Split off operations from main expr enum

11 files changed, 424 insertions, 353 deletions

diff --git a/dhall/src/semantics/builtins.rs b/dhall/src/semantics/builtins.rs
index 6007a92..45be448 100644
--- a/dhall/src/semantics/builtins.rs
+++ b/dhall/src/semantics/builtins.rs
@@ -5,8 +5,8 @@ use crate::syntax::map::DupTreeMap;
 use crate::syntax::Const::Type;
 use crate::syntax::{
     BinOp, Builtin, Const, Expr, ExprKind, InterpolatedText,
-    InterpolatedTextContents, Label, NaiveDouble, NumKind, Span, UnspannedExpr,
-    V,
+    InterpolatedTextContents, Label, NaiveDouble, NumKind, OpKind, Span,
+    UnspannedExpr, V,
 };
 use std::collections::HashMap;
 use std::convert::TryInto;
@@ -34,10 +34,10 @@ impl BuiltinClosure {
         HirKind::Expr(self.args.iter().fold(
             ExprKind::Builtin(self.b),
             |acc, v| {
-                ExprKind::App(
+                ExprKind::Op(OpKind::App(
                     Hir::new(HirKind::Expr(acc), Span::Artificial),
                     v.to_hir(venv),
-                )
+                ))
             },
         ))
     }
@@ -59,16 +59,16 @@ macro_rules! make_type {
         rc(ExprKind::Var(V(stringify!($var).into(), 0)))
     };
     (Optional $ty:ident) => {
-        rc(ExprKind::App(
+        rc(ExprKind::Op(OpKind::App(
             rc(ExprKind::Builtin(Builtin::Optional)),
             make_type!($ty)
-        ))
+        )))
     };
     (List $($rest:tt)*) => {
-        rc(ExprKind::App(
+        rc(ExprKind::Op(OpKind::App(
             rc(ExprKind::Builtin(Builtin::List)),
             make_type!($($rest)*)
-        ))
+        )))
     };
     ({ $($label:ident : $ty:ident),* }) => {{
         let mut kts = DupTreeMap::new();
@@ -214,10 +214,10 @@ macro_rules! make_closure {
     };
     (List $($ty:tt)*) => {{
         let ty = make_closure!($($ty)*);
-        rc(ExprKind::App(
+        rc(ExprKind::Op(OpKind::App(
             rc(ExprKind::Builtin(Builtin::List)),
             ty
-        ))
+        )))
     }};
     (Some($($v:tt)*)) => {
         rc(ExprKind::SomeLit(
@@ -225,20 +225,20 @@ macro_rules! make_closure {
         ))
     };
     (1 + $($v:tt)*) => {
-        rc(ExprKind::BinOp(
+        rc(ExprKind::Op(OpKind::BinOp(
             BinOp::NaturalPlus,
             make_closure!($($v)*),
             rc(ExprKind::Num(NumKind::Natural(1)))
-        ))
+        )))
     };
     ([ $($head:tt)* ] # $($tail:tt)*) => {{
         let head = make_closure!($($head)*);
         let tail = make_closure!($($tail)*);
-        rc(ExprKind::BinOp(
+        rc(ExprKind::Op(OpKind::BinOp(
             BinOp::ListAppend,
             rc(ExprKind::NEListLit(vec![head])),
             tail,
-        ))
+        )))
     }};
 }
 
diff --git a/dhall/src/semantics/nze/nir.rs b/dhall/src/semantics/nze/nir.rs
index e0d227e..73c3f30 100644
--- a/dhall/src/semantics/nze/nir.rs
+++ b/dhall/src/semantics/nze/nir.rs
@@ -8,7 +8,7 @@ use crate::semantics::{
 };
 use crate::syntax::{
     BinOp, Builtin, Const, Expr, ExprKind, InterpolatedTextContents, Label,
-    NumKind, Span,
+    NumKind, OpKind, Span,
 };
 use crate::ToExprOptions;
 
@@ -190,24 +190,24 @@ impl Nir {
                 NirKind::Const(c) => ExprKind::Const(*c),
                 NirKind::BuiltinType(b) => ExprKind::Builtin(*b),
                 NirKind::Num(l) => ExprKind::Num(l.clone()),
-                NirKind::OptionalType(t) => ExprKind::App(
+                NirKind::OptionalType(t) => ExprKind::Op(OpKind::App(
                     Nir::from_builtin(Builtin::Optional).to_hir(venv),
                     t.to_hir(venv),
-                ),
-                NirKind::EmptyOptionalLit(n) => ExprKind::App(
+                )),
+                NirKind::EmptyOptionalLit(n) => ExprKind::Op(OpKind::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(
+                NirKind::ListType(t) => ExprKind::Op(OpKind::App(
                     Nir::from_builtin(Builtin::List).to_hir(venv),
                     t.to_hir(venv),
-                ),
+                )),
                 NirKind::EmptyListLit(n) => ExprKind::EmptyListLit(Hir::new(
-                    HirKind::Expr(ExprKind::App(
+                    HirKind::Expr(ExprKind::Op(OpKind::App(
                         Nir::from_builtin(Builtin::List).to_hir(venv),
                         n.to_hir(venv),
-                    )),
+                    ))),
                     Span::Artificial,
                 )),
                 NirKind::NEListLit(elts) => ExprKind::NEListLit(
@@ -229,31 +229,33 @@ impl Nir {
                         .collect(),
                 ),
                 NirKind::UnionType(kts) => map_uniontype(kts),
-                NirKind::UnionConstructor(l, kts) => ExprKind::Field(
-                    Hir::new(
-                        HirKind::Expr(map_uniontype(kts)),
-                        Span::Artificial,
-                    ),
-                    l.clone(),
-                ),
-                NirKind::UnionLit(l, v, kts) => ExprKind::App(
+                NirKind::UnionConstructor(l, kts) => {
+                    ExprKind::Op(OpKind::Field(
+                        Hir::new(
+                            HirKind::Expr(map_uniontype(kts)),
+                            Span::Artificial,
+                        ),
+                        l.clone(),
+                    ))
+                }
+                NirKind::UnionLit(l, v, kts) => ExprKind::Op(OpKind::App(
                     Hir::new(
-                        HirKind::Expr(ExprKind::Field(
+                        HirKind::Expr(ExprKind::Op(OpKind::Field(
                             Hir::new(
                                 HirKind::Expr(map_uniontype(kts)),
                                 Span::Artificial,
                             ),
                             l.clone(),
-                        )),
+                        ))),
                         Span::Artificial,
                     ),
                     v.to_hir(venv),
-                ),
-                NirKind::Equivalence(x, y) => ExprKind::BinOp(
+                )),
+                NirKind::Equivalence(x, y) => ExprKind::Op(OpKind::BinOp(
                     BinOp::Equivalence,
                     x.to_hir(venv),
                     y.to_hir(venv),
-                ),
+                )),
                 NirKind::PartialExpr(e) => e.map_ref(|v| v.to_hir(venv)),
             }),
         };
diff --git a/dhall/src/semantics/nze/normalize.rs b/dhall/src/semantics/nze/normalize.rs
index 570e106..ebf4ae1 100644
--- a/dhall/src/semantics/nze/normalize.rs
+++ b/dhall/src/semantics/nze/normalize.rs
@@ -3,7 +3,9 @@ use std::collections::HashMap;
 
 use crate::semantics::NzEnv;
 use crate::semantics::{Binder, Closure, Hir, HirKind, Nir, NirKind, TextLit};
-use crate::syntax::{BinOp, ExprKind, InterpolatedTextContents, NumKind};
+use crate::syntax::{
+    BinOp, ExprKind, InterpolatedTextContents, NumKind, OpKind,
+};
 
 pub fn apply_any(f: Nir, a: Nir) -> NirKind {
     match f.kind() {
@@ -12,7 +14,7 @@ pub fn apply_any(f: Nir, a: Nir) -> NirKind {
         NirKind::UnionConstructor(l, kts) => {
             NirKind::UnionLit(l.clone(), a, kts.clone())
         }
-        _ => NirKind::PartialExpr(ExprKind::App(f, a)),
+        _ => NirKind::PartialExpr(ExprKind::Op(OpKind::App(f, a))),
     }
 }
 
@@ -173,11 +175,11 @@ fn apply_binop<'a>(o: BinOp, x: &'a Nir, y: &'a Nir) -> Option<Ret<'a>> {
         }
         (RecursiveRecordMerge, RecordLit(kvs1), RecordLit(kvs2)) => {
             let kvs = merge_maps(kvs1, kvs2, |_, v1, v2| {
-                Nir::from_partial_expr(ExprKind::BinOp(
+                Nir::from_partial_expr(ExprKind::Op(OpKind::BinOp(
                     RecursiveRecordMerge,
                     v1.clone(),
                     v2.clone(),
-                ))
+                )))
             });
             Ret::NirKind(RecordLit(kvs))
         }
@@ -188,11 +190,11 @@ fn apply_binop<'a>(o: BinOp, x: &'a Nir, y: &'a Nir) -> Option<Ret<'a>> {
                 kts_y,
                 // If the Label exists for both records, then we hit the recursive case.
                 |_, l: &Nir, r: &Nir| {
-                    Nir::from_partial_expr(ExprKind::BinOp(
+                    Nir::from_partial_expr(ExprKind::Op(OpKind::BinOp(
                         RecursiveRecordTypeMerge,
                         l.clone(),
                         r.clone(),
-                    ))
+                    )))
                 },
             );
             Ret::NirKind(RecordType(kts))
@@ -216,7 +218,7 @@ pub fn normalize_one_layer(expr: ExprKind<Nir>, env: &NzEnv) -> NirKind {
     use NumKind::Bool;
 
     let ret = match expr {
-        ExprKind::Import(..) | ExprKind::Completion(..) => {
+        ExprKind::Import(..) | ExprKind::Op(OpKind::Completion(..)) => {
             unreachable!("This case should have been handled in resolution")
         }
         ExprKind::Var(..)
@@ -230,7 +232,7 @@ pub fn normalize_one_layer(expr: ExprKind<Nir>, env: &NzEnv) -> NirKind {
         ExprKind::Const(c) => Ret::Nir(Nir::from_const(c)),
         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::Op(OpKind::App(v, a)) => Ret::Nir(v.app(a)),
         ExprKind::Num(l) => Ret::NirKind(Num(l)),
         ExprKind::SomeLit(e) => Ret::NirKind(NEOptionalLit(e)),
         ExprKind::EmptyListLit(t) => {
@@ -261,7 +263,7 @@ pub fn normalize_one_layer(expr: ExprKind<Nir>, env: &NzEnv) -> NirKind {
                 Ret::NirKind(NirKind::TextLit(tlit))
             }
         }
-        ExprKind::BoolIf(ref b, ref e1, ref e2) => {
+        ExprKind::Op(OpKind::BoolIf(ref b, ref e1, ref e2)) => {
             match b.kind() {
                 Num(Bool(true)) => Ret::NirRef(e1),
                 Num(Bool(false)) => Ret::NirRef(e2),
@@ -275,12 +277,14 @@ pub fn normalize_one_layer(expr: ExprKind<Nir>, env: &NzEnv) -> NirKind {
                 }
             }
         }
-        ExprKind::BinOp(o, ref x, ref y) => match apply_binop(o, x, y) {
-            Some(ret) => ret,
-            None => Ret::Expr(expr),
-        },
+        ExprKind::Op(OpKind::BinOp(o, ref x, ref y)) => {
+            match apply_binop(o, x, y) {
+                Some(ret) => ret,
+                None => Ret::Expr(expr),
+            }
+        }
 
-        ExprKind::Field(ref v, ref field) => match v.kind() {
+        ExprKind::Op(OpKind::Field(ref v, ref field)) => match v.kind() {
             RecordLit(kvs) => match kvs.get(field) {
                 Some(r) => Ret::Nir(r.clone()),
                 None => Ret::Expr(expr),
@@ -288,53 +292,65 @@ pub fn normalize_one_layer(expr: ExprKind<Nir>, env: &NzEnv) -> NirKind {
             UnionType(kts) => {
                 Ret::NirKind(UnionConstructor(field.clone(), kts.clone()))
             }
-            PartialExpr(ExprKind::Projection(x, _)) => {
+            PartialExpr(ExprKind::Op(OpKind::Projection(x, _))) => {
                 return normalize_one_layer(
-                    ExprKind::Field(x.clone(), field.clone()),
+                    ExprKind::Op(OpKind::Field(x.clone(), field.clone())),
                     env,
                 )
             }
-            PartialExpr(ExprKind::BinOp(
+            PartialExpr(ExprKind::Op(OpKind::BinOp(
                 BinOp::RightBiasedRecordMerge,
                 x,
                 y,
-            )) => match (x.kind(), y.kind()) {
+            ))) => match (x.kind(), y.kind()) {
                 (_, RecordLit(kvs)) => match kvs.get(field) {
                     Some(r) => Ret::Nir(r.clone()),
                     None => {
                         return normalize_one_layer(
-                            ExprKind::Field(x.clone(), field.clone()),
+                            ExprKind::Op(OpKind::Field(
+                                x.clone(),
+                                field.clone(),
+                            )),
                             env,
                         )
                     }
                 },
                 (RecordLit(kvs), _) => match kvs.get(field) {
-                    Some(r) => Ret::Expr(ExprKind::Field(
-                        Nir::from_kind(PartialExpr(ExprKind::BinOp(
-                            BinOp::RightBiasedRecordMerge,
-                            Nir::from_kind(RecordLit(
-                                Some((field.clone(), r.clone()))
-                                    .into_iter()
-                                    .collect(),
-                            )),
-                            y.clone(),
+                    Some(r) => Ret::Expr(ExprKind::Op(OpKind::Field(
+                        Nir::from_kind(PartialExpr(ExprKind::Op(
+                            OpKind::BinOp(
+                                BinOp::RightBiasedRecordMerge,
+                                Nir::from_kind(RecordLit(
+                                    Some((field.clone(), r.clone()))
+                                        .into_iter()
+                                        .collect(),
+                                )),
+                                y.clone(),
+                            ),
                         ))),
                         field.clone(),
-                    )),
+                    ))),
                     None => {
                         return normalize_one_layer(
-                            ExprKind::Field(y.clone(), field.clone()),
+                            ExprKind::Op(OpKind::Field(
+                                y.clone(),
+                                field.clone(),
+                            )),
                             env,
                         )
                     }
                 },
                 _ => Ret::Expr(expr),
             },
-            PartialExpr(ExprKind::BinOp(BinOp::RecursiveRecordMerge, x, y)) => {
-                match (x.kind(), y.kind()) {
-                    (RecordLit(kvs), _) => match kvs.get(field) {
-                        Some(r) => Ret::Expr(ExprKind::Field(
-                            Nir::from_kind(PartialExpr(ExprKind::BinOp(
+            PartialExpr(ExprKind::Op(OpKind::BinOp(
+                BinOp::RecursiveRecordMerge,
+                x,
+                y,
+            ))) => match (x.kind(), y.kind()) {
+                (RecordLit(kvs), _) => match kvs.get(field) {
+                    Some(r) => Ret::Expr(ExprKind::Op(OpKind::Field(
+                        Nir::from_kind(PartialExpr(ExprKind::Op(
+                            OpKind::BinOp(
                                 BinOp::RecursiveRecordMerge,
                                 Nir::from_kind(RecordLit(
                                     Some((field.clone(), r.clone()))
@@ -342,19 +358,24 @@ pub fn normalize_one_layer(expr: ExprKind<Nir>, env: &NzEnv) -> NirKind {
                                         .collect(),
                                 )),
                                 y.clone(),
-                            ))),
-                            field.clone(),
-                        )),
-                        None => {
-                            return normalize_one_layer(
-                                ExprKind::Field(y.clone(), field.clone()),
-                                env,
-                            )
-                        }
-                    },
-                    (_, RecordLit(kvs)) => match kvs.get(field) {
-                        Some(r) => Ret::Expr(ExprKind::Field(
-                            Nir::from_kind(PartialExpr(ExprKind::BinOp(
+                            ),
+                        ))),
+                        field.clone(),
+                    ))),
+                    None => {
+                        return normalize_one_layer(
+                            ExprKind::Op(OpKind::Field(
+                                y.clone(),
+                                field.clone(),
+                            )),
+                            env,
+                        )
+                    }
+                },
+                (_, RecordLit(kvs)) => match kvs.get(field) {
+                    Some(r) => Ret::Expr(ExprKind::Op(OpKind::Field(
+                        Nir::from_kind(PartialExpr(ExprKind::Op(
+                            OpKind::BinOp(
                                 BinOp::RecursiveRecordMerge,
                                 x.clone(),
                                 Nir::from_kind(RecordLit(
@@ -362,52 +383,57 @@ pub fn normalize_one_layer(expr: ExprKind<Nir>, env: &NzEnv) -> NirKind {
                                         .into_iter()
                                         .collect(),
                                 )),
-                            ))),
-                            field.clone(),
-                        )),
-                        None => {
-                            return normalize_one_layer(
-                                ExprKind::Field(x.clone(), field.clone()),
-                                env,
-                            )
-                        }
-                    },
-                    _ => Ret::Expr(expr),
-                }
-            }
+                            ),
+                        ))),
+                        field.clone(),
+                    ))),
+                    None => {
+                        return normalize_one_layer(
+                            ExprKind::Op(OpKind::Field(
+                                x.clone(),
+                                field.clone(),
+                            )),
+                            env,
+                        )
+                    }
+                },
+                _ => Ret::Expr(expr),
+            },
             _ => Ret::Expr(expr),
         },
-        ExprKind::Projection(_, ref ls) if ls.is_empty() => {
+        ExprKind::Op(OpKind::Projection(_, ref ls)) if ls.is_empty() => {
             Ret::NirKind(RecordLit(HashMap::new()))
         }
-        ExprKind::Projection(ref v, ref ls) => match v.kind() {
+        ExprKind::Op(OpKind::Projection(ref v, ref ls)) => match v.kind() {
             RecordLit(kvs) => Ret::NirKind(RecordLit(
                 ls.iter()
                     .filter_map(|l| kvs.get(l).map(|x| (l.clone(), x.clone())))
                     .collect(),
             )),
-            PartialExpr(ExprKind::Projection(v2, _)) => {
+            PartialExpr(ExprKind::Op(OpKind::Projection(v2, _))) => {
                 return normalize_one_layer(
-                    ExprKind::Projection(v2.clone(), ls.clone()),
+                    ExprKind::Op(OpKind::Projection(v2.clone(), ls.clone())),
                     env,
                 )
             }
             _ => Ret::Expr(expr),
         },
-        ExprKind::ProjectionByExpr(ref v, ref t) => match t.kind() {
-            RecordType(kts) => {
-                return normalize_one_layer(
-                    ExprKind::Projection(
-                        v.clone(),
-                        kts.keys().cloned().collect(),
-                    ),
-                    env,
-                )
+        ExprKind::Op(OpKind::ProjectionByExpr(ref v, ref t)) => {
+            match t.kind() {
+                RecordType(kts) => {
+                    return normalize_one_layer(
+                        ExprKind::Op(OpKind::Projection(
+                            v.clone(),
+                            kts.keys().cloned().collect(),
+                        )),
+                        env,
+                    )
+                }
+                _ => Ret::Expr(expr),
             }
-            _ => Ret::Expr(expr),
-        },
+        }
 
-        ExprKind::Merge(ref handlers, ref variant, _) => {
+        ExprKind::Op(OpKind::Merge(ref handlers, ref variant, _)) => {
             match handlers.kind() {
                 RecordLit(kvs) => match variant.kind() {
                     UnionConstructor(l, _) => match kvs.get(l) {
@@ -431,7 +457,7 @@ pub fn normalize_one_layer(expr: ExprKind<Nir>, env: &NzEnv) -> NirKind {
                 _ => Ret::Expr(expr),
             }
         }
-        ExprKind::ToMap(ref v, ref annot) => match v.kind() {
+        ExprKind::Op(OpKind::ToMap(ref v, ref annot)) => match v.kind() {
             RecordLit(kvs) if kvs.is_empty() => {
                 match annot.as_ref().map(|v| v.kind()) {
                     Some(NirKind::ListType(t)) => {
diff --git a/dhall/src/semantics/resolve/resolve.rs b/dhall/src/semantics/resolve/resolve.rs
index 6e50fa6..3e0022f 100644
--- a/dhall/src/semantics/resolve/resolve.rs
+++ b/dhall/src/semantics/resolve/resolve.rs
@@ -11,7 +11,7 @@ use crate::syntax;
 use crate::syntax::map::DupTreeMap;
 use crate::syntax::{
     BinOp, Builtin, Expr, ExprKind, FilePath, FilePrefix, Hash, ImportMode,
-    ImportTarget, Span, UnspannedExpr, URL,
+    ImportTarget, OpKind, Span, UnspannedExpr, URL,
 };
 use crate::{Parsed, Resolved};
 
@@ -179,12 +179,13 @@ impl ImportLocation {
         };
 
         let asloc_ty = make_aslocation_uniontype();
-        let expr = mkexpr(ExprKind::Field(asloc_ty, field_name.into()));
+        let expr =
+            mkexpr(ExprKind::Op(OpKind::Field(asloc_ty, field_name.into())));
         match arg {
-            Some(arg) => mkexpr(ExprKind::App(
+            Some(arg) => mkexpr(ExprKind::Op(OpKind::App(
                 expr,
                 mkexpr(ExprKind::TextLit(arg.into())),
-            )),
+            ))),
             None => expr,
         }
     }
@@ -261,21 +262,21 @@ fn resolve_one_import(
 /// Desugar the first level of the expression.
 fn desugar(expr: &Expr) -> Cow<'_, Expr> {
     match expr.kind() {
-        ExprKind::Completion(ty, compl) => {
+        ExprKind::Op(OpKind::Completion(ty, compl)) => {
             let ty_field_default = Expr::new(
-                ExprKind::Field(ty.clone(), "default".into()),
+                ExprKind::Op(OpKind::Field(ty.clone(), "default".into())),
                 expr.span(),
             );
             let merged = Expr::new(
-                ExprKind::BinOp(
+                ExprKind::Op(OpKind::BinOp(
                     BinOp::RightBiasedRecordMerge,
                     ty_field_default,
                     compl.clone(),
-                ),
+                )),
                 expr.span(),
             );
             let ty_field_type = Expr::new(
-                ExprKind::Field(ty.clone(), "Type".into()),
+                ExprKind::Op(OpKind::Field(ty.clone(), "Type".into())),
                 expr.span(),
             );
             Cow::Owned(Expr::new(
@@ -304,7 +305,7 @@ fn traverse_resolve_expr(
                     .format(),
             )?,
         },
-        ExprKind::BinOp(BinOp::ImportAlt, l, r) => {
+        ExprKind::Op(OpKind::BinOp(BinOp::ImportAlt, l, r)) => {
             match traverse_resolve_expr(name_env, l, f) {
                 Ok(l) => l,
                 Err(_) => {
diff --git a/dhall/src/semantics/tck/typecheck.rs b/dhall/src/semantics/tck/typecheck.rs
index c3334b5..8f3fcb2 100644
--- a/dhall/src/semantics/tck/typecheck.rs
+++ b/dhall/src/semantics/tck/typecheck.rs
@@ -9,7 +9,8 @@ use crate::semantics::{
     Type,
 };
 use crate::syntax::{
-    BinOp, Builtin, Const, ExprKind, InterpolatedTextContents, NumKind, Span,
+    BinOp, Builtin, Const, ExprKind, InterpolatedTextContents, NumKind, OpKind,
+    Span,
 };
 
 fn check_rectymerge(
@@ -75,7 +76,7 @@ fn type_one_layer(
     let span_err = |msg: &str| mk_span_err(span.clone(), msg);
 
     let ty = match &ekind {
-        ExprKind::Import(..) | ExprKind::Completion(..) => {
+        ExprKind::Import(..) | ExprKind::Op(OpKind::Completion(..)) => {
             unreachable!("This case should have been handled in resolution")
         }
         ExprKind::Var(..)
@@ -222,7 +223,7 @@ fn type_one_layer(
 
             Type::from_const(k)
         }
-        ExprKind::Field(scrut, x) => {
+        ExprKind::Op(OpKind::Field(scrut, x)) => {
             match scrut.ty().kind() {
                 NirKind::RecordType(kts) => match kts.get(&x) {
                     Some(val) => Type::new_infer_universe(env, val.clone())?,
@@ -261,7 +262,7 @@ fn type_one_layer(
             }
             t
         }
-        ExprKind::App(f, arg) => {
+        ExprKind::Op(OpKind::App(f, arg)) => {
             match f.ty().kind() {
                 // TODO: store Type in closure
                 NirKind::PiClosure { annot, closure, .. } => {
@@ -309,7 +310,7 @@ fn type_one_layer(
                 ),
             }
         }
-        ExprKind::BoolIf(x, y, z) => {
+        ExprKind::Op(OpKind::BoolIf(x, y, z)) => {
             if *x.ty().kind() != NirKind::from_builtin(Builtin::Bool) {
                 return span_err("InvalidPredicate");
             }
@@ -322,7 +323,7 @@ fn type_one_layer(
 
             y.ty().clone()
         }
-        ExprKind::BinOp(BinOp::RightBiasedRecordMerge, x, y) => {
+        ExprKind::Op(OpKind::BinOp(BinOp::RightBiasedRecordMerge, x, y)) => {
             let x_type = x.ty();
             let y_type = y.ty();
 
@@ -344,22 +345,22 @@ fn type_one_layer(
             let u = max(x.ty().ty(), y.ty().ty());
             Nir::from_kind(NirKind::RecordType(kts)).to_type(u)
         }
-        ExprKind::BinOp(BinOp::RecursiveRecordMerge, x, y) => {
+        ExprKind::Op(OpKind::BinOp(BinOp::RecursiveRecordMerge, x, y)) => {
             check_rectymerge(&span, env, x.ty().to_nir(), y.ty().to_nir())?;
 
             let hir = Hir::new(
-                HirKind::Expr(ExprKind::BinOp(
+                HirKind::Expr(ExprKind::Op(OpKind::BinOp(
                     BinOp::RecursiveRecordTypeMerge,
                     x.ty().to_hir(env.as_varenv()),
                     y.ty().to_hir(env.as_varenv()),
-                )),
+                ))),
                 span.clone(),
             );
             let x_u = x.ty().ty();
             let y_u = y.ty().ty();
             Type::new(hir.eval(env), max(x_u, y_u))
         }
-        ExprKind::BinOp(BinOp::RecursiveRecordTypeMerge, x, y) => {
+        ExprKind::Op(OpKind::BinOp(BinOp::RecursiveRecordTypeMerge, x, y)) => {
             check_rectymerge(&span, env, x.eval(env), y.eval(env))?;
 
             // A RecordType's type is always a const
@@ -367,7 +368,7 @@ fn type_one_layer(
             let yk = y.ty().as_const().unwrap();
             Type::from_const(max(xk, yk))
         }
-        ExprKind::BinOp(BinOp::ListAppend, l, r) => {
+        ExprKind::Op(OpKind::BinOp(BinOp::ListAppend, l, r)) => {
             match l.ty().kind() {
                 NirKind::ListType(..) => {}
                 _ => return span_err("BinOpTypeMismatch"),
@@ -379,7 +380,7 @@ fn type_one_layer(
 
             l.ty().clone()
         }
-        ExprKind::BinOp(BinOp::Equivalence, l, r) => {
+        ExprKind::Op(OpKind::BinOp(BinOp::Equivalence, l, r)) => {
             if l.ty() != r.ty() {
                 return span_err("EquivalenceTypeMismatch");
             }
@@ -389,7 +390,7 @@ fn type_one_layer(
 
             Type::from_const(Const::Type)
         }
-        ExprKind::BinOp(o, l, r) => {
+        ExprKind::Op(OpKind::BinOp(o, l, r)) => {
             let t = Type::from_builtin(match o {
                 BinOp::BoolAnd
                 | BinOp::BoolOr
@@ -415,7 +416,7 @@ fn type_one_layer(
 
             t
         }
-        ExprKind::Merge(record, union, type_annot) => {
+        ExprKind::Op(OpKind::Merge(record, union, type_annot)) => {
             let record_type = record.ty();
             let handlers = match record_type.kind() {
                 NirKind::RecordType(kts) => kts,
@@ -554,7 +555,7 @@ fn type_one_layer(
                 (None, None) => return span_err("MergeEmptyNeedsAnnotation"),
             }
         }
-        ExprKind::ToMap(record, annot) => {
+        ExprKind::Op(OpKind::ToMap(record, annot)) => {
             if record.ty().ty().as_const() != Some(Const::Type) {
                 return span_err("`toMap` only accepts records of type `Type`");
             }
@@ -624,7 +625,7 @@ fn type_one_layer(
                 output_type
             }
         }
-        ExprKind::Projection(record, labels) => {
+        ExprKind::Op(OpKind::Projection(record, labels)) => {
             let record_type = record.ty();
             let kts = match record_type.kind() {
                 NirKind::RecordType(kts) => kts,
@@ -652,7 +653,7 @@ fn type_one_layer(
                 Nir::from_kind(NirKind::RecordType(new_kts)),
             )?
         }
-        ExprKind::ProjectionByExpr(record, selection) => {
+        ExprKind::Op(OpKind::ProjectionByExpr(record, selection)) => {
             let record_type = record.ty();
             let rec_kts = match record_type.kind() {
                 NirKind::RecordType(kts) => kts,
diff --git a/dhall/src/syntax/ast/expr.rs b/dhall/src/syntax/ast/expr.rs
index 9e935dc..51426ce 100644
--- a/dhall/src/syntax/ast/expr.rs
+++ b/dhall/src/syntax/ast/expr.rs
@@ -126,63 +126,73 @@ pub enum NumKind {
     Double(Double),
 }
 
+/// Operations
+#[derive(Debug, Clone, PartialEq, Eq, PartialOrd, Ord, Hash)]
+pub enum OpKind<SubExpr> {
+    ///  `f a`
+    App(SubExpr, SubExpr),
+    /// Binary operations
+    BinOp(BinOp, SubExpr, SubExpr),
+    ///  `if x then y else z`
+    BoolIf(SubExpr, SubExpr, SubExpr),
+    ///  `merge x y : t`
+    Merge(SubExpr, SubExpr, Option<SubExpr>),
+    ///  `toMap x : t`
+    ToMap(SubExpr, Option<SubExpr>),
+    ///  `e.x`
+    Field(SubExpr, Label),
+    ///  `e.{ x, y, z }`
+    Projection(SubExpr, DupTreeSet<Label>),
+    ///  `e.(t)`
+    ProjectionByExpr(SubExpr, SubExpr),
+    ///  `x::y`
+    Completion(SubExpr, SubExpr),
+}
+
 /// Syntax tree for expressions
 // Having the recursion out of the enum definition enables writing
 // much more generic code and improves pattern-matching behind
 // smart pointers.
 #[derive(Debug, Clone, PartialEq, Eq, Hash)]
 pub enum ExprKind<SubExpr> {
+    /// `Type`, `Kind` and `Sort`
     Const(Const),
+    /// Numbers and booleans
     Num(NumKind),
-    ///  `x`
-    ///  `x@n`
-    Var(V),
-    ///  `λ(x : A) -> b`
-    Lam(Label, SubExpr, SubExpr),
-    ///  `A -> B`
-    ///  `∀(x : A) -> B`
-    Pi(Label, SubExpr, SubExpr),
-    ///  `f a`
-    App(SubExpr, SubExpr),
-    ///  `let x     = r in e`
-    ///  `let x : t = r in e`
-    Let(Label, Option<SubExpr>, SubExpr, SubExpr),
-    ///  `x : t`
-    Annot(SubExpr, SubExpr),
-    ///  `assert : t`
-    Assert(SubExpr),
-    /// Built-in values
+    /// Built-in functions and types
     Builtin(Builtin),
-    // Binary operations
-    BinOp(BinOp, SubExpr, SubExpr),
-    ///  `if x then y else z`
-    BoolIf(SubExpr, SubExpr, SubExpr),
+    ///  `Some e`
+    SomeLit(SubExpr),
     ///  `"Some ${interpolated} text"`
     TextLit(InterpolatedText<SubExpr>),
     ///  `[] : t`
     EmptyListLit(SubExpr),
     ///  `[x, y, z]`
     NEListLit(Vec<SubExpr>),
-    ///  `Some e`
-    SomeLit(SubExpr),
     ///  `{ k1 : t1, k2 : t1 }`
     RecordType(DupTreeMap<Label, SubExpr>),
     ///  `{ k1 = v1, k2 = v2 }`
     RecordLit(BTreeMap<Label, SubExpr>),
     ///  `< k1 : t1, k2 >`
     UnionType(DupTreeMap<Label, Option<SubExpr>>),
-    ///  `merge x y : t`
-    Merge(SubExpr, SubExpr, Option<SubExpr>),
-    ///  `toMap x : t`
-    ToMap(SubExpr, Option<SubExpr>),
-    ///  `e.x`
-    Field(SubExpr, Label),
-    ///  `e.{ x, y, z }`
-    Projection(SubExpr, DupTreeSet<Label>),
-    ///  `e.(t)`
-    ProjectionByExpr(SubExpr, SubExpr),
-    ///  `x::y`
-    Completion(SubExpr, SubExpr),
+
+    ///  `x`, `x@n`
+    Var(V),
+    ///  `λ(x : A) -> b`
+    Lam(Label, SubExpr, SubExpr),
+    ///  `A -> B`, `∀(x : A) -> B`
+    Pi(Label, SubExpr, SubExpr),
+    ///  `let x : t = r in e`
+    Let(Label, Option<SubExpr>, SubExpr, SubExpr),
+
+    /// Operations
+    Op(OpKind<SubExpr>),
+
+    ///  `x : t`
+    Annot(SubExpr, SubExpr),
+    ///  `assert : t`
+    Assert(SubExpr),
+
     /// `./some/path`
     Import(Import<SubExpr>),
 }
@@ -239,6 +249,45 @@ impl<SE> ExprKind<SE> {
     }
 }
 
+impl<SE> OpKind<SE> {
+    pub fn traverse_ref<'a, SE2, Err>(
+        &'a self,
+        mut f: impl FnMut(&'a SE) -> Result<SE2, Err>,
+    ) -> Result<OpKind<SE2>, Err> {
+        // Can't use closures because of borrowing rules
+        macro_rules! expr {
+            ($e:expr) => {
+                f($e)?
+            };
+        }
+        macro_rules! opt {
+            ($e:expr) => {
+                $e.as_ref().map(|e| Ok(expr!(e))).transpose()?
+            };
+        }
+
+        use OpKind::*;
+        Ok(match self {
+            App(f, a) => App(expr!(f), expr!(a)),
+            BinOp(o, x, y) => BinOp(*o, expr!(x), expr!(y)),
+            BoolIf(b, t, f) => BoolIf(expr!(b), expr!(t), expr!(f)),
+            Merge(x, y, t) => Merge(expr!(x), expr!(y), opt!(t)),
+            ToMap(x, t) => ToMap(expr!(x), opt!(t)),
+            Field(e, l) => Field(expr!(e), l.clone()),
+            Projection(e, ls) => Projection(expr!(e), ls.clone()),
+            ProjectionByExpr(e, x) => ProjectionByExpr(expr!(e), expr!(x)),
+            Completion(e, x) => Completion(expr!(e), expr!(x)),
+        })
+    }
+
+    pub fn map_ref<'a, SE2>(
+        &'a self,
+        mut f: impl FnMut(&'a SE) -> SE2,
+    ) -> OpKind<SE2> {
+        trivial_result(self.traverse_ref(|x| Ok(f(x))))
+    }
+}
+
 impl Expr {
     pub fn as_ref(&self) -> &UnspannedExpr {
         &self.kind
diff --git a/dhall/src/syntax/ast/visitor.rs b/dhall/src/syntax/ast/visitor.rs
index 0a0c5ef..7244d0a 100644
--- a/dhall/src/syntax/ast/visitor.rs
+++ b/dhall/src/syntax/ast/visitor.rs
@@ -1,22 +1,13 @@
+use itertools::Itertools;
 use std::iter::FromIterator;
 
 use crate::syntax::*;
 
-fn vec<'a, T, U, Err>(
-    x: &'a [T],
-    f: impl FnMut(&'a T) -> Result<U, Err>,
-) -> Result<Vec<U>, Err> {
-    x.iter().map(f).collect()
-}
-
 fn opt<'a, T, U, Err>(
     x: &'a Option<T>,
     f: impl FnOnce(&'a T) -> Result<U, Err>,
 ) -> Result<Option<U>, Err> {
-    Ok(match x {
-        Some(x) => Some(f(x)?),
-        None => None,
-    })
+    x.as_ref().map(f).transpose()
 }
 
 fn dupmap<'a, SE1, SE2, T, Err>(
@@ -30,27 +21,6 @@ where
     x.into_iter().map(|(k, x)| Ok((k.clone(), f(x)?))).collect()
 }
 
-fn optdupmap<'a, SE1, SE2, T, Err>(
-    x: impl IntoIterator<Item = (&'a Label, &'a Option<SE1>)>,
-    mut f: impl FnMut(&'a SE1) -> Result<SE2, Err>,
-) -> Result<T, Err>
-where
-    SE1: 'a,
-    T: FromIterator<(Label, Option<SE2>)>,
-{
-    x.into_iter()
-        .map(|(k, x)| {
-            Ok((
-                k.clone(),
-                match x {
-                    Some(x) => Some(f(x)?),
-                    None => None,
-                },
-            ))
-        })
-        .collect()
-}
-
 pub fn visit_ref<'a, F, SE1, SE2, Err>(
     input: &'a ExprKind<SE1>,
     mut f: F,
@@ -60,54 +30,44 @@ where
 {
     // Can't use closures because of borrowing rules
     macro_rules! expr {
+        () => {
+            |e| Ok(expr!(e))
+        };
         ($e:expr) => {
-            f(None, $e)
+            f(None, $e)?
         };
         ($l:expr, $e:expr) => {
-            f(Some($l), $e)
+            f(Some($l), $e)?
+        };
+    }
+    macro_rules! opt {
+        () => {
+            |e| Ok(opt!(e))
+        };
+        ($e:expr) => {
+            opt($e, |e| Ok(expr!(e)))?
         };
     }
 
     use crate::syntax::ExprKind::*;
     Ok(match input {
         Var(v) => Var(v.clone()),
-        Lam(l, t, e) => {
-            let t = expr!(t)?;
-            let e = expr!(l, e)?;
-            Lam(l.clone(), t, e)
-        }
-        Pi(l, t, e) => {
-            let t = expr!(t)?;
-            let e = expr!(l, e)?;
-            Pi(l.clone(), t, e)
-        }
-        Let(l, t, a, e) => {
-            let t = opt(t, &mut |e| expr!(e))?;
-            let a = expr!(a)?;
-            let e = expr!(l, e)?;
-            Let(l.clone(), t, a, e)
-        }
-        App(f, a) => App(expr!(f)?, expr!(a)?),
-        Annot(x, t) => Annot(expr!(x)?, expr!(t)?),
+        Lam(l, t, e) => Lam(l.clone(), expr!(t), expr!(l, e)),
+        Pi(l, t, e) => Pi(l.clone(), expr!(t), expr!(l, e)),
+        Let(l, t, a, e) => Let(l.clone(), opt!(t), expr!(a), expr!(l, e)),
         Const(k) => Const(*k),
-        Builtin(v) => Builtin(*v),
         Num(n) => Num(n.clone()),
-        TextLit(t) => TextLit(t.traverse_ref(|e| expr!(e))?),
-        BinOp(o, x, y) => BinOp(*o, expr!(x)?, expr!(y)?),
-        BoolIf(b, t, f) => BoolIf(expr!(b)?, expr!(t)?, expr!(f)?),
-        EmptyListLit(t) => EmptyListLit(expr!(t)?),
-        NEListLit(es) => NEListLit(vec(es, |e| expr!(e))?),
-        SomeLit(e) => SomeLit(expr!(e)?),
-        RecordType(kts) => RecordType(dupmap(kts, |e| expr!(e))?),
-        RecordLit(kvs) => RecordLit(dupmap(kvs, |e| expr!(e))?),
-        UnionType(kts) => UnionType(optdupmap(kts, |e| expr!(e))?),
-        Merge(x, y, t) => Merge(expr!(x)?, expr!(y)?, opt(t, |e| expr!(e))?),
-        ToMap(x, t) => ToMap(expr!(x)?, opt(t, |e| expr!(e))?),
-        Field(e, l) => Field(expr!(e)?, l.clone()),
-        Projection(e, ls) => Projection(expr!(e)?, ls.clone()),
-        ProjectionByExpr(e, x) => ProjectionByExpr(expr!(e)?, expr!(x)?),
-        Completion(e, x) => Completion(expr!(e)?, expr!(x)?),
-        Assert(e) => Assert(expr!(e)?),
-        Import(i) => Import(i.traverse_ref(|e| expr!(e))?),
+        Builtin(v) => Builtin(*v),
+        TextLit(t) => TextLit(t.traverse_ref(expr!())?),
+        SomeLit(e) => SomeLit(expr!(e)),
+        EmptyListLit(t) => EmptyListLit(expr!(t)),
+        NEListLit(es) => NEListLit(es.iter().map(expr!()).try_collect()?),
+        RecordType(kts) => RecordType(dupmap(kts, expr!())?),
+        RecordLit(kvs) => RecordLit(dupmap(kvs, expr!())?),
+        UnionType(kts) => UnionType(dupmap(kts, opt!())?),
+        Op(op) => Op(op.traverse_ref(expr!())?),
+        Annot(x, t) => Annot(expr!(x), expr!(t)),
+        Assert(e) => Assert(expr!(e)),
+        Import(i) => Import(i.traverse_ref(expr!())?),
     })
 }
diff --git a/dhall/src/syntax/binary/decode.rs b/dhall/src/syntax/binary/decode.rs
index 3c93419..b183f6c 100644
--- a/dhall/src/syntax/binary/decode.rs
+++ b/dhall/src/syntax/binary/decode.rs
@@ -6,7 +6,7 @@ use crate::error::DecodeError;
 use crate::syntax;
 use crate::syntax::{
     Expr, ExprKind, FilePath, FilePrefix, Hash, ImportMode, ImportTarget,
-    Integer, InterpolatedText, Label, Natural, NumKind, Scheme, Span,
+    Integer, InterpolatedText, Label, Natural, NumKind, OpKind, Scheme, Span,
     UnspannedExpr, URL, V,
 };
 type DecodedExpr = Expr;
@@ -27,6 +27,7 @@ fn cbor_value_to_dhall(data: &cbor::Value) -> Result<DecodedExpr, DecodeError> {
     use cbor::Value::*;
     use syntax::{BinOp, Builtin, Const};
     use ExprKind::*;
+    use OpKind::*;
     Ok(rc(match data {
         String(s) => match Builtin::parse(s) {
             Some(b) => ExprKind::Builtin(b),
@@ -66,7 +67,7 @@ fn cbor_value_to_dhall(data: &cbor::Value) -> Result<DecodedExpr, DecodeError> {
                 let mut f = cbor_value_to_dhall(&f)?;
                 for a in args {
                     let a = cbor_value_to_dhall(&a)?;
-                    f = rc(App(f, a))
+                    f = rc(Op(App(f, a)))
                 }
                 return Ok(f);
             }
@@ -105,7 +106,7 @@ fn cbor_value_to_dhall(data: &cbor::Value) -> Result<DecodedExpr, DecodeError> {
             [U64(3), U64(13), x, y] => {
                 let x = cbor_value_to_dhall(&x)?;
                 let y = cbor_value_to_dhall(&y)?;
-                Completion(x, y)
+                Op(Completion(x, y))
             }
             [U64(3), U64(n), x, y] => {
                 let x = cbor_value_to_dhall(&x)?;
@@ -131,11 +132,14 @@ fn cbor_value_to_dhall(data: &cbor::Value) -> Result<DecodedExpr, DecodeError> {
                         ))
                     }
                 };
-                BinOp(op, x, y)
+                Op(BinOp(op, x, y))
             }
             [U64(4), t] => {
                 let t = cbor_value_to_dhall(&t)?;
-                EmptyListLit(rc(App(rc(ExprKind::Builtin(Builtin::List)), t)))
+                EmptyListLit(rc(Op(App(
+                    rc(ExprKind::Builtin(Builtin::List)),
+                    t,
+                ))))
             }
             [U64(4), Null, rest @ ..] => {
                 let rest = rest
@@ -151,26 +155,26 @@ fn cbor_value_to_dhall(data: &cbor::Value) -> Result<DecodedExpr, DecodeError> {
             // Old-style optional literals
             [U64(5), t] => {
                 let t = cbor_value_to_dhall(&t)?;
-                App(rc(ExprKind::Builtin(Builtin::OptionalNone)), t)
+                Op(App(rc(ExprKind::Builtin(Builtin::OptionalNone)), t))
             }
             [U64(5), t, x] => {
                 let x = cbor_value_to_dhall(&x)?;
                 let t = cbor_value_to_dhall(&t)?;
                 Annot(
                     rc(SomeLit(x)),
-                    rc(App(rc(ExprKind::Builtin(Builtin::Optional)), t)),
+                    rc(Op(App(rc(ExprKind::Builtin(Builtin::Optional)), t))),
                 )
             }
             [U64(6), x, y] => {
                 let x = cbor_value_to_dhall(&x)?;
                 let y = cbor_value_to_dhall(&y)?;
-                Merge(x, y, None)
+                Op(Merge(x, y, None))
             }
             [U64(6), x, y, z] => {
                 let x = cbor_value_to_dhall(&x)?;
                 let y = cbor_value_to_dhall(&y)?;
                 let z = cbor_value_to_dhall(&z)?;
-                Merge(x, y, Some(z))
+                Op(Merge(x, y, Some(z)))
             }
             [U64(7), Object(map)] => {
                 let map = cbor_map_to_dhall_map(map)?;
@@ -183,13 +187,13 @@ fn cbor_value_to_dhall(data: &cbor::Value) -> Result<DecodedExpr, DecodeError> {
             [U64(9), x, String(l)] => {
                 let x = cbor_value_to_dhall(&x)?;
                 let l = Label::from(l.as_str());
-                Field(x, l)
+                Op(Field(x, l))
             }
             [U64(10), x, Array(arr)] => {
                 let x = cbor_value_to_dhall(&x)?;
                 if let [y] = arr.as_slice() {
                     let y = cbor_value_to_dhall(&y)?;
-                    ProjectionByExpr(x, y)
+                    Op(ProjectionByExpr(x, y))
                 } else {
                     return Err(DecodeError::WrongFormatError(
                         "projection-by-expr".to_owned(),
@@ -207,7 +211,7 @@ fn cbor_value_to_dhall(data: &cbor::Value) -> Result<DecodedExpr, DecodeError> {
                         )),
                     })
                     .collect::<Result<_, _>>()?;
-                Projection(x, labels)
+                Op(Projection(x, labels))
             }
             [U64(11), Object(map)] => {
                 let map = cbor_map_to_dhall_opt_map(map)?;
@@ -222,7 +226,7 @@ fn cbor_value_to_dhall(data: &cbor::Value) -> Result<DecodedExpr, DecodeError> {
                 let x = cbor_value_to_dhall(&x)?;
                 let y = cbor_value_to_dhall(&y)?;
                 let z = cbor_value_to_dhall(&z)?;
-                BoolIf(x, y, z)
+                Op(BoolIf(x, y, z))
             }
             [U64(15), U64(x)] => Num(NumKind::Natural(*x as Natural)),
             [U64(16), U64(x)] => Num(NumKind::Integer(*x as Integer)),
@@ -416,12 +420,12 @@ fn cbor_value_to_dhall(data: &cbor::Value) -> Result<DecodedExpr, DecodeError> {
             }
             [U64(27), x] => {
                 let x = cbor_value_to_dhall(&x)?;
-                ToMap(x, None)
+                Op(ToMap(x, None))
             }
             [U64(27), x, y] => {
                 let x = cbor_value_to_dhall(&x)?;
                 let y = cbor_value_to_dhall(&y)?;
-                ToMap(x, Some(y))
+                Op(ToMap(x, Some(y)))
             }
             [U64(28), x] => {
                 let x = cbor_value_to_dhall(&x)?;
diff --git a/dhall/src/syntax/binary/encode.rs b/dhall/src/syntax/binary/encode.rs
index 8d22a9b..f2bc6f1 100644
--- a/dhall/src/syntax/binary/encode.rs
+++ b/dhall/src/syntax/binary/encode.rs
@@ -7,7 +7,7 @@ use crate::syntax;
 use crate::syntax::map::DupTreeMap;
 use crate::syntax::{
     Expr, ExprKind, FilePrefix, Hash, Import, ImportMode, ImportTarget, Label,
-    Scheme, V,
+    OpKind, Scheme, V,
 };
 
 pub fn encode(expr: &Expr) -> Result<Vec<u8>, EncodeError> {
@@ -49,6 +49,7 @@ where
     use syntax::Builtin;
     use syntax::ExprKind::*;
     use syntax::NumKind::*;
+    use syntax::OpKind::*;
 
     use self::Serialize::{RecordDupMap, RecordMap, UnionMap};
     fn expr(x: &Expr) -> self::Serialize<'_> {
@@ -70,7 +71,9 @@ where
             let n: f64 = (*n).into();
             ser.serialize_f64(n)
         }
-        BoolIf(x, y, z) => ser_seq!(ser; tag(14), expr(x), expr(y), expr(z)),
+        Op(BoolIf(x, y, z)) => {
+            ser_seq!(ser; tag(14), expr(x), expr(y), expr(z))
+        }
         Var(V(l, n)) if l == &"_".into() => ser.serialize_u64(*n as u64),
         Var(V(l, n)) => ser_seq!(ser; label(l), U64(*n as u64)),
         Lam(l, x, y) if l == &"_".into() => {
@@ -99,7 +102,7 @@ where
             ser_seq.serialize_element(&expr(bound_e))?;
             ser_seq.end()
         }
-        App(_, _) => {
+        Op(App(_, _)) => {
             let (f, args) = collect_nested_applications(e);
             ser.collect_seq(
                 once(tag(0))
@@ -111,7 +114,7 @@ where
         Assert(x) => ser_seq!(ser; tag(19), expr(x)),
         SomeLit(x) => ser_seq!(ser; tag(5), null(), expr(x)),
         EmptyListLit(x) => match x.as_ref() {
-            App(f, a) => match f.as_ref() {
+            Op(App(f, a)) => match f.as_ref() {
                 ExprKind::Builtin(Builtin::List) => {
                     ser_seq!(ser; tag(4), expr(a))
                 }
@@ -132,8 +135,8 @@ where
         RecordType(map) => ser_seq!(ser; tag(7), RecordDupMap(map)),
         RecordLit(map) => ser_seq!(ser; tag(8), RecordMap(map)),
         UnionType(map) => ser_seq!(ser; tag(11), UnionMap(map)),
-        Field(x, l) => ser_seq!(ser; tag(9), expr(x), label(l)),
-        BinOp(op, x, y) => {
+        Op(Field(x, l)) => ser_seq!(ser; tag(9), expr(x), label(l)),
+        Op(BinOp(op, x, y)) => {
             use syntax::BinOp::*;
             let op = match op {
                 BoolOr => 0,
@@ -152,21 +155,23 @@ where
             };
             ser_seq!(ser; tag(3), U64(op), expr(x), expr(y))
         }
-        Merge(x, y, None) => ser_seq!(ser; tag(6), expr(x), expr(y)),
-        Merge(x, y, Some(z)) => {
+        Op(Merge(x, y, None)) => ser_seq!(ser; tag(6), expr(x), expr(y)),
+        Op(Merge(x, y, Some(z))) => {
             ser_seq!(ser; tag(6), expr(x), expr(y), expr(z))
         }
-        ToMap(x, None) => ser_seq!(ser; tag(27), expr(x)),
-        ToMap(x, Some(y)) => ser_seq!(ser; tag(27), expr(x), expr(y)),
-        Projection(x, ls) => ser.collect_seq(
+        Op(ToMap(x, None)) => ser_seq!(ser; tag(27), expr(x)),
+        Op(ToMap(x, Some(y))) => ser_seq!(ser; tag(27), expr(x), expr(y)),
+        Op(Projection(x, ls)) => ser.collect_seq(
             once(tag(10))
                 .chain(once(expr(x)))
                 .chain(ls.iter().map(label)),
         ),
-        ProjectionByExpr(x, y) => {
+        Op(ProjectionByExpr(x, y)) => {
             ser_seq!(ser; tag(10), expr(x), vec![expr(y)])
         }
-        Completion(x, y) => ser_seq!(ser; tag(3), tag(13), expr(x), expr(y)),
+        Op(Completion(x, y)) => {
+            ser_seq!(ser; tag(3), tag(13), expr(x), expr(y))
+        }
         Import(import) => serialize_import(ser, import),
     }
 }
@@ -286,7 +291,7 @@ impl<'a> serde::ser::Serialize for Serialize<'a> {
 fn collect_nested_applications<'a>(e: &'a Expr) -> (&'a Expr, Vec<&'a Expr>) {
     fn go<'a>(e: &'a Expr, vec: &mut Vec<&'a Expr>) -> &'a Expr {
         match e.as_ref() {
-            ExprKind::App(f, a) => {
+            ExprKind::Op(OpKind::App(f, a)) => {
                 vec.push(a);
                 go(f, vec)
             }
diff --git a/dhall/src/syntax/text/parser.rs b/dhall/src/syntax/text/parser.rs
index 6f5949f..ab9bc24 100644
--- a/dhall/src/syntax/text/parser.rs
+++ b/dhall/src/syntax/text/parser.rs
@@ -10,6 +10,7 @@ use pest_consume::{match_nodes, Parser};
 use crate::syntax::map::{DupTreeMap, DupTreeSet};
 use crate::syntax::ExprKind::*;
 use crate::syntax::NumKind::*;
+use crate::syntax::OpKind::*;
 use crate::syntax::{
     Double, Expr, FilePath, FilePrefix, Hash, ImportMode, ImportTarget,
     Integer, InterpolatedText, InterpolatedTextContents, Label, NaiveDouble,
@@ -138,7 +139,7 @@ fn insert_recordlit_entry(map: &mut BTreeMap<Label, Expr>, l: Label, e: Expr) {
             let dummy = Expr::new(Num(Bool(false)), Span::Artificial);
             let other = entry.insert(dummy);
             entry.insert(Expr::new(
-                BinOp(RecursiveRecordMerge, other, e),
+                Op(BinOp(RecursiveRecordMerge, other, e)),
                 Span::DuplicateRecordFieldsSugar,
             ));
         }
@@ -151,13 +152,16 @@ fn desugar_with_expr(x: Expr, labels: &[Label], y: Expr) -> Expr {
     match labels {
         [] => y,
         [l, rest @ ..] => {
-            let res =
-                desugar_with_expr(expr(Field(x.clone(), l.clone())), rest, y);
-            expr(BinOp(
+            let res = desugar_with_expr(
+                expr(Op(Field(x.clone(), l.clone()))),
+                rest,
+                y,
+            );
+            expr(Op(BinOp(
                 RightBiasedRecordMerge,
                 x,
                 expr(RecordLit(once((l.clone(), res)).collect())),
-            ))
+            )))
         }
     }
 }
@@ -725,7 +729,7 @@ impl DhallParser {
             },
             [if_(()), expression(cond), expression(left),
                     expression(right)] => {
-                spanned(input, BoolIf(cond, left, right))
+                spanned(input, Op(BoolIf(cond, left, right)))
             },
             [let_binding(bindings).., expression(final_expr)] => {
                 bindings.rev().fold(
@@ -747,13 +751,13 @@ impl DhallParser {
                 spanned(input, Pi("_".into(), typ, body))
             },
             [merge(()), expression(x), expression(y), expression(z)] => {
-                spanned(input, Merge(x, y, Some(z)))
+                spanned(input, Op(Merge(x, y, Some(z))))
             },
             [assert(()), expression(x)] => {
                 spanned(input, Assert(x))
             },
             [toMap(()), expression(x), expression(y)] => {
-                spanned(input, ToMap(x, Some(y)))
+                spanned(input, Op(ToMap(x, Some(y))))
             },
             [expression(e), expression(annot)] => {
                 spanned(input, Annot(e, annot))
@@ -801,7 +805,7 @@ impl DhallParser {
             }
         };
 
-        Ok(spanned_union(l.span(), r.span(), BinOp(op, l, r)))
+        Ok(spanned_union(l.span(), r.span(), Op(BinOp(op, l, r))))
     }
 
     fn Some_(_input: ParseInput) -> ParseResult<()> {
@@ -840,7 +844,7 @@ impl DhallParser {
                         spanned_union(
                             acc.span(),
                             e.span(),
-                            App(acc, e)
+                            Op(App(acc, e))
                         )
                     }
                 )
@@ -855,10 +859,10 @@ impl DhallParser {
                 spanned(input, SomeLit(e))
             },
             [merge(()), expression(x), expression(y)] => {
-                spanned(input, Merge(x, y, None))
+                spanned(input, Op(Merge(x, y, None)))
             },
             [toMap(()), expression(x)] => {
-                spanned(input, ToMap(x, None))
+                spanned(input, Op(ToMap(x, None)))
             },
             [expression(e)] => e,
         ))
@@ -875,7 +879,7 @@ impl DhallParser {
                         spanned_union(
                             acc.span(),
                             e.span(),
-                            Completion(acc, e),
+                            Op(Completion(acc, e)),
                         )
                     }
                 )
@@ -895,9 +899,9 @@ impl DhallParser {
                             acc.span(),
                             e.1,
                             match e.0 {
-                                Selector::Field(l) => Field(acc, l),
-                                Selector::Projection(ls) => Projection(acc, ls),
-                                Selector::ProjectionByExpr(e) => ProjectionByExpr(acc, e)
+                                Selector::Field(l) => Op(Field(acc, l)),
+                                Selector::Projection(ls) => Op(Projection(acc, ls)),
+                                Selector::ProjectionByExpr(e) => Op(ProjectionByExpr(acc, e))
                             }
                         )
                     }
diff --git a/dhall/src/syntax/text/printer.rs b/dhall/src/syntax/text/printer.rs
index 378f408..d655489 100644
--- a/dhall/src/syntax/text/printer.rs
+++ b/dhall/src/syntax/text/printer.rs
@@ -5,14 +5,15 @@ use std::fmt::{self, Display};
 // There is a one-to-one correspondence between the formatter and the grammar. Each phase is
 // named after a corresponding grammar group, and the structure of the formatter reflects
 // the relationship between the corresponding grammar rules. This leads to the nice property
-// of automatically getting all the parentheses and precedences right.
+// of automatically getting all the parentheses and precedences right (in a manner dual do Pratt
+// parsing).
 #[derive(Debug, Copy, Clone, Ord, PartialOrd, Eq, PartialEq)]
 enum PrintPhase {
     // `expression`
     Base,
     // `operator-expression`
     Operator,
-    // All the operator `*-expression`s
+    // All the `<operator>-expression`s
     BinOp(ast::BinOp),
     // `application-expression`
     App,
@@ -37,6 +38,7 @@ impl UnspannedExpr {
     // Annotate subexpressions with the appropriate phase, defaulting to Base
     fn annotate_with_phases(&self) -> ExprKind<PhasedExpr<'_>> {
         use crate::syntax::ExprKind::*;
+        use crate::syntax::OpKind::*;
         use PrintPhase::*;
         let with_base = self.map_ref(|e| PhasedExpr(e, Base));
         match with_base {
@@ -47,31 +49,33 @@ impl UnspannedExpr {
                     Pi(a, b, c)
                 }
             }
-            Merge(a, b, c) => Merge(
+            Op(Merge(a, b, c)) => Op(Merge(
                 a.phase(PrintPhase::Import),
                 b.phase(PrintPhase::Import),
                 c.map(|x| x.phase(PrintPhase::App)),
-            ),
-            ToMap(a, b) => ToMap(
+            )),
+            Op(ToMap(a, b)) => Op(ToMap(
                 a.phase(PrintPhase::Import),
                 b.map(|x| x.phase(PrintPhase::App)),
-            ),
+            )),
             Annot(a, b) => Annot(a.phase(Operator), b),
-            ExprKind::BinOp(op, a, b) => ExprKind::BinOp(
+            Op(OpKind::BinOp(op, a, b)) => Op(OpKind::BinOp(
                 op,
                 a.phase(PrintPhase::BinOp(op)),
                 b.phase(PrintPhase::BinOp(op)),
-            ),
+            )),
             SomeLit(e) => SomeLit(e.phase(PrintPhase::Import)),
-            ExprKind::App(f, a) => ExprKind::App(
+            Op(OpKind::App(f, a)) => Op(OpKind::App(
                 f.phase(PrintPhase::App),
                 a.phase(PrintPhase::Import),
-            ),
-            Field(a, b) => Field(a.phase(Primitive), b),
-            Projection(e, ls) => Projection(e.phase(Primitive), ls),
-            ProjectionByExpr(a, b) => ProjectionByExpr(a.phase(Primitive), b),
-            Completion(a, b) => {
-                Completion(a.phase(Primitive), b.phase(Primitive))
+            )),
+            Op(Field(a, b)) => Op(Field(a.phase(Primitive), b)),
+            Op(Projection(e, ls)) => Op(Projection(e.phase(Primitive), ls)),
+            Op(ProjectionByExpr(a, b)) => {
+                Op(ProjectionByExpr(a.phase(Primitive), b))
+            }
+            Op(Completion(a, b)) => {
+                Op(Completion(a.phase(Primitive), b.phase(Primitive)))
             }
             ExprKind::Import(a) => {
                 ExprKind::Import(a.map_ref(|x| x.phase(PrintPhase::Import)))
@@ -86,21 +90,23 @@ impl UnspannedExpr {
         phase: PrintPhase,
     ) -> Result<(), fmt::Error> {
         use crate::syntax::ExprKind::*;
+        use crate::syntax::OpKind::*;
 
         let needs_paren = match self {
             Lam(_, _, _)
-            | BoolIf(_, _, _)
             | Pi(_, _, _)
             | Let(_, _, _, _)
-            | EmptyListLit(_)
             | SomeLit(_)
-            | Merge(_, _, _)
-            | ToMap(_, _)
+            | EmptyListLit(_)
+            | Op(BoolIf(_, _, _))
+            | Op(Merge(_, _, _))
+            | Op(ToMap(_, _))
             | Annot(_, _) => phase > PrintPhase::Base,
-            // Precedence is magically handled by the ordering of BinOps.
-            ExprKind::BinOp(op, _, _) => phase > PrintPhase::BinOp(*op),
-            ExprKind::App(_, _) => phase > PrintPhase::App,
-            Completion(_, _) => phase > PrintPhase::Import,
+            // Precedence is magically handled by the ordering of BinOps. This is reverse Pratt
+            // parsing.
+            Op(BinOp(op, _, _)) => phase > PrintPhase::BinOp(*op),
+            Op(App(_, _)) => phase > PrintPhase::App,
+            Op(Completion(_, _)) => phase > PrintPhase::Import,
             _ => false,
         };
 
@@ -143,12 +149,10 @@ impl<SE: Display + Clone> Display for ExprKind<SE> {
     fn fmt(&self, f: &mut fmt::Formatter) -> Result<(), fmt::Error> {
         use crate::syntax::ExprKind::*;
         match self {
+            Var(a) => a.fmt(f)?,
             Lam(a, b, c) => {
                 write!(f, "λ({} : {}) → {}", a, b, c)?;
             }
-            BoolIf(a, b, c) => {
-                write!(f, "if {} then {} else {}", a, b, c)?;
-            }
             Pi(a, b, c) if &String::from(a) == "_" => {
                 write!(f, "{} → {}", b, c)?;
             }
@@ -162,14 +166,62 @@ impl<SE: Display + Clone> Display for ExprKind<SE> {
                 }
                 write!(f, " = {} in {}", c, d)?;
             }
+            Const(k) => k.fmt(f)?,
+            Builtin(v) => v.fmt(f)?,
+            Num(a) => a.fmt(f)?,
+            TextLit(a) => a.fmt(f)?,
+            SomeLit(e) => {
+                write!(f, "Some {}", e)?;
+            }
             EmptyListLit(t) => {
                 write!(f, "[] : {}", t)?;
             }
             NEListLit(es) => {
                 fmt_list("[", ", ", "]", es, f, Display::fmt)?;
             }
-            SomeLit(e) => {
-                write!(f, "Some {}", e)?;
+            RecordLit(a) if a.is_empty() => f.write_str("{=}")?,
+            RecordLit(a) => fmt_list("{ ", ", ", " }", a, f, |(k, v), f| {
+                write!(f, "{} = {}", k, v)
+            })?,
+            RecordType(a) if a.is_empty() => f.write_str("{}")?,
+            RecordType(a) => fmt_list("{ ", ", ", " }", a, f, |(k, t), f| {
+                write!(f, "{} : {}", k, t)
+            })?,
+            UnionType(a) => fmt_list("< ", " | ", " >", a, f, |(k, v), f| {
+                write!(f, "{}", k)?;
+                if let Some(v) = v {
+                    write!(f, ": {}", v)?;
+                }
+                Ok(())
+            })?,
+            Op(op) => {
+                op.fmt(f)?;
+            }
+            Annot(a, b) => {
+                write!(f, "{} : {}", a, b)?;
+            }
+            Assert(a) => {
+                write!(f, "assert : {}", a)?;
+            }
+            Import(a) => a.fmt(f)?,
+        }
+        Ok(())
+    }
+}
+
+/// Generic instance that delegates to subexpressions
+impl<SE: Display + Clone> Display for OpKind<SE> {
+    fn fmt(&self, f: &mut fmt::Formatter) -> Result<(), fmt::Error> {
+        use crate::syntax::OpKind::*;
+        match self {
+            App(a, b) => {
+                write!(f, "{} {}", a, b)?;
+            }
+            BinOp(op, a, b) => {
+                write!(f, "{} {} {}", a, op, b)?;
+            }
+            BoolIf(a, b, c) => {
+                write!(f, "if {} then {} else {}", a, b, c)?;
             }
             Merge(a, b, c) => {
                 write!(f, "merge {} {}", a, b)?;
@@ -183,41 +235,9 @@ impl<SE: Display + Clone> Display for ExprKind<SE> {
                     write!(f, " : {}", b)?;
                 }
             }
-            Annot(a, b) => {
-                write!(f, "{} : {}", a, b)?;
-            }
-            Assert(a) => {
-                write!(f, "assert : {}", a)?;
-            }
-            ExprKind::BinOp(op, a, b) => {
-                write!(f, "{} {} {}", a, op, b)?;
-            }
-            ExprKind::App(a, b) => {
-                write!(f, "{} {}", a, b)?;
-            }
             Field(a, b) => {
                 write!(f, "{}.{}", a, b)?;
             }
-            Var(a) => a.fmt(f)?,
-            Const(k) => k.fmt(f)?,
-            Builtin(v) => v.fmt(f)?,
-            Num(a) => a.fmt(f)?,
-            TextLit(a) => a.fmt(f)?,
-            RecordType(a) if a.is_empty() => f.write_str("{}")?,
-            RecordType(a) => fmt_list("{ ", ", ", " }", a, f, |(k, t), f| {
-                write!(f, "{} : {}", k, t)
-            })?,
-            RecordLit(a) if a.is_empty() => f.write_str("{=}")?,
-            RecordLit(a) => fmt_list("{ ", ", ", " }", a, f, |(k, v), f| {
-                write!(f, "{} = {}", k, v)
-            })?,
-            UnionType(a) => fmt_list("< ", " | ", " >", a, f, |(k, v), f| {
-                write!(f, "{}", k)?;
-                if let Some(v) = v {
-                    write!(f, ": {}", v)?;
-                }
-                Ok(())
-            })?,
             Projection(e, ls) => {
                 write!(f, "{}.", e)?;
                 fmt_list("{ ", ", ", " }", ls, f, Display::fmt)?;
@@ -228,7 +248,6 @@ impl<SE: Display + Clone> Display for ExprKind<SE> {
             Completion(a, b) => {
                 write!(f, "{}::{}", a, b)?;
             }
-            Import(a) => a.fmt(f)?,
         }
         Ok(())
     }