Merge pull request #159 from Nadrieril/operations

Factor out operations

7 files changed, 295 insertions, 985 deletions

diff --git a/dhall/src/semantics/builtins.rs b/dhall/src/builtins.rs
index 6007a92..67929a0 100644
--- a/dhall/src/semantics/builtins.rs
+++ b/dhall/src/builtins.rs
@@ -1,15 +1,91 @@
+use std::collections::{BTreeMap, HashMap};
+use std::convert::TryInto;
+
+use crate::operations::{BinOp, OpKind};
 use crate::semantics::{
     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, NaiveDouble, NumKind, Span, UnspannedExpr,
-    V,
+    Const, Expr, ExprKind, InterpolatedText, InterpolatedTextContents, Label,
+    NaiveDouble, NumKind, Span, UnspannedExpr, V,
 };
-use std::collections::HashMap;
-use std::convert::TryInto;
+
+/// Built-ins
+#[derive(Debug, Copy, Clone, PartialEq, Eq, Hash)]
+pub enum Builtin {
+    Bool,
+    Natural,
+    Integer,
+    Double,
+    Text,
+    List,
+    Optional,
+    OptionalNone,
+    NaturalBuild,
+    NaturalFold,
+    NaturalIsZero,
+    NaturalEven,
+    NaturalOdd,
+    NaturalToInteger,
+    NaturalShow,
+    NaturalSubtract,
+    IntegerToDouble,
+    IntegerShow,
+    IntegerNegate,
+    IntegerClamp,
+    DoubleShow,
+    ListBuild,
+    ListFold,
+    ListLength,
+    ListHead,
+    ListLast,
+    ListIndexed,
+    ListReverse,
+    OptionalFold,
+    OptionalBuild,
+    TextShow,
+}
+
+impl Builtin {
+    pub fn parse(s: &str) -> Option<Self> {
+        use Builtin::*;
+        match s {
+            "Bool" => Some(Bool),
+            "Natural" => Some(Natural),
+            "Integer" => Some(Integer),
+            "Double" => Some(Double),
+            "Text" => Some(Text),
+            "List" => Some(List),
+            "Optional" => Some(Optional),
+            "None" => Some(OptionalNone),
+            "Natural/build" => Some(NaturalBuild),
+            "Natural/fold" => Some(NaturalFold),
+            "Natural/isZero" => Some(NaturalIsZero),
+            "Natural/even" => Some(NaturalEven),
+            "Natural/odd" => Some(NaturalOdd),
+            "Natural/toInteger" => Some(NaturalToInteger),
+            "Natural/show" => Some(NaturalShow),
+            "Natural/subtract" => Some(NaturalSubtract),
+            "Integer/toDouble" => Some(IntegerToDouble),
+            "Integer/show" => Some(IntegerShow),
+            "Integer/negate" => Some(IntegerNegate),
+            "Integer/clamp" => Some(IntegerClamp),
+            "Double/show" => Some(DoubleShow),
+            "List/build" => Some(ListBuild),
+            "List/fold" => Some(ListFold),
+            "List/length" => Some(ListLength),
+            "List/head" => Some(ListHead),
+            "List/last" => Some(ListLast),
+            "List/indexed" => Some(ListIndexed),
+            "List/reverse" => Some(ListReverse),
+            "Optional/fold" => Some(OptionalFold),
+            "Optional/build" => Some(OptionalBuild),
+            "Text/show" => Some(TextShow),
+            _ => None,
+        }
+    }
+}
 
 /// A partially applied builtin.
 /// Invariant: the evaluation of the given args must not be able to progress further
@@ -34,10 +110,10 @@ 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),
-                )
+                ))
             },
         ))
     }
@@ -59,19 +135,19 @@ 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();
+        let mut kts = BTreeMap::new();
         $(
             kts.insert(
                 Label::from(stringify!($label)),
@@ -214,10 +290,10 @@ 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 +301,20 @@ 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,
-        ))
+        )))
     }};
 }
 
@@ -491,3 +567,42 @@ impl std::cmp::PartialEq for BuiltinClosure {
     }
 }
 impl std::cmp::Eq for BuiltinClosure {}
+
+impl std::fmt::Display for Builtin {
+    fn fmt(&self, f: &mut std::fmt::Formatter) -> std::fmt::Result {
+        use Builtin::*;
+        f.write_str(match *self {
+            Bool => "Bool",
+            Natural => "Natural",
+            Integer => "Integer",
+            Double => "Double",
+            Text => "Text",
+            List => "List",
+            Optional => "Optional",
+            OptionalNone => "None",
+            NaturalBuild => "Natural/build",
+            NaturalFold => "Natural/fold",
+            NaturalIsZero => "Natural/isZero",
+            NaturalEven => "Natural/even",
+            NaturalOdd => "Natural/odd",
+            NaturalToInteger => "Natural/toInteger",
+            NaturalShow => "Natural/show",
+            NaturalSubtract => "Natural/subtract",
+            IntegerToDouble => "Integer/toDouble",
+            IntegerNegate => "Integer/negate",
+            IntegerClamp => "Integer/clamp",
+            IntegerShow => "Integer/show",
+            DoubleShow => "Double/show",
+            ListBuild => "List/build",
+            ListFold => "List/fold",
+            ListLength => "List/length",
+            ListHead => "List/head",
+            ListLast => "List/last",
+            ListIndexed => "List/indexed",
+            ListReverse => "List/reverse",
+            OptionalFold => "Optional/fold",
+            OptionalBuild => "Optional/build",
+            TextShow => "Text/show",
+        })
+    }
+}
diff --git a/dhall/src/semantics/mod.rs b/dhall/src/semantics/mod.rs
index 468d8b1..a488c31 100644
--- a/dhall/src/semantics/mod.rs
+++ b/dhall/src/semantics/mod.rs
@@ -1,9 +1,7 @@
-pub mod builtins;
 pub mod nze;
 pub mod parse;
 pub mod resolve;
 pub mod tck;
-pub use self::builtins::*;
 pub use self::nze::*;
 pub use self::resolve::*;
 pub use self::tck::*;
diff --git a/dhall/src/semantics/nze/nir.rs b/dhall/src/semantics/nze/nir.rs
index e0d227e..12f1b14 100644
--- a/dhall/src/semantics/nze/nir.rs
+++ b/dhall/src/semantics/nze/nir.rs
@@ -1,14 +1,15 @@
 use std::collections::HashMap;
 use std::rc::Rc;
 
+use crate::builtins::{Builtin, BuiltinClosure};
+use crate::operations::{BinOp, OpKind};
 use crate::semantics::nze::lazy;
 use crate::semantics::{
-    apply_any, normalize_hir_whnf, normalize_one_layer, squash_textlit, Binder,
-    BuiltinClosure, Hir, HirKind, NzEnv, NzVar, TyEnv, Type, Universe, VarEnv,
+    apply_any, normalize_hir, normalize_one_layer, squash_textlit, Binder, Hir,
+    HirKind, NzEnv, NzVar, TyEnv, Type, Universe, VarEnv,
 };
 use crate::syntax::{
-    BinOp, Builtin, Const, Expr, ExprKind, InterpolatedTextContents, Label,
-    NumKind, Span,
+    Const, Expr, ExprKind, InterpolatedTextContents, Label, NumKind, Span,
 };
 use crate::ToExprOptions;
 
@@ -74,25 +75,27 @@ pub enum NirKind {
 
     Var(NzVar),
     Const(Const),
+    Num(NumKind),
     // Must be a number type, Bool or Text
     BuiltinType(Builtin),
-    Num(NumKind),
-    OptionalType(Nir),
+    TextLit(TextLit),
     EmptyOptionalLit(Nir),
     NEOptionalLit(Nir),
-    ListType(Nir),
+    OptionalType(Nir),
     // EmptyListLit(t) means `[] : List t`, not `[] : t`
     EmptyListLit(Nir),
     NEListLit(Vec<Nir>),
-    RecordType(HashMap<Label, Nir>),
+    ListType(Nir),
     RecordLit(HashMap<Label, Nir>),
-    UnionType(HashMap<Label, Option<Nir>>),
+    RecordType(HashMap<Label, Nir>),
     UnionConstructor(Label, HashMap<Label, Option<Nir>>),
     UnionLit(Label, Nir, HashMap<Label, Option<Nir>>),
-    TextLit(TextLit),
+    UnionType(HashMap<Label, Option<Nir>>),
     Equivalence(Nir, Nir),
-    /// Invariant: evaluation must not be able to progress with `normalize_one_layer`.
-    PartialExpr(ExprKind<Nir>),
+    Assert(Nir),
+    /// Invariant: evaluation must not be able to progress with `normalize_operation`.
+    /// This is used when an operation couldn't proceed further, for example because of variables.
+    Op(OpKind<Nir>),
 }
 
 impl Nir {
@@ -111,8 +114,7 @@ impl Nir {
         NirInternal::from_whnf(v).into_nir()
     }
     pub fn from_const(c: Const) -> Self {
-        let v = NirKind::Const(c);
-        NirInternal::from_whnf(v).into_nir()
+        Self::from_kind(NirKind::Const(c))
     }
     pub fn from_builtin(b: Builtin) -> Self {
         Self::from_builtin_env(b, &NzEnv::new())
@@ -148,7 +150,10 @@ impl Nir {
     }
 
     pub fn app(&self, v: Nir) -> Nir {
-        Nir::from_kind(apply_any(self.clone(), v))
+        Nir::from_kind(self.app_to_kind(v))
+    }
+    pub fn app_to_kind(&self, v: Nir) -> NirKind {
+        apply_any(self, v)
     }
 
     pub fn to_hir(&self, venv: VarEnv) -> Hir {
@@ -190,24 +195,24 @@ 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(
@@ -229,32 +234,35 @@ 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)),
+                )),
+                NirKind::Assert(x) => ExprKind::Assert(x.to_hir(venv)),
+                NirKind::Op(e) => ExprKind::Op(e.map_ref(|v| v.to_hir(venv))),
             }),
         };
 
@@ -307,7 +315,7 @@ impl Thunk {
     }
     fn eval(self) -> NirKind {
         match self {
-            Thunk::Thunk { env, body } => normalize_hir_whnf(&env, &body),
+            Thunk::Thunk { env, body } => normalize_hir(&env, &body),
             Thunk::PartialExpr { env, expr } => normalize_one_layer(expr, &env),
         }
     }
diff --git a/dhall/src/semantics/nze/normalize.rs b/dhall/src/semantics/nze/normalize.rs
index 570e106..d042f3f 100644
--- a/dhall/src/semantics/nze/normalize.rs
+++ b/dhall/src/semantics/nze/normalize.rs
@@ -1,18 +1,18 @@
-use itertools::Itertools;
 use std::collections::HashMap;
 
+use crate::operations::{normalize_operation, OpKind};
 use crate::semantics::NzEnv;
 use crate::semantics::{Binder, Closure, Hir, HirKind, Nir, NirKind, TextLit};
-use crate::syntax::{BinOp, ExprKind, InterpolatedTextContents, NumKind};
+use crate::syntax::{ExprKind, InterpolatedTextContents};
 
-pub 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),
         NirKind::UnionConstructor(l, kts) => {
             NirKind::UnionLit(l.clone(), a, kts.clone())
         }
-        _ => NirKind::PartialExpr(ExprKind::App(f, a)),
+        _ => NirKind::Op(OpKind::App(f.clone(), a)),
     }
 }
 
@@ -81,393 +81,83 @@ where
     kvs
 }
 
-// Small helper enum to avoid repetition
-enum Ret<'a> {
-    NirKind(NirKind),
-    Nir(Nir),
-    NirRef(&'a Nir),
-    Expr(ExprKind<Nir>),
-}
-
-fn apply_binop<'a>(o: BinOp, x: &'a Nir, y: &'a Nir) -> Option<Ret<'a>> {
-    use BinOp::{
-        BoolAnd, BoolEQ, BoolNE, BoolOr, Equivalence, ListAppend, NaturalPlus,
-        NaturalTimes, RecursiveRecordMerge, RecursiveRecordTypeMerge,
-        RightBiasedRecordMerge, TextAppend,
-    };
-    use NirKind::{EmptyListLit, NEListLit, Num, RecordLit, RecordType};
-    use NumKind::{Bool, Natural};
-
-    Some(match (o, x.kind(), y.kind()) {
-        (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, 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, 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, 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, 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),
-        (ListAppend, _, EmptyListLit(_)) => Ret::NirRef(x),
-        (ListAppend, NEListLit(xs), NEListLit(ys)) => Ret::NirKind(NEListLit(
-            xs.iter().chain(ys.iter()).cloned().collect(),
-        )),
-
-        (TextAppend, NirKind::TextLit(x), _) if x.is_empty() => Ret::NirRef(y),
-        (TextAppend, _, NirKind::TextLit(y)) if y.is_empty() => Ret::NirRef(x),
-        (TextAppend, NirKind::TextLit(x), NirKind::TextLit(y)) => {
-            Ret::NirKind(NirKind::TextLit(x.concat(y)))
-        }
-        (TextAppend, NirKind::TextLit(x), _) => Ret::NirKind(NirKind::TextLit(
-            x.concat(&TextLit::interpolate(y.clone())),
-        )),
-        (TextAppend, _, NirKind::TextLit(y)) => Ret::NirKind(NirKind::TextLit(
-            TextLit::interpolate(x.clone()).concat(y),
-        )),
+pub type Ret = NirKind;
 
-        (RightBiasedRecordMerge, _, RecordLit(kvs)) if kvs.is_empty() => {
-            Ret::NirRef(x)
-        }
-        (RightBiasedRecordMerge, RecordLit(kvs), _) if kvs.is_empty() => {
-            Ret::NirRef(y)
-        }
-        (RightBiasedRecordMerge, RecordLit(kvs1), RecordLit(kvs2)) => {
-            let mut kvs = kvs2.clone();
-            for (x, v) in kvs1 {
-                // Insert only if key not already present
-                kvs.entry(x.clone()).or_insert_with(|| v.clone());
-            }
-            Ret::NirKind(RecordLit(kvs))
-        }
-        (RightBiasedRecordMerge, _, _) if x == y => Ret::NirRef(y),
-
-        (RecursiveRecordMerge, _, RecordLit(kvs)) if kvs.is_empty() => {
-            Ret::NirRef(x)
-        }
-        (RecursiveRecordMerge, RecordLit(kvs), _) if kvs.is_empty() => {
-            Ret::NirRef(y)
-        }
-        (RecursiveRecordMerge, RecordLit(kvs1), RecordLit(kvs2)) => {
-            let kvs = merge_maps(kvs1, kvs2, |_, v1, v2| {
-                Nir::from_partial_expr(ExprKind::BinOp(
-                    RecursiveRecordMerge,
-                    v1.clone(),
-                    v2.clone(),
-                ))
-            });
-            Ret::NirKind(RecordLit(kvs))
-        }
-
-        (RecursiveRecordTypeMerge, RecordType(kts_x), RecordType(kts_y)) => {
-            let kts = merge_maps(
-                kts_x,
-                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(
-                        RecursiveRecordTypeMerge,
-                        l.clone(),
-                        r.clone(),
-                    ))
-                },
-            );
-            Ret::NirKind(RecordType(kts))
-        }
-
-        (Equivalence, _, _) => {
-            Ret::NirKind(NirKind::Equivalence(x.clone(), y.clone()))
-        }
-
-        _ => return None,
-    })
+pub fn ret_nir(x: Nir) -> Ret {
+    ret_ref(&x)
+}
+pub fn ret_kind(x: NirKind) -> Ret {
+    x
+}
+pub fn ret_ref(x: &Nir) -> Ret {
+    x.kind().clone()
+}
+pub fn ret_op(x: OpKind<Nir>) -> Ret {
+    NirKind::Op(x)
 }
 
-#[allow(clippy::cognitive_complexity)]
 pub fn normalize_one_layer(expr: ExprKind<Nir>, env: &NzEnv) -> NirKind {
     use NirKind::{
-        EmptyListLit, EmptyOptionalLit, NEListLit, NEOptionalLit, Num,
-        PartialExpr, RecordLit, RecordType, UnionConstructor, UnionLit,
+        Assert, Const, NEListLit, NEOptionalLit, Num, RecordLit, RecordType,
         UnionType,
     };
-    use NumKind::Bool;
 
-    let ret = match expr {
-        ExprKind::Import(..) | ExprKind::Completion(..) => {
-            unreachable!("This case should have been handled in resolution")
-        }
+    match expr {
         ExprKind::Var(..)
         | ExprKind::Lam(..)
         | ExprKind::Pi(..)
-        | ExprKind::Let(..) => unreachable!(
-            "This case should have been handled in normalize_hir_whnf"
-        ),
+        | ExprKind::Let(..) => {
+            unreachable!("This case should have been handled in normalize_hir")
+        }
 
-        ExprKind::Annot(x, _) => Ret::Nir(x),
-        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::Num(l) => Ret::NirKind(Num(l)),
-        ExprKind::SomeLit(e) => Ret::NirKind(NEOptionalLit(e)),
+        ExprKind::Const(c) => ret_kind(Const(c)),
+        ExprKind::Num(l) => ret_kind(Num(l)),
+        ExprKind::Builtin(b) => {
+            ret_kind(NirKind::from_builtin_env(b, env.clone()))
+        }
+        ExprKind::TextLit(elts) => {
+            let tlit = TextLit::new(elts.into_iter());
+            // Simplify bare interpolation
+            if let Some(v) = tlit.as_single_expr() {
+                ret_ref(v)
+            } else {
+                ret_kind(NirKind::TextLit(tlit))
+            }
+        }
+        ExprKind::SomeLit(e) => ret_kind(NEOptionalLit(e)),
         ExprKind::EmptyListLit(t) => {
             let arg = match t.kind() {
                 NirKind::ListType(t) => t.clone(),
                 _ => panic!("internal type error"),
             };
-            Ret::NirKind(NirKind::EmptyListLit(arg))
+            ret_kind(NirKind::EmptyListLit(arg))
         }
         ExprKind::NEListLit(elts) => {
-            Ret::NirKind(NEListLit(elts.into_iter().collect()))
+            ret_kind(NEListLit(elts.into_iter().collect()))
         }
         ExprKind::RecordLit(kvs) => {
-            Ret::NirKind(RecordLit(kvs.into_iter().collect()))
+            ret_kind(RecordLit(kvs.into_iter().collect()))
         }
         ExprKind::RecordType(kvs) => {
-            Ret::NirKind(RecordType(kvs.into_iter().collect()))
+            ret_kind(RecordType(kvs.into_iter().collect()))
         }
         ExprKind::UnionType(kvs) => {
-            Ret::NirKind(UnionType(kvs.into_iter().collect()))
-        }
-        ExprKind::TextLit(elts) => {
-            let tlit = TextLit::new(elts.into_iter());
-            // Simplify bare interpolation
-            if let Some(v) = tlit.as_single_expr() {
-                Ret::Nir(v.clone())
-            } else {
-                Ret::NirKind(NirKind::TextLit(tlit))
-            }
-        }
-        ExprKind::BoolIf(ref b, ref e1, ref e2) => {
-            match b.kind() {
-                Num(Bool(true)) => Ret::NirRef(e1),
-                Num(Bool(false)) => Ret::NirRef(e2),
-                _ => {
-                    match (e1.kind(), e2.kind()) {
-                        // Simplify `if b then True else False`
-                        (Num(Bool(true)), Num(Bool(false))) => Ret::NirRef(b),
-                        _ if e1 == e2 => Ret::NirRef(e1),
-                        _ => Ret::Expr(expr),
-                    }
-                }
-            }
-        }
-        ExprKind::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() {
-            RecordLit(kvs) => match kvs.get(field) {
-                Some(r) => Ret::Nir(r.clone()),
-                None => Ret::Expr(expr),
-            },
-            UnionType(kts) => {
-                Ret::NirKind(UnionConstructor(field.clone(), kts.clone()))
-            }
-            PartialExpr(ExprKind::Projection(x, _)) => {
-                return normalize_one_layer(
-                    ExprKind::Field(x.clone(), field.clone()),
-                    env,
-                )
-            }
-            PartialExpr(ExprKind::BinOp(
-                BinOp::RightBiasedRecordMerge,
-                x,
-                y,
-            )) => 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()),
-                            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(),
-                        ))),
-                        field.clone(),
-                    )),
-                    None => {
-                        return normalize_one_layer(
-                            ExprKind::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(
-                                BinOp::RecursiveRecordMerge,
-                                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()),
-                                env,
-                            )
-                        }
-                    },
-                    (_, RecordLit(kvs)) => match kvs.get(field) {
-                        Some(r) => Ret::Expr(ExprKind::Field(
-                            Nir::from_kind(PartialExpr(ExprKind::BinOp(
-                                BinOp::RecursiveRecordMerge,
-                                x.clone(),
-                                Nir::from_kind(RecordLit(
-                                    Some((field.clone(), r.clone()))
-                                        .into_iter()
-                                        .collect(),
-                                )),
-                            ))),
-                            field.clone(),
-                        )),
-                        None => {
-                            return normalize_one_layer(
-                                ExprKind::Field(x.clone(), field.clone()),
-                                env,
-                            )
-                        }
-                    },
-                    _ => Ret::Expr(expr),
-                }
-            }
-            _ => Ret::Expr(expr),
-        },
-        ExprKind::Projection(_, ref ls) if ls.is_empty() => {
-            Ret::NirKind(RecordLit(HashMap::new()))
+            ret_kind(UnionType(kvs.into_iter().collect()))
         }
-        ExprKind::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, _)) => {
-                return normalize_one_layer(
-                    ExprKind::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,
-                )
-            }
-            _ => Ret::Expr(expr),
-        },
-
-        ExprKind::Merge(ref handlers, ref variant, _) => {
-            match handlers.kind() {
-                RecordLit(kvs) => match variant.kind() {
-                    UnionConstructor(l, _) => match kvs.get(l) {
-                        Some(h) => Ret::Nir(h.clone()),
-                        None => Ret::Expr(expr),
-                    },
-                    UnionLit(l, v, _) => match kvs.get(l) {
-                        Some(h) => Ret::Nir(h.app(v.clone())),
-                        None => Ret::Expr(expr),
-                    },
-                    EmptyOptionalLit(_) => match kvs.get(&"None".into()) {
-                        Some(h) => Ret::Nir(h.clone()),
-                        None => Ret::Expr(expr),
-                    },
-                    NEOptionalLit(v) => match kvs.get(&"Some".into()) {
-                        Some(h) => Ret::Nir(h.app(v.clone())),
-                        None => Ret::Expr(expr),
-                    },
-                    _ => Ret::Expr(expr),
-                },
-                _ => Ret::Expr(expr),
-            }
+        ExprKind::Op(ref op) => normalize_operation(op),
+        ExprKind::Annot(x, _) => ret_nir(x),
+        ExprKind::Assert(x) => ret_kind(Assert(x)),
+        ExprKind::Import(..) => {
+            unreachable!("This case should have been handled in resolution")
         }
-        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::ListType(t)) => {
-                        Ret::NirKind(EmptyListLit(t.clone()))
-                    }
-                    _ => Ret::Expr(expr),
-                }
-            }
-            RecordLit(kvs) => Ret::NirKind(NEListLit(
-                kvs.iter()
-                    .sorted_by_key(|(k, _)| *k)
-                    .map(|(k, v)| {
-                        let mut rec = HashMap::new();
-                        rec.insert("mapKey".into(), Nir::from_text(k));
-                        rec.insert("mapValue".into(), v.clone());
-                        Nir::from_kind(NirKind::RecordLit(rec))
-                    })
-                    .collect(),
-            )),
-            _ => Ret::Expr(expr),
-        },
-    };
-
-    match ret {
-        Ret::NirKind(v) => v,
-        Ret::Nir(v) => v.kind().clone(),
-        Ret::NirRef(v) => v.kind().clone(),
-        Ret::Expr(expr) => NirKind::PartialExpr(expr),
     }
 }
 
 /// Normalize Hir into WHNF
-pub fn normalize_hir_whnf(env: &NzEnv, hir: &Hir) -> NirKind {
+pub fn normalize_hir(env: &NzEnv, hir: &Hir) -> NirKind {
     match hir.kind() {
         HirKind::Var(var) => env.lookup_val(*var),
-        HirKind::Import(hir, _) => normalize_hir_whnf(env, hir),
+        HirKind::Import(hir, _) => normalize_hir(env, hir),
         HirKind::Expr(ExprKind::Lam(binder, annot, body)) => {
             let annot = annot.eval(env);
             NirKind::LamClosure {
diff --git a/dhall/src/semantics/resolve/resolve.rs b/dhall/src/semantics/resolve/resolve.rs
index 6e50fa6..e96f16b 100644
--- a/dhall/src/semantics/resolve/resolve.rs
+++ b/dhall/src/semantics/resolve/resolve.rs
@@ -1,17 +1,19 @@
 use itertools::Itertools;
 use std::borrow::Cow;
+use std::collections::BTreeMap;
 use std::env;
 use std::path::PathBuf;
 use url::Url;
 
+use crate::builtins::Builtin;
 use crate::error::ErrorBuilder;
 use crate::error::{Error, ImportError};
+use crate::operations::{BinOp, OpKind};
 use crate::semantics::{mkerr, Hir, HirKind, ImportEnv, NameEnv, Type};
 use crate::syntax;
-use crate::syntax::map::DupTreeMap;
 use crate::syntax::{
-    BinOp, Builtin, Expr, ExprKind, FilePath, FilePrefix, Hash, ImportMode,
-    ImportTarget, Span, UnspannedExpr, URL,
+    Expr, ExprKind, FilePath, FilePrefix, Hash, ImportMode, ImportTarget, Span,
+    UnspannedExpr, URL,
 };
 use crate::{Parsed, Resolved};
 
@@ -179,12 +181,13 @@ 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,
         }
     }
@@ -196,7 +199,7 @@ fn mkexpr(kind: UnspannedExpr) -> Expr {
 
 fn make_aslocation_uniontype() -> Expr {
     let text_type = mkexpr(ExprKind::Builtin(Builtin::Text));
-    let mut union = DupTreeMap::default();
+    let mut union = BTreeMap::default();
     union.insert("Local".into(), Some(text_type.clone()));
     union.insert("Remote".into(), Some(text_type.clone()));
     union.insert("Environment".into(), Some(text_type));
@@ -261,21 +264,21 @@ 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 +307,7 @@ 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/tir.rs b/dhall/src/semantics/tck/tir.rs
index 89a8027..ec15a1f 100644
--- a/dhall/src/semantics/tck/tir.rs
+++ b/dhall/src/semantics/tck/tir.rs
@@ -1,6 +1,7 @@
+use crate::builtins::Builtin;
 use crate::error::{ErrorBuilder, TypeError};
 use crate::semantics::{mkerr, Hir, Nir, NirKind, NzEnv, TyEnv, VarEnv};
-use crate::syntax::{Builtin, Const, Expr, Span};
+use crate::syntax::{Const, Expr, Span};
 
 /// The type of a type. 0 is `Type`, 1 is `Kind`, etc...
 #[derive(Debug, Copy, Clone, PartialEq, Eq, PartialOrd, Ord, Default)]
diff --git a/dhall/src/semantics/tck/typecheck.rs b/dhall/src/semantics/tck/typecheck.rs
index c3334b5..361e1b4 100644
--- a/dhall/src/semantics/tck/typecheck.rs
+++ b/dhall/src/semantics/tck/typecheck.rs
@@ -1,49 +1,10 @@
-use std::borrow::Cow;
 use std::cmp::max;
-use std::collections::HashMap;
 
+use crate::builtins::{type_of_builtin, Builtin};
 use crate::error::{ErrorBuilder, TypeError, TypeMessage};
-use crate::semantics::merge_maps;
-use crate::semantics::{
-    type_of_builtin, Binder, Closure, Hir, HirKind, Nir, NirKind, Tir, TyEnv,
-    Type,
-};
-use crate::syntax::{
-    BinOp, Builtin, Const, ExprKind, InterpolatedTextContents, NumKind, Span,
-};
-
-fn check_rectymerge(
-    span: &Span,
-    env: &TyEnv,
-    x: Nir,
-    y: Nir,
-) -> Result<(), TypeError> {
-    let kts_x = match x.kind() {
-        NirKind::RecordType(kts) => kts,
-        _ => {
-            return mk_span_err(
-                span.clone(),
-                "RecordTypeMergeRequiresRecordType",
-            )
-        }
-    };
-    let kts_y = match y.kind() {
-        NirKind::RecordType(kts) => kts,
-        _ => {
-            return mk_span_err(
-                span.clone(),
-                "RecordTypeMergeRequiresRecordType",
-            )
-        }
-    };
-    for (k, tx) in kts_x {
-        if let Some(ty) = kts_y.get(k) {
-            // TODO: store Type in RecordType ?
-            check_rectymerge(span, env, tx.clone(), ty.clone())?;
-        }
-    }
-    Ok(())
-}
+use crate::operations::typecheck_operation;
+use crate::semantics::{Hir, HirKind, Nir, NirKind, Tir, TyEnv, Type};
+use crate::syntax::{Const, ExprKind, InterpolatedTextContents, NumKind, Span};
 
 fn function_check(a: Const, b: Const) -> Const {
     if b == Const::Type {
@@ -74,8 +35,8 @@ fn type_one_layer(
 ) -> Result<Type, TypeError> {
     let span_err = |msg: &str| mk_span_err(span.clone(), msg);
 
-    let ty = match &ekind {
-        ExprKind::Import(..) | ExprKind::Completion(..) => {
+    Ok(match &ekind {
+        ExprKind::Import(..) => {
             unreachable!("This case should have been handled in resolution")
         }
         ExprKind::Var(..)
@@ -89,20 +50,16 @@ fn type_one_layer(
 
         ExprKind::Const(Const::Type) => Type::from_const(Const::Kind),
         ExprKind::Const(Const::Kind) => Type::from_const(Const::Sort),
+        ExprKind::Num(num) => Type::from_builtin(match num {
+            NumKind::Bool(_) => Builtin::Bool,
+            NumKind::Natural(_) => Builtin::Natural,
+            NumKind::Integer(_) => Builtin::Integer,
+            NumKind::Double(_) => Builtin::Double,
+        }),
         ExprKind::Builtin(b) => {
             let t_hir = type_of_builtin(*b);
             typecheck(&t_hir)?.eval_to_type(env)?
         }
-        ExprKind::Num(NumKind::Bool(_)) => Type::from_builtin(Builtin::Bool),
-        ExprKind::Num(NumKind::Natural(_)) => {
-            Type::from_builtin(Builtin::Natural)
-        }
-        ExprKind::Num(NumKind::Integer(_)) => {
-            Type::from_builtin(Builtin::Integer)
-        }
-        ExprKind::Num(NumKind::Double(_)) => {
-            Type::from_builtin(Builtin::Double)
-        }
         ExprKind::TextLit(interpolated) => {
             let text_type = Type::from_builtin(Builtin::Text);
             for contents in interpolated.iter() {
@@ -115,6 +72,16 @@ fn type_one_layer(
             }
             text_type
         }
+        ExprKind::SomeLit(x) => {
+            if x.ty().ty().as_const() != Some(Const::Type) {
+                return span_err("InvalidOptionalType");
+            }
+
+            let t = x.ty().to_nir();
+            Nir::from_builtin(Builtin::Optional)
+                .app(t)
+                .to_type(Const::Type)
+        }
         ExprKind::EmptyListLit(t) => {
             let t = t.eval_to_type(env)?;
             match t.kind() {
@@ -138,82 +105,56 @@ fn type_one_layer(
             let t = x.ty().to_nir();
             Nir::from_builtin(Builtin::List).app(t).to_type(Const::Type)
         }
-        ExprKind::SomeLit(x) => {
-            if x.ty().ty().as_const() != Some(Const::Type) {
-                return span_err("InvalidOptionalType");
-            }
-
-            let t = x.ty().to_nir();
-            Nir::from_builtin(Builtin::Optional)
-                .app(t)
-                .to_type(Const::Type)
-        }
         ExprKind::RecordLit(kvs) => {
-            use std::collections::hash_map::Entry;
-            let mut kts = HashMap::new();
             // An empty record type has type Type
             let mut k = Const::Type;
-            for (x, v) in kvs {
-                // Check for duplicated entries
-                match kts.entry(x.clone()) {
-                    Entry::Occupied(_) => {
-                        return span_err("RecordTypeDuplicateField")
-                    }
-                    Entry::Vacant(e) => e.insert(v.ty().to_nir()),
-                };
-
+            for v in kvs.values() {
                 // Check that the fields have a valid kind
                 match v.ty().ty().as_const() {
                     Some(c) => k = max(k, c),
-                    None => return span_err("InvalidFieldType"),
+                    None => return mk_span_err(v.span(), "InvalidFieldType"),
                 }
             }
 
+            let kts = kvs
+                .iter()
+                .map(|(x, v)| (x.clone(), v.ty().to_nir()))
+                .collect();
+
             Nir::from_kind(NirKind::RecordType(kts)).to_type(k)
         }
         ExprKind::RecordType(kts) => {
-            use std::collections::hash_map::Entry;
-            let mut seen_fields = HashMap::new();
             // An empty record type has type Type
             let mut k = Const::Type;
-
-            for (x, t) in kts {
-                // Check for duplicated entries
-                match seen_fields.entry(x.clone()) {
-                    Entry::Occupied(_) => {
-                        return span_err("RecordTypeDuplicateField")
-                    }
-                    Entry::Vacant(e) => e.insert(()),
-                };
-
+            for t in kts.values() {
                 // Check the type is a Const and compute final type
                 match t.ty().as_const() {
                     Some(c) => k = max(k, c),
-                    None => return span_err("InvalidFieldType"),
+                    None => return mk_span_err(t.span(), "InvalidFieldType"),
                 }
             }
 
             Type::from_const(k)
         }
         ExprKind::UnionType(kts) => {
-            use std::collections::hash_map::Entry;
-            let mut seen_fields = HashMap::new();
             // Check that all types are the same const
             let mut k = None;
-            for (x, t) in kts {
+            for t in kts.values() {
                 if let Some(t) = t {
-                    match (k, t.ty().as_const()) {
-                        (None, Some(k2)) => k = Some(k2),
-                        (Some(k1), Some(k2)) if k1 == k2 => {}
-                        _ => return span_err("InvalidFieldType"),
+                    let c = match t.ty().as_const() {
+                        Some(c) => c,
+                        None => {
+                            return mk_span_err(t.span(), "InvalidVariantType")
+                        }
+                    };
+                    match k {
+                        None => k = Some(c),
+                        Some(k) if k == c => {}
+                        _ => {
+                            return mk_span_err(t.span(), "InvalidVariantType")
+                        }
                     }
                 }
-                match seen_fields.entry(x) {
-                    Entry::Occupied(_) => {
-                        return span_err("UnionTypeDuplicateField")
-                    }
-                    Entry::Vacant(e) => e.insert(()),
-                };
             }
 
             // An empty union type has type Type;
@@ -222,36 +163,7 @@ fn type_one_layer(
 
             Type::from_const(k)
         }
-        ExprKind::Field(scrut, x) => {
-            match scrut.ty().kind() {
-                NirKind::RecordType(kts) => match kts.get(&x) {
-                    Some(val) => Type::new_infer_universe(env, val.clone())?,
-                    None => return span_err("MissingRecordField"),
-                },
-                NirKind::Const(_) => {
-                    let scrut = scrut.eval_to_type(env)?;
-                    match scrut.kind() {
-                        NirKind::UnionType(kts) => match kts.get(x) {
-                            // Constructor has type T -> < x: T, ... >
-                            Some(Some(ty)) => {
-                                Nir::from_kind(NirKind::PiClosure {
-                                    binder: Binder::new(x.clone()),
-                                    annot: ty.clone(),
-                                    closure: Closure::new_constant(
-                                        scrut.to_nir(),
-                                    ),
-                                })
-                                .to_type(scrut.ty())
-                            }
-                            Some(None) => scrut,
-                            None => return span_err("MissingUnionField"),
-                        },
-                        _ => return span_err("NotARecord"),
-                    }
-                }
-                _ => return span_err("NotARecord"),
-            }
-        }
+        ExprKind::Op(op) => typecheck_operation(env, span, op)?,
         ExprKind::Assert(t) => {
             let t = t.eval_to_type(env)?;
             match t.kind() {
@@ -261,430 +173,13 @@ fn type_one_layer(
             }
             t
         }
-        ExprKind::App(f, arg) => {
-            match f.ty().kind() {
-                // TODO: store Type in closure
-                NirKind::PiClosure { annot, closure, .. } => {
-                    if arg.ty().as_nir() != annot {
-                        return mkerr(
-                            ErrorBuilder::new(format!(
-                                "wrong type of function argument"
-                            ))
-                            .span_err(
-                                f.span(),
-                                format!(
-                                    "this expects an argument of type: {}",
-                                    annot.to_expr_tyenv(env),
-                                ),
-                            )
-                            .span_err(
-                                arg.span(),
-                                format!(
-                                    "but this has type: {}",
-                                    arg.ty().to_expr_tyenv(env),
-                                ),
-                            )
-                            .note(format!(
-                                "expected type `{}`\n   found type `{}`",
-                                annot.to_expr_tyenv(env),
-                                arg.ty().to_expr_tyenv(env),
-                            ))
-                            .format(),
-                        );
-                    }
-
-                    let arg_nf = arg.eval(env);
-                    Type::new_infer_universe(env, closure.apply(arg_nf))?
-                }
-                _ => return mkerr(
-                    ErrorBuilder::new(format!(
-                        "expected function, found `{}`",
-                        f.ty().to_expr_tyenv(env)
-                    ))
-                    .span_err(
-                        f.span(),
-                        format!("function application requires a function",),
-                    )
-                    .format(),
-                ),
-            }
-        }
-        ExprKind::BoolIf(x, y, z) => {
-            if *x.ty().kind() != NirKind::from_builtin(Builtin::Bool) {
-                return span_err("InvalidPredicate");
-            }
-            if y.ty().ty().as_const() != Some(Const::Type) {
-                return span_err("IfBranchMustBeTerm");
-            }
-            if y.ty() != z.ty() {
-                return span_err("IfBranchMismatch");
-            }
-
-            y.ty().clone()
-        }
-        ExprKind::BinOp(BinOp::RightBiasedRecordMerge, x, y) => {
-            let x_type = x.ty();
-            let y_type = y.ty();
-
-            // Extract the LHS record type
-            let kts_x = match x_type.kind() {
-                NirKind::RecordType(kts) => kts,
-                _ => return span_err("MustCombineRecord"),
-            };
-            // Extract the RHS record type
-            let kts_y = match y_type.kind() {
-                NirKind::RecordType(kts) => kts,
-                _ => return span_err("MustCombineRecord"),
-            };
-
-            // Union the two records, prefering
-            // the values found in the RHS.
-            let kts = merge_maps(kts_x, kts_y, |_, _, r_t| r_t.clone());
-
-            let u = max(x.ty().ty(), y.ty().ty());
-            Nir::from_kind(NirKind::RecordType(kts)).to_type(u)
-        }
-        ExprKind::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(
-                    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) => {
-            check_rectymerge(&span, env, x.eval(env), y.eval(env))?;
-
-            // A RecordType's type is always a const
-            let xk = x.ty().as_const().unwrap();
-            let yk = y.ty().as_const().unwrap();
-            Type::from_const(max(xk, yk))
-        }
-        ExprKind::BinOp(BinOp::ListAppend, l, r) => {
-            match l.ty().kind() {
-                NirKind::ListType(..) => {}
-                _ => return span_err("BinOpTypeMismatch"),
-            }
-
-            if l.ty() != r.ty() {
-                return span_err("BinOpTypeMismatch");
-            }
-
-            l.ty().clone()
-        }
-        ExprKind::BinOp(BinOp::Equivalence, l, r) => {
-            if l.ty() != r.ty() {
-                return span_err("EquivalenceTypeMismatch");
-            }
-            if l.ty().ty().as_const() != Some(Const::Type) {
-                return span_err("EquivalenceArgumentsMustBeTerms");
-            }
-
-            Type::from_const(Const::Type)
-        }
-        ExprKind::BinOp(o, l, r) => {
-            let t = Type::from_builtin(match o {
-                BinOp::BoolAnd
-                | BinOp::BoolOr
-                | BinOp::BoolEQ
-                | BinOp::BoolNE => Builtin::Bool,
-                BinOp::NaturalPlus | BinOp::NaturalTimes => Builtin::Natural,
-                BinOp::TextAppend => Builtin::Text,
-                BinOp::ListAppend
-                | BinOp::RightBiasedRecordMerge
-                | BinOp::RecursiveRecordMerge
-                | BinOp::RecursiveRecordTypeMerge
-                | BinOp::Equivalence => unreachable!(),
-                BinOp::ImportAlt => unreachable!("ImportAlt leftover in tck"),
-            });
-
-            if *l.ty() != t {
-                return span_err("BinOpTypeMismatch");
-            }
-
-            if *r.ty() != t {
-                return span_err("BinOpTypeMismatch");
-            }
-
-            t
-        }
-        ExprKind::Merge(record, union, type_annot) => {
-            let record_type = record.ty();
-            let handlers = match record_type.kind() {
-                NirKind::RecordType(kts) => kts,
-                _ => return span_err("Merge1ArgMustBeRecord"),
-            };
-
-            let union_type = union.ty();
-            let variants = match union_type.kind() {
-                NirKind::UnionType(kts) => Cow::Borrowed(kts),
-                NirKind::OptionalType(ty) => {
-                    let mut kts = HashMap::new();
-                    kts.insert("None".into(), None);
-                    kts.insert("Some".into(), Some(ty.clone()));
-                    Cow::Owned(kts)
-                }
-                _ => return span_err("Merge2ArgMustBeUnionOrOptional"),
-            };
-
-            let mut inferred_type = None;
-            for (x, handler_type) in handlers {
-                let handler_return_type: Type = match variants.get(x) {
-                    // Union alternative with type
-                    Some(Some(variant_type)) => match handler_type.kind() {
-                        NirKind::PiClosure { closure, annot, .. } => {
-                            if variant_type != annot {
-                                return mkerr(
-                                    ErrorBuilder::new(format!(
-                                        "Wrong handler input type"
-                                    ))
-                                    .span_err(
-                                        span,
-                                        format!("in this merge expression",),
-                                    )
-                                    .span_err(
-                                        record.span(),
-                                        format!(
-                                            "the handler for `{}` expects a \
-                                             value of type: `{}`",
-                                            x,
-                                            annot.to_expr_tyenv(env)
-                                        ),
-                                    )
-                                    .span_err(
-                                        union.span(),
-                                        format!(
-                                            "but the corresponding variant \
-                                             has type: `{}`",
-                                            variant_type.to_expr_tyenv(env)
-                                        ),
-                                    )
-                                    .format(),
-                                );
-                            }
-
-                            // TODO: this actually doesn't check anything yet
-                            match closure.remove_binder() {
-                                Ok(v) => {
-                                    Type::new_infer_universe(env, v.clone())?
-                                }
-                                Err(()) => {
-                                    return span_err(
-                                        "MergeReturnTypeIsDependent",
-                                    )
-                                }
-                            }
-                        }
-                        _ => {
-                            return mkerr(
-                                ErrorBuilder::new(format!(
-                                    "merge handler is not a function"
-                                ))
-                                .span_err(
-                                    span,
-                                    format!("in this merge expression"),
-                                )
-                                .span_err(
-                                    record.span(),
-                                    format!(
-                                        "the handler for `{}` has type: `{}`",
-                                        x,
-                                        handler_type.to_expr_tyenv(env)
-                                    ),
-                                )
-                                .span_help(
-                                    union.span(),
-                                    format!(
-                                        "the corresponding variant has type: \
-                                         `{}`",
-                                        variant_type.to_expr_tyenv(env)
-                                    ),
-                                )
-                                .help(format!(
-                                    "a handler for this variant must be a \
-                                     function that takes an input of type: \
-                                     `{}`",
-                                    variant_type.to_expr_tyenv(env)
-                                ))
-                                .format(),
-                            )
-                        }
-                    },
-                    // Union alternative without type
-                    Some(None) => {
-                        Type::new_infer_universe(env, handler_type.clone())?
-                    }
-                    None => return span_err("MergeHandlerMissingVariant"),
-                };
-                match &inferred_type {
-                    None => inferred_type = Some(handler_return_type),
-                    Some(t) => {
-                        if t != &handler_return_type {
-                            return span_err("MergeHandlerTypeMismatch");
-                        }
-                    }
-                }
-            }
-            for x in variants.keys() {
-                if !handlers.contains_key(x) {
-                    return span_err("MergeVariantMissingHandler");
-                }
-            }
-
-            let type_annot = type_annot
-                .as_ref()
-                .map(|t| t.eval_to_type(env))
-                .transpose()?;
-            match (inferred_type, type_annot) {
-                (Some(t1), Some(t2)) => {
-                    if t1 != t2 {
-                        return span_err("MergeAnnotMismatch");
-                    }
-                    t1
-                }
-                (Some(t), None) => t,
-                (None, Some(t)) => t,
-                (None, None) => return span_err("MergeEmptyNeedsAnnotation"),
-            }
-        }
-        ExprKind::ToMap(record, annot) => {
-            if record.ty().ty().as_const() != Some(Const::Type) {
-                return span_err("`toMap` only accepts records of type `Type`");
-            }
-            let record_t = record.ty();
-            let kts = match record_t.kind() {
-                NirKind::RecordType(kts) => kts,
-                _ => {
-                    return span_err("The argument to `toMap` must be a record")
-                }
-            };
-
-            if kts.is_empty() {
-                let annot = if let Some(annot) = annot {
-                    annot
-                } else {
-                    return span_err(
-                        "`toMap` applied to an empty record requires a type \
-                         annotation",
-                    );
-                };
-                let annot_val = annot.eval_to_type(env)?;
-
-                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::ListType(t) => t,
-                    _ => return span_err(err_msg),
-                };
-                let kts = match arg.kind() {
-                    NirKind::RecordType(kts) => kts,
-                    _ => return span_err(err_msg),
-                };
-                if kts.len() != 2 {
-                    return span_err(err_msg);
-                }
-                match kts.get(&"mapKey".into()) {
-                    Some(t) if *t == Nir::from_builtin(Builtin::Text) => {}
-                    _ => return span_err(err_msg),
-                }
-                match kts.get(&"mapValue".into()) {
-                    Some(_) => {}
-                    None => return span_err(err_msg),
-                }
-                annot_val
-            } else {
-                let entry_type = kts.iter().next().unwrap().1.clone();
-                for (_, t) in kts.iter() {
-                    if *t != entry_type {
-                        return span_err(
-                            "Every field of the record must have the same type",
-                        );
-                    }
-                }
-
-                let mut kts = HashMap::new();
-                kts.insert("mapKey".into(), Nir::from_builtin(Builtin::Text));
-                kts.insert("mapValue".into(), entry_type);
-                let output_type: Type = Nir::from_builtin(Builtin::List)
-                    .app(Nir::from_kind(NirKind::RecordType(kts)))
-                    .to_type(Const::Type);
-                if let Some(annot) = annot {
-                    let annot_val = annot.eval_to_type(env)?;
-                    if output_type != annot_val {
-                        return span_err("Annotation mismatch");
-                    }
-                }
-                output_type
-            }
-        }
-        ExprKind::Projection(record, labels) => {
-            let record_type = record.ty();
-            let kts = match record_type.kind() {
-                NirKind::RecordType(kts) => kts,
-                _ => return span_err("ProjectionMustBeRecord"),
-            };
-
-            let mut new_kts = HashMap::new();
-            for l in labels {
-                match kts.get(l) {
-                    None => return span_err("ProjectionMissingEntry"),
-                    Some(t) => {
-                        use std::collections::hash_map::Entry;
-                        match new_kts.entry(l.clone()) {
-                            Entry::Occupied(_) => {
-                                return span_err("ProjectionDuplicateField")
-                            }
-                            Entry::Vacant(e) => e.insert(t.clone()),
-                        }
-                    }
-                };
-            }
-
-            Type::new_infer_universe(
-                env,
-                Nir::from_kind(NirKind::RecordType(new_kts)),
-            )?
-        }
-        ExprKind::ProjectionByExpr(record, selection) => {
-            let record_type = record.ty();
-            let rec_kts = match record_type.kind() {
-                NirKind::RecordType(kts) => kts,
-                _ => return span_err("ProjectionMustBeRecord"),
-            };
-
-            let selection_val = selection.eval_to_type(env)?;
-            let sel_kts = match selection_val.kind() {
-                NirKind::RecordType(kts) => kts,
-                _ => return span_err("ProjectionByExprTakesRecordType"),
-            };
-
-            for (l, sel_ty) in sel_kts {
-                match rec_kts.get(l) {
-                    Some(rec_ty) => {
-                        if rec_ty != sel_ty {
-                            return span_err("ProjectionWrongType");
-                        }
-                    }
-                    None => return span_err("ProjectionMissingEntry"),
-                }
-            }
-
-            selection_val
-        }
-    };
-
-    Ok(ty)
+    })
 }
 
 /// `type_with` typechecks an expression in the provided environment. Optionally pass an annotation
 /// to compare with.
+// We pass the annotation to avoid duplicating the annot checking logic. I hope one day we can use
+// it to handle the annotations in merge/toMap/etc. uniformly.
 pub fn type_with<'hir>(
     env: &TyEnv,
     hir: &'hir Hir,
@@ -780,7 +275,7 @@ pub fn type_with<'hir>(
     Ok(tir)
 }
 
-/// Typecheck an expression and return the expression annotated with types if type-checking
+/// Typecheck an expression and return the expression annotated with its type if type-checking
 /// succeeded, or an error if type-checking failed.
 pub fn typecheck<'hir>(hir: &'hir Hir) -> Result<Tir<'hir>, TypeError> {
     type_with(&TyEnv::new(), hir, None)