Merge pull request #154 from Nadrieril/cleanup-api

Rewrite serde_dhall API

16 files changed, 217 insertions, 319 deletions

diff --git a/dhall/src/semantics/builtins.rs b/dhall/src/semantics/builtins.rs
index 803630b..6007a92 100644
--- a/dhall/src/semantics/builtins.rs
+++ b/dhall/src/semantics/builtins.rs
@@ -1,48 +1,35 @@
 use crate::semantics::{
-    skip_resolve, typecheck, Hir, HirKind, Nir, NirKind, NzEnv, VarEnv,
+    skip_resolve_expr, typecheck, Hir, HirKind, Nir, NirKind, NzEnv, VarEnv,
 };
 use crate::syntax::map::DupTreeMap;
 use crate::syntax::Const::Type;
 use crate::syntax::{
     BinOp, Builtin, Const, Expr, ExprKind, InterpolatedText,
-    InterpolatedTextContents, Label, LitKind, NaiveDouble, Span, UnspannedExpr,
+    InterpolatedTextContents, Label, NaiveDouble, NumKind, Span, UnspannedExpr,
     V,
 };
-use crate::Normalized;
 use std::collections::HashMap;
 use std::convert::TryInto;
 
 /// A partially applied builtin.
 /// Invariant: the evaluation of the given args must not be able to progress further
 #[derive(Debug, Clone)]
-pub(crate) struct BuiltinClosure<Nir> {
-    pub env: NzEnv,
-    pub b: Builtin,
+pub struct BuiltinClosure {
+    env: NzEnv,
+    b: Builtin,
     /// Arguments applied to the closure so far.
-    pub args: Vec<Nir>,
+    args: Vec<Nir>,
 }
 
-impl BuiltinClosure<Nir> {
-    pub fn new(b: Builtin, env: NzEnv) -> Self {
-        BuiltinClosure {
-            env,
-            b,
-            args: Vec::new(),
-        }
+impl BuiltinClosure {
+    pub fn new(b: Builtin, env: NzEnv) -> NirKind {
+        apply_builtin(b, Vec::new(), env)
     }
-
     pub fn apply(&self, a: Nir) -> NirKind {
         use std::iter::once;
         let args = self.args.iter().cloned().chain(once(a)).collect();
         apply_builtin(self.b, args, self.env.clone())
     }
-    /// This doesn't break the invariant because we already checked that the appropriate arguments
-    /// did not normalize to something that allows evaluation to proceed.
-    pub fn normalize(&self) {
-        for x in self.args.iter() {
-            x.normalize();
-        }
-    }
     pub fn to_hirkind(&self, venv: VarEnv) -> HirKind {
         HirKind::Expr(self.args.iter().fold(
             ExprKind::Builtin(self.b),
@@ -56,7 +43,7 @@ impl BuiltinClosure<Nir> {
     }
 }
 
-pub(crate) fn rc(x: UnspannedExpr) -> Expr {
+pub fn rc(x: UnspannedExpr) -> Expr {
     Expr::new(x, Span::Artificial)
 }
 
@@ -116,7 +103,7 @@ macro_rules! make_type {
     };
 }
 
-pub(crate) fn type_of_builtin(b: Builtin) -> Hir {
+pub fn type_of_builtin(b: Builtin) -> Hir {
     use Builtin::*;
     let expr = match b {
         Bool | Natural | Integer | Double | Text => make_type!(Type),
@@ -202,7 +189,7 @@ pub(crate) fn type_of_builtin(b: Builtin) -> Hir {
             forall (A: Type) -> Optional A
         ),
     };
-    skip_resolve(&expr).unwrap()
+    skip_resolve_expr(&expr).unwrap()
 }
 
 // Ad-hoc macro to help construct closures
@@ -241,7 +228,7 @@ macro_rules! make_closure {
         rc(ExprKind::BinOp(
             BinOp::NaturalPlus,
             make_closure!($($v)*),
-            rc(ExprKind::Lit(LitKind::Natural(1)))
+            rc(ExprKind::Num(NumKind::Natural(1)))
         ))
     };
     ([ $($head:tt)* ] # $($tail:tt)*) => {{
@@ -257,8 +244,8 @@ macro_rules! make_closure {
 
 #[allow(clippy::cognitive_complexity)]
 fn apply_builtin(b: Builtin, args: Vec<Nir>, env: NzEnv) -> NirKind {
-    use LitKind::{Bool, Double, Integer, Natural};
     use NirKind::*;
+    use NumKind::{Bool, Double, Integer, Natural};
 
     // Small helper enum
     enum Ret {
@@ -267,46 +254,54 @@ fn apply_builtin(b: Builtin, args: Vec<Nir>, env: NzEnv) -> NirKind {
         DoneAsIs,
     }
     let make_closure = |e| {
-        typecheck(&skip_resolve(&e).unwrap())
+        typecheck(&skip_resolve_expr(&e).unwrap())
             .unwrap()
             .eval(env.clone())
     };
 
     let ret = match (b, args.as_slice()) {
+        (Builtin::Bool, [])
+        | (Builtin::Natural, [])
+        | (Builtin::Integer, [])
+        | (Builtin::Double, [])
+        | (Builtin::Text, []) => Ret::NirKind(BuiltinType(b)),
+        (Builtin::Optional, [t]) => Ret::NirKind(OptionalType(t.clone())),
+        (Builtin::List, [t]) => Ret::NirKind(ListType(t.clone())),
+
         (Builtin::OptionalNone, [t]) => {
             Ret::NirKind(EmptyOptionalLit(t.clone()))
         }
         (Builtin::NaturalIsZero, [n]) => match &*n.kind() {
-            Lit(Natural(n)) => Ret::NirKind(Lit(Bool(*n == 0))),
+            Num(Natural(n)) => Ret::NirKind(Num(Bool(*n == 0))),
             _ => Ret::DoneAsIs,
         },
         (Builtin::NaturalEven, [n]) => match &*n.kind() {
-            Lit(Natural(n)) => Ret::NirKind(Lit(Bool(*n % 2 == 0))),
+            Num(Natural(n)) => Ret::NirKind(Num(Bool(*n % 2 == 0))),
             _ => Ret::DoneAsIs,
         },
         (Builtin::NaturalOdd, [n]) => match &*n.kind() {
-            Lit(Natural(n)) => Ret::NirKind(Lit(Bool(*n % 2 != 0))),
+            Num(Natural(n)) => Ret::NirKind(Num(Bool(*n % 2 != 0))),
             _ => Ret::DoneAsIs,
         },
         (Builtin::NaturalToInteger, [n]) => match &*n.kind() {
-            Lit(Natural(n)) => Ret::NirKind(Lit(Integer(*n as isize))),
+            Num(Natural(n)) => Ret::NirKind(Num(Integer(*n as isize))),
             _ => Ret::DoneAsIs,
         },
         (Builtin::NaturalShow, [n]) => match &*n.kind() {
-            Lit(Natural(n)) => Ret::Nir(Nir::from_text(n)),
+            Num(Natural(n)) => Ret::Nir(Nir::from_text(n)),
             _ => Ret::DoneAsIs,
         },
         (Builtin::NaturalSubtract, [a, b]) => match (&*a.kind(), &*b.kind()) {
-            (Lit(Natural(a)), Lit(Natural(b))) => {
-                Ret::NirKind(Lit(Natural(if b > a { b - a } else { 0 })))
+            (Num(Natural(a)), Num(Natural(b))) => {
+                Ret::NirKind(Num(Natural(if b > a { b - a } else { 0 })))
             }
-            (Lit(Natural(0)), _) => Ret::Nir(b.clone()),
-            (_, Lit(Natural(0))) => Ret::NirKind(Lit(Natural(0))),
-            _ if a == b => Ret::NirKind(Lit(Natural(0))),
+            (Num(Natural(0)), _) => Ret::Nir(b.clone()),
+            (_, Num(Natural(0))) => Ret::NirKind(Num(Natural(0))),
+            _ if a == b => Ret::NirKind(Num(Natural(0))),
             _ => Ret::DoneAsIs,
         },
         (Builtin::IntegerShow, [n]) => match &*n.kind() {
-            Lit(Integer(n)) => {
+            Num(Integer(n)) => {
                 let s = if *n < 0 {
                     n.to_string()
                 } else {
@@ -317,30 +312,30 @@ fn apply_builtin(b: Builtin, args: Vec<Nir>, env: NzEnv) -> NirKind {
             _ => Ret::DoneAsIs,
         },
         (Builtin::IntegerToDouble, [n]) => match &*n.kind() {
-            Lit(Integer(n)) => {
-                Ret::NirKind(Lit(Double(NaiveDouble::from(*n as f64))))
+            Num(Integer(n)) => {
+                Ret::NirKind(Num(Double(NaiveDouble::from(*n as f64))))
             }
             _ => Ret::DoneAsIs,
         },
         (Builtin::IntegerNegate, [n]) => match &*n.kind() {
-            Lit(Integer(n)) => Ret::NirKind(Lit(Integer(-n))),
+            Num(Integer(n)) => Ret::NirKind(Num(Integer(-n))),
             _ => Ret::DoneAsIs,
         },
         (Builtin::IntegerClamp, [n]) => match &*n.kind() {
-            Lit(Integer(n)) => {
-                Ret::NirKind(Lit(Natural((*n).try_into().unwrap_or(0))))
+            Num(Integer(n)) => {
+                Ret::NirKind(Num(Natural((*n).try_into().unwrap_or(0))))
             }
             _ => Ret::DoneAsIs,
         },
         (Builtin::DoubleShow, [n]) => match &*n.kind() {
-            Lit(Double(n)) => Ret::Nir(Nir::from_text(n)),
+            Num(Double(n)) => Ret::Nir(Nir::from_text(n)),
             _ => Ret::DoneAsIs,
         },
         (Builtin::TextShow, [v]) => match &*v.kind() {
             TextLit(tlit) => {
                 if let Some(s) = tlit.as_text() {
                     // Printing InterpolatedText takes care of all the escaping
-                    let txt: InterpolatedText<Normalized> =
+                    let txt: InterpolatedText<Expr> =
                         std::iter::once(InterpolatedTextContents::Text(s))
                             .collect();
                     Ret::Nir(Nir::from_text(txt))
@@ -351,8 +346,8 @@ fn apply_builtin(b: Builtin, args: Vec<Nir>, env: NzEnv) -> NirKind {
             _ => Ret::DoneAsIs,
         },
         (Builtin::ListLength, [_, l]) => match &*l.kind() {
-            EmptyListLit(_) => Ret::NirKind(Lit(Natural(0))),
-            NEListLit(xs) => Ret::NirKind(Lit(Natural(xs.len()))),
+            EmptyListLit(_) => Ret::NirKind(Num(Natural(0))),
+            NEListLit(xs) => Ret::NirKind(Num(Natural(xs.len()))),
             _ => Ret::DoneAsIs,
         },
         (Builtin::ListHead, [_, l]) => match &*l.kind() {
@@ -398,7 +393,7 @@ fn apply_builtin(b: Builtin, args: Vec<Nir>, env: NzEnv) -> NirKind {
                                     let mut kvs = HashMap::new();
                                     kvs.insert(
                                         "index".into(),
-                                        Nir::from_kind(Lit(Natural(i))),
+                                        Nir::from_kind(Num(Natural(i))),
                                     );
                                     kvs.insert("value".into(), e.clone());
                                     Nir::from_kind(RecordLit(kvs))
@@ -466,14 +461,14 @@ fn apply_builtin(b: Builtin, args: Vec<Nir>, env: NzEnv) -> NirKind {
                     λ(x : Natural) ->
                     1 + var(x)
                 )))
-                .app(Lit(Natural(0)).into_nir()),
+                .app(Num(Natural(0)).into_nir()),
         ),
 
         (Builtin::NaturalFold, [n, t, succ, zero]) => match &*n.kind() {
-            Lit(Natural(0)) => Ret::Nir(zero.clone()),
-            Lit(Natural(n)) => {
+            Num(Natural(0)) => Ret::Nir(zero.clone()),
+            Num(Natural(n)) => {
                 let fold = Nir::from_builtin(Builtin::NaturalFold)
-                    .app(Lit(Natural(n - 1)).into_nir())
+                    .app(Num(Natural(n - 1)).into_nir())
                     .app(t.clone())
                     .app(succ.clone())
                     .app(zero.clone());
@@ -490,9 +485,9 @@ fn apply_builtin(b: Builtin, args: Vec<Nir>, env: NzEnv) -> NirKind {
     }
 }
 
-impl<Nir: std::cmp::PartialEq> std::cmp::PartialEq for BuiltinClosure<Nir> {
+impl std::cmp::PartialEq for BuiltinClosure {
     fn eq(&self, other: &Self) -> bool {
         self.b == other.b && self.args == other.args
     }
 }
-impl<Nir: std::cmp::Eq> std::cmp::Eq for BuiltinClosure<Nir> {}
+impl std::cmp::Eq for BuiltinClosure {}
diff --git a/dhall/src/semantics/mod.rs b/dhall/src/semantics/mod.rs
index 87033c9..468d8b1 100644
--- a/dhall/src/semantics/mod.rs
+++ b/dhall/src/semantics/mod.rs
@@ -3,7 +3,7 @@ pub mod nze;
 pub mod parse;
 pub mod resolve;
 pub mod tck;
-pub(crate) use self::builtins::*;
-pub(crate) use self::nze::*;
-pub(crate) use self::resolve::*;
-pub(crate) use self::tck::*;
+pub use self::builtins::*;
+pub use self::nze::*;
+pub use self::resolve::*;
+pub use self::tck::*;
diff --git a/dhall/src/semantics/nze/env.rs b/dhall/src/semantics/nze/env.rs
index ef2bee6..ec99dbe 100644
--- a/dhall/src/semantics/nze/env.rs
+++ b/dhall/src/semantics/nze/env.rs
@@ -1,7 +1,7 @@
 use crate::semantics::{AlphaVar, Nir, NirKind};
 
 #[derive(Debug, Clone, Copy, PartialEq, Eq)]
-pub(crate) enum NzVar {
+pub enum NzVar {
     /// Reverse-debruijn index: counts number of binders from the bottom of the stack.
     Bound(usize),
     /// Fake fresh variable generated for expression equality checking.
@@ -17,11 +17,11 @@ enum EnvItem<Type> {
 }
 
 #[derive(Debug, Clone)]
-pub(crate) struct ValEnv<Type> {
+pub struct ValEnv<Type> {
     items: Vec<EnvItem<Type>>,
 }
 
-pub(crate) type NzEnv = ValEnv<()>;
+pub type NzEnv = ValEnv<()>;
 
 impl NzVar {
     pub fn new(idx: usize) -> Self {
diff --git a/dhall/src/semantics/nze/mod.rs b/dhall/src/semantics/nze/mod.rs
index 2648339..23022e0 100644
--- a/dhall/src/semantics/nze/mod.rs
+++ b/dhall/src/semantics/nze/mod.rs
@@ -3,7 +3,7 @@ pub mod lazy;
 pub mod nir;
 pub mod normalize;
 pub mod var;
-pub(crate) use env::*;
-pub(crate) use nir::*;
-pub(crate) use normalize::*;
-pub(crate) use var::*;
+pub use env::*;
+pub use nir::*;
+pub use normalize::*;
+pub use var::*;
diff --git a/dhall/src/semantics/nze/nir.rs b/dhall/src/semantics/nze/nir.rs
index 32ef590..e0d227e 100644
--- a/dhall/src/semantics/nze/nir.rs
+++ b/dhall/src/semantics/nze/nir.rs
@@ -7,10 +7,10 @@ use crate::semantics::{
     BuiltinClosure, Hir, HirKind, NzEnv, NzVar, TyEnv, Type, Universe, VarEnv,
 };
 use crate::syntax::{
-    BinOp, Builtin, Const, ExprKind, InterpolatedTextContents, Label, LitKind,
-    Span,
+    BinOp, Builtin, Const, Expr, ExprKind, InterpolatedTextContents, Label,
+    NumKind, Span,
 };
-use crate::{NormalizedExpr, ToExprOptions};
+use crate::ToExprOptions;
 
 /// Stores a possibly unevaluated value. Gets (partially) normalized on-demand, sharing computation
 /// automatically. Uses a Rc<RefCell> to share computation.
@@ -19,7 +19,7 @@ use crate::{NormalizedExpr, ToExprOptions};
 /// normalize as needed.
 /// Stands for "Normalized intermediate representation"
 #[derive(Clone)]
-pub(crate) struct Nir(Rc<NirInternal>);
+pub struct Nir(Rc<NirInternal>);
 
 #[derive(Debug)]
 struct NirInternal {
@@ -28,7 +28,7 @@ struct NirInternal {
 
 /// An unevaluated subexpression
 #[derive(Debug, Clone)]
-pub(crate) enum Thunk {
+pub enum Thunk {
     /// A completely unnormalized expression.
     Thunk { env: NzEnv, body: Hir },
     /// A partially normalized expression that may need to go through `normalize_one_layer`.
@@ -37,7 +37,7 @@ pub(crate) enum Thunk {
 
 /// An unevaluated subexpression that takes an argument.
 #[derive(Debug, Clone)]
-pub(crate) enum Closure {
+pub enum Closure {
     /// Normal closure
     Closure { env: NzEnv, body: Hir },
     /// Closure that ignores the argument passed
@@ -48,7 +48,7 @@ pub(crate) enum Closure {
 // Invariant: this must not contain interpolations that are themselves TextLits, and contiguous
 // text values must be merged.
 #[derive(Debug, Clone, PartialEq, Eq)]
-pub(crate) struct TextLit(Vec<InterpolatedTextContents<Nir>>);
+pub struct TextLit(Vec<InterpolatedTextContents<Nir>>);
 
 /// This represents a value in Weak Head Normal Form (WHNF). This means that the value is
 /// normalized up to the first constructor, but subexpressions may not be fully normalized.
@@ -58,7 +58,7 @@ pub(crate) struct TextLit(Vec<InterpolatedTextContents<Nir>>);
 /// In particular, this means that once we get a `NirKind`, it can be considered immutable, and
 /// we only need to recursively normalize its sub-`Nir`s to get to the NF.
 #[derive(Debug, Clone, PartialEq, Eq)]
-pub(crate) enum NirKind {
+pub enum NirKind {
     /// Closures
     LamClosure {
         binder: Binder,
@@ -70,13 +70,17 @@ pub(crate) enum NirKind {
         annot: Nir,
         closure: Closure,
     },
-    AppliedBuiltin(BuiltinClosure<Nir>),
+    AppliedBuiltin(BuiltinClosure),
 
     Var(NzVar),
     Const(Const),
-    Lit(LitKind),
+    // Must be a number type, Bool or Text
+    BuiltinType(Builtin),
+    Num(NumKind),
+    OptionalType(Nir),
     EmptyOptionalLit(Nir),
     NEOptionalLit(Nir),
+    ListType(Nir),
     // EmptyListLit(t) means `[] : List t`, not `[] : t`
     EmptyListLit(Nir),
     NEListLit(Vec<Nir>),
@@ -93,34 +97,34 @@ pub(crate) enum NirKind {
 
 impl Nir {
     /// Construct a Nir from a completely unnormalized expression.
-    pub(crate) fn new_thunk(env: NzEnv, hir: Hir) -> Nir {
+    pub fn new_thunk(env: NzEnv, hir: Hir) -> Nir {
         NirInternal::from_thunk(Thunk::new(env, hir)).into_nir()
     }
     /// Construct a Nir from a partially normalized expression that's not in WHNF.
-    pub(crate) fn from_partial_expr(e: ExprKind<Nir>) -> Nir {
+    pub fn from_partial_expr(e: ExprKind<Nir>) -> Nir {
         // TODO: env
         let env = NzEnv::new();
         NirInternal::from_thunk(Thunk::from_partial_expr(env, e)).into_nir()
     }
     /// Make a Nir from a NirKind
-    pub(crate) fn from_kind(v: NirKind) -> Nir {
+    pub fn from_kind(v: NirKind) -> Nir {
         NirInternal::from_whnf(v).into_nir()
     }
-    pub(crate) fn from_const(c: Const) -> Self {
+    pub fn from_const(c: Const) -> Self {
         let v = NirKind::Const(c);
         NirInternal::from_whnf(v).into_nir()
     }
-    pub(crate) fn from_builtin(b: Builtin) -> Self {
+    pub fn from_builtin(b: Builtin) -> Self {
         Self::from_builtin_env(b, &NzEnv::new())
     }
-    pub(crate) fn from_builtin_env(b: Builtin, env: &NzEnv) -> Self {
+    pub fn from_builtin_env(b: Builtin, env: &NzEnv) -> Self {
         Nir::from_kind(NirKind::from_builtin_env(b, env.clone()))
     }
-    pub(crate) fn from_text(txt: impl ToString) -> Self {
+    pub fn from_text(txt: impl ToString) -> Self {
         Nir::from_kind(NirKind::TextLit(TextLit::from_text(txt.to_string())))
     }
 
-    pub(crate) fn as_const(&self) -> Option<Const> {
+    pub fn as_const(&self) -> Option<Const> {
         match &*self.kind() {
             NirKind::Const(c) => Some(*c),
             _ => None,
@@ -128,26 +132,22 @@ impl Nir {
     }
 
     /// This is what you want if you want to pattern-match on the value.
-    pub(crate) fn kind(&self) -> &NirKind {
+    pub fn kind(&self) -> &NirKind {
         self.0.kind()
     }
 
-    pub(crate) fn to_type(&self, u: impl Into<Universe>) -> Type {
+    pub fn to_type(&self, u: impl Into<Universe>) -> Type {
         Type::new(self.clone(), u.into())
     }
     /// Converts a value back to the corresponding AST expression.
-    pub(crate) fn to_expr(&self, opts: ToExprOptions) -> NormalizedExpr {
+    pub fn to_expr(&self, opts: ToExprOptions) -> Expr {
         self.to_hir_noenv().to_expr(opts)
     }
-    pub(crate) fn to_expr_tyenv(&self, tyenv: &TyEnv) -> NormalizedExpr {
+    pub fn to_expr_tyenv(&self, tyenv: &TyEnv) -> Expr {
         self.to_hir(tyenv.as_varenv()).to_expr_tyenv(tyenv)
     }
 
-    pub(crate) fn normalize(&self) {
-        self.0.normalize()
-    }
-
-    pub(crate) fn app(&self, v: Nir) -> Nir {
+    pub fn app(&self, v: Nir) -> Nir {
         Nir::from_kind(apply_any(self.clone(), v))
     }
 
@@ -188,12 +188,21 @@ impl Nir {
                     closure.to_hir(venv),
                 ),
                 NirKind::Const(c) => ExprKind::Const(*c),
-                NirKind::Lit(l) => ExprKind::Lit(l.clone()),
+                NirKind::BuiltinType(b) => ExprKind::Builtin(*b),
+                NirKind::Num(l) => ExprKind::Num(l.clone()),
+                NirKind::OptionalType(t) => ExprKind::App(
+                    Nir::from_builtin(Builtin::Optional).to_hir(venv),
+                    t.to_hir(venv),
+                ),
                 NirKind::EmptyOptionalLit(n) => ExprKind::App(
                     Nir::from_builtin(Builtin::OptionalNone).to_hir(venv),
                     n.to_hir(venv),
                 ),
                 NirKind::NEOptionalLit(n) => ExprKind::SomeLit(n.to_hir(venv)),
+                NirKind::ListType(t) => ExprKind::App(
+                    Nir::from_builtin(Builtin::List).to_hir(venv),
+                    t.to_hir(venv),
+                ),
                 NirKind::EmptyListLit(n) => ExprKind::EmptyListLit(Hir::new(
                     HirKind::Expr(ExprKind::App(
                         Nir::from_builtin(Builtin::List).to_hir(venv),
@@ -274,75 +283,18 @@ impl NirInternal {
     fn kind(&self) -> &NirKind {
         &self.kind
     }
-    fn normalize(&self) {
-        self.kind().normalize();
-    }
 }
 
 impl NirKind {
-    pub(crate) fn into_nir(self) -> Nir {
+    pub fn into_nir(self) -> Nir {
         Nir::from_kind(self)
     }
 
-    pub(crate) fn normalize(&self) {
-        match self {
-            NirKind::Var(..) | NirKind::Const(_) | NirKind::Lit(_) => {}
-
-            NirKind::EmptyOptionalLit(tth) | NirKind::EmptyListLit(tth) => {
-                tth.normalize();
-            }
-
-            NirKind::NEOptionalLit(th) => {
-                th.normalize();
-            }
-            NirKind::LamClosure { annot, closure, .. }
-            | NirKind::PiClosure { annot, closure, .. } => {
-                annot.normalize();
-                closure.normalize();
-            }
-            NirKind::AppliedBuiltin(closure) => closure.normalize(),
-            NirKind::NEListLit(elts) => {
-                for x in elts.iter() {
-                    x.normalize();
-                }
-            }
-            NirKind::RecordLit(kvs) => {
-                for x in kvs.values() {
-                    x.normalize();
-                }
-            }
-            NirKind::RecordType(kvs) => {
-                for x in kvs.values() {
-                    x.normalize();
-                }
-            }
-            NirKind::UnionType(kts) | NirKind::UnionConstructor(_, kts) => {
-                for x in kts.values().flatten() {
-                    x.normalize();
-                }
-            }
-            NirKind::UnionLit(_, v, kts) => {
-                v.normalize();
-                for x in kts.values().flatten() {
-                    x.normalize();
-                }
-            }
-            NirKind::TextLit(tlit) => tlit.normalize(),
-            NirKind::Equivalence(x, y) => {
-                x.normalize();
-                y.normalize();
-            }
-            NirKind::PartialExpr(e) => {
-                e.map_ref(Nir::normalize);
-            }
-        }
-    }
-
-    pub(crate) fn from_builtin(b: Builtin) -> NirKind {
+    pub fn from_builtin(b: Builtin) -> NirKind {
         NirKind::from_builtin_env(b, NzEnv::new())
     }
-    pub(crate) fn from_builtin_env(b: Builtin, env: NzEnv) -> NirKind {
-        NirKind::AppliedBuiltin(BuiltinClosure::new(b, env))
+    pub fn from_builtin_env(b: Builtin, env: NzEnv) -> NirKind {
+        BuiltinClosure::new(b, env)
     }
 }
 
@@ -390,9 +342,6 @@ impl Closure {
         }
     }
 
-    // TODO: somehow normalize the body. Might require to pass an env.
-    pub fn normalize(&self) {}
-
     /// Convert this closure to a Hir expression
     pub fn to_hir(&self, venv: VarEnv) -> Hir {
         self.apply_var(NzVar::new(venv.size()))
@@ -456,13 +405,6 @@ impl TextLit {
     pub fn iter(&self) -> impl Iterator<Item = &InterpolatedTextContents<Nir>> {
         self.0.iter()
     }
-    /// Normalize the contained values. This does not break the invariant because we have already
-    /// ensured that no contained values normalize to a TextLit.
-    pub fn normalize(&self) {
-        for x in self.0.iter() {
-            x.map_ref(Nir::normalize);
-        }
-    }
 }
 
 impl lazy::Eval<NirKind> for Thunk {
diff --git a/dhall/src/semantics/nze/normalize.rs b/dhall/src/semantics/nze/normalize.rs
index 79d55e8..570e106 100644
--- a/dhall/src/semantics/nze/normalize.rs
+++ b/dhall/src/semantics/nze/normalize.rs
@@ -2,14 +2,10 @@ use itertools::Itertools;
 use std::collections::HashMap;
 
 use crate::semantics::NzEnv;
-use crate::semantics::{
-    Binder, BuiltinClosure, Closure, Hir, HirKind, Nir, NirKind, TextLit,
-};
-use crate::syntax::{
-    BinOp, Builtin, ExprKind, InterpolatedTextContents, LitKind,
-};
+use crate::semantics::{Binder, Closure, Hir, HirKind, Nir, NirKind, TextLit};
+use crate::syntax::{BinOp, ExprKind, InterpolatedTextContents, NumKind};
 
-pub(crate) fn apply_any(f: Nir, a: Nir) -> NirKind {
+pub fn apply_any(f: Nir, a: Nir) -> NirKind {
     match f.kind() {
         NirKind::LamClosure { closure, .. } => closure.apply(a).kind().clone(),
         NirKind::AppliedBuiltin(closure) => closure.apply(a),
@@ -20,7 +16,7 @@ pub(crate) fn apply_any(f: Nir, a: Nir) -> NirKind {
     }
 }
 
-pub(crate) fn squash_textlit(
+pub fn squash_textlit(
     elts: impl Iterator<Item = InterpolatedTextContents<Nir>>,
 ) -> Vec<InterpolatedTextContents<Nir>> {
     use std::mem::replace;
@@ -58,7 +54,7 @@ pub(crate) fn squash_textlit(
     ret
 }
 
-pub(crate) fn merge_maps<K, V, F>(
+pub fn merge_maps<K, V, F>(
     map1: &HashMap<K, V>,
     map2: &HashMap<K, V>,
     mut f: F,
@@ -99,40 +95,40 @@ fn apply_binop<'a>(o: BinOp, x: &'a Nir, y: &'a Nir) -> Option<Ret<'a>> {
         NaturalTimes, RecursiveRecordMerge, RecursiveRecordTypeMerge,
         RightBiasedRecordMerge, TextAppend,
     };
-    use LitKind::{Bool, Natural};
-    use NirKind::{EmptyListLit, Lit, NEListLit, RecordLit, RecordType};
+    use NirKind::{EmptyListLit, NEListLit, Num, RecordLit, RecordType};
+    use NumKind::{Bool, Natural};
 
     Some(match (o, x.kind(), y.kind()) {
-        (BoolAnd, Lit(Bool(true)), _) => Ret::NirRef(y),
-        (BoolAnd, _, Lit(Bool(true))) => Ret::NirRef(x),
-        (BoolAnd, Lit(Bool(false)), _) => Ret::NirKind(Lit(Bool(false))),
-        (BoolAnd, _, Lit(Bool(false))) => Ret::NirKind(Lit(Bool(false))),
+        (BoolAnd, Num(Bool(true)), _) => Ret::NirRef(y),
+        (BoolAnd, _, Num(Bool(true))) => Ret::NirRef(x),
+        (BoolAnd, Num(Bool(false)), _) => Ret::NirKind(Num(Bool(false))),
+        (BoolAnd, _, Num(Bool(false))) => Ret::NirKind(Num(Bool(false))),
         (BoolAnd, _, _) if x == y => Ret::NirRef(x),
-        (BoolOr, Lit(Bool(true)), _) => Ret::NirKind(Lit(Bool(true))),
-        (BoolOr, _, Lit(Bool(true))) => Ret::NirKind(Lit(Bool(true))),
-        (BoolOr, Lit(Bool(false)), _) => Ret::NirRef(y),
-        (BoolOr, _, Lit(Bool(false))) => Ret::NirRef(x),
+        (BoolOr, Num(Bool(true)), _) => Ret::NirKind(Num(Bool(true))),
+        (BoolOr, _, Num(Bool(true))) => Ret::NirKind(Num(Bool(true))),
+        (BoolOr, Num(Bool(false)), _) => Ret::NirRef(y),
+        (BoolOr, _, Num(Bool(false))) => Ret::NirRef(x),
         (BoolOr, _, _) if x == y => Ret::NirRef(x),
-        (BoolEQ, Lit(Bool(true)), _) => Ret::NirRef(y),
-        (BoolEQ, _, Lit(Bool(true))) => Ret::NirRef(x),
-        (BoolEQ, Lit(Bool(x)), Lit(Bool(y))) => Ret::NirKind(Lit(Bool(x == y))),
-        (BoolEQ, _, _) if x == y => Ret::NirKind(Lit(Bool(true))),
-        (BoolNE, Lit(Bool(false)), _) => Ret::NirRef(y),
-        (BoolNE, _, Lit(Bool(false))) => Ret::NirRef(x),
-        (BoolNE, Lit(Bool(x)), Lit(Bool(y))) => Ret::NirKind(Lit(Bool(x != y))),
-        (BoolNE, _, _) if x == y => Ret::NirKind(Lit(Bool(false))),
+        (BoolEQ, Num(Bool(true)), _) => Ret::NirRef(y),
+        (BoolEQ, _, Num(Bool(true))) => Ret::NirRef(x),
+        (BoolEQ, Num(Bool(x)), Num(Bool(y))) => Ret::NirKind(Num(Bool(x == y))),
+        (BoolEQ, _, _) if x == y => Ret::NirKind(Num(Bool(true))),
+        (BoolNE, Num(Bool(false)), _) => Ret::NirRef(y),
+        (BoolNE, _, Num(Bool(false))) => Ret::NirRef(x),
+        (BoolNE, Num(Bool(x)), Num(Bool(y))) => Ret::NirKind(Num(Bool(x != y))),
+        (BoolNE, _, _) if x == y => Ret::NirKind(Num(Bool(false))),
 
-        (NaturalPlus, Lit(Natural(0)), _) => Ret::NirRef(y),
-        (NaturalPlus, _, Lit(Natural(0))) => Ret::NirRef(x),
-        (NaturalPlus, Lit(Natural(x)), Lit(Natural(y))) => {
-            Ret::NirKind(Lit(Natural(x + y)))
+        (NaturalPlus, Num(Natural(0)), _) => Ret::NirRef(y),
+        (NaturalPlus, _, Num(Natural(0))) => Ret::NirRef(x),
+        (NaturalPlus, Num(Natural(x)), Num(Natural(y))) => {
+            Ret::NirKind(Num(Natural(x + y)))
         }
-        (NaturalTimes, Lit(Natural(0)), _) => Ret::NirKind(Lit(Natural(0))),
-        (NaturalTimes, _, Lit(Natural(0))) => Ret::NirKind(Lit(Natural(0))),
-        (NaturalTimes, Lit(Natural(1)), _) => Ret::NirRef(y),
-        (NaturalTimes, _, Lit(Natural(1))) => Ret::NirRef(x),
-        (NaturalTimes, Lit(Natural(x)), Lit(Natural(y))) => {
-            Ret::NirKind(Lit(Natural(x * y)))
+        (NaturalTimes, Num(Natural(0)), _) => Ret::NirKind(Num(Natural(0))),
+        (NaturalTimes, _, Num(Natural(0))) => Ret::NirKind(Num(Natural(0))),
+        (NaturalTimes, Num(Natural(1)), _) => Ret::NirRef(y),
+        (NaturalTimes, _, Num(Natural(1))) => Ret::NirRef(x),
+        (NaturalTimes, Num(Natural(x)), Num(Natural(y))) => {
+            Ret::NirKind(Num(Natural(x * y)))
         }
 
         (ListAppend, EmptyListLit(_), _) => Ret::NirRef(y),
@@ -211,13 +207,13 @@ fn apply_binop<'a>(o: BinOp, x: &'a Nir, y: &'a Nir) -> Option<Ret<'a>> {
 }
 
 #[allow(clippy::cognitive_complexity)]
-pub(crate) fn normalize_one_layer(expr: ExprKind<Nir>, env: &NzEnv) -> NirKind {
-    use LitKind::Bool;
+pub fn normalize_one_layer(expr: ExprKind<Nir>, env: &NzEnv) -> NirKind {
     use NirKind::{
-        EmptyListLit, EmptyOptionalLit, Lit, NEListLit, NEOptionalLit,
+        EmptyListLit, EmptyOptionalLit, NEListLit, NEOptionalLit, Num,
         PartialExpr, RecordLit, RecordType, UnionConstructor, UnionLit,
         UnionType,
     };
+    use NumKind::Bool;
 
     let ret = match expr {
         ExprKind::Import(..) | ExprKind::Completion(..) => {
@@ -235,15 +231,11 @@ pub(crate) fn normalize_one_layer(expr: ExprKind<Nir>, env: &NzEnv) -> NirKind {
         ExprKind::Builtin(b) => Ret::Nir(Nir::from_builtin_env(b, env)),
         ExprKind::Assert(_) => Ret::Expr(expr),
         ExprKind::App(v, a) => Ret::Nir(v.app(a)),
-        ExprKind::Lit(l) => Ret::NirKind(Lit(l)),
+        ExprKind::Num(l) => Ret::NirKind(Num(l)),
         ExprKind::SomeLit(e) => Ret::NirKind(NEOptionalLit(e)),
         ExprKind::EmptyListLit(t) => {
             let arg = match t.kind() {
-                NirKind::AppliedBuiltin(BuiltinClosure {
-                    b: Builtin::List,
-                    args,
-                    ..
-                }) if args.len() == 1 => args[0].clone(),
+                NirKind::ListType(t) => t.clone(),
                 _ => panic!("internal type error"),
             };
             Ret::NirKind(NirKind::EmptyListLit(arg))
@@ -271,12 +263,12 @@ pub(crate) fn normalize_one_layer(expr: ExprKind<Nir>, env: &NzEnv) -> NirKind {
         }
         ExprKind::BoolIf(ref b, ref e1, ref e2) => {
             match b.kind() {
-                Lit(Bool(true)) => Ret::NirRef(e1),
-                Lit(Bool(false)) => Ret::NirRef(e2),
+                Num(Bool(true)) => Ret::NirRef(e1),
+                Num(Bool(false)) => Ret::NirRef(e2),
                 _ => {
                     match (e1.kind(), e2.kind()) {
                         // Simplify `if b then True else False`
-                        (Lit(Bool(true)), Lit(Bool(false))) => Ret::NirRef(b),
+                        (Num(Bool(true)), Num(Bool(false))) => Ret::NirRef(b),
                         _ if e1 == e2 => Ret::NirRef(e1),
                         _ => Ret::Expr(expr),
                     }
@@ -442,12 +434,8 @@ pub(crate) fn normalize_one_layer(expr: ExprKind<Nir>, env: &NzEnv) -> NirKind {
         ExprKind::ToMap(ref v, ref annot) => match v.kind() {
             RecordLit(kvs) if kvs.is_empty() => {
                 match annot.as_ref().map(|v| v.kind()) {
-                    Some(NirKind::AppliedBuiltin(BuiltinClosure {
-                        b: Builtin::List,
-                        args,
-                        ..
-                    })) if args.len() == 1 => {
-                        Ret::NirKind(EmptyListLit(args[0].clone()))
+                    Some(NirKind::ListType(t)) => {
+                        Ret::NirKind(EmptyListLit(t.clone()))
                     }
                     _ => Ret::Expr(expr),
                 }
@@ -476,7 +464,7 @@ pub(crate) fn normalize_one_layer(expr: ExprKind<Nir>, env: &NzEnv) -> NirKind {
 }
 
 /// Normalize Hir into WHNF
-pub(crate) fn normalize_hir_whnf(env: &NzEnv, hir: &Hir) -> NirKind {
+pub fn normalize_hir_whnf(env: &NzEnv, hir: &Hir) -> NirKind {
     match hir.kind() {
         HirKind::Var(var) => env.lookup_val(*var),
         HirKind::Import(hir, _) => normalize_hir_whnf(env, hir),
diff --git a/dhall/src/semantics/nze/var.rs b/dhall/src/semantics/nze/var.rs
index 413c759..302dbb7 100644
--- a/dhall/src/semantics/nze/var.rs
+++ b/dhall/src/semantics/nze/var.rs
@@ -8,10 +8,10 @@ pub struct Binder {
 }
 
 impl Binder {
-    pub(crate) fn new(name: Label) -> Self {
+    pub fn new(name: Label) -> Self {
         Binder { name }
     }
-    pub(crate) fn to_label(&self) -> Label {
+    pub fn to_label(&self) -> Label {
         self.clone().into()
     }
 }
diff --git a/dhall/src/semantics/parse.rs b/dhall/src/semantics/parse.rs
index 45860d0..2326471 100644
--- a/dhall/src/semantics/parse.rs
+++ b/dhall/src/semantics/parse.rs
@@ -9,33 +9,33 @@ use crate::syntax::binary;
 use crate::syntax::parse_expr;
 use crate::Parsed;
 
-pub(crate) fn parse_file(f: &Path) -> Result<Parsed, Error> {
+pub fn parse_file(f: &Path) -> Result<Parsed, Error> {
     let text = std::fs::read_to_string(f)?;
     let expr = parse_expr(&text)?;
     let root = ImportLocation::Local(f.to_owned());
     Ok(Parsed(expr, root))
 }
 
-pub(crate) fn parse_remote(url: Url) -> Result<Parsed, Error> {
+pub fn parse_remote(url: Url) -> Result<Parsed, Error> {
     let body = reqwest::blocking::get(url.clone()).unwrap().text().unwrap();
     let expr = parse_expr(&body)?;
     let root = ImportLocation::Remote(url);
     Ok(Parsed(expr, root))
 }
 
-pub(crate) fn parse_str(s: &str) -> Result<Parsed, Error> {
+pub fn parse_str(s: &str) -> Result<Parsed, Error> {
     let expr = parse_expr(s)?;
     let root = ImportLocation::Missing;
     Ok(Parsed(expr, root))
 }
 
-pub(crate) fn parse_binary(data: &[u8]) -> Result<Parsed, Error> {
+pub fn parse_binary(data: &[u8]) -> Result<Parsed, Error> {
     let expr = binary::decode(data)?;
     let root = ImportLocation::Missing;
     Ok(Parsed(expr, root))
 }
 
-pub(crate) fn parse_binary_file(f: &Path) -> Result<Parsed, Error> {
+pub fn parse_binary_file(f: &Path) -> Result<Parsed, Error> {
     let mut buffer = Vec::new();
     File::open(f)?.read_to_end(&mut buffer)?;
     let expr = binary::decode(&buffer)?;
diff --git a/dhall/src/semantics/resolve/env.rs b/dhall/src/semantics/resolve/env.rs
index fe8c178..d7ff0ae 100644
--- a/dhall/src/semantics/resolve/env.rs
+++ b/dhall/src/semantics/resolve/env.rs
@@ -5,24 +5,24 @@ use crate::semantics::{AlphaVar, ImportLocation, TypedHir, VarEnv};
 use crate::syntax::{Label, V};
 
 /// Environment for resolving names.
-#[derive(Debug, Clone)]
-pub(crate) struct NameEnv {
+#[derive(Debug, Clone, Default)]
+pub struct NameEnv {
     names: Vec<Label>,
 }
 
-pub(crate) type ImportCache = HashMap<ImportLocation, TypedHir>;
-pub(crate) type ImportStack = Vec<ImportLocation>;
+pub type ImportCache = HashMap<ImportLocation, TypedHir>;
+pub type ImportStack = Vec<ImportLocation>;
 
 /// Environment for resolving imports
-#[derive(Debug, Clone)]
-pub(crate) struct ImportEnv {
+#[derive(Debug, Clone, Default)]
+pub struct ImportEnv {
     cache: ImportCache,
     stack: ImportStack,
 }
 
 impl NameEnv {
     pub fn new() -> Self {
-        NameEnv { names: Vec::new() }
+        NameEnv::default()
     }
     pub fn as_varenv(&self) -> VarEnv {
         VarEnv::from_size(self.names.len())
@@ -66,10 +66,7 @@ impl NameEnv {
 
 impl ImportEnv {
     pub fn new() -> Self {
-        ImportEnv {
-            cache: HashMap::new(),
-            stack: Vec::new(),
-        }
+        ImportEnv::default()
     }
 
     pub fn handle_import(
diff --git a/dhall/src/semantics/resolve/hir.rs b/dhall/src/semantics/resolve/hir.rs
index fa2989f..9256425 100644
--- a/dhall/src/semantics/resolve/hir.rs
+++ b/dhall/src/semantics/resolve/hir.rs
@@ -1,7 +1,7 @@
 use crate::error::TypeError;
 use crate::semantics::{type_with, NameEnv, Nir, NzEnv, Tir, TyEnv, Type};
 use crate::syntax::{Expr, ExprKind, Span, V};
-use crate::{NormalizedExpr, ToExprOptions};
+use crate::ToExprOptions;
 
 /// Stores an alpha-normalized variable.
 #[derive(Debug, Clone, Copy, PartialEq, Eq, Hash)]
@@ -10,7 +10,7 @@ pub struct AlphaVar {
 }
 
 #[derive(Debug, Clone, PartialEq, Eq)]
-pub(crate) enum HirKind {
+pub enum HirKind {
     /// A resolved variable (i.e. a DeBruijn index)
     Var(AlphaVar),
     /// Result of resolving an import.
@@ -21,16 +21,16 @@ pub(crate) enum HirKind {
 
 // An expression with resolved variables and imports.
 #[derive(Debug, Clone)]
-pub(crate) struct Hir {
+pub struct Hir {
     kind: Box<HirKind>,
     span: Span,
 }
 
 impl AlphaVar {
-    pub(crate) fn new(idx: usize) -> Self {
+    pub fn new(idx: usize) -> Self {
         AlphaVar { idx }
     }
-    pub(crate) fn idx(self) -> usize {
+    pub fn idx(self) -> usize {
         self.idx
     }
 }
@@ -51,15 +51,15 @@ impl Hir {
     }
 
     /// Converts a closed Hir expr back to the corresponding AST expression.
-    pub fn to_expr(&self, opts: ToExprOptions) -> NormalizedExpr {
+    pub fn to_expr(&self, opts: ToExprOptions) -> Expr {
         hir_to_expr(self, opts, &mut NameEnv::new())
     }
     /// Converts a closed Hir expr back to the corresponding AST expression.
-    pub fn to_expr_noopts(&self) -> NormalizedExpr {
+    pub fn to_expr_noopts(&self) -> Expr {
         let opts = ToExprOptions { alpha: false };
         self.to_expr(opts)
     }
-    pub fn to_expr_tyenv(&self, env: &TyEnv) -> NormalizedExpr {
+    pub fn to_expr_tyenv(&self, env: &TyEnv) -> Expr {
         let opts = ToExprOptions { alpha: false };
         let mut env = env.as_nameenv().clone();
         hir_to_expr(self, opts, &mut env)
@@ -85,19 +85,9 @@ impl Hir {
     pub fn eval_closed_expr(&self) -> Nir {
         self.eval(NzEnv::new())
     }
-    /// Eval a closed Hir fully and recursively;
-    pub fn rec_eval_closed_expr(&self) -> Nir {
-        let val = self.eval_closed_expr();
-        val.normalize();
-        val
-    }
 }
 
-fn hir_to_expr(
-    hir: &Hir,
-    opts: ToExprOptions,
-    env: &mut NameEnv,
-) -> NormalizedExpr {
+fn hir_to_expr(hir: &Hir, opts: ToExprOptions, env: &mut NameEnv) -> Expr {
     let kind = match hir.kind() {
         HirKind::Var(v) if opts.alpha => ExprKind::Var(V("_".into(), v.idx())),
         HirKind::Var(v) => ExprKind::Var(env.label_var(*v)),
diff --git a/dhall/src/semantics/resolve/mod.rs b/dhall/src/semantics/resolve/mod.rs
index 517907b..33b477e 100644
--- a/dhall/src/semantics/resolve/mod.rs
+++ b/dhall/src/semantics/resolve/mod.rs
@@ -1,6 +1,6 @@
 pub mod env;
 pub mod hir;
 pub mod resolve;
-pub(crate) use env::*;
-pub(crate) use hir::*;
-pub(crate) use resolve::*;
+pub use env::*;
+pub use hir::*;
+pub use resolve::*;
diff --git a/dhall/src/semantics/resolve/resolve.rs b/dhall/src/semantics/resolve/resolve.rs
index f3fda4b..7745e0b 100644
--- a/dhall/src/semantics/resolve/resolve.rs
+++ b/dhall/src/semantics/resolve/resolve.rs
@@ -13,17 +13,17 @@ use crate::syntax::{
     BinOp, Builtin, Expr, ExprKind, FilePath, FilePrefix, ImportMode,
     ImportTarget, Span, UnspannedExpr, URL,
 };
-use crate::{Parsed, ParsedExpr, Resolved};
+use crate::{Parsed, Resolved};
 
 // TODO: evaluate import headers
-pub(crate) type Import = syntax::Import<()>;
+pub type Import = syntax::Import<()>;
 
 /// Owned Hir with a type. Different from Tir because the Hir is owned.
-pub(crate) type TypedHir = (Hir, Type);
+pub type TypedHir = (Hir, Type);
 
 /// The location of some data, usually some dhall code.
 #[derive(Debug, Clone, PartialEq, Eq, Hash)]
-pub(crate) enum ImportLocation {
+pub enum ImportLocation {
     /// Local file
     Local(PathBuf),
     /// Remote file
@@ -227,7 +227,7 @@ fn resolve_one_import(
         }
         ImportMode::Location => {
             let expr = location.into_location();
-            let hir = skip_resolve(&expr)?;
+            let hir = skip_resolve_expr(&expr)?;
             let ty = hir.typecheck_noenv()?.ty().clone();
             Ok((hir, ty))
         }
@@ -329,16 +329,22 @@ fn resolve_with_env(
     Ok(Resolved(resolved))
 }
 
-pub(crate) fn resolve(parsed: Parsed) -> Result<Resolved, Error> {
+pub fn resolve(parsed: Parsed) -> Result<Resolved, Error> {
     resolve_with_env(&mut ImportEnv::new(), parsed)
 }
 
-pub(crate) fn skip_resolve(expr: &ParsedExpr) -> Result<Hir, Error> {
+pub fn skip_resolve_expr(expr: &Expr) -> Result<Hir, Error> {
     traverse_resolve_expr(&mut NameEnv::new(), expr, &mut |import| {
         Err(ImportError::UnexpectedImport(import).into())
     })
 }
 
+pub fn skip_resolve(parsed: Parsed) -> Result<Resolved, Error> {
+    let Parsed(expr, _) = parsed;
+    let resolved = skip_resolve_expr(&expr)?;
+    Ok(Resolved(resolved))
+}
+
 pub trait Canonicalize {
     fn canonicalize(&self) -> Self;
 }
diff --git a/dhall/src/semantics/tck/env.rs b/dhall/src/semantics/tck/env.rs
index 6dd5076..1fa66f0 100644
--- a/dhall/src/semantics/tck/env.rs
+++ b/dhall/src/semantics/tck/env.rs
@@ -2,21 +2,21 @@ use crate::semantics::{AlphaVar, NameEnv, Nir, NzEnv, NzVar, Type, ValEnv};
 use crate::syntax::Label;
 
 /// Environment for indexing variables.
-#[derive(Debug, Clone, Copy)]
-pub(crate) struct VarEnv {
+#[derive(Debug, Clone, Copy, Default)]
+pub struct VarEnv {
     size: usize,
 }
 
 /// Environment for typing expressions.
 #[derive(Debug, Clone)]
-pub(crate) struct TyEnv {
+pub struct TyEnv {
     names: NameEnv,
     items: ValEnv<Type>,
 }
 
 impl VarEnv {
     pub fn new() -> Self {
-        VarEnv { size: 0 }
+        VarEnv::default()
     }
     pub fn from_size(size: usize) -> Self {
         VarEnv { size }
diff --git a/dhall/src/semantics/tck/mod.rs b/dhall/src/semantics/tck/mod.rs
index 93c8f48..6dddfc5 100644
--- a/dhall/src/semantics/tck/mod.rs
+++ b/dhall/src/semantics/tck/mod.rs
@@ -1,6 +1,6 @@
 pub mod env;
 pub mod tir;
 pub mod typecheck;
-pub(crate) use env::*;
-pub(crate) use tir::*;
-pub(crate) use typecheck::*;
+pub use env::*;
+pub use tir::*;
+pub use typecheck::*;
diff --git a/dhall/src/semantics/tck/tir.rs b/dhall/src/semantics/tck/tir.rs
index aeb7bf9..89a8027 100644
--- a/dhall/src/semantics/tck/tir.rs
+++ b/dhall/src/semantics/tck/tir.rs
@@ -1,15 +1,14 @@
 use crate::error::{ErrorBuilder, TypeError};
 use crate::semantics::{mkerr, Hir, Nir, NirKind, NzEnv, TyEnv, VarEnv};
-use crate::syntax::{Builtin, Const, Span};
-use crate::NormalizedExpr;
+use crate::syntax::{Builtin, Const, Expr, Span};
 
 /// The type of a type. 0 is `Type`, 1 is `Kind`, etc...
 #[derive(Debug, Copy, Clone, PartialEq, Eq, PartialOrd, Ord, Default)]
-pub(crate) struct Universe(u8);
+pub struct Universe(u8);
 
 /// An expression representing a type
 #[derive(Debug, Clone, PartialEq, Eq)]
-pub(crate) struct Type {
+pub struct Type {
     val: Nir,
     univ: Universe,
 }
@@ -17,7 +16,7 @@ pub(crate) struct Type {
 /// A hir expression plus its inferred type.
 /// Stands for "Typed intermediate representation"
 #[derive(Debug, Clone)]
-pub(crate) struct Tir<'hir> {
+pub struct Tir<'hir> {
     hir: &'hir Hir,
     ty: Type,
 }
@@ -101,7 +100,7 @@ impl Type {
     pub fn to_hir(&self, venv: VarEnv) -> Hir {
         self.val.to_hir(venv)
     }
-    pub fn to_expr_tyenv(&self, tyenv: &TyEnv) -> NormalizedExpr {
+    pub fn to_expr_tyenv(&self, tyenv: &TyEnv) -> Expr {
         self.val.to_hir(tyenv.as_varenv()).to_expr_tyenv(tyenv)
     }
 }
@@ -124,7 +123,7 @@ impl<'hir> Tir<'hir> {
     pub fn as_hir(&self) -> &Hir {
         &self.hir
     }
-    pub fn to_expr_tyenv(&self, env: &TyEnv) -> NormalizedExpr {
+    pub fn to_expr_tyenv(&self, env: &TyEnv) -> Expr {
         self.as_hir().to_expr_tyenv(env)
     }
 
diff --git a/dhall/src/semantics/tck/typecheck.rs b/dhall/src/semantics/tck/typecheck.rs
index 173b76d..c3334b5 100644
--- a/dhall/src/semantics/tck/typecheck.rs
+++ b/dhall/src/semantics/tck/typecheck.rs
@@ -5,11 +5,11 @@ use std::collections::HashMap;
 use crate::error::{ErrorBuilder, TypeError, TypeMessage};
 use crate::semantics::merge_maps;
 use crate::semantics::{
-    type_of_builtin, Binder, BuiltinClosure, Closure, Hir, HirKind, Nir,
-    NirKind, Tir, TyEnv, Type,
+    type_of_builtin, Binder, Closure, Hir, HirKind, Nir, NirKind, Tir, TyEnv,
+    Type,
 };
 use crate::syntax::{
-    BinOp, Builtin, Const, ExprKind, InterpolatedTextContents, LitKind, Span,
+    BinOp, Builtin, Const, ExprKind, InterpolatedTextContents, NumKind, Span,
 };
 
 fn check_rectymerge(
@@ -53,14 +53,11 @@ fn function_check(a: Const, b: Const) -> Const {
     }
 }
 
-pub(crate) fn mkerr<T, S: ToString>(msg: S) -> Result<T, TypeError> {
+pub fn mkerr<T, S: ToString>(msg: S) -> Result<T, TypeError> {
     Err(TypeError::new(TypeMessage::Custom(msg.to_string())))
 }
 
-pub(crate) fn mk_span_err<T, S: ToString>(
-    span: Span,
-    msg: S,
-) -> Result<T, TypeError> {
+pub fn mk_span_err<T, S: ToString>(span: Span, msg: S) -> Result<T, TypeError> {
     mkerr(
         ErrorBuilder::new(msg.to_string())
             .span_err(span, msg.to_string())
@@ -96,14 +93,14 @@ fn type_one_layer(
             let t_hir = type_of_builtin(*b);
             typecheck(&t_hir)?.eval_to_type(env)?
         }
-        ExprKind::Lit(LitKind::Bool(_)) => Type::from_builtin(Builtin::Bool),
-        ExprKind::Lit(LitKind::Natural(_)) => {
+        ExprKind::Num(NumKind::Bool(_)) => Type::from_builtin(Builtin::Bool),
+        ExprKind::Num(NumKind::Natural(_)) => {
             Type::from_builtin(Builtin::Natural)
         }
-        ExprKind::Lit(LitKind::Integer(_)) => {
+        ExprKind::Num(NumKind::Integer(_)) => {
             Type::from_builtin(Builtin::Integer)
         }
-        ExprKind::Lit(LitKind::Double(_)) => {
+        ExprKind::Num(NumKind::Double(_)) => {
             Type::from_builtin(Builtin::Double)
         }
         ExprKind::TextLit(interpolated) => {
@@ -121,11 +118,7 @@ fn type_one_layer(
         ExprKind::EmptyListLit(t) => {
             let t = t.eval_to_type(env)?;
             match t.kind() {
-                NirKind::AppliedBuiltin(BuiltinClosure {
-                    b: Builtin::List,
-                    args,
-                    ..
-                }) if args.len() == 1 => {}
+                NirKind::ListType(..) => {}
                 _ => return span_err("InvalidListType"),
             };
             t
@@ -376,10 +369,7 @@ fn type_one_layer(
         }
         ExprKind::BinOp(BinOp::ListAppend, l, r) => {
             match l.ty().kind() {
-                NirKind::AppliedBuiltin(BuiltinClosure {
-                    b: Builtin::List,
-                    ..
-                }) => {}
+                NirKind::ListType(..) => {}
                 _ => return span_err("BinOpTypeMismatch"),
             }
 
@@ -435,12 +425,7 @@ fn type_one_layer(
             let union_type = union.ty();
             let variants = match union_type.kind() {
                 NirKind::UnionType(kts) => Cow::Borrowed(kts),
-                NirKind::AppliedBuiltin(BuiltinClosure {
-                    b: Builtin::Optional,
-                    args,
-                    ..
-                }) if args.len() == 1 => {
-                    let ty = &args[0];
+                NirKind::OptionalType(ty) => {
                     let mut kts = HashMap::new();
                     kts.insert("None".into(), None);
                     kts.insert("Some".into(), Some(ty.clone()));
@@ -595,11 +580,7 @@ fn type_one_layer(
                 let err_msg = "The type of `toMap x` must be of the form \
                                `List { mapKey : Text, mapValue : T }`";
                 let arg = match annot_val.kind() {
-                    NirKind::AppliedBuiltin(BuiltinClosure {
-                        b: Builtin::List,
-                        args,
-                        ..
-                    }) if args.len() == 1 => &args[0],
+                    NirKind::ListType(t) => t,
                     _ => return span_err(err_msg),
                 };
                 let kts = match arg.kind() {
@@ -704,7 +685,7 @@ fn type_one_layer(
 
 /// `type_with` typechecks an expression in the provided environment. Optionally pass an annotation
 /// to compare with.
-pub(crate) fn type_with<'hir>(
+pub fn type_with<'hir>(
     env: &TyEnv,
     hir: &'hir Hir,
     annot: Option<Type>,
@@ -801,15 +782,15 @@ pub(crate) fn type_with<'hir>(
 
 /// Typecheck an expression and return the expression annotated with types if type-checking
 /// succeeded, or an error if type-checking failed.
-pub(crate) fn typecheck<'hir>(hir: &'hir Hir) -> Result<Tir<'hir>, TypeError> {
+pub fn typecheck<'hir>(hir: &'hir Hir) -> Result<Tir<'hir>, TypeError> {
     type_with(&TyEnv::new(), hir, None)
 }
 
 /// Like `typecheck`, but additionally checks that the expression's type matches the provided type.
-pub(crate) fn typecheck_with<'hir>(
+pub fn typecheck_with<'hir>(
     hir: &'hir Hir,
-    ty: Hir,
+    ty: &Hir,
 ) -> Result<Tir<'hir>, TypeError> {
-    let ty = typecheck(&ty)?.eval_to_type(&TyEnv::new())?;
+    let ty = typecheck(ty)?.eval_to_type(&TyEnv::new())?;
     type_with(&TyEnv::new(), hir, Some(ty))
 }