Merge pull request #104 from Nadrieril/rework-value

Rework Value

16 files changed, 1501 insertions, 1963 deletions

diff --git a/Cargo.lock b/Cargo.lock
index ccd8520..c073fad 100644
--- a/Cargo.lock
+++ b/Cargo.lock
@@ -75,6 +75,7 @@ dependencies = [
  "pretty_assertions 0.6.1 (registry+https://github.com/rust-lang/crates.io-index)",
  "serde 1.0.90 (registry+https://github.com/rust-lang/crates.io-index)",
  "serde_cbor 0.9.0 (registry+https://github.com/rust-lang/crates.io-index)",
+ "take_mut 0.2.2 (registry+https://github.com/rust-lang/crates.io-index)",
  "term-painter 0.2.4 (registry+https://github.com/rust-lang/crates.io-index)",
  "walkdir 2.2.7 (registry+https://github.com/rust-lang/crates.io-index)",
 ]
diff --git a/dhall-lang b/dhall-lang
-Subproject 235d2c0b11a539003d2de6110f8666e93ae1ccd
+Subproject 3d66b4cd56627a39b6c615882beab97fbdf9d13
diff --git a/dhall/Cargo.toml b/dhall/Cargo.toml
index 0a257e4..16c1c78 100644
--- a/dhall/Cargo.toml
+++ b/dhall/Cargo.toml
@@ -9,6 +9,7 @@ build = "build.rs"
 [dependencies]
 bytecount = "0.5.1"
 itertools = "0.8.0"
+take_mut = "0.2.2"
 term-painter = "0.2.3"
 serde = { version = "1.0" }
 serde_cbor = "0.9.0"
diff --git a/dhall/build.rs b/dhall/build.rs
index 2305208..166b036 100644
--- a/dhall/build.rs
+++ b/dhall/build.rs
@@ -213,7 +213,10 @@ fn main() -> std::io::Result<()> {
         "alpha_normalize",
         "alpha-normalization/",
         "AlphaNormalization",
-        |_| false,
+        |path| {
+            // This test doesn't typecheck
+            path == "success/unit/FunctionNestedBindingXXFree"
+        },
     )?;
 
     make_test_module(
diff --git a/dhall/src/core/context.rs b/dhall/src/core/context.rs
index 9230a2e..2bf39c5 100644
--- a/dhall/src/core/context.rs
+++ b/dhall/src/core/context.rs
@@ -3,64 +3,56 @@ use std::rc::Rc;
 
 use dhall_syntax::{Label, V};
 
-use crate::core::thunk::Thunk;
 use crate::core::value::Value;
+use crate::core::valuef::ValueF;
 use crate::core::var::{AlphaVar, Shift, Subst};
 use crate::error::TypeError;
-use crate::phase::{Type, Typed};
 
 #[derive(Debug, Clone)]
-enum CtxItem<T> {
-    Kept(AlphaVar, T),
-    Replaced(Thunk, T),
+enum CtxItem {
+    Kept(AlphaVar, Value),
+    Replaced(Value),
 }
 
 #[derive(Debug, Clone)]
-struct Context<T>(Rc<Vec<(Label, CtxItem<T>)>>);
+pub(crate) struct TypecheckContext(Rc<Vec<(Label, CtxItem)>>);
 
-#[derive(Debug, Clone)]
-pub(crate) struct NormalizationContext(Context<()>);
-
-#[derive(Debug, Clone)]
-pub(crate) struct TypecheckContext(Context<Type>);
-
-impl<T> Context<T> {
+impl TypecheckContext {
     pub fn new() -> Self {
-        Context(Rc::new(Vec::new()))
+        TypecheckContext(Rc::new(Vec::new()))
     }
-    pub fn insert_kept(&self, x: &Label, t: T) -> Self
-    where
-        T: Shift + Clone,
-    {
+    pub fn insert_type(&self, x: &Label, t: Value) -> Self {
         let mut vec = self.0.as_ref().clone();
         vec.push((x.clone(), CtxItem::Kept(x.into(), t.under_binder(x))));
-        Context(Rc::new(vec))
+        TypecheckContext(Rc::new(vec))
     }
-    pub fn insert_replaced(&self, x: &Label, th: Thunk, t: T) -> Self
-    where
-        T: Clone,
-    {
+    pub fn insert_value(&self, x: &Label, e: Value) -> Result<Self, TypeError> {
         let mut vec = self.0.as_ref().clone();
-        vec.push((x.clone(), CtxItem::Replaced(th, t)));
-        Context(Rc::new(vec))
+        vec.push((x.clone(), CtxItem::Replaced(e)));
+        Ok(TypecheckContext(Rc::new(vec)))
     }
-    pub fn lookup(&self, var: &V<Label>) -> Result<CtxItem<T>, V<Label>>
-    where
-        T: Clone + Shift,
-    {
+    pub fn lookup(&self, var: &V<Label>) -> Option<Value> {
         let mut var = var.clone();
         let mut shift_map: HashMap<Label, _> = HashMap::new();
         for (l, i) in self.0.iter().rev() {
             match var.over_binder(l) {
-                None => return Ok(i.under_multiple_binders(&shift_map)),
+                None => {
+                    let i = i.under_multiple_binders(&shift_map);
+                    return Some(match i {
+                        CtxItem::Kept(newvar, t) => {
+                            Value::from_valuef_and_type(ValueF::Var(newvar), t)
+                        }
+                        CtxItem::Replaced(v) => v,
+                    });
+                }
                 Some(newvar) => var = newvar,
             };
             if let CtxItem::Kept(_, _) = i {
                 *shift_map.entry(l.clone()).or_insert(0) += 1;
             }
         }
-        // Free variable
-        Err(var)
+        // Unbound variable
+        None
     }
     /// Given a var that makes sense in the current context, map the given function in such a way
     /// that the passed variable always makes sense in the context of the passed item.
@@ -69,11 +61,8 @@ impl<T> Context<T> {
     fn do_with_var<E>(
         &self,
         var: &AlphaVar,
-        mut f: impl FnMut(&AlphaVar, &CtxItem<T>) -> Result<CtxItem<T>, E>,
-    ) -> Result<Self, E>
-    where
-        T: Clone,
-    {
+        mut f: impl FnMut(&AlphaVar, &CtxItem) -> Result<CtxItem, E>,
+    ) -> Result<Self, E> {
         let mut vec = Vec::new();
         vec.reserve(self.0.len());
         let mut var = var.clone();
@@ -91,16 +80,13 @@ impl<T> Context<T> {
             vec.push((l.clone(), (*i).clone()));
         }
         vec.reverse();
-        Ok(Context(Rc::new(vec)))
+        Ok(TypecheckContext(Rc::new(vec)))
     }
-    fn shift(&self, delta: isize, var: &AlphaVar) -> Option<Self>
-    where
-        T: Clone + Shift,
-    {
+    fn shift(&self, delta: isize, var: &AlphaVar) -> Option<Self> {
         if delta < 0 {
             Some(self.do_with_var(var, |var, i| Ok(i.shift(delta, &var)?))?)
         } else {
-            Some(Context(Rc::new(
+            Some(TypecheckContext(Rc::new(
                 self.0
                     .iter()
                     .map(|(l, i)| Ok((l.clone(), i.shift(delta, &var)?)))
@@ -108,117 +94,51 @@ impl<T> Context<T> {
             )))
         }
     }
-    fn subst_shift(&self, var: &AlphaVar, val: &Typed) -> Self
-    where
-        T: Clone + Subst<Typed>,
-    {
+    fn subst_shift(&self, var: &AlphaVar, val: &Value) -> Self {
         self.do_with_var(var, |var, i| Ok::<_, !>(i.subst_shift(&var, val)))
             .unwrap()
     }
 }
 
-impl NormalizationContext {
-    pub fn new() -> Self {
-        NormalizationContext(Context::new())
-    }
-    pub fn skip(&self, x: &Label) -> Self {
-        NormalizationContext(self.0.insert_kept(x, ()))
-    }
-    pub fn lookup(&self, var: &V<Label>) -> Value {
-        match self.0.lookup(var) {
-            Ok(CtxItem::Replaced(t, ())) => t.to_value(),
-            Ok(CtxItem::Kept(newvar, ())) => Value::Var(newvar.clone()),
-            Err(var) => Value::Var(AlphaVar::from_var(var)),
-        }
-    }
-}
-
-impl TypecheckContext {
-    pub fn new() -> Self {
-        TypecheckContext(Context::new())
-    }
-    pub fn insert_type(&self, x: &Label, t: Type) -> Self {
-        TypecheckContext(self.0.insert_kept(x, t))
-    }
-    pub fn insert_value(&self, x: &Label, e: Typed) -> Result<Self, TypeError> {
-        Ok(TypecheckContext(self.0.insert_replaced(
-            x,
-            e.to_thunk(),
-            e.get_type()?.into_owned(),
-        )))
-    }
-    pub fn lookup(&self, var: &V<Label>) -> Option<Typed> {
-        match self.0.lookup(var) {
-            Ok(CtxItem::Kept(newvar, t)) => Some(Typed::from_thunk_and_type(
-                Thunk::from_value(Value::Var(newvar.clone())),
-                t.clone(),
-            )),
-            Ok(CtxItem::Replaced(th, t)) => {
-                Some(Typed::from_thunk_and_type(th.clone(), t.clone()))
-            }
-            Err(_) => None,
-        }
-    }
-}
-
-impl<T: Shift> Shift for CtxItem<T> {
+impl Shift for CtxItem {
     fn shift(&self, delta: isize, var: &AlphaVar) -> Option<Self> {
         Some(match self {
             CtxItem::Kept(v, t) => {
                 CtxItem::Kept(v.shift(delta, var)?, t.shift(delta, var)?)
             }
-            CtxItem::Replaced(e, t) => {
-                CtxItem::Replaced(e.shift(delta, var)?, t.shift(delta, var)?)
-            }
+            CtxItem::Replaced(e) => CtxItem::Replaced(e.shift(delta, var)?),
         })
     }
 }
 
-impl<T: Clone + Shift> Shift for Context<T> {
+impl Shift for TypecheckContext {
     fn shift(&self, delta: isize, var: &AlphaVar) -> Option<Self> {
         self.shift(delta, var)
     }
 }
 
-impl Shift for NormalizationContext {
-    fn shift(&self, delta: isize, var: &AlphaVar) -> Option<Self> {
-        Some(NormalizationContext(self.0.shift(delta, var)?))
-    }
-}
-
-impl<T: Subst<Typed>> Subst<Typed> for CtxItem<T> {
-    fn subst_shift(&self, var: &AlphaVar, val: &Typed) -> Self {
+impl Subst<Value> for CtxItem {
+    fn subst_shift(&self, var: &AlphaVar, val: &Value) -> Self {
         match self {
-            CtxItem::Replaced(e, t) => CtxItem::Replaced(
-                e.subst_shift(var, val),
-                t.subst_shift(var, val),
-            ),
+            CtxItem::Replaced(e) => CtxItem::Replaced(e.subst_shift(var, val)),
             CtxItem::Kept(v, t) => match v.shift(-1, var) {
-                None => {
-                    CtxItem::Replaced(val.to_thunk(), t.subst_shift(var, val))
-                }
+                None => CtxItem::Replaced(val.clone()),
                 Some(newvar) => CtxItem::Kept(newvar, t.subst_shift(var, val)),
             },
         }
     }
 }
 
-impl<T: Clone + Subst<Typed>> Subst<Typed> for Context<T> {
-    fn subst_shift(&self, var: &AlphaVar, val: &Typed) -> Self {
+impl Subst<Value> for TypecheckContext {
+    fn subst_shift(&self, var: &AlphaVar, val: &Value) -> Self {
         self.subst_shift(var, val)
     }
 }
 
-impl Subst<Typed> for NormalizationContext {
-    fn subst_shift(&self, var: &AlphaVar, val: &Typed) -> Self {
-        NormalizationContext(self.0.subst_shift(var, val))
-    }
-}
-
+/// Don't count contexts when comparing stuff.
+/// This is dirty but needed.
 impl PartialEq for TypecheckContext {
     fn eq(&self, _: &Self) -> bool {
-        // don't count contexts when comparing stuff
-        // this is dirty but needed for now
         true
     }
 }
diff --git a/dhall/src/core/mod.rs b/dhall/src/core/mod.rs
index 0667df8..08213f7 100644
--- a/dhall/src/core/mod.rs
+++ b/dhall/src/core/mod.rs
@@ -1,4 +1,4 @@
 pub mod context;
-pub mod thunk;
 pub mod value;
+pub mod valuef;
 pub mod var;
diff --git a/dhall/src/core/thunk.rs b/dhall/src/core/thunk.rs
deleted file mode 100644
index 54a5442..0000000
--- a/dhall/src/core/thunk.rs
+++ /dev/null
@@ -1,414 +0,0 @@
-use std::borrow::Cow;
-use std::cell::{Ref, RefCell};
-use std::rc::Rc;
-
-use dhall_syntax::{Const, ExprF};
-
-use crate::core::context::{NormalizationContext, TypecheckContext};
-use crate::core::value::Value;
-use crate::core::var::{AlphaVar, Shift, Subst};
-use crate::error::{TypeError, TypeMessage};
-use crate::phase::normalize::{
-    apply_any, normalize_one_layer, normalize_whnf, InputSubExpr, OutputSubExpr,
-};
-use crate::phase::typecheck::type_of_const;
-use crate::phase::{Normalized, NormalizedSubExpr, Type, Typed};
-
-#[derive(Debug, Clone, Copy)]
-enum Marker {
-    /// Weak Head Normal Form, i.e. subexpressions may not be normalized
-    WHNF,
-    /// Normal form, i.e. completely normalized
-    NF,
-}
-use Marker::{NF, WHNF};
-
-#[derive(Debug)]
-enum ThunkInternal {
-    /// Non-normalized value alongside a normalization context
-    Unnormalized(NormalizationContext, InputSubExpr),
-    /// Partially normalized value whose subexpressions have been thunked (this is returned from
-    /// typechecking). Note that this is different from `Value::PartialExpr` because there is no
-    /// requirement of WHNF here.
-    PartialExpr(ExprF<Thunk, Normalized>),
-    /// Partially normalized value.
-    /// Invariant: if the marker is `NF`, the value must be fully normalized
-    Value(Marker, Value),
-}
-
-/// Stores a possibly unevaluated value. Gets (partially) normalized on-demand,
-/// sharing computation automatically.
-/// Uses a RefCell to share computation.
-#[derive(Clone)]
-pub struct Thunk(Rc<RefCell<ThunkInternal>>);
-
-/// A thunk in type position. Can optionally store a Type from the typechecking phase to preserve
-/// type information through the normalization phase.
-#[derive(Debug, Clone)]
-pub enum TypedThunk {
-    // Any value, along with (optionally) its type
-    Untyped(Thunk),
-    Typed(Thunk, Box<Type>),
-    // One of the base higher-kinded types.
-    // Used to avoid storing the same tower ot Type->Kind->Sort
-    // over and over again. Also enables having Sort as a value
-    // even though it doesn't itself have a type.
-    Const(Const),
-}
-
-impl ThunkInternal {
-    fn into_thunk(self) -> Thunk {
-        Thunk(Rc::new(RefCell::new(self)))
-    }
-
-    fn normalize_whnf(&mut self) {
-        match self {
-            ThunkInternal::Unnormalized(ctx, e) => {
-                *self = ThunkInternal::Value(
-                    WHNF,
-                    normalize_whnf(ctx.clone(), e.clone()),
-                )
-            }
-            ThunkInternal::PartialExpr(e) => {
-                *self =
-                    ThunkInternal::Value(WHNF, normalize_one_layer(e.clone()))
-            }
-            // Already at least in WHNF
-            ThunkInternal::Value(_, _) => {}
-        }
-    }
-
-    fn normalize_nf(&mut self) {
-        match self {
-            ThunkInternal::Unnormalized(_, _)
-            | ThunkInternal::PartialExpr(_) => {
-                self.normalize_whnf();
-                self.normalize_nf();
-            }
-            ThunkInternal::Value(m @ WHNF, v) => {
-                v.normalize_mut();
-                *m = NF;
-            }
-            // Already in NF
-            ThunkInternal::Value(NF, _) => {}
-        }
-    }
-
-    // Always use normalize_whnf before
-    fn as_whnf(&self) -> &Value {
-        match self {
-            ThunkInternal::Unnormalized(_, _)
-            | ThunkInternal::PartialExpr(_) => unreachable!(),
-            ThunkInternal::Value(_, v) => v,
-        }
-    }
-
-    // Always use normalize_nf before
-    fn as_nf(&self) -> &Value {
-        match self {
-            ThunkInternal::Unnormalized(_, _)
-            | ThunkInternal::PartialExpr(_)
-            | ThunkInternal::Value(WHNF, _) => unreachable!(),
-            ThunkInternal::Value(NF, v) => v,
-        }
-    }
-}
-
-impl Thunk {
-    pub(crate) fn new(ctx: NormalizationContext, e: InputSubExpr) -> Thunk {
-        ThunkInternal::Unnormalized(ctx, e).into_thunk()
-    }
-
-    pub(crate) fn from_value(v: Value) -> Thunk {
-        ThunkInternal::Value(WHNF, v).into_thunk()
-    }
-
-    pub(crate) fn from_partial_expr(e: ExprF<Thunk, Normalized>) -> Thunk {
-        ThunkInternal::PartialExpr(e).into_thunk()
-    }
-
-    // Normalizes contents to normal form; faster than `normalize_nf` if
-    // no one else shares this thunk
-    pub(crate) fn normalize_mut(&mut self) {
-        match Rc::get_mut(&mut self.0) {
-            // Mutate directly if sole owner
-            Some(refcell) => RefCell::get_mut(refcell).normalize_nf(),
-            // Otherwise mutate through the refcell
-            None => self.0.borrow_mut().normalize_nf(),
-        }
-    }
-
-    fn do_normalize_whnf(&self) {
-        let borrow = self.0.borrow();
-        match &*borrow {
-            ThunkInternal::Unnormalized(_, _)
-            | ThunkInternal::PartialExpr(_) => {
-                drop(borrow);
-                self.0.borrow_mut().normalize_whnf();
-            }
-            // Already at least in WHNF
-            ThunkInternal::Value(_, _) => {}
-        }
-    }
-
-    fn do_normalize_nf(&self) {
-        let borrow = self.0.borrow();
-        match &*borrow {
-            ThunkInternal::Unnormalized(_, _)
-            | ThunkInternal::PartialExpr(_)
-            | ThunkInternal::Value(WHNF, _) => {
-                drop(borrow);
-                self.0.borrow_mut().normalize_nf();
-            }
-            // Already in NF
-            ThunkInternal::Value(NF, _) => {}
-        }
-    }
-
-    // WARNING: avoid normalizing any thunk while holding on to this ref
-    // or you could run into BorrowMut panics
-    pub(crate) fn normalize_nf(&self) -> Ref<Value> {
-        self.do_normalize_nf();
-        Ref::map(self.0.borrow(), ThunkInternal::as_nf)
-    }
-
-    // WARNING: avoid normalizing any thunk while holding on to this ref
-    // or you could run into BorrowMut panics
-    pub(crate) fn as_value(&self) -> Ref<Value> {
-        self.do_normalize_whnf();
-        Ref::map(self.0.borrow(), ThunkInternal::as_whnf)
-    }
-
-    pub(crate) fn to_value(&self) -> Value {
-        self.as_value().clone()
-    }
-
-    pub(crate) fn normalize_to_expr_maybe_alpha(&self, alpha: bool) -> OutputSubExpr {
-        self.normalize_nf().normalize_to_expr_maybe_alpha(alpha)
-    }
-
-    pub(crate) fn app_val(&self, val: Value) -> Value {
-        self.app_thunk(val.into_thunk())
-    }
-
-    pub(crate) fn app_thunk(&self, th: Thunk) -> Value {
-        apply_any(self.clone(), th)
-    }
-}
-
-impl TypedThunk {
-    pub(crate) fn from_value(v: Value) -> TypedThunk {
-        TypedThunk::from_thunk(Thunk::from_value(v))
-    }
-
-    pub fn from_thunk(th: Thunk) -> TypedThunk {
-        TypedThunk::from_thunk_untyped(th)
-    }
-
-    pub(crate) fn from_type(t: Type) -> TypedThunk {
-        t.into_typethunk()
-    }
-
-    pub(crate) fn normalize_nf(&self) -> Value {
-        match self {
-            TypedThunk::Const(c) => Value::Const(*c),
-            TypedThunk::Untyped(thunk) | TypedThunk::Typed(thunk, _) => {
-                thunk.normalize_nf().clone()
-            }
-        }
-    }
-
-    pub(crate) fn to_typed(&self) -> Typed {
-        self.clone().into_typed()
-    }
-
-    pub(crate) fn normalize_to_expr_maybe_alpha(&self, alpha: bool) -> OutputSubExpr {
-        self.normalize_nf().normalize_to_expr_maybe_alpha(alpha)
-    }
-
-    pub(crate) fn from_thunk_and_type(th: Thunk, t: Type) -> Self {
-        TypedThunk::Typed(th, Box::new(t))
-    }
-    pub(crate) fn from_thunk_untyped(th: Thunk) -> Self {
-        TypedThunk::Untyped(th)
-    }
-    pub(crate) fn from_const(c: Const) -> Self {
-        TypedThunk::Const(c)
-    }
-    pub(crate) fn from_value_untyped(v: Value) -> Self {
-        TypedThunk::from_thunk_untyped(Thunk::from_value(v))
-    }
-
-    // TODO: Avoid cloning if possible
-    pub(crate) fn to_value(&self) -> Value {
-        match self {
-            TypedThunk::Untyped(th) | TypedThunk::Typed(th, _) => th.to_value(),
-            TypedThunk::Const(c) => Value::Const(*c),
-        }
-    }
-    pub(crate) fn to_expr(&self) -> NormalizedSubExpr {
-        self.to_value().normalize_to_expr()
-    }
-    pub(crate) fn to_expr_alpha(&self) -> NormalizedSubExpr {
-        self.to_value().normalize_to_expr_maybe_alpha(true)
-    }
-    pub(crate) fn to_thunk(&self) -> Thunk {
-        match self {
-            TypedThunk::Untyped(th) | TypedThunk::Typed(th, _) => th.clone(),
-            TypedThunk::Const(c) => Thunk::from_value(Value::Const(*c)),
-        }
-    }
-    pub(crate) fn to_type(&self) -> Type {
-        self.clone().into_typed().into_type()
-    }
-    pub(crate) fn into_typed(self) -> Typed {
-        Typed::from_typethunk(self)
-    }
-    pub(crate) 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) {
-        match self {
-            TypedThunk::Untyped(th) | TypedThunk::Typed(th, _) => {
-                th.normalize_mut()
-            }
-            TypedThunk::Const(_) => {}
-        }
-    }
-
-    pub(crate) fn get_type(&self) -> Result<Cow<'_, Type>, TypeError> {
-        match self {
-            TypedThunk::Untyped(_) => Err(TypeError::new(
-                &TypecheckContext::new(),
-                TypeMessage::Untyped,
-            )),
-            TypedThunk::Typed(_, t) => Ok(Cow::Borrowed(t)),
-            TypedThunk::Const(c) => Ok(Cow::Owned(type_of_const(*c)?)),
-        }
-    }
-}
-
-impl Shift for Thunk {
-    fn shift(&self, delta: isize, var: &AlphaVar) -> Option<Self> {
-        Some(self.0.borrow().shift(delta, var)?.into_thunk())
-    }
-}
-
-impl Shift for ThunkInternal {
-    fn shift(&self, delta: isize, var: &AlphaVar) -> Option<Self> {
-        Some(match self {
-            ThunkInternal::Unnormalized(ctx, e) => {
-                ThunkInternal::Unnormalized(ctx.shift(delta, var)?, e.clone())
-            }
-            ThunkInternal::PartialExpr(e) => ThunkInternal::PartialExpr(
-                e.traverse_ref_with_special_handling_of_binders(
-                    |v| Ok(v.shift(delta, var)?),
-                    |x, v| Ok(v.shift(delta, &var.under_binder(x))?),
-                )?,
-            ),
-            ThunkInternal::Value(m, v) => {
-                ThunkInternal::Value(*m, v.shift(delta, var)?)
-            }
-        })
-    }
-}
-
-impl Shift for TypedThunk {
-    fn shift(&self, delta: isize, var: &AlphaVar) -> Option<Self> {
-        Some(match self {
-            TypedThunk::Untyped(th) => {
-                TypedThunk::Untyped(th.shift(delta, var)?)
-            }
-            TypedThunk::Typed(th, t) => TypedThunk::Typed(
-                th.shift(delta, var)?,
-                Box::new(t.shift(delta, var)?),
-            ),
-            TypedThunk::Const(c) => TypedThunk::Const(*c),
-        })
-    }
-}
-
-impl Subst<Typed> for Thunk {
-    fn subst_shift(&self, var: &AlphaVar, val: &Typed) -> Self {
-        self.0.borrow().subst_shift(var, val).into_thunk()
-    }
-}
-
-impl Subst<Typed> for ThunkInternal {
-    fn subst_shift(&self, var: &AlphaVar, val: &Typed) -> Self {
-        match self {
-            ThunkInternal::Unnormalized(ctx, e) => ThunkInternal::Unnormalized(
-                ctx.subst_shift(var, val),
-                e.clone(),
-            ),
-            ThunkInternal::PartialExpr(e) => ThunkInternal::PartialExpr(
-                e.map_ref_with_special_handling_of_binders(
-                    |v| v.subst_shift(var, val),
-                    |x, v| {
-                        v.subst_shift(
-                            &var.under_binder(x),
-                            &val.under_binder(x),
-                        )
-                    },
-                ),
-            ),
-            ThunkInternal::Value(_, v) => {
-                // The resulting value may not stay in normal form after substitution
-                ThunkInternal::Value(WHNF, v.subst_shift(var, val))
-            }
-        }
-    }
-}
-
-impl Subst<Typed> for TypedThunk {
-    fn subst_shift(&self, var: &AlphaVar, val: &Typed) -> Self {
-        match self {
-            TypedThunk::Untyped(th) => {
-                TypedThunk::Untyped(th.subst_shift(var, val))
-            }
-            TypedThunk::Typed(th, t) => TypedThunk::Typed(
-                th.subst_shift(var, val),
-                Box::new(t.subst_shift(var, val)),
-            ),
-            TypedThunk::Const(c) => TypedThunk::Const(*c),
-        }
-    }
-}
-
-impl std::cmp::PartialEq for Thunk {
-    fn eq(&self, other: &Self) -> bool {
-        *self.as_value() == *other.as_value()
-    }
-}
-impl std::cmp::Eq for Thunk {}
-
-impl std::cmp::PartialEq for TypedThunk {
-    fn eq(&self, other: &Self) -> bool {
-        self.to_value() == other.to_value()
-    }
-}
-impl std::cmp::Eq for TypedThunk {}
-
-impl std::fmt::Debug for Thunk {
-    fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result {
-        let b: &ThunkInternal = &self.0.borrow();
-        match b {
-            ThunkInternal::Value(m, v) => {
-                f.debug_tuple(&format!("Thunk@{:?}", m)).field(v).finish()
-            }
-            ThunkInternal::PartialExpr(e) => {
-                f.debug_tuple("Thunk@PartialExpr").field(e).finish()
-            }
-            ThunkInternal::Unnormalized(ctx, e) => f
-                .debug_tuple("Thunk@Unnormalized")
-                .field(ctx)
-                .field(e)
-                .finish(),
-        }
-    }
-}
diff --git a/dhall/src/core/value.rs b/dhall/src/core/value.rs
index 61a8eea..0af7c8c 100644
--- a/dhall/src/core/value.rs
+++ b/dhall/src/core/value.rs
@@ -1,490 +1,272 @@
-use std::collections::HashMap;
+use std::borrow::Cow;
+use std::cell::{Ref, RefCell, RefMut};
+use std::rc::Rc;
 
-use dhall_syntax::{
-    rc, Builtin, Const, ExprF, Integer, InterpolatedTextContents, Label,
-    NaiveDouble, Natural,
-};
+use dhall_syntax::Const;
 
-use crate::core::thunk::{Thunk, TypedThunk};
-use crate::core::var::{AlphaLabel, AlphaVar, Shift, Subst};
-use crate::phase::normalize::{
-    apply_builtin, normalize_one_layer, squash_textlit, OutputSubExpr,
-};
-use crate::phase::{Normalized, Typed};
+use crate::core::context::TypecheckContext;
+use crate::core::valuef::ValueF;
+use crate::core::var::{AlphaVar, Shift, Subst};
+use crate::error::{TypeError, TypeMessage};
+use crate::phase::normalize::{apply_any, normalize_whnf, OutputSubExpr};
+use crate::phase::typecheck::type_of_const;
+use crate::phase::{NormalizedSubExpr, Typed};
 
-/// A semantic value. The invariants ensure this value represents a Weak-Head
-/// Normal Form (WHNF). This means that this first constructor is the first constructor of the
-/// final Normal Form (NF).
-/// This WHNF must be preserved by operations on `Value`s. In particular, `subst_shift` could break
-/// the invariants so need to be careful to reevaluate as needed.
-/// Subexpressions are Thunks, which are partially evaluated expressions that are normalized
-/// on-demand. When all the Thunks in a Value are at least in WHNF, and recursively so, then the
-/// Value is in NF. This is because WHNF ensures that we have the first constructor of the NF; so
-/// if we have the first constructor of the NF at all levels, we actually have the NF.
-/// Equality is up to alpha-equivalence (renaming of bound variables) and beta-equivalence
-/// (normalization). Equality will normalize only as needed.
-#[derive(Debug, Clone, PartialEq, Eq)]
-pub enum Value {
-    /// Closures
-    Lam(AlphaLabel, TypedThunk, Thunk),
-    Pi(AlphaLabel, TypedThunk, TypedThunk),
-    // Invariant: the evaluation must not be able to progress further.
-    AppliedBuiltin(Builtin, Vec<Thunk>),
+#[derive(Debug, Clone, Copy)]
+enum Form {
+    /// No constraints; expression may not be normalized at all.
+    Unevaled,
+    /// Weak Head Normal Form, i.e. normalized up to the first constructor, but subexpressions may
+    /// not be normalized. This means that the first constructor of the contained ValueF is the first
+    /// constructor of the final Normal Form (NF).
+    WHNF,
+    /// Normal Form, i.e. completely normalized.
+    /// When all the Values in a ValueF are at least in WHNF, and recursively so, then the
+    /// ValueF is in NF. This is because WHNF ensures that we have the first constructor of the NF; so
+    /// if we have the first constructor of the NF at all levels, we actually have the NF.
+    NF,
+}
+use Form::{Unevaled, NF, WHNF};
 
-    Var(AlphaVar),
-    Const(Const),
-    BoolLit(bool),
-    NaturalLit(Natural),
-    IntegerLit(Integer),
-    DoubleLit(NaiveDouble),
-    EmptyOptionalLit(TypedThunk),
-    NEOptionalLit(Thunk),
-    // EmptyListLit(t) means `[] : List t`, not `[] : t`
-    EmptyListLit(TypedThunk),
-    NEListLit(Vec<Thunk>),
-    RecordLit(HashMap<Label, Thunk>),
-    RecordType(HashMap<Label, TypedThunk>),
-    UnionType(HashMap<Label, Option<TypedThunk>>),
-    UnionConstructor(Label, HashMap<Label, Option<TypedThunk>>),
-    UnionLit(Label, Thunk, HashMap<Label, Option<TypedThunk>>),
-    // Invariant: this must not contain interpolations that are themselves TextLits, and
-    // contiguous text values must be merged.
-    TextLit(Vec<InterpolatedTextContents<Thunk>>),
-    Equivalence(TypedThunk, TypedThunk),
-    // Invariant: this must not contain a value captured by one of the variants above.
-    PartialExpr(ExprF<Thunk, Normalized>),
+#[derive(Debug)]
+/// Partially normalized value.
+/// Invariant: if `form` is `WHNF`, `value` must be in Weak Head Normal Form
+/// Invariant: if `form` is `NF`, `value` must be fully normalized
+struct ValueInternal {
+    form: Form,
+    value: ValueF,
+    ty: Option<Value>,
 }
 
-impl Value {
-    pub(crate) fn into_thunk(self) -> Thunk {
-        Thunk::from_value(self)
+/// Stores a possibly unevaluated value. Gets (partially) normalized on-demand,
+/// sharing computation automatically. Uses a RefCell to share computation.
+/// Can optionally store a type from typechecking to preserve type information.
+#[derive(Clone)]
+pub struct Value(Rc<RefCell<ValueInternal>>);
+
+impl ValueInternal {
+    fn into_value(self) -> Value {
+        Value(Rc::new(RefCell::new(self)))
+    }
+    fn as_valuef(&self) -> &ValueF {
+        &self.value
     }
 
-    /// Convert the value to a fully normalized syntactic expression
-    pub(crate) fn normalize_to_expr(&self) -> OutputSubExpr {
-        self.normalize_to_expr_maybe_alpha(false)
-    }
-    /// Convert the value to a fully normalized syntactic expression. Also alpha-normalize
-    /// if alpha is `true`
-    pub(crate) fn normalize_to_expr_maybe_alpha(&self, alpha: bool) -> OutputSubExpr {
-        match self {
-            Value::Lam(x, t, e) => rc(ExprF::Lam(
-                x.to_label_maybe_alpha(alpha),
-                t.normalize_to_expr_maybe_alpha(alpha),
-                e.normalize_to_expr_maybe_alpha(alpha),
-            )),
-            Value::AppliedBuiltin(b, args) => {
-                let mut e = rc(ExprF::Builtin(*b));
-                for v in args {
-                    e = rc(ExprF::App(
-                        e,
-                        v.normalize_to_expr_maybe_alpha(alpha),
-                    ));
-                }
-                e
-            }
-            Value::Pi(x, t, e) => rc(ExprF::Pi(
-                x.to_label_maybe_alpha(alpha),
-                t.normalize_to_expr_maybe_alpha(alpha),
-                e.normalize_to_expr_maybe_alpha(alpha),
-            )),
-            Value::Var(v) => rc(ExprF::Var(v.to_var(alpha))),
-            Value::Const(c) => rc(ExprF::Const(*c)),
-            Value::BoolLit(b) => rc(ExprF::BoolLit(*b)),
-            Value::NaturalLit(n) => rc(ExprF::NaturalLit(*n)),
-            Value::IntegerLit(n) => rc(ExprF::IntegerLit(*n)),
-            Value::DoubleLit(n) => rc(ExprF::DoubleLit(*n)),
-            Value::EmptyOptionalLit(n) => rc(ExprF::App(
-                rc(ExprF::Builtin(Builtin::OptionalNone)),
-                n.normalize_to_expr_maybe_alpha(alpha),
-            )),
-            Value::NEOptionalLit(n) => {
-                rc(ExprF::SomeLit(n.normalize_to_expr_maybe_alpha(alpha)))
-            }
-            Value::EmptyListLit(n) => rc(ExprF::EmptyListLit(rc(ExprF::App(
-                rc(ExprF::Builtin(Builtin::List)),
-                n.normalize_to_expr_maybe_alpha(alpha),
-            )))),
-            Value::NEListLit(elts) => rc(ExprF::NEListLit(
-                elts.iter()
-                    .map(|n| n.normalize_to_expr_maybe_alpha(alpha))
-                    .collect(),
-            )),
-            Value::RecordLit(kvs) => rc(ExprF::RecordLit(
-                kvs.iter()
-                    .map(|(k, v)| {
-                        (k.clone(), v.normalize_to_expr_maybe_alpha(alpha))
-                    })
-                    .collect(),
-            )),
-            Value::RecordType(kts) => rc(ExprF::RecordType(
-                kts.iter()
-                    .map(|(k, v)| {
-                        (k.clone(), v.normalize_to_expr_maybe_alpha(alpha))
-                    })
-                    .collect(),
-            )),
-            Value::UnionType(kts) => rc(ExprF::UnionType(
-                kts.iter()
-                    .map(|(k, v)| {
-                        (
-                            k.clone(),
-                            v.as_ref().map(|v| {
-                                v.normalize_to_expr_maybe_alpha(alpha)
-                            }),
-                        )
-                    })
-                    .collect(),
-            )),
-            Value::UnionConstructor(l, kts) => {
-                let kts = kts
-                    .iter()
-                    .map(|(k, v)| {
-                        (
-                            k.clone(),
-                            v.as_ref().map(|v| {
-                                v.normalize_to_expr_maybe_alpha(alpha)
-                            }),
-                        )
-                    })
-                    .collect();
-                rc(ExprF::Field(rc(ExprF::UnionType(kts)), l.clone()))
+    fn normalize_whnf(&mut self) {
+        take_mut::take(self, |vint| match &vint.form {
+            Unevaled => ValueInternal {
+                form: WHNF,
+                value: normalize_whnf(vint.value),
+                ty: vint.ty,
+            },
+            // Already in WHNF
+            WHNF | NF => vint,
+        })
+    }
+    fn normalize_nf(&mut self) {
+        match self.form {
+            Unevaled => {
+                self.normalize_whnf();
+                self.normalize_nf();
             }
-            Value::UnionLit(l, v, kts) => rc(ExprF::App(
-                Value::UnionConstructor(l.clone(), kts.clone())
-                    .normalize_to_expr_maybe_alpha(alpha),
-                v.normalize_to_expr_maybe_alpha(alpha),
-            )),
-            Value::TextLit(elts) => {
-                use InterpolatedTextContents::{Expr, Text};
-                rc(ExprF::TextLit(
-                    elts.iter()
-                        .map(|contents| match contents {
-                            Expr(e) => {
-                                Expr(e.normalize_to_expr_maybe_alpha(alpha))
-                            }
-                            Text(s) => Text(s.clone()),
-                        })
-                        .collect(),
-                ))
+            WHNF => {
+                self.value.normalize_mut();
+                self.form = NF;
             }
-            Value::Equivalence(x, y) => rc(ExprF::BinOp(
-                dhall_syntax::BinOp::Equivalence,
-                x.normalize_to_expr_maybe_alpha(alpha),
-                y.normalize_to_expr_maybe_alpha(alpha),
+            // Already in NF
+            NF => {}
+        }
+    }
+
+    fn get_type(&self) -> Result<&Value, TypeError> {
+        match &self.ty {
+            Some(t) => Ok(t),
+            None => Err(TypeError::new(
+                &TypecheckContext::new(),
+                TypeMessage::Untyped,
             )),
-            Value::PartialExpr(e) => {
-                rc(e.map_ref(|v| v.normalize_to_expr_maybe_alpha(alpha)))
-            }
         }
     }
+}
 
-    pub(crate) fn normalize_mut(&mut self) {
-        match self {
-            Value::Var(_)
-            | Value::Const(_)
-            | Value::BoolLit(_)
-            | Value::NaturalLit(_)
-            | Value::IntegerLit(_)
-            | Value::DoubleLit(_) => {}
+impl Value {
+    pub(crate) fn from_valuef_untyped(v: ValueF) -> Value {
+        ValueInternal {
+            form: Unevaled,
+            value: v,
+            ty: None,
+        }
+        .into_value()
+    }
+    pub(crate) fn from_valuef_and_type(v: ValueF, t: Value) -> Value {
+        ValueInternal {
+            form: Unevaled,
+            value: v,
+            ty: Some(t),
+        }
+        .into_value()
+    }
+    pub(crate) fn from_valuef_simple_type(v: ValueF) -> Value {
+        Value::from_valuef_and_type(v, Value::from_const(Const::Type))
+    }
+    pub(crate) fn from_const(c: Const) -> Self {
+        match type_of_const(c) {
+            Ok(t) => Value::from_valuef_and_type(ValueF::Const(c), t),
+            Err(_) => Value::from_valuef_untyped(ValueF::Const(c)),
+        }
+    }
+    pub fn const_type() -> Self {
+        Value::from_const(Const::Type)
+    }
 
-            Value::EmptyOptionalLit(tth) | Value::EmptyListLit(tth) => {
-                tth.normalize_mut();
-            }
+    pub(crate) fn as_const(&self) -> Option<Const> {
+        match &*self.as_whnf() {
+            ValueF::Const(c) => Some(*c),
+            _ => None,
+        }
+    }
 
-            Value::NEOptionalLit(th) => {
-                th.normalize_mut();
-            }
-            Value::Lam(_, t, e) => {
-                t.normalize_mut();
-                e.normalize_mut();
-            }
-            Value::Pi(_, t, e) => {
-                t.normalize_mut();
-                e.normalize_mut();
-            }
-            Value::AppliedBuiltin(_, args) => {
-                for x in args.iter_mut() {
-                    x.normalize_mut();
-                }
-            }
-            Value::NEListLit(elts) => {
-                for x in elts.iter_mut() {
-                    x.normalize_mut();
-                }
-            }
-            Value::RecordLit(kvs) => {
-                for x in kvs.values_mut() {
-                    x.normalize_mut();
-                }
-            }
-            Value::RecordType(kvs) => {
-                for x in kvs.values_mut() {
-                    x.normalize_mut();
-                }
-            }
-            Value::UnionType(kts) | Value::UnionConstructor(_, kts) => {
-                for x in kts.values_mut().flat_map(|opt| opt) {
-                    x.normalize_mut();
-                }
-            }
-            Value::UnionLit(_, v, kts) => {
-                v.normalize_mut();
-                for x in kts.values_mut().flat_map(|opt| opt) {
-                    x.normalize_mut();
-                }
-            }
-            Value::TextLit(elts) => {
-                for x in elts.iter_mut() {
-                    use InterpolatedTextContents::{Expr, Text};
-                    match x {
-                        Expr(n) => n.normalize_mut(),
-                        Text(_) => {}
-                    }
-                }
-            }
-            Value::Equivalence(x, y) => {
-                x.normalize_mut();
-                y.normalize_mut();
+    fn as_internal(&self) -> Ref<ValueInternal> {
+        self.0.borrow()
+    }
+    fn as_internal_mut(&self) -> RefMut<ValueInternal> {
+        self.0.borrow_mut()
+    }
+    /// WARNING: The returned ValueF may be entirely unnormalized, in aprticular it may just be an
+    /// unevaled PartialExpr. You probably want to use `as_whnf`.
+    fn as_valuef(&self) -> Ref<ValueF> {
+        Ref::map(self.as_internal(), ValueInternal::as_valuef)
+    }
+    /// This is what you want if you want to pattern-match on the value.
+    /// WARNING: drop this ref before normalizing the same value or you will run into BorrowMut
+    /// panics.
+    pub(crate) fn as_whnf(&self) -> Ref<ValueF> {
+        self.normalize_whnf();
+        self.as_valuef()
+    }
+    /// WARNING: drop this ref before normalizing the same value or you will run into BorrowMut
+    /// panics.
+    pub(crate) fn as_nf(&self) -> Ref<ValueF> {
+        self.normalize_nf();
+        self.as_valuef()
+    }
+
+    // TODO: rename `normalize_to_expr`
+    pub(crate) fn to_expr(&self) -> NormalizedSubExpr {
+        self.as_whnf().normalize_to_expr()
+    }
+    // TODO: rename `normalize_to_expr_maybe_alpha`
+    pub(crate) fn to_expr_alpha(&self) -> NormalizedSubExpr {
+        self.as_whnf().normalize_to_expr_maybe_alpha(true)
+    }
+    /// TODO: cloning a valuef can often be avoided
+    pub(crate) fn to_whnf(&self) -> ValueF {
+        self.as_whnf().clone()
+    }
+    pub(crate) fn into_typed(self) -> Typed {
+        Typed::from_value(self)
+    }
+
+    /// Mutates the contents. If no one else shares this, this avoids a RefCell lock.
+    fn mutate_internal(&mut self, f: impl FnOnce(&mut ValueInternal)) {
+        match Rc::get_mut(&mut self.0) {
+            // Mutate directly if sole owner
+            Some(refcell) => f(RefCell::get_mut(refcell)),
+            // Otherwise mutate through the refcell
+            None => f(&mut self.as_internal_mut()),
+        }
+    }
+    /// Normalizes contents to normal form; faster than `normalize_nf` if
+    /// no one else shares this.
+    pub(crate) fn normalize_mut(&mut self) {
+        self.mutate_internal(|vint| vint.normalize_nf())
+    }
+
+    pub(crate) fn normalize_whnf(&self) {
+        let borrow = self.as_internal();
+        match borrow.form {
+            Unevaled => {
+                drop(borrow);
+                self.as_internal_mut().normalize_whnf();
             }
-            Value::PartialExpr(e) => {
-                // TODO: need map_mut
-                e.map_ref(|v| {
-                    v.normalize_nf();
-                });
+            // Already at least in WHNF
+            WHNF | NF => {}
+        }
+    }
+    pub(crate) fn normalize_nf(&self) {
+        let borrow = self.as_internal();
+        match borrow.form {
+            Unevaled | WHNF => {
+                drop(borrow);
+                self.as_internal_mut().normalize_nf();
             }
+            // Already in NF
+            NF => {}
         }
     }
 
-    /// Apply to a value
-    pub(crate) fn app(self, val: Value) -> Value {
-        self.app_val(val)
+    pub(crate) fn normalize_to_expr_maybe_alpha(
+        &self,
+        alpha: bool,
+    ) -> OutputSubExpr {
+        self.as_nf().normalize_to_expr_maybe_alpha(alpha)
     }
 
-    /// Apply to a value
-    pub(crate) fn app_val(self, val: Value) -> Value {
-        self.app_thunk(val.into_thunk())
+    pub(crate) fn app_value(&self, th: Value) -> ValueF {
+        apply_any(self.clone(), th)
     }
 
-    /// Apply to a thunk
-    pub fn app_thunk(self, th: Thunk) -> Value {
-        Thunk::from_value(self).app_thunk(th)
+    pub(crate) fn get_type(&self) -> Result<Cow<'_, Value>, TypeError> {
+        Ok(Cow::Owned(self.as_internal().get_type()?.clone()))
     }
+}
 
-    pub fn from_builtin(b: Builtin) -> Value {
-        Value::AppliedBuiltin(b, vec![])
+impl Shift for Value {
+    fn shift(&self, delta: isize, var: &AlphaVar) -> Option<Self> {
+        Some(Value(self.0.shift(delta, var)?))
     }
 }
 
-impl Shift for Value {
+impl Shift for ValueInternal {
     fn shift(&self, delta: isize, var: &AlphaVar) -> Option<Self> {
-        Some(match self {
-            Value::Lam(x, t, e) => Value::Lam(
-                x.clone(),
-                t.shift(delta, var)?,
-                e.shift(delta, &var.under_binder(x))?,
-            ),
-            Value::AppliedBuiltin(b, args) => Value::AppliedBuiltin(
-                *b,
-                args.iter()
-                    .map(|v| Ok(v.shift(delta, var)?))
-                    .collect::<Result<_, _>>()?,
-            ),
-            Value::Pi(x, t, e) => Value::Pi(
-                x.clone(),
-                t.shift(delta, var)?,
-                e.shift(delta, &var.under_binder(x))?,
-            ),
-            Value::Var(v) => Value::Var(v.shift(delta, var)?),
-            Value::Const(c) => Value::Const(*c),
-            Value::BoolLit(b) => Value::BoolLit(*b),
-            Value::NaturalLit(n) => Value::NaturalLit(*n),
-            Value::IntegerLit(n) => Value::IntegerLit(*n),
-            Value::DoubleLit(n) => Value::DoubleLit(*n),
-            Value::EmptyOptionalLit(tth) => {
-                Value::EmptyOptionalLit(tth.shift(delta, var)?)
-            }
-            Value::NEOptionalLit(th) => {
-                Value::NEOptionalLit(th.shift(delta, var)?)
-            }
-            Value::EmptyListLit(tth) => {
-                Value::EmptyListLit(tth.shift(delta, var)?)
-            }
-            Value::NEListLit(elts) => Value::NEListLit(
-                elts.iter()
-                    .map(|v| Ok(v.shift(delta, var)?))
-                    .collect::<Result<_, _>>()?,
-            ),
-            Value::RecordLit(kvs) => Value::RecordLit(
-                kvs.iter()
-                    .map(|(k, v)| Ok((k.clone(), v.shift(delta, var)?)))
-                    .collect::<Result<_, _>>()?,
-            ),
-            Value::RecordType(kvs) => Value::RecordType(
-                kvs.iter()
-                    .map(|(k, v)| Ok((k.clone(), v.shift(delta, var)?)))
-                    .collect::<Result<_, _>>()?,
-            ),
-            Value::UnionType(kts) => Value::UnionType(
-                kts.iter()
-                    .map(|(k, v)| {
-                        Ok((
-                            k.clone(),
-                            v.as_ref()
-                                .map(|v| Ok(v.shift(delta, var)?))
-                                .transpose()?,
-                        ))
-                    })
-                    .collect::<Result<_, _>>()?,
-            ),
-            Value::UnionConstructor(x, kts) => Value::UnionConstructor(
-                x.clone(),
-                kts.iter()
-                    .map(|(k, v)| {
-                        Ok((
-                            k.clone(),
-                            v.as_ref()
-                                .map(|v| Ok(v.shift(delta, var)?))
-                                .transpose()?,
-                        ))
-                    })
-                    .collect::<Result<_, _>>()?,
-            ),
-            Value::UnionLit(x, v, kts) => Value::UnionLit(
-                x.clone(),
-                v.shift(delta, var)?,
-                kts.iter()
-                    .map(|(k, v)| {
-                        Ok((
-                            k.clone(),
-                            v.as_ref()
-                                .map(|v| Ok(v.shift(delta, var)?))
-                                .transpose()?,
-                        ))
-                    })
-                    .collect::<Result<_, _>>()?,
-            ),
-            Value::TextLit(elts) => Value::TextLit(
-                elts.iter()
-                    .map(|contents| {
-                        use InterpolatedTextContents::{Expr, Text};
-                        Ok(match contents {
-                            Expr(th) => Expr(th.shift(delta, var)?),
-                            Text(s) => Text(s.clone()),
-                        })
-                    })
-                    .collect::<Result<_, _>>()?,
-            ),
-            Value::Equivalence(x, y) => {
-                Value::Equivalence(x.shift(delta, var)?, y.shift(delta, var)?)
-            }
-            Value::PartialExpr(e) => Value::PartialExpr(
-                e.traverse_ref_with_special_handling_of_binders(
-                    |v| Ok(v.shift(delta, var)?),
-                    |x, v| Ok(v.shift(delta, &var.under_binder(x))?),
-                )?,
-            ),
+        Some(ValueInternal {
+            form: self.form,
+            value: self.value.shift(delta, var)?,
+            ty: self.ty.shift(delta, var)?,
         })
     }
 }
 
-impl Subst<Typed> for Value {
-    fn subst_shift(&self, var: &AlphaVar, val: &Typed) -> Self {
-        match self {
-            // Retry normalizing since substituting may allow progress
-            Value::AppliedBuiltin(b, args) => apply_builtin(
-                *b,
-                args.iter().map(|v| v.subst_shift(var, val)).collect(),
-            ),
-            // Retry normalizing since substituting may allow progress
-            Value::PartialExpr(e) => {
-                normalize_one_layer(e.map_ref_with_special_handling_of_binders(
-                    |v| v.subst_shift(var, val),
-                    |x, v| {
-                        v.subst_shift(
-                            &var.under_binder(x),
-                            &val.under_binder(x),
-                        )
-                    },
-                ))
-            }
-            // Retry normalizing since substituting may allow progress
-            Value::TextLit(elts) => {
-                Value::TextLit(squash_textlit(elts.iter().map(|contents| {
-                    use InterpolatedTextContents::{Expr, Text};
-                    match contents {
-                        Expr(th) => Expr(th.subst_shift(var, val)),
-                        Text(s) => Text(s.clone()),
-                    }
-                })))
-            }
-            Value::Lam(x, t, e) => Value::Lam(
-                x.clone(),
-                t.subst_shift(var, val),
-                e.subst_shift(&var.under_binder(x), &val.under_binder(x)),
-            ),
-            Value::Pi(x, t, e) => Value::Pi(
-                x.clone(),
-                t.subst_shift(var, val),
-                e.subst_shift(&var.under_binder(x), &val.under_binder(x)),
-            ),
-            Value::Var(v) if v == var => val.to_value(),
-            Value::Var(v) => Value::Var(v.shift(-1, var).unwrap()),
-            Value::Const(c) => Value::Const(*c),
-            Value::BoolLit(b) => Value::BoolLit(*b),
-            Value::NaturalLit(n) => Value::NaturalLit(*n),
-            Value::IntegerLit(n) => Value::IntegerLit(*n),
-            Value::DoubleLit(n) => Value::DoubleLit(*n),
-            Value::EmptyOptionalLit(tth) => {
-                Value::EmptyOptionalLit(tth.subst_shift(var, val))
-            }
-            Value::NEOptionalLit(th) => {
-                Value::NEOptionalLit(th.subst_shift(var, val))
-            }
-            Value::EmptyListLit(tth) => {
-                Value::EmptyListLit(tth.subst_shift(var, val))
-            }
-            Value::NEListLit(elts) => Value::NEListLit(
-                elts.iter().map(|v| v.subst_shift(var, val)).collect(),
-            ),
-            Value::RecordLit(kvs) => Value::RecordLit(
-                kvs.iter()
-                    .map(|(k, v)| (k.clone(), v.subst_shift(var, val)))
-                    .collect(),
-            ),
-            Value::RecordType(kvs) => Value::RecordType(
-                kvs.iter()
-                    .map(|(k, v)| (k.clone(), v.subst_shift(var, val)))
-                    .collect(),
-            ),
-            Value::UnionType(kts) => Value::UnionType(
-                kts.iter()
-                    .map(|(k, v)| {
-                        (k.clone(), v.as_ref().map(|v| v.subst_shift(var, val)))
-                    })
-                    .collect(),
-            ),
-            Value::UnionConstructor(x, kts) => Value::UnionConstructor(
-                x.clone(),
-                kts.iter()
-                    .map(|(k, v)| {
-                        (k.clone(), v.as_ref().map(|v| v.subst_shift(var, val)))
-                    })
-                    .collect(),
-            ),
-            Value::UnionLit(x, v, kts) => Value::UnionLit(
-                x.clone(),
-                v.subst_shift(var, val),
-                kts.iter()
-                    .map(|(k, v)| {
-                        (k.clone(), v.as_ref().map(|v| v.subst_shift(var, val)))
-                    })
-                    .collect(),
-            ),
-            Value::Equivalence(x, y) => Value::Equivalence(
-                x.subst_shift(var, val),
-                y.subst_shift(var, val),
-            ),
+impl Subst<Value> for Value {
+    fn subst_shift(&self, var: &AlphaVar, val: &Value) -> Self {
+        Value(self.0.subst_shift(var, val))
+    }
+}
+
+impl Subst<Value> for ValueInternal {
+    fn subst_shift(&self, var: &AlphaVar, val: &Value) -> Self {
+        ValueInternal {
+            // The resulting value may not stay in wnhf after substitution
+            form: Unevaled,
+            value: self.value.subst_shift(var, val),
+            ty: self.ty.subst_shift(var, val),
         }
     }
 }
+
+// TODO: use Rc comparison to shortcut on identical pointers
+impl std::cmp::PartialEq for Value {
+    fn eq(&self, other: &Self) -> bool {
+        *self.as_whnf() == *other.as_whnf()
+    }
+}
+impl std::cmp::Eq for Value {}
+
+impl std::fmt::Debug for Value {
+    fn fmt(&self, fmt: &mut std::fmt::Formatter<'_>) -> std::fmt::Result {
+        let vint: &ValueInternal = &self.as_internal();
+        fmt.debug_tuple(&format!("Value@{:?}", &vint.form))
+            .field(&vint.value)
+            .finish()
+    }
+}
diff --git a/dhall/src/core/valuef.rs b/dhall/src/core/valuef.rs
new file mode 100644
index 0000000..0c3058d
--- /dev/null
+++ b/dhall/src/core/valuef.rs
@@ -0,0 +1,400 @@
+use std::collections::HashMap;
+
+use dhall_syntax::{
+    rc, Builtin, Const, ExprF, Integer, InterpolatedTextContents, Label,
+    NaiveDouble, Natural,
+};
+
+use crate::core::value::Value;
+use crate::core::var::{AlphaLabel, AlphaVar, Shift, Subst};
+use crate::phase::normalize::OutputSubExpr;
+use crate::phase::Normalized;
+
+/// A semantic value. Subexpressions are Values, which are partially evaluated expressions that are
+/// normalized on-demand.
+/// If you compare for equality two `ValueF`s in WHNF, then equality will be up to
+/// alpha-equivalence (renaming of bound variables) and beta-equivalence (normalization). It will
+/// recursively normalize as needed.
+#[derive(Debug, Clone, PartialEq, Eq)]
+pub enum ValueF {
+    /// Closures
+    Lam(AlphaLabel, Value, Value),
+    Pi(AlphaLabel, Value, Value),
+    // Invariant: the evaluation must not be able to progress further.
+    AppliedBuiltin(Builtin, Vec<Value>),
+
+    Var(AlphaVar),
+    Const(Const),
+    BoolLit(bool),
+    NaturalLit(Natural),
+    IntegerLit(Integer),
+    DoubleLit(NaiveDouble),
+    EmptyOptionalLit(Value),
+    NEOptionalLit(Value),
+    // EmptyListLit(t) means `[] : List t`, not `[] : t`
+    EmptyListLit(Value),
+    NEListLit(Vec<Value>),
+    RecordLit(HashMap<Label, Value>),
+    RecordType(HashMap<Label, Value>),
+    UnionType(HashMap<Label, Option<Value>>),
+    UnionConstructor(Label, HashMap<Label, Option<Value>>),
+    UnionLit(Label, Value, HashMap<Label, Option<Value>>),
+    // Invariant: this must not contain interpolations that are themselves TextLits, and
+    // contiguous text values must be merged.
+    TextLit(Vec<InterpolatedTextContents<Value>>),
+    Equivalence(Value, Value),
+    // Invariant: this must not contain a value captured by one of the variants above.
+    PartialExpr(ExprF<Value, Normalized>),
+}
+
+impl ValueF {
+    pub(crate) fn into_value_untyped(self) -> Value {
+        Value::from_valuef_untyped(self)
+    }
+    pub(crate) fn into_value_with_type(self, t: Value) -> Value {
+        Value::from_valuef_and_type(self, t)
+    }
+    pub(crate) fn into_value_simple_type(self) -> Value {
+        Value::from_valuef_simple_type(self)
+    }
+
+    /// Convert the value to a fully normalized syntactic expression
+    pub(crate) fn normalize_to_expr(&self) -> OutputSubExpr {
+        self.normalize_to_expr_maybe_alpha(false)
+    }
+    /// Convert the value to a fully normalized syntactic expression. Also alpha-normalize
+    /// if alpha is `true`
+    pub(crate) fn normalize_to_expr_maybe_alpha(
+        &self,
+        alpha: bool,
+    ) -> OutputSubExpr {
+        match self {
+            ValueF::Lam(x, t, e) => rc(ExprF::Lam(
+                x.to_label_maybe_alpha(alpha),
+                t.normalize_to_expr_maybe_alpha(alpha),
+                e.normalize_to_expr_maybe_alpha(alpha),
+            )),
+            ValueF::AppliedBuiltin(b, args) => {
+                let mut e = rc(ExprF::Builtin(*b));
+                for v in args {
+                    e = rc(ExprF::App(
+                        e,
+                        v.normalize_to_expr_maybe_alpha(alpha),
+                    ));
+                }
+                e
+            }
+            ValueF::Pi(x, t, e) => rc(ExprF::Pi(
+                x.to_label_maybe_alpha(alpha),
+                t.normalize_to_expr_maybe_alpha(alpha),
+                e.normalize_to_expr_maybe_alpha(alpha),
+            )),
+            ValueF::Var(v) => rc(ExprF::Var(v.to_var(alpha))),
+            ValueF::Const(c) => rc(ExprF::Const(*c)),
+            ValueF::BoolLit(b) => rc(ExprF::BoolLit(*b)),
+            ValueF::NaturalLit(n) => rc(ExprF::NaturalLit(*n)),
+            ValueF::IntegerLit(n) => rc(ExprF::IntegerLit(*n)),
+            ValueF::DoubleLit(n) => rc(ExprF::DoubleLit(*n)),
+            ValueF::EmptyOptionalLit(n) => rc(ExprF::App(
+                rc(ExprF::Builtin(Builtin::OptionalNone)),
+                n.normalize_to_expr_maybe_alpha(alpha),
+            )),
+            ValueF::NEOptionalLit(n) => {
+                rc(ExprF::SomeLit(n.normalize_to_expr_maybe_alpha(alpha)))
+            }
+            ValueF::EmptyListLit(n) => rc(ExprF::EmptyListLit(rc(ExprF::App(
+                rc(ExprF::Builtin(Builtin::List)),
+                n.normalize_to_expr_maybe_alpha(alpha),
+            )))),
+            ValueF::NEListLit(elts) => rc(ExprF::NEListLit(
+                elts.iter()
+                    .map(|n| n.normalize_to_expr_maybe_alpha(alpha))
+                    .collect(),
+            )),
+            ValueF::RecordLit(kvs) => rc(ExprF::RecordLit(
+                kvs.iter()
+                    .map(|(k, v)| {
+                        (k.clone(), v.normalize_to_expr_maybe_alpha(alpha))
+                    })
+                    .collect(),
+            )),
+            ValueF::RecordType(kts) => rc(ExprF::RecordType(
+                kts.iter()
+                    .map(|(k, v)| {
+                        (k.clone(), v.normalize_to_expr_maybe_alpha(alpha))
+                    })
+                    .collect(),
+            )),
+            ValueF::UnionType(kts) => rc(ExprF::UnionType(
+                kts.iter()
+                    .map(|(k, v)| {
+                        (
+                            k.clone(),
+                            v.as_ref().map(|v| {
+                                v.normalize_to_expr_maybe_alpha(alpha)
+                            }),
+                        )
+                    })
+                    .collect(),
+            )),
+            ValueF::UnionConstructor(l, kts) => {
+                let kts = kts
+                    .iter()
+                    .map(|(k, v)| {
+                        (
+                            k.clone(),
+                            v.as_ref().map(|v| {
+                                v.normalize_to_expr_maybe_alpha(alpha)
+                            }),
+                        )
+                    })
+                    .collect();
+                rc(ExprF::Field(rc(ExprF::UnionType(kts)), l.clone()))
+            }
+            ValueF::UnionLit(l, v, kts) => rc(ExprF::App(
+                ValueF::UnionConstructor(l.clone(), kts.clone())
+                    .normalize_to_expr_maybe_alpha(alpha),
+                v.normalize_to_expr_maybe_alpha(alpha),
+            )),
+            ValueF::TextLit(elts) => {
+                use InterpolatedTextContents::{Expr, Text};
+                rc(ExprF::TextLit(
+                    elts.iter()
+                        .map(|contents| match contents {
+                            Expr(e) => {
+                                Expr(e.normalize_to_expr_maybe_alpha(alpha))
+                            }
+                            Text(s) => Text(s.clone()),
+                        })
+                        .collect(),
+                ))
+            }
+            ValueF::Equivalence(x, y) => rc(ExprF::BinOp(
+                dhall_syntax::BinOp::Equivalence,
+                x.normalize_to_expr_maybe_alpha(alpha),
+                y.normalize_to_expr_maybe_alpha(alpha),
+            )),
+            ValueF::PartialExpr(e) => {
+                rc(e.map_ref(|v| v.normalize_to_expr_maybe_alpha(alpha)))
+            }
+        }
+    }
+
+    pub(crate) fn normalize_mut(&mut self) {
+        match self {
+            ValueF::Var(_)
+            | ValueF::Const(_)
+            | ValueF::BoolLit(_)
+            | ValueF::NaturalLit(_)
+            | ValueF::IntegerLit(_)
+            | ValueF::DoubleLit(_) => {}
+
+            ValueF::EmptyOptionalLit(tth) | ValueF::EmptyListLit(tth) => {
+                tth.normalize_mut();
+            }
+
+            ValueF::NEOptionalLit(th) => {
+                th.normalize_mut();
+            }
+            ValueF::Lam(_, t, e) => {
+                t.normalize_mut();
+                e.normalize_mut();
+            }
+            ValueF::Pi(_, t, e) => {
+                t.normalize_mut();
+                e.normalize_mut();
+            }
+            ValueF::AppliedBuiltin(_, args) => {
+                for x in args.iter_mut() {
+                    x.normalize_mut();
+                }
+            }
+            ValueF::NEListLit(elts) => {
+                for x in elts.iter_mut() {
+                    x.normalize_mut();
+                }
+            }
+            ValueF::RecordLit(kvs) => {
+                for x in kvs.values_mut() {
+                    x.normalize_mut();
+                }
+            }
+            ValueF::RecordType(kvs) => {
+                for x in kvs.values_mut() {
+                    x.normalize_mut();
+                }
+            }
+            ValueF::UnionType(kts) | ValueF::UnionConstructor(_, kts) => {
+                for x in kts.values_mut().flat_map(|opt| opt) {
+                    x.normalize_mut();
+                }
+            }
+            ValueF::UnionLit(_, v, kts) => {
+                v.normalize_mut();
+                for x in kts.values_mut().flat_map(|opt| opt) {
+                    x.normalize_mut();
+                }
+            }
+            ValueF::TextLit(elts) => {
+                for x in elts.iter_mut() {
+                    use InterpolatedTextContents::{Expr, Text};
+                    match x {
+                        Expr(n) => n.normalize_mut(),
+                        Text(_) => {}
+                    }
+                }
+            }
+            ValueF::Equivalence(x, y) => {
+                x.normalize_mut();
+                y.normalize_mut();
+            }
+            ValueF::PartialExpr(e) => {
+                // TODO: need map_mut
+                e.map_ref(|v| {
+                    v.normalize_nf();
+                });
+            }
+        }
+    }
+
+    /// Apply to a valuef
+    pub(crate) fn app(self, val: ValueF) -> ValueF {
+        self.app_valuef(val)
+    }
+
+    /// Apply to a valuef
+    pub(crate) fn app_valuef(self, val: ValueF) -> ValueF {
+        self.app_value(val.into_value_untyped())
+    }
+
+    /// Apply to a value
+    pub fn app_value(self, th: Value) -> ValueF {
+        Value::from_valuef_untyped(self).app_value(th)
+    }
+
+    pub fn from_builtin(b: Builtin) -> ValueF {
+        ValueF::AppliedBuiltin(b, vec![])
+    }
+}
+
+impl Shift for ValueF {
+    fn shift(&self, delta: isize, var: &AlphaVar) -> Option<Self> {
+        Some(match self {
+            ValueF::Lam(x, t, e) => ValueF::Lam(
+                x.clone(),
+                t.shift(delta, var)?,
+                e.shift(delta, &var.under_binder(x))?,
+            ),
+            ValueF::AppliedBuiltin(b, args) => {
+                ValueF::AppliedBuiltin(*b, args.shift(delta, var)?)
+            }
+            ValueF::Pi(x, t, e) => ValueF::Pi(
+                x.clone(),
+                t.shift(delta, var)?,
+                e.shift(delta, &var.under_binder(x))?,
+            ),
+            ValueF::Var(v) => ValueF::Var(v.shift(delta, var)?),
+            ValueF::Const(c) => ValueF::Const(*c),
+            ValueF::BoolLit(b) => ValueF::BoolLit(*b),
+            ValueF::NaturalLit(n) => ValueF::NaturalLit(*n),
+            ValueF::IntegerLit(n) => ValueF::IntegerLit(*n),
+            ValueF::DoubleLit(n) => ValueF::DoubleLit(*n),
+            ValueF::EmptyOptionalLit(tth) => {
+                ValueF::EmptyOptionalLit(tth.shift(delta, var)?)
+            }
+            ValueF::NEOptionalLit(th) => {
+                ValueF::NEOptionalLit(th.shift(delta, var)?)
+            }
+            ValueF::EmptyListLit(tth) => {
+                ValueF::EmptyListLit(tth.shift(delta, var)?)
+            }
+            ValueF::NEListLit(elts) => {
+                ValueF::NEListLit(elts.shift(delta, var)?)
+            }
+            ValueF::RecordLit(kvs) => ValueF::RecordLit(kvs.shift(delta, var)?),
+            ValueF::RecordType(kvs) => {
+                ValueF::RecordType(kvs.shift(delta, var)?)
+            }
+            ValueF::UnionType(kts) => ValueF::UnionType(kts.shift(delta, var)?),
+            ValueF::UnionConstructor(x, kts) => {
+                ValueF::UnionConstructor(x.clone(), kts.shift(delta, var)?)
+            }
+            ValueF::UnionLit(x, v, kts) => ValueF::UnionLit(
+                x.clone(),
+                v.shift(delta, var)?,
+                kts.shift(delta, var)?,
+            ),
+            ValueF::TextLit(elts) => ValueF::TextLit(elts.shift(delta, var)?),
+            ValueF::Equivalence(x, y) => {
+                ValueF::Equivalence(x.shift(delta, var)?, y.shift(delta, var)?)
+            }
+            ValueF::PartialExpr(e) => ValueF::PartialExpr(e.shift(delta, var)?),
+        })
+    }
+}
+
+impl Subst<Value> for ValueF {
+    fn subst_shift(&self, var: &AlphaVar, val: &Value) -> Self {
+        match self {
+            ValueF::AppliedBuiltin(b, args) => {
+                ValueF::AppliedBuiltin(*b, args.subst_shift(var, val))
+            }
+            ValueF::PartialExpr(e) => {
+                ValueF::PartialExpr(e.subst_shift(var, val))
+            }
+            ValueF::TextLit(elts) => {
+                ValueF::TextLit(elts.subst_shift(var, val))
+            }
+            ValueF::Lam(x, t, e) => ValueF::Lam(
+                x.clone(),
+                t.subst_shift(var, val),
+                e.subst_shift(&var.under_binder(x), &val.under_binder(x)),
+            ),
+            ValueF::Pi(x, t, e) => ValueF::Pi(
+                x.clone(),
+                t.subst_shift(var, val),
+                e.subst_shift(&var.under_binder(x), &val.under_binder(x)),
+            ),
+            ValueF::Var(v) if v == var => val.to_whnf(),
+            ValueF::Var(v) => ValueF::Var(v.shift(-1, var).unwrap()),
+            ValueF::Const(c) => ValueF::Const(*c),
+            ValueF::BoolLit(b) => ValueF::BoolLit(*b),
+            ValueF::NaturalLit(n) => ValueF::NaturalLit(*n),
+            ValueF::IntegerLit(n) => ValueF::IntegerLit(*n),
+            ValueF::DoubleLit(n) => ValueF::DoubleLit(*n),
+            ValueF::EmptyOptionalLit(tth) => {
+                ValueF::EmptyOptionalLit(tth.subst_shift(var, val))
+            }
+            ValueF::NEOptionalLit(th) => {
+                ValueF::NEOptionalLit(th.subst_shift(var, val))
+            }
+            ValueF::EmptyListLit(tth) => {
+                ValueF::EmptyListLit(tth.subst_shift(var, val))
+            }
+            ValueF::NEListLit(elts) => {
+                ValueF::NEListLit(elts.subst_shift(var, val))
+            }
+            ValueF::RecordLit(kvs) => {
+                ValueF::RecordLit(kvs.subst_shift(var, val))
+            }
+            ValueF::RecordType(kvs) => {
+                ValueF::RecordType(kvs.subst_shift(var, val))
+            }
+            ValueF::UnionType(kts) => {
+                ValueF::UnionType(kts.subst_shift(var, val))
+            }
+            ValueF::UnionConstructor(x, kts) => {
+                ValueF::UnionConstructor(x.clone(), kts.subst_shift(var, val))
+            }
+            ValueF::UnionLit(x, v, kts) => ValueF::UnionLit(
+                x.clone(),
+                v.subst_shift(var, val),
+                kts.subst_shift(var, val),
+            ),
+            ValueF::Equivalence(x, y) => ValueF::Equivalence(
+                x.subst_shift(var, val),
+                y.subst_shift(var, val),
+            ),
+        }
+    }
+}
diff --git a/dhall/src/core/var.rs b/dhall/src/core/var.rs
index 4ef1b93..ce4d137 100644
--- a/dhall/src/core/var.rs
+++ b/dhall/src/core/var.rs
@@ -2,17 +2,17 @@ use std::collections::HashMap;
 
 use dhall_syntax::{Label, V};
 
-/// Stores a pair of variables: a normal one and if relevant one
+/// Stores a pair of variables: a normal one and one
 /// that corresponds to the alpha-normalized version of the first one.
-/// Equality is up to alpha-equivalence.
+/// Equality is up to alpha-equivalence (compares on the second one only).
 #[derive(Clone, Eq)]
 pub struct AlphaVar {
     normal: V<Label>,
-    alpha: Option<V<()>>,
+    alpha: V<()>,
 }
 
 // Exactly like a Label, but equality returns always true.
-// This is so that Value equality is exactly alpha-equivalence.
+// This is so that ValueF equality is exactly alpha-equivalence.
 #[derive(Clone, Eq)]
 pub struct AlphaLabel(Label);
 
@@ -50,27 +50,22 @@ pub(crate) trait Shift: Sized {
     }
 }
 
-pub(crate) trait Subst<T> {
-    fn subst_shift(&self, var: &AlphaVar, val: &T) -> Self;
+pub(crate) trait Subst<S> {
+    fn subst_shift(&self, var: &AlphaVar, val: &S) -> Self;
 }
 
 impl AlphaVar {
     pub(crate) fn to_var(&self, alpha: bool) -> V<Label> {
-        match (alpha, &self.alpha) {
-            (true, Some(x)) => V("_".into(), x.1),
-            _ => self.normal.clone(),
-        }
-    }
-    pub(crate) fn from_var(normal: V<Label>) -> Self {
-        AlphaVar {
-            normal,
-            alpha: None,
+        if alpha {
+            V("_".into(), self.alpha.1)
+        } else {
+            self.normal.clone()
         }
     }
     pub(crate) fn from_var_and_alpha(normal: V<Label>, alpha: usize) -> Self {
         AlphaVar {
             normal,
-            alpha: Some(V((), alpha)),
+            alpha: V((), alpha),
         }
     }
 }
@@ -92,31 +87,15 @@ impl Shift for AlphaVar {
     fn shift(&self, delta: isize, var: &AlphaVar) -> Option<Self> {
         Some(AlphaVar {
             normal: self.normal.shift(delta, &var.normal)?,
-            alpha: match (&self.alpha, &var.alpha) {
-                (Some(x), Some(v)) => Some(x.shift(delta, v)?),
-                _ => None,
-            },
+            alpha: self.alpha.shift(delta, &var.alpha)?,
         })
     }
 }
 
-impl Shift for () {
-    fn shift(&self, _delta: isize, _var: &AlphaVar) -> Option<Self> {
-        Some(())
-    }
-}
-
-impl<T> Subst<T> for () {
-    fn subst_shift(&self, _var: &AlphaVar, _val: &T) -> Self {}
-}
-
+/// Equality up to alpha-equivalence
 impl std::cmp::PartialEq for AlphaVar {
     fn eq(&self, other: &Self) -> bool {
-        match (&self.alpha, &other.alpha) {
-            (Some(x), Some(y)) => x == y,
-            (None, None) => self.normal == other.normal,
-            _ => false,
-        }
+        self.alpha == other.alpha
     }
 }
 impl std::cmp::PartialEq for AlphaLabel {
@@ -127,10 +106,7 @@ impl std::cmp::PartialEq for AlphaLabel {
 
 impl std::fmt::Debug for AlphaVar {
     fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result {
-        match &self.alpha {
-            Some(a) => write!(f, "AlphaVar({}, {})", self.normal, a.1),
-            None => write!(f, "AlphaVar({}, free)", self.normal),
-        }
+        write!(f, "AlphaVar({}, {})", self.normal, self.alpha.1)
     }
 }
 
@@ -144,7 +120,7 @@ impl From<Label> for AlphaVar {
     fn from(x: Label) -> AlphaVar {
         AlphaVar {
             normal: V(x, 0),
-            alpha: Some(V((), 0)),
+            alpha: V((), 0),
         }
     }
 }
@@ -175,3 +151,153 @@ impl From<AlphaLabel> for Label {
         x.0
     }
 }
+impl Shift for () {
+    fn shift(&self, _delta: isize, _var: &AlphaVar) -> Option<Self> {
+        Some(())
+    }
+}
+
+impl<A: Shift, B: Shift> Shift for (A, B) {
+    fn shift(&self, delta: isize, var: &AlphaVar) -> Option<Self> {
+        Some((self.0.shift(delta, var)?, self.1.shift(delta, var)?))
+    }
+}
+
+impl<T: Shift> Shift for Option<T> {
+    fn shift(&self, delta: isize, var: &AlphaVar) -> Option<Self> {
+        Some(match self {
+            None => None,
+            Some(x) => Some(x.shift(delta, var)?),
+        })
+    }
+}
+
+impl<T: Shift> Shift for Box<T> {
+    fn shift(&self, delta: isize, var: &AlphaVar) -> Option<Self> {
+        Some(Box::new(self.as_ref().shift(delta, var)?))
+    }
+}
+
+impl<T: Shift> Shift for std::rc::Rc<T> {
+    fn shift(&self, delta: isize, var: &AlphaVar) -> Option<Self> {
+        Some(std::rc::Rc::new(self.as_ref().shift(delta, var)?))
+    }
+}
+
+impl<T: Shift> Shift for std::cell::RefCell<T> {
+    fn shift(&self, delta: isize, var: &AlphaVar) -> Option<Self> {
+        Some(std::cell::RefCell::new(self.borrow().shift(delta, var)?))
+    }
+}
+
+impl<T: Shift, E: Clone> Shift for dhall_syntax::ExprF<T, E> {
+    fn shift(&self, delta: isize, var: &AlphaVar) -> Option<Self> {
+        Some(self.traverse_ref_with_special_handling_of_binders(
+            |v| Ok(v.shift(delta, var)?),
+            |x, v| Ok(v.shift(delta, &var.under_binder(x))?),
+        )?)
+    }
+}
+
+impl<T: Shift> Shift for Vec<T> {
+    fn shift(&self, delta: isize, var: &AlphaVar) -> Option<Self> {
+        Some(
+            self.iter()
+                .map(|v| Ok(v.shift(delta, var)?))
+                .collect::<Result<_, _>>()?,
+        )
+    }
+}
+
+impl<K, T: Shift> Shift for HashMap<K, T>
+where
+    K: Clone + std::hash::Hash + Eq,
+{
+    fn shift(&self, delta: isize, var: &AlphaVar) -> Option<Self> {
+        Some(
+            self.iter()
+                .map(|(k, v)| Ok((k.clone(), v.shift(delta, var)?)))
+                .collect::<Result<_, _>>()?,
+        )
+    }
+}
+
+impl<T: Shift> Shift for dhall_syntax::InterpolatedTextContents<T> {
+    fn shift(&self, delta: isize, var: &AlphaVar) -> Option<Self> {
+        use dhall_syntax::InterpolatedTextContents::{Expr, Text};
+        Some(match self {
+            Expr(x) => Expr(x.shift(delta, var)?),
+            Text(s) => Text(s.clone()),
+        })
+    }
+}
+
+impl<S> Subst<S> for () {
+    fn subst_shift(&self, _var: &AlphaVar, _val: &S) -> Self {}
+}
+
+impl<S, A: Subst<S>, B: Subst<S>> Subst<S> for (A, B) {
+    fn subst_shift(&self, var: &AlphaVar, val: &S) -> Self {
+        (self.0.subst_shift(var, val), self.1.subst_shift(var, val))
+    }
+}
+
+impl<S, T: Subst<S>> Subst<S> for Option<T> {
+    fn subst_shift(&self, var: &AlphaVar, val: &S) -> Self {
+        self.as_ref().map(|x| x.subst_shift(var, val))
+    }
+}
+
+impl<S, T: Subst<S>> Subst<S> for Box<T> {
+    fn subst_shift(&self, var: &AlphaVar, val: &S) -> Self {
+        Box::new(self.as_ref().subst_shift(var, val))
+    }
+}
+
+impl<S, T: Subst<S>> Subst<S> for std::rc::Rc<T> {
+    fn subst_shift(&self, var: &AlphaVar, val: &S) -> Self {
+        std::rc::Rc::new(self.as_ref().subst_shift(var, val))
+    }
+}
+
+impl<S, T: Subst<S>> Subst<S> for std::cell::RefCell<T> {
+    fn subst_shift(&self, var: &AlphaVar, val: &S) -> Self {
+        std::cell::RefCell::new(self.borrow().subst_shift(var, val))
+    }
+}
+
+impl<S: Shift, T: Subst<S>, E: Clone> Subst<S> for dhall_syntax::ExprF<T, E> {
+    fn subst_shift(&self, var: &AlphaVar, val: &S) -> Self {
+        self.map_ref_with_special_handling_of_binders(
+            |v| v.subst_shift(var, val),
+            |x, v| v.subst_shift(&var.under_binder(x), &val.under_binder(x)),
+        )
+    }
+}
+
+impl<S, T: Subst<S>> Subst<S> for Vec<T> {
+    fn subst_shift(&self, var: &AlphaVar, val: &S) -> Self {
+        self.iter().map(|v| v.subst_shift(var, val)).collect()
+    }
+}
+
+impl<S, T: Subst<S>> Subst<S> for dhall_syntax::InterpolatedTextContents<T> {
+    fn subst_shift(&self, var: &AlphaVar, val: &S) -> Self {
+        use dhall_syntax::InterpolatedTextContents::{Expr, Text};
+        match self {
+            Expr(x) => Expr(x.subst_shift(var, val)),
+            Text(s) => Text(s.clone()),
+        }
+    }
+}
+
+impl<S, K, T: Subst<S>> Subst<S> for HashMap<K, T>
+where
+    K: Clone + std::hash::Hash + Eq,
+{
+    fn subst_shift(&self, var: &AlphaVar, val: &S) -> Self {
+        self.iter()
+            .map(|(k, v)| (k.clone(), v.subst_shift(var, val)))
+            .collect()
+    }
+}
diff --git a/dhall/src/error/mod.rs b/dhall/src/error/mod.rs
index 8f6ff51..13a9d7e 100644
--- a/dhall/src/error/mod.rs
+++ b/dhall/src/error/mod.rs
@@ -3,8 +3,9 @@ use std::io::Error as IOError;
 use dhall_syntax::{BinOp, Import, Label, ParseError, V};
 
 use crate::core::context::TypecheckContext;
+use crate::core::value::Value;
 use crate::phase::resolve::ImportStack;
-use crate::phase::{Normalized, NormalizedSubExpr, Type, Typed};
+use crate::phase::NormalizedSubExpr;
 
 pub type Result<T> = std::result::Result<T, Error>;
 
@@ -48,28 +49,27 @@ pub struct TypeError {
 #[derive(Debug)]
 pub(crate) enum TypeMessage {
     UnboundVariable(V<Label>),
-    InvalidInputType(Normalized),
-    InvalidOutputType(Normalized),
-    NotAFunction(Typed),
-    TypeMismatch(Typed, Normalized, Typed),
-    AnnotMismatch(Typed, Normalized),
+    InvalidInputType(Value),
+    InvalidOutputType(Value),
+    NotAFunction(Value),
+    TypeMismatch(Value, Value, Value),
+    AnnotMismatch(Value, Value),
     Untyped,
-    FieldCollision(Label),
-    InvalidListElement(usize, Normalized, Typed),
-    InvalidListType(Normalized),
-    InvalidOptionalType(Normalized),
-    InvalidPredicate(Typed),
-    IfBranchMismatch(Typed, Typed),
-    IfBranchMustBeTerm(bool, Typed),
-    InvalidFieldType(Label, Type),
-    NotARecord(Label, Normalized),
-    MustCombineRecord(Typed),
-    MissingRecordField(Label, Typed),
-    MissingUnionField(Label, Normalized),
-    BinOpTypeMismatch(BinOp, Typed),
-    InvalidTextInterpolation(Typed),
-    Merge1ArgMustBeRecord(Typed),
-    Merge2ArgMustBeUnion(Typed),
+    InvalidListElement(usize, Value, Value),
+    InvalidListType(Value),
+    InvalidOptionalType(Value),
+    InvalidPredicate(Value),
+    IfBranchMismatch(Value, Value),
+    IfBranchMustBeTerm(bool, Value),
+    InvalidFieldType(Label, Value),
+    NotARecord(Label, Value),
+    MustCombineRecord(Value),
+    MissingRecordField(Label, Value),
+    MissingUnionField(Label, Value),
+    BinOpTypeMismatch(BinOp, Value),
+    InvalidTextInterpolation(Value),
+    Merge1ArgMustBeRecord(Value),
+    Merge2ArgMustBeUnion(Value),
     MergeEmptyNeedsAnnotation,
     MergeHandlerMissingVariant(Label),
     MergeVariantMissingHandler(Label),
@@ -79,14 +79,12 @@ pub(crate) enum TypeMessage {
     ProjectionMustBeRecord,
     ProjectionMissingEntry,
     Sort,
-    RecordMismatch(Typed, Typed),
     RecordTypeDuplicateField,
-    RecordTypeMergeRequiresRecordType(Type),
-    RecordTypeMismatch(Type, Type, Type, Type),
+    RecordTypeMergeRequiresRecordType(Value),
     UnionTypeDuplicateField,
-    EquivalenceArgumentMustBeTerm(bool, Typed),
-    EquivalenceTypeMismatch(Typed, Typed),
-    AssertMismatch(Typed, Typed),
+    EquivalenceArgumentMustBeTerm(bool, Value),
+    EquivalenceTypeMismatch(Value, Value),
+    AssertMismatch(Value, Value),
     AssertMustTakeEquivalence,
 }
 
diff --git a/dhall/src/phase/mod.rs b/dhall/src/phase/mod.rs
index 778f990..1f7e5f0 100644
--- a/dhall/src/phase/mod.rs
+++ b/dhall/src/phase/mod.rs
@@ -4,8 +4,8 @@ use std::path::Path;
 
 use dhall_syntax::{Const, SubExpr};
 
-use crate::core::thunk::{Thunk, TypedThunk};
 use crate::core::value::Value;
+use crate::core::valuef::ValueF;
 use crate::core::var::{AlphaVar, Shift, Subst};
 use crate::error::{EncodeError, Error, ImportError, TypeError};
 
@@ -33,7 +33,7 @@ pub struct Resolved(ResolvedSubExpr);
 
 /// A typed expression
 #[derive(Debug, Clone)]
-pub struct Typed(TypedThunk);
+pub struct Typed(Value);
 
 /// A normalized expression.
 ///
@@ -41,8 +41,6 @@ pub struct Typed(TypedThunk);
 #[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)
@@ -71,15 +69,10 @@ impl Parsed {
 
 impl Resolved {
     pub fn typecheck(self) -> Result<Typed, TypeError> {
-        typecheck::typecheck(self)
-    }
-    pub fn typecheck_with(self, ty: &Type) -> Result<Typed, TypeError> {
-        typecheck::typecheck_with(self, ty)
+        Ok(typecheck::typecheck(self.0)?.into_typed())
     }
-    /// Pretends this expression has been typechecked. Use with care.
-    #[allow(dead_code)]
-    pub(crate) 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.to_expr())?.into_typed())
     }
 }
 
@@ -97,58 +90,39 @@ impl Typed {
         Normalized(self)
     }
 
-    pub(crate) fn from_thunk_and_type(th: Thunk, t: Type) -> Self {
-        Typed(TypedThunk::from_thunk_and_type(th, t))
-    }
-    pub(crate) fn from_thunk_untyped(th: Thunk) -> Self {
-        Typed(TypedThunk::from_thunk_untyped(th))
-    }
     pub(crate) fn from_const(c: Const) -> Self {
-        Typed(TypedThunk::from_const(c))
+        Typed(Value::from_const(c))
     }
-    pub fn from_value_untyped(v: Value) -> Self {
-        Typed(TypedThunk::from_value_untyped(v))
+    pub fn from_valuef_and_type(v: ValueF, t: Typed) -> Self {
+        Typed(Value::from_valuef_and_type(v, t.into_value()))
     }
-    pub(crate) fn from_typethunk(th: TypedThunk) -> Self {
+    pub(crate) fn from_value(th: Value) -> Self {
         Typed(th)
     }
-
-    pub(crate) fn to_value(&self) -> Value {
-        self.0.to_value()
+    pub fn const_type() -> Self {
+        Typed::from_const(Const::Type)
     }
+
     pub fn to_expr(&self) -> NormalizedSubExpr {
         self.0.to_expr()
     }
     pub(crate) fn to_expr_alpha(&self) -> NormalizedSubExpr {
         self.0.to_expr_alpha()
     }
-    pub fn to_thunk(&self) -> Thunk {
-        self.0.to_thunk()
-    }
-    // Deprecated
-    pub fn to_type(&self) -> Type {
-        self.clone()
+    pub fn to_value(&self) -> Value {
+        self.0.clone()
     }
-    // Deprecated
-    pub(crate) fn into_type(self) -> Type {
-        self
-    }
-    pub(crate) fn into_typethunk(self) -> TypedThunk {
+    pub(crate) fn into_value(self) -> Value {
         self.0
     }
-    pub(crate) fn to_normalized(&self) -> Normalized {
-        self.clone().normalize()
-    }
-    pub(crate) fn as_const(&self) -> Option<Const> {
-        self.0.as_const()
-    }
 
     pub(crate) fn normalize_mut(&mut self) {
         self.0.normalize_mut()
     }
 
-    pub(crate) fn get_type(&self) -> Result<Cow<'_, Type>, TypeError> {
-        self.0.get_type()
+    #[allow(dead_code)]
+    pub(crate) fn get_type(&self) -> Result<Cow<'_, Typed>, TypeError> {
+        Ok(Cow::Owned(self.0.get_type()?.into_owned().into_typed()))
     }
 }
 
@@ -164,13 +138,6 @@ impl Normalized {
     pub(crate) fn to_expr_alpha(&self) -> NormalizedSubExpr {
         self.0.to_expr_alpha()
     }
-    #[allow(dead_code)]
-    pub(crate) fn to_type(&self) -> Type {
-        self.0.to_type()
-    }
-    pub(crate) fn to_value(&self) -> Value {
-        self.0.to_value()
-    }
     pub(crate) fn into_typed(self) -> Typed {
         self.0
     }
@@ -188,8 +155,8 @@ impl Shift for Normalized {
     }
 }
 
-impl Subst<Typed> for Typed {
-    fn subst_shift(&self, var: &AlphaVar, val: &Typed) -> Self {
+impl Subst<Value> for Typed {
+    fn subst_shift(&self, var: &AlphaVar, val: &Value) -> Self {
         Typed(self.0.subst_shift(var, val))
     }
 }
@@ -234,7 +201,7 @@ impl std::hash::Hash for Normalized {
 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 fd0197d..a379a4b 100644
--- a/dhall/src/phase/normalize.rs
+++ b/dhall/src/phase/normalize.rs
@@ -5,13 +5,11 @@ use dhall_syntax::{
     NaiveDouble,
 };
 
-use crate::core::context::NormalizationContext;
-use crate::core::thunk::{Thunk, TypedThunk};
 use crate::core::value::Value;
+use crate::core::valuef::ValueF;
 use crate::core::var::{Shift, Subst};
-use crate::phase::{Normalized, NormalizedSubExpr, ResolvedSubExpr, Typed};
+use crate::phase::{Normalized, NormalizedSubExpr};
 
-pub(crate) type InputSubExpr = ResolvedSubExpr;
 pub(crate) type OutputSubExpr = NormalizedSubExpr;
 
 // Ad-hoc macro to help construct closures
@@ -22,67 +20,76 @@ macro_rules! make_closure {
             Label::from(stringify!($var)).into(),
             $n
         );
-        Value::Var(var).into_thunk()
+        ValueF::Var(var).into_value_untyped()
     }};
+    // Warning: assumes that $ty, as a dhall value, has type `Type`
     (λ($var:ident : $($ty:tt)*) -> $($rest:tt)*) => {
-        Value::Lam(
+        ValueF::Lam(
             Label::from(stringify!($var)).into(),
-            TypedThunk::from_thunk_untyped(make_closure!($($ty)*)),
+            make_closure!($($ty)*),
             make_closure!($($rest)*),
-        ).into_thunk()
+        ).into_value_untyped()
+    };
+    (Natural) => {
+        ValueF::from_builtin(Builtin::Natural)
+            .into_value_simple_type()
     };
-    (Natural) => { Value::from_builtin(Builtin::Natural).into_thunk() };
     (List $($rest:tt)*) => {
-        Value::from_builtin(Builtin::List)
-            .app_thunk(make_closure!($($rest)*))
-            .into_thunk()
+        ValueF::from_builtin(Builtin::List)
+            .app_value(make_closure!($($rest)*))
+            .into_value_simple_type()
     };
-    (Some $($rest:tt)*) => {
-        Value::NEOptionalLit(make_closure!($($rest)*)).into_thunk()
+    (Some($($rest:tt)*)) => {
+        ValueF::NEOptionalLit(make_closure!($($rest)*))
+            .into_value_untyped()
     };
     (1 + $($rest:tt)*) => {
-        Value::PartialExpr(ExprF::BinOp(
+        ValueF::PartialExpr(ExprF::BinOp(
             dhall_syntax::BinOp::NaturalPlus,
             make_closure!($($rest)*),
-            Thunk::from_value(Value::NaturalLit(1)),
-        )).into_thunk()
+            Value::from_valuef_and_type(
+                ValueF::NaturalLit(1),
+                make_closure!(Natural)
+            ),
+        )).into_value_with_type(
+            make_closure!(Natural)
+        )
     };
     ([ $($head:tt)* ] # $($tail:tt)*) => {
-        Value::PartialExpr(ExprF::BinOp(
+        ValueF::PartialExpr(ExprF::BinOp(
             dhall_syntax::BinOp::ListAppend,
-            Value::NEListLit(vec![make_closure!($($head)*)]).into_thunk(),
+            ValueF::NEListLit(vec![make_closure!($($head)*)])
+                .into_value_untyped(),
             make_closure!($($tail)*),
-        )).into_thunk()
+        )).into_value_untyped()
     };
 }
 
 #[allow(clippy::cognitive_complexity)]
-pub(crate) fn apply_builtin(b: Builtin, args: Vec<Thunk>) -> Value {
+pub(crate) fn apply_builtin(b: Builtin, args: Vec<Value>) -> ValueF {
     use dhall_syntax::Builtin::*;
-    use Value::*;
+    use ValueF::*;
 
     // 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(TypedThunk::from_thunk(t.clone()))))
-        }
-        (NaturalIsZero, [n, r..]) => match &*n.as_value() {
+        (OptionalNone, [t, r..]) => Ok((r, EmptyOptionalLit(t.clone()))),
+        (NaturalIsZero, [n, r..]) => match &*n.as_whnf() {
             NaturalLit(n) => Ok((r, BoolLit(*n == 0))),
             _ => Err(()),
         },
-        (NaturalEven, [n, r..]) => match &*n.as_value() {
+        (NaturalEven, [n, r..]) => match &*n.as_whnf() {
             NaturalLit(n) => Ok((r, BoolLit(*n % 2 == 0))),
             _ => Err(()),
         },
-        (NaturalOdd, [n, r..]) => match &*n.as_value() {
+        (NaturalOdd, [n, r..]) => match &*n.as_whnf() {
             NaturalLit(n) => Ok((r, BoolLit(*n % 2 != 0))),
             _ => Err(()),
         },
-        (NaturalToInteger, [n, r..]) => match &*n.as_value() {
+        (NaturalToInteger, [n, r..]) => match &*n.as_whnf() {
             NaturalLit(n) => Ok((r, IntegerLit(*n as isize))),
             _ => Err(()),
         },
-        (NaturalShow, [n, r..]) => match &*n.as_value() {
+        (NaturalShow, [n, r..]) => match &*n.as_whnf() {
             NaturalLit(n) => Ok((
                 r,
                 TextLit(vec![InterpolatedTextContents::Text(n.to_string())]),
@@ -90,7 +97,7 @@ pub(crate) fn apply_builtin(b: Builtin, args: Vec<Thunk>) -> Value {
             _ => Err(()),
         },
         (NaturalSubtract, [a, b, r..]) => {
-            match (&*a.as_value(), &*b.as_value()) {
+            match (&*a.as_whnf(), &*b.as_whnf()) {
                 (NaturalLit(a), NaturalLit(b)) => {
                     Ok((r, NaturalLit(if b > a { b - a } else { 0 })))
                 }
@@ -100,7 +107,7 @@ pub(crate) fn apply_builtin(b: Builtin, args: Vec<Thunk>) -> Value {
                 _ => Err(()),
             }
         }
-        (IntegerShow, [n, r..]) => match &*n.as_value() {
+        (IntegerShow, [n, r..]) => match &*n.as_whnf() {
             IntegerLit(n) => {
                 let s = if *n < 0 {
                     n.to_string()
@@ -111,18 +118,18 @@ pub(crate) fn apply_builtin(b: Builtin, args: Vec<Thunk>) -> Value {
             }
             _ => Err(()),
         },
-        (IntegerToDouble, [n, r..]) => match &*n.as_value() {
+        (IntegerToDouble, [n, r..]) => match &*n.as_whnf() {
             IntegerLit(n) => Ok((r, DoubleLit(NaiveDouble::from(*n as f64)))),
             _ => Err(()),
         },
-        (DoubleShow, [n, r..]) => match &*n.as_value() {
+        (DoubleShow, [n, r..]) => match &*n.as_whnf() {
             DoubleLit(n) => Ok((
                 r,
                 TextLit(vec![InterpolatedTextContents::Text(n.to_string())]),
             )),
             _ => Err(()),
         },
-        (TextShow, [v, r..]) => match &*v.as_value() {
+        (TextShow, [v, r..]) => match &*v.as_whnf() {
             TextLit(elts) => {
                 match elts.as_slice() {
                     // Empty string literal.
@@ -156,41 +163,44 @@ pub(crate) fn apply_builtin(b: Builtin, args: Vec<Thunk>) -> Value {
             }
             _ => Err(()),
         },
-        (ListLength, [_, l, r..]) => match &*l.as_value() {
+        (ListLength, [_, l, r..]) => match &*l.as_whnf() {
             EmptyListLit(_) => Ok((r, NaturalLit(0))),
             NEListLit(xs) => Ok((r, NaturalLit(xs.len()))),
             _ => Err(()),
         },
-        (ListHead, [_, l, r..]) => match &*l.as_value() {
+        (ListHead, [_, l, r..]) => match &*l.as_whnf() {
             EmptyListLit(n) => Ok((r, EmptyOptionalLit(n.clone()))),
             NEListLit(xs) => {
                 Ok((r, NEOptionalLit(xs.iter().next().unwrap().clone())))
             }
             _ => Err(()),
         },
-        (ListLast, [_, l, r..]) => match &*l.as_value() {
+        (ListLast, [_, l, r..]) => match &*l.as_whnf() {
             EmptyListLit(n) => Ok((r, EmptyOptionalLit(n.clone()))),
             NEListLit(xs) => {
                 Ok((r, NEOptionalLit(xs.iter().rev().next().unwrap().clone())))
             }
             _ => Err(()),
         },
-        (ListReverse, [_, l, r..]) => match &*l.as_value() {
+        (ListReverse, [_, l, r..]) => match &*l.as_whnf() {
             EmptyListLit(n) => Ok((r, EmptyListLit(n.clone()))),
             NEListLit(xs) => {
                 Ok((r, NEListLit(xs.iter().rev().cloned().collect())))
             }
             _ => Err(()),
         },
-        (ListIndexed, [_, l, r..]) => match &*l.as_value() {
+        (ListIndexed, [_, l, r..]) => match &*l.as_whnf() {
             EmptyListLit(t) => {
                 let mut kts = HashMap::new();
                 kts.insert(
                     "index".into(),
-                    TypedThunk::from_value(Value::from_builtin(Natural)),
+                    Value::from_valuef_untyped(ValueF::from_builtin(Natural)),
                 );
                 kts.insert("value".into(), t.clone());
-                Ok((r, EmptyListLit(TypedThunk::from_value(RecordType(kts)))))
+                Ok((
+                    r,
+                    EmptyListLit(Value::from_valuef_untyped(RecordType(kts))),
+                ))
             }
             NEListLit(xs) => {
                 let xs = xs
@@ -199,105 +209,131 @@ pub(crate) fn apply_builtin(b: Builtin, args: Vec<Thunk>) -> Value {
                     .map(|(i, e)| {
                         let i = NaturalLit(i);
                         let mut kvs = HashMap::new();
-                        kvs.insert("index".into(), Thunk::from_value(i));
+                        kvs.insert(
+                            "index".into(),
+                            Value::from_valuef_untyped(i),
+                        );
                         kvs.insert("value".into(), e.clone());
-                        Thunk::from_value(RecordLit(kvs))
+                        Value::from_valuef_untyped(RecordLit(kvs))
                     })
                     .collect();
                 Ok((r, NEListLit(xs)))
             }
             _ => Err(()),
         },
-        (ListBuild, [t, f, r..]) => match &*f.as_value() {
+        (ListBuild, [t, f, r..]) => 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()))
+                    Ok((r, args[1].to_whnf()))
                 } else {
                     // Do we really need to handle this case ?
                     unimplemented!()
                 }
             }
-            _ => Ok((
-                r,
-                f.app_val(Value::from_builtin(List).app_thunk(t.clone()))
-                    .app_thunk({
-                        // Move `t` under new `x` variable
-                        let t1 = t.under_binder(Label::from("x"));
-                        make_closure!(
-                            λ(x : #t) ->
-                            λ(xs : List #t1) ->
-                            [ var(x, 1) ] # var(xs, 0)
-                        )
-                    })
-                    .app_val(EmptyListLit(TypedThunk::from_thunk(t.clone()))),
-            )),
+            _ => {
+                let list_t = ValueF::from_builtin(List)
+                    .app_value(t.clone())
+                    .into_value_simple_type();
+                Ok((
+                    r,
+                    f.app_value(list_t.clone())
+                        .app_value({
+                            // Move `t` under new `x` variable
+                            let t1 = t.under_binder(Label::from("x"));
+                            make_closure!(
+                                λ(x : #t) ->
+                                λ(xs : List #t1) ->
+                                [ var(x, 1) ] # var(xs, 0)
+                            )
+                        })
+                        .app_value(
+                            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(_) => Ok((r, nil.to_whnf())),
             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();
+                        .app_value(x.clone())
+                        .app_value(v)
+                        .into_value_untyped();
                 }
-                Ok((r, v.to_value()))
+                Ok((r, v.to_whnf()))
             }
             _ => Err(()),
         },
-        (OptionalBuild, [t, f, r..]) => match &*f.as_value() {
+        (OptionalBuild, [t, f, r..]) => 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()))
+                    Ok((r, args[1].to_whnf()))
                 } else {
                     // Do we really need to handle this case ?
                     unimplemented!()
                 }
             }
-            _ => Ok((
-                r,
-                f.app_val(Value::from_builtin(Optional).app_thunk(t.clone()))
-                    .app_thunk(make_closure!(λ(x: #t) -> Some var(x, 0)))
-                    .app_val(EmptyOptionalLit(TypedThunk::from_thunk(
-                        t.clone(),
-                    ))),
-            )),
+            _ => {
+                let optional_t = ValueF::from_builtin(Optional)
+                    .app_value(t.clone())
+                    .into_value_simple_type();
+                Ok((
+                    r,
+                    f.app_value(optional_t.clone())
+                        .app_value(make_closure!(λ(x: #t) -> Some(var(x, 0))))
+                        .app_value(
+                            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()))),
+        (OptionalFold, [_, v, _, just, nothing, r..]) => match &*v.as_whnf() {
+            EmptyOptionalLit(_) => Ok((r, nothing.to_whnf())),
+            NEOptionalLit(x) => Ok((r, just.app_value(x.clone()))),
             _ => Err(()),
         },
-        (NaturalBuild, [f, r..]) => match &*f.as_value() {
+        (NaturalBuild, [f, r..]) => 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()))
+                    Ok((r, args[0].to_whnf()))
                 } else {
                     // Do we really need to handle this case ?
                     unimplemented!()
                 }
             }
-            _ => Ok((
-                r,
-                f.app_val(Value::from_builtin(Natural))
-                    .app_thunk(make_closure!(λ(x : Natural) -> 1 + var(x, 0)))
-                    .app_val(NaturalLit(0)),
-            )),
+            _ => {
+                let nat_type =
+                    ValueF::from_builtin(Natural).into_value_simple_type();
+                Ok((
+                    r,
+                    f.app_value(nat_type.clone())
+                        .app_value(
+                            make_closure!(λ(x : Natural) -> 1 + var(x, 0)),
+                        )
+                        .app_value(
+                            NaturalLit(0).into_value_with_type(nat_type),
+                        ),
+                ))
+            }
         },
-        (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) => Ok((r, zero.to_whnf())),
             NaturalLit(n) => {
-                let fold = Value::from_builtin(NaturalFold)
+                let fold = ValueF::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_value(t.clone())
+                    .app_value(succ.clone())
+                    .app_value(zero.clone())
+                    .into_value_with_type(t.clone());
+                Ok((r, succ.app_value(fold)))
             }
             _ => Err(()),
         },
@@ -307,7 +343,7 @@ pub(crate) fn apply_builtin(b: Builtin, args: Vec<Thunk>) -> Value {
         Ok((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_value(x);
             }
             v
         }
@@ -315,22 +351,19 @@ pub(crate) fn apply_builtin(b: Builtin, args: Vec<Thunk>) -> Value {
     }
 }
 
-pub(crate) fn apply_any(f: Thunk, a: Thunk) -> Value {
-    let fallback = |f: Thunk, a: Thunk| Value::PartialExpr(ExprF::App(f, a));
+pub(crate) fn apply_any(f: Value, a: Value) -> ValueF {
+    let fallback = |f: Value, a: Value| ValueF::PartialExpr(ExprF::App(f, a));
 
-    let f_borrow = f.as_value();
+    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()
-        }
-        Value::AppliedBuiltin(b, args) => {
+        ValueF::Lam(x, _, e) => e.subst_shift(&x.into(), &a).to_whnf(),
+        ValueF::AppliedBuiltin(b, args) => {
             use std::iter::once;
             let args = args.iter().cloned().chain(once(a.clone())).collect();
             apply_builtin(*b, args)
         }
-        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);
@@ -340,23 +373,23 @@ pub(crate) fn apply_any(f: Thunk, a: Thunk) -> Value {
 }
 
 pub(crate) fn squash_textlit(
-    elts: impl Iterator<Item = InterpolatedTextContents<Thunk>>,
-) -> Vec<InterpolatedTextContents<Thunk>> {
+    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)
                         }
                         _ => {
@@ -381,32 +414,6 @@ pub(crate) fn squash_textlit(
     ret
 }
 
-/// Reduces the imput expression to a Value. Evaluates as little as possible.
-pub(crate) fn normalize_whnf(ctx: NormalizationContext, expr: InputSubExpr) -> Value {
-    match expr.as_ref() {
-        ExprF::Embed(e) => return e.to_value(),
-        ExprF::Var(v) => return ctx.lookup(v),
-        _ => {}
-    }
-
-    // Thunk subexpressions
-    let expr: ExprF<Thunk, Normalized> =
-        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()),
-        );
-
-    normalize_one_layer(expr)
-}
-
-// Small helper enum to avoid repetition
-enum Ret<'a> {
-    Value(Value),
-    Thunk(Thunk),
-    ThunkRef(&'a Thunk),
-    Expr(ExprF<Thunk, Normalized>),
-}
-
 /// Performs an intersection of two HashMaps.
 ///
 /// # Arguments
@@ -441,60 +448,6 @@ where
     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>(
     map1: &HashMap<K, V>,
     map2: &HashMap<K, V>,
@@ -520,82 +473,90 @@ where
     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) -> 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();
@@ -603,54 +564,53 @@ 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(
+                Value::from_valuef_untyped(ValueF::PartialExpr(ExprF::BinOp(
                     RecursiveRecordMerge,
                     v1.clone(),
                     v2.clone(),
-                ))
+                )))
             });
-            Ret::Value(RecordLit(kvs))
+            Ret::ValueF(RecordLit(kvs))
         }
 
         (RecursiveRecordTypeMerge, _, RecordType(kvs)) if kvs.is_empty() => {
-            Ret::ThunkRef(x)
+            Ret::ValueRef(x)
         }
         (RecursiveRecordTypeMerge, RecordType(kvs), _) if kvs.is_empty() => {
-            Ret::ThunkRef(y)
+            Ret::ValueRef(y)
         }
         (RecursiveRecordTypeMerge, RecordType(kvs1), RecordType(kvs2)) => {
             let kvs = merge_maps(kvs1, kvs2, |v1, v2| {
-                TypedThunk::from_thunk(Thunk::from_partial_expr(ExprF::BinOp(
+                Value::from_valuef_untyped(ValueF::PartialExpr(ExprF::BinOp(
                     RecursiveRecordTypeMerge,
-                    v1.to_thunk(),
-                    v2.to_thunk(),
+                    v1.clone(),
+                    v2.clone(),
                 )))
             });
-            Ret::Value(RecordType(kvs))
+            Ret::ValueF(RecordType(kvs))
         }
 
-        (Equivalence, _, _) => Ret::Value(Value::Equivalence(
-            TypedThunk::from_thunk(x.clone()),
-            TypedThunk::from_thunk(y.clone()),
-        )),
+        (Equivalence, _, _) => {
+            Ret::ValueF(ValueF::Equivalence(x.clone(), y.clone()))
+        }
 
         _ => return None,
     })
 }
 
-pub(crate) fn normalize_one_layer(expr: ExprF<Thunk, Normalized>) -> Value {
-    use Value::{
+pub(crate) fn normalize_one_layer(expr: ExprF<Value, Normalized>) -> ValueF {
+    use ValueF::{
         AppliedBuiltin, BoolLit, DoubleLit, EmptyListLit, IntegerLit, Lam,
         NEListLit, NEOptionalLit, NaturalLit, Pi, RecordLit, RecordType,
         TextLit, UnionConstructor, UnionLit, UnionType,
@@ -662,36 +622,25 @@ pub(crate) fn normalize_one_layer(expr: ExprF<Thunk, Normalized>) -> Value {
         ),
         ExprF::Embed(_) => unreachable!(),
         ExprF::Var(_) => unreachable!(),
-        ExprF::Annot(x, _) => Ret::Thunk(x),
+        ExprF::Annot(x, _) => Ret::Value(x),
         ExprF::Assert(_) => Ret::Expr(expr),
-        ExprF::Lam(x, t, e) => {
-            Ret::Value(Lam(x.into(), TypedThunk::from_thunk(t), e))
-        }
-        ExprF::Pi(x, t, e) => Ret::Value(Pi(
-            x.into(),
-            TypedThunk::from_thunk(t),
-            TypedThunk::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::Lam(x, t, e) => Ret::ValueF(Lam(x.into(), t, e)),
+        ExprF::Pi(x, t, e) => Ret::ValueF(Pi(x.into(), t, e)),
+        ExprF::Let(x, _, v, b) => Ret::Value(b.subst_shift(&x.into(), &v)),
+        ExprF::App(v, a) => Ret::ValueF(v.app_value(a)),
+        ExprF::Builtin(b) => Ret::ValueF(ValueF::from_builtin(b)),
+        ExprF::Const(c) => Ret::ValueF(ValueF::Const(c)),
+        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(TypedThunk::from_thunk(
-                        args[0].clone(),
-                    )))
+                    Ret::ValueF(EmptyListLit(args[0].clone()))
                 }
                 _ => {
                     drop(t_borrow);
@@ -700,43 +649,39 @@ pub(crate) fn normalize_one_layer(expr: ExprF<Thunk, Normalized>) -> 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::ValueF(RecordType(kts.into_iter().collect()))
+        }
+        ExprF::UnionType(kts) => {
+            Ret::ValueF(UnionType(kts.into_iter().collect()))
         }
-        ExprF::RecordType(kts) => Ret::Value(RecordType(
-            kts.into_iter()
-                .map(|(k, t)| (k, TypedThunk::from_thunk(t)))
-                .collect(),
-        )),
-        ExprF::UnionType(kts) => Ret::Value(UnionType(
-            kts.into_iter()
-                .map(|(k, t)| (k, t.map(|t| TypedThunk::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);
@@ -753,12 +698,12 @@ pub(crate) fn normalize_one_layer(expr: ExprF<Thunk, Normalized>) -> Value {
         },
 
         ExprF::Projection(_, ref ls) if ls.is_empty() => {
-            Ret::Value(RecordLit(HashMap::new()))
+            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()))
@@ -772,17 +717,17 @@ pub(crate) fn normalize_one_layer(expr: ExprF<Thunk, Normalized>) -> 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);
@@ -792,11 +737,11 @@ pub(crate) fn normalize_one_layer(expr: ExprF<Thunk, Normalized>) -> 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);
@@ -804,7 +749,7 @@ pub(crate) fn normalize_one_layer(expr: ExprF<Thunk, Normalized>) -> Value {
                     }
                 },
                 (RecordLit(kvs), UnionLit(l, v, _)) => match kvs.get(l) {
-                    Some(h) => Ret::Value(h.app_thunk(v.clone())),
+                    Some(h) => Ret::ValueF(h.app_value(v.clone())),
                     None => {
                         drop(handlers_borrow);
                         drop(variant_borrow);
@@ -821,9 +766,22 @@ pub(crate) fn normalize_one_layer(expr: ExprF<Thunk, Normalized>) -> Value {
     };
 
     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(th) => th.as_whnf().clone(),
+        Ret::ValueRef(th) => th.as_whnf().clone(),
+        Ret::Expr(expr) => ValueF::PartialExpr(expr),
+    }
+}
+
+/// Normalize a ValueF into WHNF
+pub(crate) fn normalize_whnf(v: ValueF) -> ValueF {
+    match v {
+        ValueF::AppliedBuiltin(b, args) => apply_builtin(b, args),
+        ValueF::PartialExpr(e) => normalize_one_layer(e),
+        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/typecheck.rs b/dhall/src/phase/typecheck.rs
index 56fb5ed..c47eb78 100644
--- a/dhall/src/phase/typecheck.rs
+++ b/dhall/src/phase/typecheck.rs
@@ -1,33 +1,29 @@
+use std::cmp::max;
 use std::collections::HashMap;
 
 use dhall_syntax::{
     rc, Builtin, Const, Expr, ExprF, InterpolatedTextContents, Label, SubExpr,
 };
 
-use crate::core::context::{NormalizationContext, TypecheckContext};
-use crate::core::thunk::{Thunk, TypedThunk};
+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() {
@@ -35,68 +31,58 @@ fn tck_pi_type(
         _ => {
             return Err(TypeError::new(
                 &ctx2,
-                InvalidOutputType(te.get_type()?.to_normalized()),
+                InvalidOutputType(te.get_type()?.into_owned()),
             ))
         }
     };
 
     let k = function_check(ka, kb);
 
-    Ok(Typed::from_thunk_and_type(
-        Value::Pi(
-            x.into(),
-            TypedThunk::from_type(tx),
-            TypedThunk::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(|| TypedThunk::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();
@@ -111,46 +97,42 @@ 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| TypedThunk::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(crate) fn type_of_const(c: Const) -> Result<Type, TypeError> {
+pub(crate) fn type_of_const(c: Const) -> Result<Value, TypeError> {
     match c {
-        Const::Type => Ok(Type::from_const(Const::Kind)),
-        Const::Kind => Ok(Type::from_const(Const::Sort)),
+        Const::Type => Ok(Value::from_const(Const::Kind)),
+        Const::Kind => Ok(Value::from_const(Const::Sort)),
         Const::Sort => {
             Err(TypeError::new(&TypecheckContext::new(), TypeMessage::Sort))
         }
@@ -298,25 +280,9 @@ fn type_of_builtin<E>(b: Builtin) -> Expr<E> {
     }
 }
 
-/// Takes an expression that is meant to contain a Type
-/// and turn it into a type, typechecking it along the way.
-pub(crate) fn mktype(
-    ctx: &TypecheckContext,
-    e: SubExpr<Normalized>,
-) -> Result<Type, TypeError> {
-    Ok(type_with(ctx, e)?.to_type())
-}
-
-pub(crate) 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),
+// TODO: this can't fail in practise
+pub(crate) fn builtin_to_type(b: Builtin) -> Result<Value, TypeError> {
+    type_with(&TypecheckContext::new(), SubExpr::from_builtin(b))
 }
 
 /// Type-check an expression and return the expression alongside its type if type-checking
@@ -326,28 +292,23 @@ enum Ret {
 fn type_with(
     ctx: &TypecheckContext,
     e: SubExpr<Normalized>,
-) -> Result<Typed, TypeError> {
+) -> 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 tx = type_with(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(),
-                TypedThunk::from_type(tx.clone()),
-                b.to_thunk(),
-            );
+            let v = ValueF::Lam(x.clone().into(), tx.clone(), b.clone());
             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)
+            let t = tck_pi_type(ctx, x.clone(), tx, tb)?;
+            Value::from_valuef_and_type(v, t)
         }
         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) => {
@@ -360,9 +321,9 @@ 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,
@@ -370,24 +331,13 @@ 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!(),
-                )?;
-            let ret = type_last_layer(ctx, &expr)?;
-            match ret {
-                RetTypeOnly(typ) => {
-                    let expr = expr.map_ref(|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)?
         }
     })
 }
@@ -396,17 +346,25 @@ fn type_with(
 /// layer.
 fn type_last_layer(
     ctx: &TypecheckContext,
-    e: &ExprF<Typed, Normalized>,
-) -> 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"
         ),
@@ -415,456 +373,296 @@ fn type_last_layer(
         }
         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()?.as_ref() != 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 t != x.get_type()?.as_ref() {
+                return mkerr(AnnotMismatch(x.clone(), t.clone()));
             }
-            Ok(RetTypeOnly(x.get_type()?.into_owned()))
+            RetTypeOnly(x.get_type()?.into_owned())
         }
         Assert(t) => {
-            match t.to_value() {
-                Value::Equivalence(ref x, ref 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())));
+                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()?.into_owned())
         }
         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()?.into_owned(),
                         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.into_owned()));
             }
 
-            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_valuef_and_type(
+                ValueF::from_builtin(dhall_syntax::Builtin::List)
+                    .app_value(t.into_owned()),
+                Value::from_const(Type),
             ))
         }
         SomeLit(x) => {
             let t = x.get_type()?.into_owned();
             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_valuef_and_type(
+                ValueF::from_builtin(dhall_syntax::Builtin::Optional)
+                    .app_value(t),
+                Value::from_const(Type),
             ))
         }
-        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()?.into_owned()))),
+        )?),
         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)))?)),
-        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(Value::from_const(*c)),
+        Builtin(b) => RetTypeOnly(type_with(ctx, rc(type_of_builtin(*b)))?),
+        BoolLit(_) => RetTypeOnly(builtin_to_type(Bool)?),
+        NaturalLit(_) => RetTypeOnly(builtin_to_type(Natural)?),
+        IntegerLit(_) => RetTypeOnly(builtin_to_type(Integer)?),
+        DoubleLit(_) => RetTypeOnly(builtin_to_type(Double)?),
         TextLit(interpolated) => {
             let text_type = builtin_to_type(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())));
+                        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| 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, TypedThunk>,
-                kts_r: HashMap<Label, TypedThunk>,
-            ) -> 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: &TypedThunk,
-                               inner_r: &TypedThunk|
-                 -> 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: &TypedThunk, r: &TypedThunk| {
-                        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()?.into_owned(),
+                r.get_type()?.into_owned(),
+            ),
+        )?),
         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, TypedThunk>,
-                kts_r: HashMap<Label, TypedThunk>,
-            ) -> 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: &TypedThunk,
-                               kts_r_inner: &TypedThunk|
-                 -> 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: &TypedThunk, r: &TypedThunk| {
-                        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())
-            };
+            use crate::phase::normalize::intersection_with_key;
 
             // Extract the Const of the LHS
-            let k_l = match l.get_type()?.to_value() {
-                Value::Const(k) => k,
+            let k_l = match l.get_type()?.as_const() {
+                Some(k) => k,
                 _ => {
-                    return Err(mkerr(RecordTypeMergeRequiresRecordType(
-                        l.clone(),
-                    )))
+                    return mkerr(RecordTypeMergeRequiresRecordType(l.clone()))
                 }
             };
 
             // Extract the Const of the RHS
-            let k_r = match r.get_type()?.to_value() {
-                Value::Const(k) => k,
+            let k_r = match r.get_type()?.as_const() {
+                Some(k) => k,
                 _ => {
-                    return Err(mkerr(RecordTypeMergeRequiresRecordType(
-                        r.clone(),
-                    )))
+                    return 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(),
-                )));
-            };
+            let k = max(k_l, k_r);
 
             // 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 = intersection_with_key(
+                // If the Label exists for both records, then we hit the recursive case.
+                |_: &Label, l: &Value, r: &Value| {
+                    type_last_layer(
+                        ctx,
+                        ExprF::BinOp(
+                            RecursiveRecordTypeMerge,
+                            l.clone(),
+                            r.clone(),
+                        ),
+                    )
+                },
+                kts_x,
+                kts_y,
+            );
+            tck_record_type(ctx, kts.into_iter().map(|(x, v)| Ok((x, v?))))?;
+
+            RetTypeOnly(Value::from_const(k))
         }
         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()?.into_owned())
         }
         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()))
+            RetTypeOnly(Value::from_const(Type))
         }
         BinOp(o, l, r) => {
             let t = builtin_to_type(match o {
@@ -884,140 +682,136 @@ fn type_last_layer(
             })?;
 
             if l.get_type()?.as_ref() != &t {
-                return Err(mkerr(BinOpTypeMismatch(*o, l.clone())));
+                return mkerr(BinOpTypeMismatch(*o, l.clone()));
             }
 
             if r.get_type()?.as_ref() != &t {
-                return Err(mkerr(BinOpTypeMismatch(*o, r.clone())));
+                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),
             }
         }
         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()?.into_owned(),
             ))
         }
-    }
+    };
+
+    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<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: SubExpr<Normalized>) -> Result<Value, TypeError> {
+    type_with(&TypecheckContext::new(), e)
 }
 
-pub(crate) fn typecheck(e: Resolved) -> Result<Typed, TypeError> {
-    type_of(e.0)
-}
-
-pub(crate) fn typecheck_with(e: Resolved, ty: &Type) -> Result<Typed, TypeError> {
-    let expr: SubExpr<_> = e.0;
-    let ty: SubExpr<_> = ty.to_expr();
-    type_of(expr.rewrap(ExprF::Annot(expr.clone(), ty)))
-}
-pub(crate) fn skip_typecheck(e: Resolved) -> Typed {
-    Typed::from_thunk_untyped(Thunk::new(NormalizationContext::new(), e.0))
+pub(crate) fn typecheck_with(
+    expr: SubExpr<Normalized>,
+    ty: SubExpr<Normalized>,
+) -> Result<Value, TypeError> {
+    typecheck(expr.rewrap(ExprF::Annot(expr.clone(), ty)))
 }
diff --git a/dhall/src/tests.rs b/dhall/src/tests.rs
index d269523..be4805d 100644
--- a/dhall/src/tests.rs
+++ b/dhall/src/tests.rs
@@ -169,7 +169,7 @@ pub fn run_test(
             let expected_file_path = base_path + "B.dhall";
             let expected = parse_file_str(&expected_file_path)?
                 .resolve()?
-                .skip_typecheck()
+                .typecheck()?
                 .normalize();
 
             match feature {
@@ -177,24 +177,23 @@ pub fn run_test(
                     unreachable!()
                 }
                 Import => {
-                    let expr = expr.skip_typecheck().normalize();
+                    let expr = expr.typecheck()?.normalize();
                     assert_eq_display!(expr, expected);
                 }
                 Typecheck => {
-                    expr.typecheck_with(&expected.to_type())?;
+                    expr.typecheck_with(&expected.into_typed())?.get_type()?;
                 }
                 TypeInference => {
                     let expr = expr.typecheck()?;
-                    let ty = expr.get_type()?.into_owned();
-                    assert_eq_display!(ty.to_normalized(), expected);
+                    let ty = expr.get_type()?.into_owned().normalize();
+                    assert_eq_display!(ty, expected);
                 }
                 Normalization => {
-                    let expr = expr.skip_typecheck().normalize();
+                    let expr = expr.typecheck()?.normalize();
                     assert_eq_display!(expr, expected);
                 }
                 AlphaNormalization => {
-                    let expr =
-                        expr.skip_typecheck().normalize().to_expr_alpha();
+                    let expr = expr.typecheck()?.normalize().to_expr_alpha();
                     assert_eq_display!(expr, expected.to_expr());
                 }
             }
@@ -226,10 +225,15 @@ pub fn run_test(
                 }
                 Normalization | AlphaNormalization => unreachable!(),
                 Typecheck | TypeInference => {
-                    parse_file_str(&file_path)?
-                        .skip_resolve()?
-                        .typecheck()
-                        .unwrap_err();
+                    let res =
+                        parse_file_str(&file_path)?.skip_resolve()?.typecheck();
+                    match res {
+                        Err(_) => {}
+                        // If e did typecheck, check that it doesn't have a type
+                        Ok(e) => {
+                            e.get_type().unwrap_err();
+                        }
+                    }
                 }
             }
         }
diff --git a/serde_dhall/src/lib.rs b/serde_dhall/src/lib.rs
index 71674a9..cef11dd 100644
--- a/serde_dhall/src/lib.rs
+++ b/serde_dhall/src/lib.rs
@@ -124,9 +124,9 @@ pub use value::Value;
 
 // A Dhall value.
 pub mod value {
-    use dhall::core::thunk::{Thunk, TypedThunk};
     use dhall::core::value::Value as DhallValue;
-    use dhall::phase::{NormalizedSubExpr, Parsed, Type, Typed};
+    use dhall::core::valuef::ValueF as DhallValueF;
+    use dhall::phase::{NormalizedSubExpr, Parsed, Typed};
     use dhall_syntax::Builtin;
 
     use super::de::{Error, Result};
@@ -146,34 +146,37 @@ pub mod value {
             let resolved = Parsed::parse_str(s)?.resolve()?;
             let typed = match ty {
                 None => resolved.typecheck()?,
-                Some(t) => resolved.typecheck_with(&t.to_type())?,
+                Some(t) => resolved.typecheck_with(t.as_typed())?,
             };
             Ok(Value(typed))
         }
         pub(crate) fn to_expr(&self) -> NormalizedSubExpr {
             self.0.to_expr()
         }
-        pub(crate) fn to_thunk(&self) -> Thunk {
-            self.0.to_thunk()
+        pub(crate) fn to_value(&self) -> DhallValue {
+            self.0.to_value()
         }
-        pub(crate) fn to_type(&self) -> Type {
-            self.0.to_type()
+        pub(crate) fn as_typed(&self) -> &Typed {
+            &self.0
         }
 
-        pub(crate) fn from_dhall_value(v: DhallValue) -> Self {
-            Value(Typed::from_value_untyped(v))
+        /// Assumes that the given value has type `Type`.
+        pub(crate) fn make_simple_type(v: DhallValueF) -> Self {
+            Value(Typed::from_valuef_and_type(v, Typed::const_type()))
         }
         pub(crate) fn make_builtin_type(b: Builtin) -> Self {
-            Self::from_dhall_value(DhallValue::from_builtin(b))
+            Self::make_simple_type(DhallValueF::from_builtin(b))
         }
         pub(crate) fn make_optional_type(t: Value) -> Self {
-            Self::from_dhall_value(
-                DhallValue::from_builtin(Builtin::Optional).app_thunk(t.to_thunk()),
+            Self::make_simple_type(
+                DhallValueF::from_builtin(Builtin::Optional)
+                    .app_value(t.to_value()),
             )
         }
         pub(crate) fn make_list_type(t: Value) -> Self {
-            Self::from_dhall_value(
-                DhallValue::from_builtin(Builtin::List).app_thunk(t.to_thunk()),
+            Self::make_simple_type(
+                DhallValueF::from_builtin(Builtin::List)
+                    .app_value(t.to_value()),
             )
         }
         // Made public for the StaticType derive macro
@@ -181,22 +184,17 @@ pub mod value {
         pub fn make_record_type(
             kts: impl Iterator<Item = (String, Value)>,
         ) -> Self {
-            Self::from_dhall_value(DhallValue::RecordType(
-                kts.map(|(k, t)| {
-                    (k.into(), TypedThunk::from_thunk(t.to_thunk()))
-                })
-                .collect(),
+            Self::make_simple_type(DhallValueF::RecordType(
+                kts.map(|(k, t)| (k.into(), t.to_value())).collect(),
             ))
         }
         #[doc(hidden)]
         pub fn make_union_type(
             kts: impl Iterator<Item = (String, Option<Value>)>,
         ) -> Self {
-            Self::from_dhall_value(DhallValue::UnionType(
-                kts.map(|(k, t)| {
-                    (k.into(), t.map(|t| TypedThunk::from_thunk(t.to_thunk())))
-                })
-                .collect(),
+            Self::make_simple_type(DhallValueF::UnionType(
+                kts.map(|(k, t)| (k.into(), t.map(|t| t.to_value())))
+                    .collect(),
             ))
         }
     }