnionType(kts) => {
-                    Ret::Value(UnionConstructor(l.clone(), kts.clone()))
+                    Ret::ValueF(UnionConstructor(l.clone(), kts.clone()))
                 }
                 _ => {
                     drop(v_borrow);
@@ -776,11 +739,11 @@ pub fn normalize_one_layer(expr: ExprF<Thunk, X>) -> Value {
         }
 
         ExprF::Merge(ref handlers, ref variant, _) => {
-            let handlers_borrow = handlers.as_value();
-            let variant_borrow = variant.as_value();
+            let handlers_borrow = handlers.as_whnf();
+            let variant_borrow = variant.as_whnf();
             match (&*handlers_borrow, &*variant_borrow) {
                 (RecordLit(kvs), UnionConstructor(l, _)) => match kvs.get(l) {
-                    Some(h) => Ret::Thunk(h.clone()),
+                    Some(h) => Ret::Value(h.clone()),
                     None => {
                         drop(handlers_borrow);
                         drop(variant_borrow);
@@ -788,7 +751,7 @@ pub fn normalize_one_layer(expr: ExprF<Thunk, X>) -> Value {
                     }
                 },
                 (RecordLit(kvs), UnionLit(l, v, _)) => match kvs.get(l) {
-                    Some(h) => Ret::Value(h.app_thunk(v.clone())),
+                    Some(h) => Ret::Value(h.app(v.clone())),
                     None => {
                         drop(handlers_borrow);
                         drop(variant_borrow);
@@ -802,12 +765,26 @@ pub fn normalize_one_layer(expr: ExprF<Thunk, X>) -> Value {
                 }
             }
         }
+        ExprF::ToMap(_, _) => unimplemented!("toMap"),
     };
 
     match ret {
-        Ret::Value(v) => v,
-        Ret::Thunk(th) => th.to_value(),
-        Ret::ThunkRef(th) => th.to_value(),
-        Ret::Expr(expr) => Value::PartialExpr(expr),
+        Ret::ValueF(v) => v,
+        Ret::Value(v) => v.to_whnf_check_type(ty),
+        Ret::ValueRef(v) => v.to_whnf_check_type(ty),
+        Ret::Expr(expr) => ValueF::PartialExpr(expr),
+    }
+}
+
+/// Normalize a ValueF into WHNF
+pub(crate) fn normalize_whnf(v: ValueF, ty: &Value) -> ValueF {
+    match v {
+        ValueF::AppliedBuiltin(b, args) => apply_builtin(b, args, ty),
+        ValueF::PartialExpr(e) => normalize_one_layer(e, ty),
+        ValueF::TextLit(elts) => {
+            ValueF::TextLit(squash_textlit(elts.into_iter()))
+        }
+        // All other cases are already in WHNF
+        v => v,
     }
 }
diff --git a/dhall/src/phase/parse.rs b/dhall/src/phase/parse.rs
index 734f6e1..540ceea 100644
--- a/dhall/src/phase/parse.rs
+++ b/dhall/src/phase/parse.rs
@@ -8,7 +8,7 @@ use crate::error::Error;
 use crate::phase::resolve::ImportRoot;
 use crate::phase::Parsed;
 
-pub fn parse_file(f: &Path) -> Result<Parsed, Error> {
+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)?;
@@ -16,22 +16,22 @@ pub fn parse_file(f: &Path) -> Result<Parsed, Error> {
     Ok(Parsed(expr, root))
 }
 
-pub fn parse_str(s: &str) -> Result<Parsed, Error> {
+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 fn parse_binary(data: &[u8]) -> Result<Parsed, Error> {
+pub(crate) fn parse_binary(data: &[u8]) -> Result<Parsed, Error> {
     let expr = crate::phase::binary::decode(data)?;
     let root = ImportRoot::LocalDir(std::env::current_dir()?);
-    Ok(Parsed(expr.note_absurd(), root))
+    Ok(Parsed(expr, root))
 }
 
-pub fn parse_binary_file(f: &Path) -> Result<Parsed, Error> {
+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))
+    Ok(Parsed(expr, root))
 }
diff --git a/dhall/src/phase/resolve.rs b/dhall/src/phase/resolve.rs
index ac264e6..5bde68a 100644
--- a/dhall/src/phase/resolve.rs
+++ b/dhall/src/phase/resolve.rs
@@ -1,20 +1,20 @@
 use std::collections::HashMap;
 use std::path::{Path, PathBuf};
 
-use dhall_syntax::Import;
-
 use crate::error::{Error, ImportError};
-use crate::phase::{Normalized, Parsed, Resolved};
+use crate::phase::{Normalized, NormalizedExpr, Parsed, Resolved};
+
+type Import = dhall_syntax::Import<NormalizedExpr>;
 
 /// A root from which to resolve relative imports.
 #[derive(Debug, Clone, PartialEq, Eq)]
-pub enum ImportRoot {
+pub(crate) enum ImportRoot {
     LocalDir(PathBuf),
 }
 
 type ImportCache = HashMap<Import, Normalized>;
 
-pub type ImportStack = Vec<Import>;
+pub(crate) type ImportStack = Vec<Import>;
 
 
 fn resolve_import(
@@ -29,9 +29,9 @@ fn resolve_import(
     let cwd = match root {
         LocalDir(cwd) => cwd,
     };
-    match &import.location_hashed.location {
+    match &import.location {
         Local(prefix, path) => {
-            let path_buf: PathBuf = path.clone().into_iter().collect();
+            let path_buf: PathBuf = path.file_path.iter().collect();
             let path_buf = match prefix {
                 // TODO: fail gracefully
                 Parent => cwd.parent().unwrap().join(path_buf),
@@ -91,11 +91,11 @@ fn do_resolve_expr(
     Ok(Resolved(expr))
 }
 
-pub fn resolve(e: Parsed) -> Result<Resolved, ImportError> {
+pub(crate) fn resolve(e: Parsed) -> Result<Resolved, ImportError> {
     do_resolve_expr(e, &mut HashMap::new(), &Vec::new())
 }
 
-pub fn skip_resolve_expr(
+pub(crate) fn skip_resolve_expr(
     Parsed(expr, _root): Parsed,
 ) -> Result<Resolved, ImportError> {
     let resolve = |import: &Import| -> Result<Normalized, ImportError> {
@@ -106,18 +106,26 @@ pub fn skip_resolve_expr(
 }
 
 #[cfg(test)]
+#[rustfmt::skip]
 mod spec_tests {
-    #![rustfmt::skip]
-
     macro_rules! import_success {
         ($name:ident, $path:expr) => {
-            make_spec_test!(Import, Success, $name, &("../dhall-lang/tests/import/success/".to_owned() + $path));
+            make_spec_test!(
+                ImportSuccess(
+                    &("../dhall-lang/tests/import/success/".to_owned() + $path + "A.dhall"),
+                    &("../dhall-lang/tests/import/success/".to_owned() + $path + "B.dhall")
+                ),
+                $name
+            );
         };
     }
 
     // macro_rules! import_failure {
     //     ($name:ident, $path:expr) => {
-    //         make_spec_test!(Import, Failure, $name, &("../dhall-lang/tests/import/failure/".to_owned() + $path));
+    //         make_spec_test!(
+    //             ImportFailure(&("../dhall-lang/tests/import/failure/".to_owned() + $path + ".dhall")),
+    //             $name
+    //         );
     //     };
     // }
 
diff --git a/dhall/src/phase/typecheck.rs b/dhall/src/phase/typecheck.rs
index 299997a..9013c1f 100644
--- a/dhall/src/phase/typecheck.rs
+++ b/dhall/src/phase/typecheck.rs
@@ -1,34 +1,29 @@
+use std::cmp::max;
 use std::collections::HashMap;
 
 use dhall_syntax::{
-    rc, Builtin, Const, Expr, ExprF, InterpolatedTextContents, Label, Span,
-    SubExpr, X,
+    rc, Builtin, Const, Expr, ExprF, InterpolatedTextContents, Label,
 };
 
-use crate::core::context::{NormalizationContext, TypecheckContext};
-use crate::core::thunk::{Thunk, TypeThunk};
+use crate::core::context::TypecheckContext;
 use crate::core::value::Value;
+use crate::core::valuef::ValueF;
 use crate::core::var::{Shift, Subst};
 use crate::error::{TypeError, TypeMessage};
-use crate::phase::{Normalized, Resolved, Type, Typed};
+use crate::phase::Normalized;
 
 fn tck_pi_type(
     ctx: &TypecheckContext,
     x: Label,
-    tx: Type,
-    te: Type,
-) -> Result<Typed, TypeError> {
+    tx: Value,
+    te: Value,
+) -> Result<Value, TypeError> {
     use crate::error::TypeMessage::*;
     let ctx2 = ctx.insert_type(&x, tx.clone());
 
     let ka = match tx.get_type()?.as_const() {
         Some(k) => k,
-        _ => {
-            return Err(TypeError::new(
-                ctx,
-                InvalidInputType(tx.to_normalized()),
-            ))
-        }
+        _ => return Err(TypeError::new(ctx, InvalidInputType(tx))),
     };
 
     let kb = match te.get_type()?.as_const() {
@@ -36,64 +31,58 @@ fn tck_pi_type(
         _ => {
             return Err(TypeError::new(
                 &ctx2,
-                InvalidOutputType(te.get_type()?.to_normalized()),
+                InvalidOutputType(te.get_type()?),
             ))
         }
     };
 
     let k = function_check(ka, kb);
 
-    Ok(Typed::from_thunk_and_type(
-        Value::Pi(x.into(), TypeThunk::from_type(tx), TypeThunk::from_type(te))
-            .into_thunk(),
-        Type::from_const(k),
+    Ok(Value::from_valuef_and_type(
+        ValueF::Pi(x.into(), tx, te),
+        Value::from_const(k),
     ))
 }
 
 fn tck_record_type(
     ctx: &TypecheckContext,
-    kts: impl IntoIterator<Item = Result<(Label, Type), TypeError>>,
-) -> Result<Typed, TypeError> {
+    kts: impl IntoIterator<Item = Result<(Label, Value), TypeError>>,
+) -> Result<Value, TypeError> {
     use crate::error::TypeMessage::*;
     use std::collections::hash_map::Entry;
     let mut new_kts = HashMap::new();
-    // Check that all types are the same const
-    let mut k = None;
+    // An empty record type has type Type
+    let mut k = Const::Type;
     for e in kts {
         let (x, t) = e?;
-        match (k, t.get_type()?.as_const()) {
-            (None, Some(k2)) => k = Some(k2),
-            (Some(k1), Some(k2)) if k1 == k2 => {}
-            _ => {
-                return Err(TypeError::new(
-                    ctx,
-                    InvalidFieldType(x.clone(), t.clone()),
-                ))
-            }
+        // Construct the union of the contained `Const`s
+        match t.get_type()?.as_const() {
+            Some(k2) => k = max(k, k2),
+            None => return Err(TypeError::new(ctx, InvalidFieldType(x, t))),
         }
-        let entry = new_kts.entry(x.clone());
+        // Check for duplicated entries
+        let entry = new_kts.entry(x);
         match &entry {
             Entry::Occupied(_) => {
                 return Err(TypeError::new(ctx, RecordTypeDuplicateField))
             }
-            Entry::Vacant(_) => {
-                entry.or_insert_with(|| TypeThunk::from_type(t.clone()))
-            }
+            Entry::Vacant(_) => entry.or_insert_with(|| t),
         };
     }
-    // An empty record type has type Type
-    let k = k.unwrap_or(dhall_syntax::Const::Type);
 
-    Ok(Typed::from_thunk_and_type(
-        Value::RecordType(new_kts).into_thunk(),
-        Type::from_const(k),
+    Ok(Value::from_valuef_and_type(
+        ValueF::RecordType(new_kts),
+        Value::from_const(k),
     ))
 }
 
-fn tck_union_type(
+fn tck_union_type<Iter>(
     ctx: &TypecheckContext,
-    kts: impl IntoIterator<Item = Result<(Label, Option<Type>), TypeError>>,
-) -> Result<Typed, TypeError> {
+    kts: Iter,
+) -> Result<Value, TypeError>
+where
+    Iter: IntoIterator<Item = Result<(Label, Option<Value>), TypeError>>,
+{
     use crate::error::TypeMessage::*;
     use std::collections::hash_map::Entry;
     let mut new_kts = HashMap::new();
@@ -108,49 +97,48 @@ fn tck_union_type(
                 _ => {
                     return Err(TypeError::new(
                         ctx,
-                        InvalidFieldType(x.clone(), t.clone()),
+                        InvalidFieldType(x, t.clone()),
                     ))
                 }
             }
         }
-        let entry = new_kts.entry(x.clone());
+        let entry = new_kts.entry(x);
         match &entry {
             Entry::Occupied(_) => {
                 return Err(TypeError::new(ctx, UnionTypeDuplicateField))
             }
-            Entry::Vacant(_) => entry.or_insert_with(|| {
-                t.as_ref().map(|t| TypeThunk::from_type(t.clone()))
-            }),
+            Entry::Vacant(_) => entry.or_insert_with(|| t),
         };
     }
 
     // An empty union type has type Type;
     // an union type with only unary variants also has type Type
-    let k = k.unwrap_or(dhall_syntax::Const::Type);
+    let k = k.unwrap_or(Const::Type);
 
-    Ok(Typed::from_thunk_and_type(
-        Value::UnionType(new_kts).into_thunk(),
-        Type::from_const(k),
+    Ok(Value::from_valuef_and_type(
+        ValueF::UnionType(new_kts),
+        Value::from_const(k),
     ))
 }
 
 fn function_check(a: Const, b: Const) -> Const {
-    use dhall_syntax::Const::Type;
-    use std::cmp::max;
-    if b == Type {
-        Type
+    if b == Const::Type {
+        Const::Type
     } else {
         max(a, b)
     }
 }
 
-pub fn type_of_const(c: Const) -> Result<Type, TypeError> {
+pub(crate) fn const_to_value(c: Const) -> Value {
+    let v = ValueF::Const(c);
     match c {
-        Const::Type => Ok(Type::from_const(Const::Kind)),
-        Const::Kind => Ok(Type::from_const(Const::Sort)),
-        Const::Sort => {
-            Err(TypeError::new(&TypecheckContext::new(), TypeMessage::Sort))
+        Const::Type => {
+            Value::from_valuef_and_type(v, const_to_value(Const::Kind))
         }
+        Const::Kind => {
+            Value::from_valuef_and_type(v, const_to_value(Const::Sort))
+        }
+        Const::Sort => Value::const_sort(),
     }
 }
 
@@ -210,9 +198,9 @@ macro_rules! make_type {
     };
 }
 
-fn type_of_builtin(b: Builtin) -> Expr<X, X> {
+fn type_of_builtin<E>(b: Builtin) -> Expr<E> {
     use dhall_syntax::Builtin::*;
-    match b {
+    rc(match b {
         Bool | Natural | Integer | Double | Text => make_type!(Type),
         List | Optional => make_type!(
             Type -> Type
@@ -292,28 +280,15 @@ fn type_of_builtin(b: Builtin) -> Expr<X, X> {
         OptionalNone => make_type!(
             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.
-pub fn mktype(
-    ctx: &TypecheckContext,
-    e: SubExpr<Span, Normalized>,
-) -> Result<Type, TypeError> {
-    Ok(type_with(ctx, e)?.to_type())
-}
-
-pub fn builtin_to_type(b: Builtin) -> Result<Type, TypeError> {
-    mktype(&TypecheckContext::new(), SubExpr::from_builtin(b))
+    })
 }
 
-/// Intermediary return type
-enum Ret {
-    /// Returns the contained value as is
-    RetWhole(Typed),
-    /// Use the contained Type as the type of the input expression
-    RetTypeOnly(Type),
+pub(crate) fn builtin_to_value(b: Builtin) -> Value {
+    let ctx = TypecheckContext::new();
+    Value::from_valuef_and_type(
+        ValueF::from_builtin(b),
+        type_with(&ctx, type_of_builtin(b)).unwrap(),
+    )
 }
 
 /// Type-check an expression and return the expression alongside its type if type-checking
@@ -322,29 +297,25 @@ enum Ret {
 /// normalized as well.
 fn type_with(
     ctx: &TypecheckContext,
-    e: SubExpr<Span, Normalized>,
-) -> Result<Typed, TypeError> {
+    e: Expr<Normalized>,
+) -> Result<Value, TypeError> {
     use dhall_syntax::ExprF::{Annot, Embed, Lam, Let, Pi, Var};
 
-    use Ret::*;
     Ok(match e.as_ref() {
-        Lam(x, t, b) => {
-            let tx = mktype(ctx, t.clone())?;
-            let ctx2 = ctx.insert_type(x, tx.clone());
-            let b = type_with(&ctx2, b.clone())?;
-            let v = Value::Lam(
-                x.clone().into(),
-                TypeThunk::from_type(tx.clone()),
-                b.to_thunk(),
-            );
-            let tb = b.get_type()?.into_owned();
-            let t = tck_pi_type(ctx, x.clone(), tx, tb)?.to_type();
-            Typed::from_thunk_and_type(Thunk::from_value(v), t)
+        Lam(var, annot, body) => {
+            let annot = type_with(ctx, annot.clone())?;
+            let ctx2 = ctx.insert_type(var, annot.clone());
+            let body = type_with(&ctx2, body.clone())?;
+            let body_type = body.get_type()?;
+            Value::from_valuef_and_type(
+                ValueF::Lam(var.clone().into(), annot.clone(), body),
+                tck_pi_type(ctx, var.clone(), annot, body_type)?,
+            )
         }
         Pi(x, ta, tb) => {
-            let ta = mktype(ctx, ta.clone())?;
+            let ta = type_with(ctx, ta.clone())?;
             let ctx2 = ctx.insert_type(x, ta.clone());
-            let tb = mktype(&ctx2, tb.clone())?;
+            let tb = type_with(&ctx2, tb.clone())?;
             return tck_pi_type(ctx, x.clone(), ta, tb);
         }
         Let(x, t, v, e) => {
@@ -357,9 +328,9 @@ fn type_with(
             let v = type_with(ctx, v)?;
             return type_with(&ctx.insert_value(x, v.clone())?, e.clone());
         }
-        Embed(p) => p.clone().into_typed(),
+        Embed(p) => p.clone().into_typed().into_value(),
         Var(var) => match ctx.lookup(&var) {
-            Some(typed) => typed,
+            Some(typed) => typed.clone(),
             None => {
                 return Err(TypeError::new(
                     ctx,
@@ -367,25 +338,13 @@ fn type_with(
                 ))
             }
         },
-        _ => {
+        e => {
             // Typecheck recursively all subexpressions
-            let expr =
-                e.as_ref().traverse_ref_with_special_handling_of_binders(
-                    |e| type_with(ctx, e.clone()),
-                    |_, _| unreachable!(),
-                    |_| unreachable!(),
-                )?;
-            let ret = type_last_layer(ctx, &expr)?;
-            match ret {
-                RetTypeOnly(typ) => {
-                    let expr = expr.map_ref_simple(|typed| typed.to_thunk());
-                    Typed::from_thunk_and_type(
-                        Thunk::from_partial_expr(expr),
-                        typ,
-                    )
-                }
-                RetWhole(tt) => tt,
-            }
+            let expr = e.traverse_ref_with_special_handling_of_binders(
+                |e| type_with(ctx, e.clone()),
+                |_, _| unreachable!(),
+            )?;
+            type_last_layer(ctx, expr)?
         }
     })
 }
@@ -394,473 +353,305 @@ fn type_with(
 /// layer.
 fn type_last_layer(
     ctx: &TypecheckContext,
-    e: &ExprF<Typed, X>,
-) -> Result<Ret, TypeError> {
+    e: ExprF<Value, Normalized>,
+) -> Result<Value, TypeError> {
     use crate::error::TypeMessage::*;
     use dhall_syntax::BinOp::*;
     use dhall_syntax::Builtin::*;
     use dhall_syntax::Const::Type;
     use dhall_syntax::ExprF::*;
+    let mkerr = |msg: TypeMessage| Err(TypeError::new(ctx, msg));
+
+    /// Intermediary return type
+    enum Ret {
+        /// Returns the contained value as is
+        RetWhole(Value),
+        /// Returns the input expression `e` with the contained value as its type
+        RetTypeOnly(Value),
+    }
     use Ret::*;
-    let mkerr = |msg: TypeMessage| TypeError::new(ctx, msg);
 
-    match e {
+    let ret = match &e {
+        Import(_) => unreachable!(
+            "There should remain no imports in a resolved expression"
+        ),
         Lam(_, _, _) | Pi(_, _, _) | Let(_, _, _, _) | Embed(_) | Var(_) => {
             unreachable!()
         }
         App(f, a) => {
             let tf = f.get_type()?;
-            let (x, tx, tb) = match &tf.to_value() {
-                Value::Pi(x, tx, tb) => (x.clone(), tx.to_type(), tb.to_type()),
-                _ => return Err(mkerr(NotAFunction(f.clone()))),
+            let tf_borrow = tf.as_whnf();
+            let (x, tx, tb) = match &*tf_borrow {
+                ValueF::Pi(x, tx, tb) => (x, tx, tb),
+                _ => return mkerr(NotAFunction(f.clone())),
             };
-            if a.get_type()?.as_ref() != &tx {
-                return Err(mkerr(TypeMismatch(
-                    f.clone(),
-                    tx.to_normalized(),
-                    a.clone(),
-                )));
+            if &a.get_type()? != tx {
+                return mkerr(TypeMismatch(f.clone(), tx.clone(), a.clone()));
             }
 
-            Ok(RetTypeOnly(tb.subst_shift(&x.into(), &a)))
+            RetTypeOnly(tb.subst_shift(&x.into(), a))
         }
         Annot(x, t) => {
-            let t = t.to_type();
-            if &t != x.get_type()?.as_ref() {
-                return Err(mkerr(AnnotMismatch(x.clone(), t.to_normalized())));
+            if &x.get_type()? != t {
+                return mkerr(AnnotMismatch(x.clone(), t.clone()));
             }
-            Ok(RetTypeOnly(x.get_type()?.into_owned()))
+            RetWhole(x.clone())
         }
         Assert(t) => {
-            match t.to_value() {
-                Value::Equivalence(x, y) if x == y => {}
-                Value::Equivalence(x, y) => {
-                    return Err(mkerr(AssertMismatch(
-                        x.to_typed(),
-                        y.to_typed(),
-                    )))
+            match &*t.as_whnf() {
+                ValueF::Equivalence(x, y) if x == y => {}
+                ValueF::Equivalence(x, y) => {
+                    return mkerr(AssertMismatch(x.clone(), y.clone()))
                 }
-                _ => return Err(mkerr(AssertMustTakeEquivalence)),
+                _ => return mkerr(AssertMustTakeEquivalence),
             }
-            Ok(RetTypeOnly(t.to_type()))
+            RetTypeOnly(t.clone())
         }
         BoolIf(x, y, z) => {
-            if x.get_type()?.as_ref() != &builtin_to_type(Bool)? {
-                return Err(mkerr(InvalidPredicate(x.clone())));
+            if *x.get_type()?.as_whnf() != ValueF::from_builtin(Bool) {
+                return mkerr(InvalidPredicate(x.clone()));
             }
 
             if y.get_type()?.get_type()?.as_const() != Some(Type) {
-                return Err(mkerr(IfBranchMustBeTerm(true, y.clone())));
+                return mkerr(IfBranchMustBeTerm(true, y.clone()));
             }
 
             if z.get_type()?.get_type()?.as_const() != Some(Type) {
-                return Err(mkerr(IfBranchMustBeTerm(false, z.clone())));
+                return mkerr(IfBranchMustBeTerm(false, z.clone()));
             }
 
             if y.get_type()? != z.get_type()? {
-                return Err(mkerr(IfBranchMismatch(y.clone(), z.clone())));
+                return mkerr(IfBranchMismatch(y.clone(), z.clone()));
             }
 
-            Ok(RetTypeOnly(y.get_type()?.into_owned()))
+            RetTypeOnly(y.get_type()?)
         }
         EmptyListLit(t) => {
-            let t = t.to_type();
-            match &t.to_value() {
-                Value::AppliedBuiltin(dhall_syntax::Builtin::List, args)
+            match &*t.as_whnf() {
+                ValueF::AppliedBuiltin(dhall_syntax::Builtin::List, args)
                     if args.len() == 1 => {}
-                _ => {
-                    return Err(TypeError::new(
-                        ctx,
-                        InvalidListType(t.to_normalized()),
-                    ))
-                }
+                _ => return mkerr(InvalidListType(t.clone())),
             }
-            Ok(RetTypeOnly(t))
+            RetTypeOnly(t.clone())
         }
         NEListLit(xs) => {
             let mut iter = xs.iter().enumerate();
             let (_, x) = iter.next().unwrap();
             for (i, y) in iter {
                 if x.get_type()? != y.get_type()? {
-                    return Err(mkerr(InvalidListElement(
+                    return mkerr(InvalidListElement(
                         i,
-                        x.get_type()?.to_normalized(),
+                        x.get_type()?,
                         y.clone(),
-                    )));
+                    ));
                 }
             }
             let t = x.get_type()?;
             if t.get_type()?.as_const() != Some(Type) {
-                return Err(TypeError::new(
-                    ctx,
-                    InvalidListType(t.to_normalized()),
-                ));
+                return mkerr(InvalidListType(t));
             }
 
-            Ok(RetTypeOnly(
-                Typed::from_thunk_and_type(
-                    Value::from_builtin(dhall_syntax::Builtin::List)
-                        .app(t.to_value())
-                        .into_thunk(),
-                    Typed::from_const(Type),
-                )
-                .to_type(),
-            ))
+            RetTypeOnly(Value::from_builtin(dhall_syntax::Builtin::List).app(t))
         }
         SomeLit(x) => {
-            let t = x.get_type()?.into_owned();
+            let t = x.get_type()?;
             if t.get_type()?.as_const() != Some(Type) {
-                return Err(TypeError::new(
-                    ctx,
-                    InvalidOptionalType(t.to_normalized()),
-                ));
+                return mkerr(InvalidOptionalType(t));
             }
 
-            Ok(RetTypeOnly(
-                Typed::from_thunk_and_type(
-                    Value::from_builtin(dhall_syntax::Builtin::Optional)
-                        .app(t.to_value())
-                        .into_thunk(),
-                    Typed::from_const(Type).into_type(),
-                )
-                .to_type(),
-            ))
+            RetTypeOnly(
+                Value::from_builtin(dhall_syntax::Builtin::Optional).app(t),
+            )
         }
-        RecordType(kts) => Ok(RetWhole(tck_record_type(
+        RecordType(kts) => RetWhole(tck_record_type(
             ctx,
-            kts.iter().map(|(x, t)| Ok((x.clone(), t.to_type()))),
-        )?)),
-        UnionType(kts) => Ok(RetWhole(tck_union_type(
+            kts.iter().map(|(x, t)| Ok((x.clone(), t.clone()))),
+        )?),
+        UnionType(kts) => RetWhole(tck_union_type(
             ctx,
-            kts.iter()
-                .map(|(x, t)| Ok((x.clone(), t.as_ref().map(|t| t.to_type())))),
-        )?)),
-        RecordLit(kvs) => Ok(RetTypeOnly(
-            tck_record_type(
-                ctx,
-                kvs.iter()
-                    .map(|(x, v)| Ok((x.clone(), v.get_type()?.into_owned()))),
-            )?
-            .into_type(),
-        )),
+            kts.iter().map(|(x, t)| Ok((x.clone(), t.clone()))),
+        )?),
+        RecordLit(kvs) => RetTypeOnly(tck_record_type(
+            ctx,
+            kvs.iter().map(|(x, v)| Ok((x.clone(), v.get_type()?))),
+        )?),
         Field(r, x) => {
-            match &r.get_type()?.to_value() {
-                Value::RecordType(kts) => match kts.get(&x) {
+            match &*r.get_type()?.as_whnf() {
+                ValueF::RecordType(kts) => match kts.get(&x) {
                     Some(tth) => {
-                        Ok(RetTypeOnly(tth.to_type()))
+                        RetTypeOnly(tth.clone())
                     },
-                    None => Err(mkerr(MissingRecordField(x.clone(),
-                                        r.clone()))),
+                    None => return mkerr(MissingRecordField(x.clone(),
+                                        r.clone())),
                 },
                 // TODO: branch here only when r.get_type() is a Const
                 _ => {
-                    let r = r.to_type();
-                    match &r.to_value() {
-                        Value::UnionType(kts) => match kts.get(&x) {
+                    match &*r.as_whnf() {
+                        ValueF::UnionType(kts) => match kts.get(&x) {
                             // Constructor has type T -> < x: T, ... >
                             Some(Some(t)) => {
-                                // TODO: avoid capture
-                                Ok(RetTypeOnly(
+                                RetTypeOnly(
                                     tck_pi_type(
                                         ctx,
                                         "_".into(),
-                                        t.to_type(),
-                                        r.clone(),
-                                    )?.to_type()
-                                ))
+                                        t.clone(),
+                                        r.under_binder(Label::from("_")),
+                                    )?
+                                )
                             },
                             Some(None) => {
-                                Ok(RetTypeOnly(r.clone()))
+                                RetTypeOnly(r.clone())
                             },
                             None => {
-                                Err(mkerr(MissingUnionField(
+                                return mkerr(MissingUnionField(
                                     x.clone(),
-                                    r.to_normalized(),
-                                )))
+                                    r.clone(),
+                                ))
                             },
                         },
                         _ => {
-                            Err(mkerr(NotARecord(
+                            return mkerr(NotARecord(
                                 x.clone(),
-                                r.to_normalized()
-                            )))
+                                r.clone()
+                            ))
                         },
                     }
                 }
-                // _ => Err(mkerr(NotARecord(
+                // _ => mkerr(NotARecord(
                 //     x,
-                //     r.to_type()?.to_normalized(),
-                // ))),
+                //     r?,
+                // )),
             }
         }
-        Const(c) => Ok(RetWhole(Typed::from_const(*c))),
-        Builtin(b) => {
-            Ok(RetTypeOnly(mktype(ctx, rc(type_of_builtin(*b)).absurd())?))
-        }
-        BoolLit(_) => Ok(RetTypeOnly(builtin_to_type(Bool)?)),
-        NaturalLit(_) => Ok(RetTypeOnly(builtin_to_type(Natural)?)),
-        IntegerLit(_) => Ok(RetTypeOnly(builtin_to_type(Integer)?)),
-        DoubleLit(_) => Ok(RetTypeOnly(builtin_to_type(Double)?)),
+        Const(c) => RetWhole(const_to_value(*c)),
+        Builtin(b) => RetWhole(builtin_to_value(*b)),
+        BoolLit(_) => RetTypeOnly(builtin_to_value(Bool)),
+        NaturalLit(_) => RetTypeOnly(builtin_to_value(Natural)),
+        IntegerLit(_) => RetTypeOnly(builtin_to_value(Integer)),
+        DoubleLit(_) => RetTypeOnly(builtin_to_value(Double)),
         TextLit(interpolated) => {
-            let text_type = builtin_to_type(Text)?;
+            let text_type = builtin_to_value(Text);
             for contents in interpolated.iter() {
                 use InterpolatedTextContents::Expr;
                 if let Expr(x) = contents {
-                    if x.get_type()?.as_ref() != &text_type {
-                        return Err(mkerr(InvalidTextInterpolation(x.clone())));
+                    if x.get_type()? != text_type {
+                        return mkerr(InvalidTextInterpolation(x.clone()));
                     }
                 }
             }
-            Ok(RetTypeOnly(text_type))
+            RetTypeOnly(text_type)
         }
         BinOp(RightBiasedRecordMerge, l, r) => {
             use crate::phase::normalize::merge_maps;
 
             let l_type = l.get_type()?;
-            let l_kind = l_type.get_type()?;
             let r_type = r.get_type()?;
-            let r_kind = r_type.get_type()?;
-
-            // Check the equality of kinds.
-            // This is to disallow expression such as:
-            // "{ x = Text } // { y = 1 }"
-            if l_kind != r_kind {
-                return Err(mkerr(RecordMismatch(l.clone(), r.clone())));
-            }
 
             // Extract the LHS record type
-            let kts_x = match l_type.to_value() {
-                Value::RecordType(kts) => kts,
-                _ => return Err(mkerr(MustCombineRecord(l.clone()))),
+            let l_type_borrow = l_type.as_whnf();
+            let kts_x = match &*l_type_borrow {
+                ValueF::RecordType(kts) => kts,
+                _ => return mkerr(MustCombineRecord(l.clone())),
             };
 
             // Extract the RHS record type
-            let kts_y = match r_type.to_value() {
-                Value::RecordType(kts) => kts,
-                _ => return Err(mkerr(MustCombineRecord(r.clone()))),
+            let r_type_borrow = r_type.as_whnf();
+            let kts_y = match &*r_type_borrow {
+                ValueF::RecordType(kts) => kts,
+                _ => return mkerr(MustCombineRecord(r.clone())),
             };
 
             // Union the two records, prefering
             // the values found in the RHS.
-            let kts = merge_maps(&kts_x, &kts_y, |_, r_t| r_t.clone());
+            let kts = merge_maps::<_, _, _, !>(kts_x, kts_y, |_, _, r_t| {
+                Ok(r_t.clone())
+            })?;
 
             // Construct the final record type from the union
-            Ok(RetTypeOnly(
-                tck_record_type(
-                    ctx,
-                    kts.iter().map(|(x, v)| Ok((x.clone(), v.to_type()))),
-                )?
-                .into_type(),
-            ))
-        }
-        BinOp(RecursiveRecordMerge, l, r) => {
-            // A recursive function to dig down into
-            // records of records when merging.
-            fn combine_record_types(
-                ctx: &TypecheckContext,
-                kts_l: HashMap<Label, TypeThunk>,
-                kts_r: HashMap<Label, TypeThunk>,
-            ) -> Result<Typed, TypeError> {
-                use crate::phase::normalize::outer_join;
-
-                // If the Label exists for both records and Type for the values
-                // are records themselves, then we hit the recursive case.
-                // Otherwise we have a field collision.
-                let combine = |k: &Label,
-                               inner_l: &TypeThunk,
-                               inner_r: &TypeThunk|
-                 -> Result<Typed, TypeError> {
-                    match (inner_l.to_value(), inner_r.to_value()) {
-                        (
-                            Value::RecordType(inner_l_kvs),
-                            Value::RecordType(inner_r_kvs),
-                        ) => {
-                            combine_record_types(ctx, inner_l_kvs, inner_r_kvs)
-                        }
-                        (_, _) => {
-                            Err(TypeError::new(ctx, FieldCollision(k.clone())))
-                        }
-                    }
-                };
-
-                let kts: HashMap<Label, Result<Typed, TypeError>> = outer_join(
-                    |l| Ok(l.to_type()),
-                    |r| Ok(r.to_type()),
-                    |k: &Label, l: &TypeThunk, r: &TypeThunk| combine(k, l, r),
-                    &kts_l,
-                    &kts_r,
-                );
-
-                Ok(tck_record_type(
-                    ctx,
-                    kts.into_iter().map(|(x, v)| v.map(|r| (x.clone(), r))),
-                )?
-                .into_type())
-            };
-
-            let l_type = l.get_type()?;
-            let l_kind = l_type.get_type()?;
-            let r_type = r.get_type()?;
-            let r_kind = r_type.get_type()?;
-
-            // Check the equality of kinds.
-            // This is to disallow expression such as:
-            // "{ x = Text } // { y = 1 }"
-            if l_kind != r_kind {
-                return Err(mkerr(RecordMismatch(l.clone(), r.clone())));
-            }
-
-            // Extract the LHS record type
-            let kts_x = match l_type.to_value() {
-                Value::RecordType(kts) => kts,
-                _ => return Err(mkerr(MustCombineRecord(l.clone()))),
-            };
-
-            // Extract the RHS record type
-            let kts_y = match r_type.to_value() {
-                Value::RecordType(kts) => kts,
-                _ => return Err(mkerr(MustCombineRecord(r.clone()))),
-            };
-
-            combine_record_types(ctx, kts_x, kts_y).map(|r| RetTypeOnly(r))
+            RetTypeOnly(tck_record_type(
+                ctx,
+                kts.into_iter().map(|(x, v)| Ok((x.clone(), v))),
+            )?)
         }
+        BinOp(RecursiveRecordMerge, l, r) => RetTypeOnly(type_last_layer(
+            ctx,
+            ExprF::BinOp(
+                RecursiveRecordTypeMerge,
+                l.get_type()?,
+                r.get_type()?,
+            ),
+        )?),
         BinOp(RecursiveRecordTypeMerge, l, r) => {
-            // A recursive function to dig down into
-            // records of records when merging.
-            fn combine_record_types(
-                ctx: &TypecheckContext,
-                kts_l: HashMap<Label, TypeThunk>,
-                kts_r: HashMap<Label, TypeThunk>,
-            ) -> Result<Typed, TypeError> {
-                use crate::phase::normalize::intersection_with_key;
-
-                // If the Label exists for both records and Type for the values
-                // are records themselves, then we hit the recursive case.
-                // Otherwise we have a field collision.
-                let combine = |k: &Label,
-                               kts_l_inner: &TypeThunk,
-                               kts_r_inner: &TypeThunk|
-                 -> Result<Typed, TypeError> {
-                    match (kts_l_inner.to_value(), kts_r_inner.to_value()) {
-                        (
-                            Value::RecordType(kvs_l_inner),
-                            Value::RecordType(kvs_r_inner),
-                        ) => {
-                            combine_record_types(ctx, kvs_l_inner, kvs_r_inner)
-                        }
-                        (_, _) => {
-                            Err(TypeError::new(ctx, FieldCollision(k.clone())))
-                        }
-                    }
-                };
-
-                let kts = intersection_with_key(
-                    |k: &Label, l: &TypeThunk, r: &TypeThunk| combine(k, l, r),
-                    &kts_l,
-                    &kts_r,
-                );
-
-                Ok(tck_record_type(
-                    ctx,
-                    kts.into_iter().map(|(x, v)| v.map(|r| (x.clone(), r))),
-                )?
-                .into_type())
-            };
-
-            // Extract the Const of the LHS
-            let k_l = match l.get_type()?.to_value() {
-                Value::Const(k) => k,
-                _ => {
-                    return Err(mkerr(RecordTypeMergeRequiresRecordType(
-                        l.clone(),
-                    )))
-                }
-            };
-
-            // Extract the Const of the RHS
-            let k_r = match r.get_type()?.to_value() {
-                Value::Const(k) => k,
-                _ => {
-                    return Err(mkerr(RecordTypeMergeRequiresRecordType(
-                        r.clone(),
-                    )))
-                }
-            };
-
-            // Const values must match for the Records
-            let k = if k_l == k_r {
-                k_l
-            } else {
-                return Err(mkerr(RecordTypeMismatch(
-                    Typed::from_const(k_l),
-                    Typed::from_const(k_r),
-                    l.clone(),
-                    r.clone(),
-                )));
-            };
+            use crate::phase::normalize::merge_maps;
 
             // Extract the LHS record type
-            let kts_x = match l.to_value() {
-                Value::RecordType(kts) => kts,
+            let borrow_l = l.as_whnf();
+            let kts_x = match &*borrow_l {
+                ValueF::RecordType(kts) => kts,
                 _ => {
-                    return Err(mkerr(RecordTypeMergeRequiresRecordType(
-                        l.clone(),
-                    )))
+                    return mkerr(RecordTypeMergeRequiresRecordType(l.clone()))
                 }
             };
 
             // Extract the RHS record type
-            let kts_y = match r.to_value() {
-                Value::RecordType(kts) => kts,
+            let borrow_r = r.as_whnf();
+            let kts_y = match &*borrow_r {
+                ValueF::RecordType(kts) => kts,
                 _ => {
-                    return Err(mkerr(RecordTypeMergeRequiresRecordType(
-                        r.clone(),
-                    )))
+                    return mkerr(RecordTypeMergeRequiresRecordType(r.clone()))
                 }
             };
 
             // Ensure that the records combine without a type error
-            // and if not output the final Const value.
-            combine_record_types(ctx, kts_x, kts_y)
-                .and(Ok(RetTypeOnly(Typed::from_const(k))))
+            let kts = merge_maps(
+                kts_x,
+                kts_y,
+                // If the Label exists for both records, then we hit the recursive case.
+                |_, l: &Value, r: &Value| {
+                    type_last_layer(
+                        ctx,
+                        ExprF::BinOp(
+                            RecursiveRecordTypeMerge,
+                            l.clone(),
+                            r.clone(),
+                        ),
+                    )
+                },
+            )?;
+
+            RetWhole(tck_record_type(ctx, kts.into_iter().map(Ok))?)
         }
         BinOp(o @ ListAppend, l, r) => {
-            match l.get_type()?.to_value() {
-                Value::AppliedBuiltin(List, _) => {}
-                _ => return Err(mkerr(BinOpTypeMismatch(*o, l.clone()))),
+            match &*l.get_type()?.as_whnf() {
+                ValueF::AppliedBuiltin(List, _) => {}
+                _ => return mkerr(BinOpTypeMismatch(*o, l.clone())),
             }
 
             if l.get_type()? != r.get_type()? {
-                return Err(mkerr(BinOpTypeMismatch(*o, r.clone())));
+                return mkerr(BinOpTypeMismatch(*o, r.clone()));
             }
 
-            Ok(RetTypeOnly(l.get_type()?.into_owned()))
+            RetTypeOnly(l.get_type()?)
         }
         BinOp(Equivalence, l, r) => {
             if l.get_type()?.get_type()?.as_const() != Some(Type) {
-                return Err(mkerr(EquivalenceArgumentMustBeTerm(
-                    true,
-                    l.clone(),
-                )));
+                return mkerr(EquivalenceArgumentMustBeTerm(true, l.clone()));
             }
             if r.get_type()?.get_type()?.as_const() != Some(Type) {
-                return Err(mkerr(EquivalenceArgumentMustBeTerm(
-                    false,
-                    r.clone(),
-                )));
+                return mkerr(EquivalenceArgumentMustBeTerm(false, r.clone()));
             }
 
             if l.get_type()? != r.get_type()? {
-                return Err(mkerr(EquivalenceTypeMismatch(
-                    r.clone(),
-                    l.clone(),
-                )));
+                return mkerr(EquivalenceTypeMismatch(r.clone(), l.clone()));
             }
 
-            Ok(RetTypeOnly(Typed::from_const(Type).into_type()))
+            RetWhole(Value::from_valuef_and_type(
+                ValueF::Equivalence(l.clone(), r.clone()),
+                Value::from_const(Type),
+            ))
         }
         BinOp(o, l, r) => {
-            let t = builtin_to_type(match o {
+            let t = builtin_to_value(match o {
                 BoolAnd => Bool,
                 BoolOr => Bool,
                 BoolEQ => Bool,
@@ -874,143 +665,140 @@ fn type_last_layer(
                 RecursiveRecordTypeMerge => unreachable!(),
                 ImportAlt => unreachable!("There should remain no import alternatives in a resolved expression"),
                 Equivalence => unreachable!(),
-            })?;
+            });
 
-            if l.get_type()?.as_ref() != &t {
-                return Err(mkerr(BinOpTypeMismatch(*o, l.clone())));
+            if l.get_type()? != t {
+                return mkerr(BinOpTypeMismatch(*o, l.clone()));
             }
 
-            if r.get_type()?.as_ref() != &t {
-                return Err(mkerr(BinOpTypeMismatch(*o, r.clone())));
+            if r.get_type()? != t {
+                return mkerr(BinOpTypeMismatch(*o, r.clone()));
             }
 
-            Ok(RetTypeOnly(t))
+            RetTypeOnly(t)
         }
         Merge(record, union, type_annot) => {
-            let handlers = match record.get_type()?.to_value() {
-                Value::RecordType(kts) => kts,
-                _ => return Err(mkerr(Merge1ArgMustBeRecord(record.clone()))),
+            let record_type = record.get_type()?;
+            let record_borrow = record_type.as_whnf();
+            let handlers = match &*record_borrow {
+                ValueF::RecordType(kts) => kts,
+                _ => return mkerr(Merge1ArgMustBeRecord(record.clone())),
             };
 
-            let variants = match union.get_type()?.to_value() {
-                Value::UnionType(kts) => kts,
-                _ => return Err(mkerr(Merge2ArgMustBeUnion(union.clone()))),
+            let union_type = union.get_type()?;
+            let union_borrow = union_type.as_whnf();
+            let variants = match &*union_borrow {
+                ValueF::UnionType(kts) => kts,
+                _ => return mkerr(Merge2ArgMustBeUnion(union.clone())),
             };
 
             let mut inferred_type = None;
-            for (x, handler) in handlers.iter() {
-                let handler_return_type = match variants.get(x) {
-                    // Union alternative with type
-                    Some(Some(variant_type)) => {
-                        let variant_type = variant_type.to_type();
-                        let handler_type = handler.to_type();
-                        let (x, tx, tb) = match &handler_type.to_value() {
-                            Value::Pi(x, tx, tb) => {
-                                (x.clone(), tx.to_type(), tb.to_type())
+            for (x, handler_type) in handlers {
+                let handler_return_type =
+                    match variants.get(x) {
+                        // Union alternative with type
+                        Some(Some(variant_type)) => {
+                            let handler_type_borrow = handler_type.as_whnf();
+                            let (x, tx, tb) = match &*handler_type_borrow {
+                                ValueF::Pi(x, tx, tb) => (x, tx, tb),
+                                _ => {
+                                    return mkerr(NotAFunction(
+                                        handler_type.clone(),
+                                    ))
+                                }
+                            };
+
+                            if variant_type != tx {
+                                return mkerr(TypeMismatch(
+                                    handler_type.clone(),
+                                    tx.clone(),
+                                    variant_type.clone(),
+                                ));
                             }
-                            _ => return Err(mkerr(NotAFunction(handler_type))),
-                        };
-
-                        if &variant_type != &tx {
-                            return Err(mkerr(TypeMismatch(
-                                handler_type,
-                                tx.to_normalized(),
-                                variant_type,
-                            )));
-                        }
 
-                        // Extract `tb` from under the `x` binder. Fails is `x` was free in `tb`.
-                        match tb.over_binder(x) {
-                            Some(x) => x,
-                            None => {
-                                return Err(mkerr(
+                            // Extract `tb` from under the `x` binder. Fails is `x` was free in `tb`.
+                            match tb.over_binder(x) {
+                                Some(x) => x,
+                                None => return mkerr(
                                     MergeHandlerReturnTypeMustNotBeDependent,
-                                ))
+                                ),
                             }
                         }
-                    }
-                    // Union alternative without type
-                    Some(None) => handler.to_type(),
-                    None => {
-                        return Err(mkerr(MergeHandlerMissingVariant(
-                            x.clone(),
-                        )))
-                    }
-                };
+                        // Union alternative without type
+                        Some(None) => handler_type.clone(),
+                        None => {
+                            return mkerr(MergeHandlerMissingVariant(x.clone()))
+                        }
+                    };
                 match &inferred_type {
                     None => inferred_type = Some(handler_return_type),
                     Some(t) => {
                         if t != &handler_return_type {
-                            return Err(mkerr(MergeHandlerTypeMismatch));
+                            return mkerr(MergeHandlerTypeMismatch);
                         }
                     }
                 }
             }
             for x in variants.keys() {
                 if !handlers.contains_key(x) {
-                    return Err(mkerr(MergeVariantMissingHandler(x.clone())));
+                    return mkerr(MergeVariantMissingHandler(x.clone()));
                 }
             }
 
             match (inferred_type, type_annot) {
                 (Some(ref t1), Some(t2)) => {
-                    let t2 = t2.to_type();
-                    if t1 != &t2 {
-                        return Err(mkerr(MergeAnnotMismatch));
+                    if t1 != t2 {
+                        return mkerr(MergeAnnotMismatch);
                     }
-                    Ok(RetTypeOnly(t2))
+                    RetTypeOnly(t2.clone())
                 }
-                (Some(t), None) => Ok(RetTypeOnly(t)),
-                (None, Some(t)) => Ok(RetTypeOnly(t.to_type())),
-                (None, None) => Err(mkerr(MergeEmptyNeedsAnnotation)),
+                (Some(t), None) => RetTypeOnly(t),
+                (None, Some(t)) => RetTypeOnly(t.clone()),
+                (None, None) => return mkerr(MergeEmptyNeedsAnnotation),
             }
         }
+        ToMap(_, _) => unimplemented!("toMap"),
         Projection(record, labels) => {
-            let trecord = record.get_type()?;
-            let kts = match trecord.to_value() {
-                Value::RecordType(kts) => kts,
-                _ => return Err(mkerr(ProjectionMustBeRecord)),
+            let record_type = record.get_type()?;
+            let record_borrow = record_type.as_whnf();
+            let kts = match &*record_borrow {
+                ValueF::RecordType(kts) => kts,
+                _ => return mkerr(ProjectionMustBeRecord),
             };
 
             let mut new_kts = HashMap::new();
             for l in labels {
                 match kts.get(l) {
-                    None => return Err(mkerr(ProjectionMissingEntry)),
+                    None => return mkerr(ProjectionMissingEntry),
                     Some(t) => new_kts.insert(l.clone(), t.clone()),
                 };
             }
 
-            Ok(RetTypeOnly(
-                Typed::from_thunk_and_type(
-                    Value::RecordType(new_kts).into_thunk(),
-                    trecord.get_type()?.into_owned(),
-                )
-                .to_type(),
+            RetTypeOnly(Value::from_valuef_and_type(
+                ValueF::RecordType(new_kts),
+                record_type.get_type()?,
             ))
         }
-    }
+    };
+
+    Ok(match ret {
+        RetTypeOnly(typ) => {
+            Value::from_valuef_and_type(ValueF::PartialExpr(e), typ)
+        }
+        RetWhole(v) => v,
+    })
 }
 
-/// `typeOf` is the same as `type_with` with an empty context, meaning that the
+/// `type_of` is the same as `type_with` with an empty context, meaning that the
 /// expression must be closed (i.e. no free variables), otherwise type-checking
 /// will fail.
-fn type_of(e: SubExpr<Span, Normalized>) -> Result<Typed, TypeError> {
-    let ctx = TypecheckContext::new();
-    let e = type_with(&ctx, e)?;
-    // Ensure `e` has a type (i.e. `e` is not `Sort`)
-    e.get_type()?;
-    Ok(e)
+pub(crate) fn typecheck(e: Expr<Normalized>) -> Result<Value, TypeError> {
+    type_with(&TypecheckContext::new(), e)
 }
 
-pub fn typecheck(e: Resolved) -> Result<Typed, TypeError> {
-    type_of(e.0)
-}
-
-pub 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)))
-}
-pub fn skip_typecheck(e: Resolved) -> Typed {
-    Typed::from_thunk_untyped(Thunk::new(NormalizationContext::new(), e.0))
+pub(crate) fn typecheck_with(
+    expr: Expr<Normalized>,
+    ty: Expr<Normalized>,
+) -> Result<Value, TypeError> {
+    typecheck(expr.rewrap(ExprF::Annot(expr.clone(), ty)))
 }