7 files changed, 230 insertions, 366 deletions

diff --git a/dhall_syntax/src/core/context.rs b/dhall_syntax/src/core/context.rs
index eeec121..6844baa 100644
--- a/dhall_syntax/src/core/context.rs
+++ b/dhall_syntax/src/core/context.rs
@@ -4,7 +4,7 @@ use std::hash::Hash;
 
 /// A `(Context a)` associates `Text` labels with values of type `a`
 ///
-/// The `Context` is used for type-checking when `(a = Expr X)`
+/// The `Context` is used for type-checking when `(a = Expr)`
 ///
 /// * You create a `Context` using `empty` and `insert`
 /// * You transform a `Context` using `fmap`
diff --git a/dhall_syntax/src/core/expr.rs b/dhall_syntax/src/core/expr.rs
index 0cbece3..30ac4eb 100644
--- a/dhall_syntax/src/core/expr.rs
+++ b/dhall_syntax/src/core/expr.rs
@@ -10,9 +10,15 @@ pub type Double = NaiveDouble;
 
 /// An empty type
 #[derive(Debug, Copy, Clone, PartialEq, Eq)]
-pub enum X {}
+pub enum Void {}
 
-pub fn trivial_result<T>(x: Result<T, X>) -> T {
+impl std::fmt::Display for Void {
+    fn fmt(&self, _f: &mut std::fmt::Formatter) -> Result<(), std::fmt::Error> {
+        match *self {}
+    }
+}
+
+pub fn trivial_result<T>(x: Result<T, Void>) -> T {
     match x {
         Ok(x) => x,
         Err(e) => match e {},
@@ -55,6 +61,15 @@ impl PartialEq for NaiveDouble {
 
 impl Eq for NaiveDouble {}
 
+impl std::hash::Hash for NaiveDouble {
+    fn hash<H>(&self, state: &mut H)
+    where
+        H: std::hash::Hasher,
+    {
+        self.0.to_bits().hash(state)
+    }
+}
+
 impl From<f64> for NaiveDouble {
     fn from(x: f64) -> Self {
         NaiveDouble(x)
@@ -68,7 +83,7 @@ impl From<NaiveDouble> for f64 {
 }
 
 /// Constants for a pure type system
-#[derive(Debug, Copy, Clone, PartialEq, Eq, PartialOrd, Ord)]
+#[derive(Debug, Copy, Clone, PartialEq, Eq, PartialOrd, Ord, Hash)]
 pub enum Const {
     Type,
     Kind,
@@ -80,7 +95,7 @@ pub enum Const {
 /// The `Label` field is the variable's name (i.e. \"`x`\").
 /// The `Int` field is a DeBruijn index.
 /// See dhall-lang/standard/semantics.md for details
-#[derive(Debug, Clone, PartialEq, Eq)]
+#[derive(Debug, Clone, PartialEq, Eq, Hash)]
 pub struct V<Label>(pub Label, pub usize);
 
 // This is only for the specific `Label` type, not generic
@@ -97,7 +112,7 @@ impl<'a> From<&'a Label> for V<Label> {
 
 // Definition order must match precedence order for
 // pretty-printing to work correctly
-#[derive(Debug, Copy, Clone, PartialEq, Eq, PartialOrd, Ord)]
+#[derive(Debug, Copy, Clone, PartialEq, Eq, PartialOrd, Ord, Hash)]
 pub enum BinOp {
     /// `x ? y`
     ImportAlt,
@@ -128,7 +143,7 @@ pub enum BinOp {
 }
 
 /// Built-ins
-#[derive(Debug, Copy, Clone, PartialEq, Eq)]
+#[derive(Debug, Copy, Clone, PartialEq, Eq, Hash)]
 pub enum Builtin {
     Bool,
     Natural,
@@ -162,8 +177,8 @@ pub enum Builtin {
 }
 
 // Each node carries an annotation. In practice it's either X (no annotation) or a Span.
-#[derive(Debug)]
-pub struct SubExpr<Embed>(Rc<(Expr<Embed>, Option<Span>)>);
+#[derive(Debug, Clone)]
+pub struct SubExpr<Embed>(Box<(Expr<Embed>, Option<Span>)>);
 
 impl<Embed: PartialEq> std::cmp::PartialEq for SubExpr<Embed> {
     fn eq(&self, other: &Self) -> bool {
@@ -173,13 +188,22 @@ impl<Embed: PartialEq> std::cmp::PartialEq for SubExpr<Embed> {
 
 impl<Embed: Eq> std::cmp::Eq for SubExpr<Embed> {}
 
+impl<Embed: std::hash::Hash> std::hash::Hash for SubExpr<Embed> {
+    fn hash<H>(&self, state: &mut H)
+    where
+        H: std::hash::Hasher,
+    {
+        (self.0).0.hash(state)
+    }
+}
+
 pub type Expr<Embed> = ExprF<SubExpr<Embed>, Embed>;
 
 /// 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)]
+#[derive(Debug, Clone, PartialEq, Eq, Hash)]
 pub enum ExprF<SubExpr, Embed> {
     Const(Const),
     ///  `x`
@@ -233,7 +257,9 @@ pub enum ExprF<SubExpr, Embed> {
     Field(SubExpr, Label),
     ///  `e.{ x, y, z }`
     Projection(SubExpr, DupTreeSet<Label>),
-    /// Embeds an import or the result of resolving the import
+    /// `./some/path`
+    Import(Import<SubExpr>),
+    /// Embeds the result of resolving an import
     Embed(Embed),
 }
 
@@ -245,92 +271,62 @@ impl<SE, E> ExprF<SE, E> {
         v.visit(self)
     }
 
-    pub fn traverse_ref_with_special_handling_of_binders<'a, SE2, E2, Err>(
+    pub fn traverse_ref_with_special_handling_of_binders<'a, SE2, Err>(
         &'a self,
         visit_subexpr: impl FnMut(&'a SE) -> Result<SE2, Err>,
         visit_under_binder: impl FnOnce(&'a Label, &'a SE) -> Result<SE2, Err>,
-        visit_embed: impl FnOnce(&'a E) -> Result<E2, Err>,
-    ) -> Result<ExprF<SE2, E2>, Err> {
+    ) -> Result<ExprF<SE2, E>, Err>
+    where
+        E: Clone,
+    {
         self.visit(visitor::TraverseRefWithBindersVisitor {
             visit_subexpr,
             visit_under_binder,
-            visit_embed,
         })
     }
 
-    fn traverse_ref<'a, SE2, E2, Err>(
+    fn traverse_ref<'a, SE2, Err>(
         &'a self,
         visit_subexpr: impl FnMut(&'a SE) -> Result<SE2, Err>,
-        visit_embed: impl FnOnce(&'a E) -> Result<E2, Err>,
-    ) -> Result<ExprF<SE2, E2>, Err> {
-        self.visit(visitor::TraverseRefVisitor {
-            visit_subexpr,
-            visit_embed,
-        })
+    ) -> Result<ExprF<SE2, E>, Err>
+    where
+        E: Clone,
+    {
+        self.visit(visitor::TraverseRefVisitor { visit_subexpr })
     }
 
-    pub fn map_ref_with_special_handling_of_binders<'a, SE2, E2>(
+    pub fn map_ref_with_special_handling_of_binders<'a, SE2>(
         &'a self,
         mut map_subexpr: impl FnMut(&'a SE) -> SE2,
         mut map_under_binder: impl FnMut(&'a Label, &'a SE) -> SE2,
-        map_embed: impl FnOnce(&'a E) -> E2,
-    ) -> ExprF<SE2, E2> {
+    ) -> ExprF<SE2, E>
+    where
+        E: Clone,
+    {
         trivial_result(self.traverse_ref_with_special_handling_of_binders(
             |x| Ok(map_subexpr(x)),
             |l, x| Ok(map_under_binder(l, x)),
-            |x| Ok(map_embed(x)),
         ))
     }
 
-    pub fn map_ref<'a, SE2, E2>(
+    pub fn map_ref<'a, SE2>(
         &'a self,
         mut map_subexpr: impl FnMut(&'a SE) -> SE2,
-        map_embed: impl FnOnce(&'a E) -> E2,
-    ) -> ExprF<SE2, E2> {
-        trivial_result(
-            self.traverse_ref(|x| Ok(map_subexpr(x)), |x| Ok(map_embed(x))),
-        )
-    }
-
-    pub fn traverse_ref_simple<'a, SE2, Err>(
-        &'a self,
-        visit_subexpr: impl FnMut(&'a SE) -> Result<SE2, Err>,
-    ) -> Result<ExprF<SE2, E>, Err>
-    where
-        E: Clone,
-    {
-        self.traverse_ref(visit_subexpr, |x| Ok(E::clone(x)))
-    }
-
-    pub fn map_ref_simple<'a, SE2>(
-        &'a self,
-        map_subexpr: impl Fn(&'a SE) -> SE2,
     ) -> ExprF<SE2, E>
     where
         E: Clone,
     {
-        self.map_ref(map_subexpr, E::clone)
+        trivial_result(self.traverse_ref(|x| Ok(map_subexpr(x))))
     }
 }
 
 impl<E> Expr<E> {
-    fn traverse_embed<E2, Err>(
-        &self,
-        visit_embed: impl FnMut(&E) -> Result<E2, Err>,
-    ) -> Result<Expr<E2>, Err> {
-        self.visit(&mut visitor::TraverseEmbedVisitor(visit_embed))
-    }
-
-    fn map_embed<E2>(&self, mut map_embed: impl FnMut(&E) -> E2) -> Expr<E2> {
-        trivial_result(self.traverse_embed(|x| Ok(map_embed(x))))
-    }
-
     pub fn traverse_resolve<E2, Err>(
         &self,
-        visit_embed: impl FnMut(&E) -> Result<E2, Err>,
+        visit_import: impl FnMut(&Import<SubExpr<E2>>) -> Result<E2, Err>,
     ) -> Result<Expr<E2>, Err> {
         self.traverse_resolve_with_visitor(&mut visitor::ResolveVisitor(
-            visit_embed,
+            visit_import,
         ))
     }
 
@@ -339,35 +335,35 @@ impl<E> Expr<E> {
         visitor: &mut visitor::ResolveVisitor<F1>,
     ) -> Result<Expr<E2>, Err>
     where
-        F1: FnMut(&E) -> Result<E2, Err>,
+        F1: FnMut(&Import<SubExpr<E2>>) -> Result<E2, Err>,
     {
         match self {
             ExprF::BinOp(BinOp::ImportAlt, l, r) => l
                 .as_ref()
                 .traverse_resolve_with_visitor(visitor)
                 .or(r.as_ref().traverse_resolve_with_visitor(visitor)),
-            _ => self.visit(visitor),
+            _ => {
+                let e = self.visit(&mut *visitor)?;
+                Ok(match &e {
+                    ExprF::Import(import) => ExprF::Embed((visitor.0)(import)?),
+                    _ => e,
+                })
+            }
         }
     }
 }
 
-impl Expr<X> {
-    pub fn absurd<E>(&self) -> Expr<E> {
-        self.visit(&mut visitor::AbsurdVisitor)
-    }
-}
-
 impl<E> SubExpr<E> {
     pub fn as_ref(&self) -> &Expr<E> {
         &self.0.as_ref().0
     }
 
     pub fn new(x: Expr<E>, n: Span) -> Self {
-        SubExpr(Rc::new((x, Some(n))))
+        SubExpr(Box::new((x, Some(n))))
     }
 
     pub fn from_expr_no_span(x: Expr<E>) -> Self {
-        SubExpr(Rc::new((x, None)))
+        SubExpr(Box::new((x, None)))
     }
 
     pub fn from_builtin(b: Builtin) -> Self {
@@ -375,56 +371,16 @@ impl<E> SubExpr<E> {
     }
 
     pub fn rewrap<E2>(&self, x: Expr<E2>) -> SubExpr<E2> {
-        SubExpr(Rc::new((x, (self.0).1.clone())))
-    }
-
-    pub fn traverse_embed<E2, Err>(
-        &self,
-        visit_embed: impl FnMut(&E) -> Result<E2, Err>,
-    ) -> Result<SubExpr<E2>, Err> {
-        Ok(self.rewrap(self.as_ref().traverse_embed(visit_embed)?))
-    }
-
-    pub fn map_embed<E2>(
-        &self,
-        map_embed: impl FnMut(&E) -> E2,
-    ) -> SubExpr<E2> {
-        self.rewrap(self.as_ref().map_embed(map_embed))
-    }
-
-    pub fn map_subexprs_with_special_handling_of_binders<'a>(
-        &'a self,
-        map_expr: impl FnMut(&'a Self) -> Self,
-        map_under_binder: impl FnMut(&'a Label, &'a Self) -> Self,
-    ) -> Self {
-        match self.as_ref() {
-            ExprF::Embed(_) => SubExpr::clone(self),
-            // This calls ExprF::map_ref
-            e => self.rewrap(e.map_ref_with_special_handling_of_binders(
-                map_expr,
-                map_under_binder,
-                |_| unreachable!(),
-            )),
-        }
+        SubExpr(Box::new((x, (self.0).1.clone())))
     }
+}
 
+impl<E> SubExpr<E> {
     pub fn traverse_resolve<E2, Err>(
         &self,
-        visit_embed: impl FnMut(&E) -> Result<E2, Err>,
+        visit_import: impl FnMut(&Import<SubExpr<E2>>) -> Result<E2, Err>,
     ) -> Result<SubExpr<E2>, Err> {
-        Ok(self.rewrap(self.as_ref().traverse_resolve(visit_embed)?))
-    }
-}
-
-impl SubExpr<X> {
-    pub fn absurd<T>(&self) -> SubExpr<T> {
-        SubExpr::from_expr_no_span(self.as_ref().absurd())
-    }
-}
-
-impl<E> Clone for SubExpr<E> {
-    fn clone(&self) -> Self {
-        SubExpr(Rc::clone(&self.0))
+        Ok(self.rewrap(self.as_ref().traverse_resolve(visit_import)?))
     }
 }
 
diff --git a/dhall_syntax/src/core/import.rs b/dhall_syntax/src/core/import.rs
index d41eae2..9329d48 100644
--- a/dhall_syntax/src/core/import.rs
+++ b/dhall_syntax/src/core/import.rs
@@ -13,21 +13,20 @@ pub enum FilePrefix {
 
 /// The location of import (i.e. local vs. remote vs. environment)
 #[derive(Debug, Clone, PartialEq, Eq, Hash)]
-pub enum ImportLocation {
+pub enum ImportLocation<SubExpr> {
     Local(FilePrefix, Vec<String>),
-    Remote(URL),
+    Remote(URL<SubExpr>),
     Env(String),
     Missing,
 }
 
 #[derive(Debug, Clone, PartialEq, Eq, Hash)]
-pub struct URL {
+pub struct URL<SubExpr> {
     pub scheme: Scheme,
     pub authority: String,
     pub path: Vec<String>,
     pub query: Option<String>,
-    // TODO: implement inline headers
-    pub headers: Option<Box<ImportHashed>>,
+    pub headers: Option<SubExpr>,
 }
 
 #[derive(Debug, Copy, Clone, PartialEq, Eq, Hash)]
@@ -49,15 +48,54 @@ pub enum Hash {
     SHA256(Vec<u8>),
 }
 
+/// Reference to an external resource
 #[derive(Debug, Clone, PartialEq, Eq, Hash)]
-pub struct ImportHashed {
-    pub location: ImportLocation,
+pub struct Import<SubExpr> {
+    pub mode: ImportMode,
+    pub location: ImportLocation<SubExpr>,
     pub hash: Option<Hash>,
 }
 
-/// Reference to an external resource
-#[derive(Debug, Clone, PartialEq, Eq, Hash)]
-pub struct Import {
-    pub mode: ImportMode,
-    pub location_hashed: ImportHashed,
+impl<SE> URL<SE> {
+    pub fn visit_subexpr<'a, Err, SE2>(
+        &'a self,
+        f: impl FnOnce(&'a SE) -> Result<SE2, Err>,
+    ) -> Result<URL<SE2>, Err> {
+        let headers = self.headers.as_ref().map(f).transpose()?;
+        Ok(URL {
+            scheme: self.scheme,
+            authority: self.authority.clone(),
+            path: self.path.clone(),
+            query: self.query.clone(),
+            headers,
+        })
+    }
+}
+
+impl<SE> ImportLocation<SE> {
+    pub fn visit_subexpr<'a, Err, SE2>(
+        &'a self,
+        f: impl FnOnce(&'a SE) -> Result<SE2, Err>,
+    ) -> Result<ImportLocation<SE2>, Err> {
+        use ImportLocation::*;
+        Ok(match self {
+            Local(prefix, path) => Local(prefix.clone(), path.clone()),
+            Remote(url) => Remote(url.visit_subexpr(f)?),
+            Env(env) => Env(env.clone()),
+            Missing => Missing,
+        })
+    }
+}
+
+impl<SE> Import<SE> {
+    pub fn visit_subexpr<'a, Err, SE2>(
+        &'a self,
+        f: impl FnOnce(&'a SE) -> Result<SE2, Err>,
+    ) -> Result<Import<SE2>, Err> {
+        Ok(Import {
+            mode: self.mode,
+            location: self.location.visit_subexpr(f)?,
+            hash: self.hash.clone(),
+        })
+    }
 }
diff --git a/dhall_syntax/src/core/text.rs b/dhall_syntax/src/core/text.rs
index 0ce1e6f..10fd68a 100644
--- a/dhall_syntax/src/core/text.rs
+++ b/dhall_syntax/src/core/text.rs
@@ -1,6 +1,6 @@
 use std::iter::FromIterator;
 
-#[derive(Debug, Clone, PartialEq, Eq)]
+#[derive(Debug, Clone, PartialEq, Eq, Hash)]
 pub struct InterpolatedText<SubExpr> {
     head: String,
     tail: Vec<(SubExpr, String)>,
diff --git a/dhall_syntax/src/core/visitor.rs b/dhall_syntax/src/core/visitor.rs
index 50ec68a..7b4ed4b 100644
--- a/dhall_syntax/src/core/visitor.rs
+++ b/dhall_syntax/src/core/visitor.rs
@@ -2,52 +2,56 @@ use crate::*;
 use std::iter::FromIterator;
 
 /// A way too generic Visitor trait.
-pub trait GenericVisitor<Input, Return>: Sized {
-    fn visit(self, input: Input) -> Return;
+pub trait GenericVisitor<Input, Output>: Sized {
+    fn visit(self, input: Input) -> Output;
 }
 
-/// A visitor trait that can be used to traverse `ExprF`s. We need this pattern
-/// so that Rust lets us have as much mutability as we can.
-/// For example, `traverse_embed` cannot be made using only `traverse_ref`, because
-/// `traverse_ref` takes a `FnMut` so we would need to pass multiple mutable
-/// reverences to this argument to `traverse_ref`. But Rust's ownership system
-/// is all about preventing exactly this ! So we have to be more clever.
-/// The visitor pattern allows us to have only one mutable thing the whole
-/// time: the visitor itself. The visitor can then carry around multiple closures
-/// or just one, and Rust is ok with either. See for example TraverseRefVisitor
-/// and TraverseEmbedVisitor.
-/// This is very generic. For a more legible trait, see ExprFInFallibleVisitor
-pub trait ExprFVeryGenericVisitor<'a, Ret, SE1, E1>: Sized {
+/// A visitor trait that can be used to traverse `ExprF`s. We need this pattern so that Rust lets
+/// us have as much mutability as we can.
+/// For example, `traverse_ref_with_special_handling_of_binders` cannot be made using only
+/// `traverse_ref`, because `traverse_ref` takes a `FnMut` so we would need to pass multiple
+/// mutable reverences to this argument to `traverse_ref`. But Rust's ownership system is all about
+/// preventing exactly this ! So we have to be more clever. The visitor pattern allows us to have
+/// only one mutable thing the whole time: the visitor itself. The visitor can then carry around
+/// multiple closures or just one, and Rust is ok with either. See for example TraverseRefVisitor.
+pub trait ExprFFallibleVisitor<'a, SE1, SE2, E1, E2>: Sized {
     type Error;
-    type SE2;
-    type E2;
 
-    fn visit_subexpr(
-        &mut self,
-        subexpr: &'a SE1,
-    ) -> Result<Self::SE2, Self::Error>;
+    fn visit_subexpr(&mut self, subexpr: &'a SE1) -> Result<SE2, Self::Error>;
+    fn visit_embed(self, embed: &'a E1) -> Result<E2, Self::Error>;
 
     fn visit_subexpr_under_binder(
-        self,
-        label: &'a Label,
+        mut self,
+        _label: &'a Label,
         subexpr: &'a SE1,
-    ) -> Result<Self::SE2, Self::Error>;
+    ) -> Result<SE2, Self::Error> {
+        self.visit_subexpr(subexpr)
+    }
+}
 
-    fn visit_embed_squash(self, embed: &'a E1) -> Result<Ret, Self::Error>;
+/// Like ExprFFallibleVisitor, but without the error handling.
+pub trait ExprFInFallibleVisitor<'a, SE1, SE2, E1, E2>: Sized {
+    fn visit_subexpr(&mut self, subexpr: &'a SE1) -> SE2;
+    fn visit_embed(self, embed: &'a E1) -> E2;
 
-    // Called with the result of the map, in the non-embed case.
-    // Useful to change the result type, and/or avoid some loss of info
-    fn visit_resulting_exprf(
-        result: ExprF<Self::SE2, Self::E2>,
-    ) -> Result<Ret, Self::Error>;
+    fn visit_subexpr_under_binder(
+        mut self,
+        _label: &'a Label,
+        subexpr: &'a SE1,
+    ) -> SE2 {
+        self.visit_subexpr(subexpr)
+    }
 }
 
-impl<'a, T, Ret, SE1, E1>
-    GenericVisitor<&'a ExprF<SE1, E1>, Result<Ret, T::Error>> for T
+impl<'a, T, SE1, SE2, E1, E2>
+    GenericVisitor<&'a ExprF<SE1, E1>, Result<ExprF<SE2, E2>, T::Error>> for T
 where
-    T: ExprFVeryGenericVisitor<'a, Ret, SE1, E1>,
+    T: ExprFFallibleVisitor<'a, SE1, SE2, E1, E2>,
 {
-    fn visit(self, input: &'a ExprF<SE1, E1>) -> Result<Ret, T::Error> {
+    fn visit(
+        self,
+        input: &'a ExprF<SE1, E1>,
+    ) -> Result<ExprF<SE2, E2>, T::Error> {
         fn vec<'a, T, U, Err, F: FnMut(&'a T) -> Result<U, Err>>(
             x: &'a [T],
             f: F,
@@ -63,27 +67,27 @@ where
                 None => None,
             })
         }
-        fn dupmap<'a, V, Ret, SE, E, T>(
-            x: impl IntoIterator<Item = (&'a Label, &'a SE)>,
+        fn dupmap<'a, V, SE1, SE2, E1, E2, T>(
+            x: impl IntoIterator<Item = (&'a Label, &'a SE1)>,
             mut v: V,
         ) -> Result<T, V::Error>
         where
-            SE: 'a,
-            T: FromIterator<(Label, V::SE2)>,
-            V: ExprFVeryGenericVisitor<'a, Ret, SE, E>,
+            SE1: 'a,
+            T: FromIterator<(Label, SE2)>,
+            V: ExprFFallibleVisitor<'a, SE1, SE2, E1, E2>,
         {
             x.into_iter()
                 .map(|(k, x)| Ok((k.clone(), v.visit_subexpr(x)?)))
                 .collect()
         }
-        fn optdupmap<'a, V, Ret, SE, E, T>(
-            x: impl IntoIterator<Item = (&'a Label, &'a Option<SE>)>,
+        fn optdupmap<'a, V, SE1, SE2, E1, E2, T>(
+            x: impl IntoIterator<Item = (&'a Label, &'a Option<SE1>)>,
             mut v: V,
         ) -> Result<T, V::Error>
         where
-            SE: 'a,
-            T: FromIterator<(Label, Option<V::SE2>)>,
-            V: ExprFVeryGenericVisitor<'a, Ret, SE, E>,
+            SE1: 'a,
+            T: FromIterator<(Label, Option<SE2>)>,
+            V: ExprFFallibleVisitor<'a, SE1, SE2, E1, E2>,
         {
             x.into_iter()
                 .map(|(k, x)| {
@@ -100,7 +104,7 @@ where
 
         let mut v = self;
         use crate::ExprF::*;
-        T::visit_resulting_exprf(match input {
+        Ok(match input {
             Var(v) => Var(v.clone()),
             Lam(l, t, e) => {
                 let t = v.visit_subexpr(t)?;
@@ -149,90 +153,19 @@ where
             Field(e, l) => Field(v.visit_subexpr(e)?, l.clone()),
             Projection(e, ls) => Projection(v.visit_subexpr(e)?, ls.clone()),
             Assert(e) => Assert(v.visit_subexpr(e)?),
-            Embed(a) => return v.visit_embed_squash(a),
+            Import(i) => Import(i.visit_subexpr(|e| v.visit_subexpr(e))?),
+            Embed(a) => Embed(v.visit_embed(a)?),
         })
     }
 }
 
-/// Like ExprFVeryGenericVisitor, but sets the return
-/// type to ExprF<_>
-pub trait ExprFFallibleVisitor<'a, SE1, SE2, E1, E2>: Sized {
-    type Error;
-
-    fn visit_subexpr(&mut self, subexpr: &'a SE1) -> Result<SE2, Self::Error>;
-    fn visit_embed(self, embed: &'a E1) -> Result<E2, Self::Error>;
-
-    fn visit_subexpr_under_binder(
-        mut self,
-        _label: &'a Label,
-        subexpr: &'a SE1,
-    ) -> Result<SE2, Self::Error> {
-        self.visit_subexpr(subexpr)
-    }
-
-    fn visit_embed_squash(
-        self,
-        embed: &'a E1,
-    ) -> Result<ExprF<SE2, E2>, Self::Error> {
-        Ok(ExprF::Embed(self.visit_embed(embed)?))
-    }
-}
-
-impl<'a, T, SE1, SE2, E1, E2>
-    ExprFVeryGenericVisitor<'a, ExprF<SE2, E2>, SE1, E1> for T
+impl<'a, T, SE1, SE2, E1, E2> GenericVisitor<&'a ExprF<SE1, E1>, ExprF<SE2, E2>>
+    for T
 where
-    T: ExprFFallibleVisitor<'a, SE1, SE2, E1, E2>,
+    T: ExprFInFallibleVisitor<'a, SE1, SE2, E1, E2>,
 {
-    type Error = T::Error;
-    type SE2 = SE2;
-    type E2 = E2;
-
-    fn visit_subexpr(
-        &mut self,
-        subexpr: &'a SE1,
-    ) -> Result<Self::SE2, Self::Error> {
-        self.visit_subexpr(subexpr)
-    }
-
-    fn visit_subexpr_under_binder(
-        self,
-        label: &'a Label,
-        subexpr: &'a SE1,
-    ) -> Result<Self::SE2, Self::Error> {
-        self.visit_subexpr_under_binder(label, subexpr)
-    }
-
-    fn visit_embed_squash(
-        self,
-        embed: &'a E1,
-    ) -> Result<ExprF<SE2, E2>, Self::Error> {
-        self.visit_embed_squash(embed)
-    }
-
-    // Called with the result of the map, in the non-embed case.
-    // Useful to change the result type, and/or avoid some loss of info
-    fn visit_resulting_exprf(
-        result: ExprF<Self::SE2, Self::E2>,
-    ) -> Result<ExprF<SE2, E2>, Self::Error> {
-        Ok(result)
-    }
-}
-
-/// Like ExprFFallibleVisitor, but without the error handling.
-pub trait ExprFInFallibleVisitor<'a, SE1, SE2, E1, E2>: Sized {
-    fn visit_subexpr(&mut self, subexpr: &'a SE1) -> SE2;
-    fn visit_embed(self, embed: &'a E1) -> E2;
-
-    fn visit_subexpr_under_binder(
-        mut self,
-        _label: &'a Label,
-        subexpr: &'a SE1,
-    ) -> SE2 {
-        self.visit_subexpr(subexpr)
-    }
-
-    fn visit_embed_squash(self, embed: &'a E1) -> ExprF<SE2, E2> {
-        ExprF::Embed(self.visit_embed(embed))
+    fn visit(self, input: &'a ExprF<SE1, E1>) -> ExprF<SE2, E2> {
+        trivial_result(InfallibleWrapper(self).visit(input))
     }
 }
 
@@ -243,7 +176,7 @@ impl<'a, T, SE1, SE2, E1, E2> ExprFFallibleVisitor<'a, SE1, SE2, E1, E2>
 where
     T: ExprFInFallibleVisitor<'a, SE1, SE2, E1, E2>,
 {
-    type Error = X;
+    type Error = Void;
 
     fn visit_subexpr(&mut self, subexpr: &'a SE1) -> Result<SE2, Self::Error> {
         Ok(self.0.visit_subexpr(subexpr))
@@ -259,40 +192,20 @@ where
     ) -> Result<SE2, Self::Error> {
         Ok(self.0.visit_subexpr_under_binder(label, subexpr))
     }
-
-    fn visit_embed_squash(
-        self,
-        embed: &'a E1,
-    ) -> Result<ExprF<SE2, E2>, Self::Error> {
-        Ok(self.0.visit_embed_squash(embed))
-    }
 }
 
-impl<'a, T, SE1, SE2, E1, E2> GenericVisitor<&'a ExprF<SE1, E1>, ExprF<SE2, E2>>
-    for T
-where
-    T: ExprFInFallibleVisitor<'a, SE1, SE2, E1, E2>,
-{
-    fn visit(self, input: &'a ExprF<SE1, E1>) -> ExprF<SE2, E2> {
-        trivial_result(InfallibleWrapper(self).visit(input))
-    }
-}
-
-pub struct TraverseRefWithBindersVisitor<F1, F2, F4> {
+pub struct TraverseRefWithBindersVisitor<F1, F2> {
     pub visit_subexpr: F1,
     pub visit_under_binder: F2,
-    pub visit_embed: F4,
 }
 
-impl<'a, SE, E, SE2, E2, Err, F1, F2, F4>
-    ExprFFallibleVisitor<'a, SE, SE2, E, E2>
-    for TraverseRefWithBindersVisitor<F1, F2, F4>
+impl<'a, SE, E, SE2, Err, F1, F2> ExprFFallibleVisitor<'a, SE, SE2, E, E>
+    for TraverseRefWithBindersVisitor<F1, F2>
 where
     SE: 'a,
-    E: 'a,
+    E: 'a + Clone,
     F1: FnMut(&'a SE) -> Result<SE2, Err>,
     F2: FnOnce(&'a Label, &'a SE) -> Result<SE2, Err>,
-    F4: FnOnce(&'a E) -> Result<E2, Err>,
 {
     type Error = Err;
 
@@ -306,52 +219,29 @@ where
     ) -> Result<SE2, Self::Error> {
         (self.visit_under_binder)(label, subexpr)
     }
-    fn visit_embed(self, embed: &'a E) -> Result<E2, Self::Error> {
-        (self.visit_embed)(embed)
+    fn visit_embed(self, embed: &'a E) -> Result<E, Self::Error> {
+        Ok(embed.clone())
     }
 }
 
-pub struct TraverseRefVisitor<F1, F3> {
+pub struct TraverseRefVisitor<F1> {
     pub visit_subexpr: F1,
-    pub visit_embed: F3,
 }
 
-impl<'a, SE, E, SE2, E2, Err, F1, F3> ExprFFallibleVisitor<'a, SE, SE2, E, E2>
-    for TraverseRefVisitor<F1, F3>
+impl<'a, SE, E, SE2, Err, F1> ExprFFallibleVisitor<'a, SE, SE2, E, E>
+    for TraverseRefVisitor<F1>
 where
     SE: 'a,
-    E: 'a,
+    E: 'a + Clone,
     F1: FnMut(&'a SE) -> Result<SE2, Err>,
-    F3: FnOnce(&'a E) -> Result<E2, Err>,
 {
     type Error = Err;
 
     fn visit_subexpr(&mut self, subexpr: &'a SE) -> Result<SE2, Self::Error> {
         (self.visit_subexpr)(subexpr)
     }
-    fn visit_embed(self, embed: &'a E) -> Result<E2, Self::Error> {
-        (self.visit_embed)(embed)
-    }
-}
-
-pub struct TraverseEmbedVisitor<F1>(pub F1);
-
-impl<'a, 'b, E, E2, Err, F1>
-    ExprFFallibleVisitor<'a, SubExpr<E>, SubExpr<E2>, E, E2>
-    for &'b mut TraverseEmbedVisitor<F1>
-where
-    F1: FnMut(&E) -> Result<E2, Err>,
-{
-    type Error = Err;
-
-    fn visit_subexpr(
-        &mut self,
-        subexpr: &'a SubExpr<E>,
-    ) -> Result<SubExpr<E2>, Self::Error> {
-        Ok(subexpr.rewrap(subexpr.as_ref().visit(&mut **self)?))
-    }
-    fn visit_embed(self, embed: &'a E) -> Result<E2, Self::Error> {
-        (self.0)(embed)
+    fn visit_embed(self, embed: &'a E) -> Result<E, Self::Error> {
+        Ok(embed.clone())
     }
 }
 
@@ -361,7 +251,7 @@ impl<'a, 'b, E, E2, Err, F1>
     ExprFFallibleVisitor<'a, SubExpr<E>, SubExpr<E2>, E, E2>
     for &'b mut ResolveVisitor<F1>
 where
-    F1: FnMut(&E) -> Result<E2, Err>,
+    F1: FnMut(&Import<SubExpr<E2>>) -> Result<E2, Err>,
 {
     type Error = Err;
 
@@ -375,20 +265,7 @@ where
                 .traverse_resolve_with_visitor(&mut **self)?,
         ))
     }
-    fn visit_embed(self, embed: &'a E) -> Result<E2, Self::Error> {
-        (self.0)(embed)
-    }
-}
-
-pub struct AbsurdVisitor;
-
-impl<'a, 'b, E> ExprFInFallibleVisitor<'a, SubExpr<X>, SubExpr<E>, X, E>
-    for &'b mut AbsurdVisitor
-{
-    fn visit_subexpr(&mut self, subexpr: &'a SubExpr<X>) -> SubExpr<E> {
-        SubExpr::from_expr_no_span(subexpr.as_ref().visit(&mut **self))
-    }
-    fn visit_embed(self, embed: &'a X) -> E {
-        match *embed {}
+    fn visit_embed(self, _embed: &'a E) -> Result<E2, Self::Error> {
+        unimplemented!()
     }
 }
diff --git a/dhall_syntax/src/parser.rs b/dhall_syntax/src/parser.rs
index 1ab6e6d..8ecd0ab 100644
--- a/dhall_syntax/src/parser.rs
+++ b/dhall_syntax/src/parser.rs
@@ -15,10 +15,10 @@ use crate::*;
 // their own crate because they are quite general and useful. For now they
 // are here and hopefully you can figure out how they work.
 
-pub(crate) type ParsedExpr = Expr<Import>;
-pub(crate) type ParsedSubExpr = SubExpr<Import>;
-type ParsedText = InterpolatedText<SubExpr<Import>>;
-type ParsedTextContents = InterpolatedTextContents<SubExpr<Import>>;
+pub(crate) type ParsedExpr = Expr<Void>;
+pub(crate) type ParsedSubExpr = SubExpr<Void>;
+type ParsedText = InterpolatedText<ParsedSubExpr>;
+type ParsedTextContents = InterpolatedTextContents<ParsedSubExpr>;
 
 pub type ParseError = pest::error::Error<Rule>;
 
@@ -598,7 +598,7 @@ make_parser! {
         _ => unreachable!(),
     });
 
-    rule!(http_raw<URL>; children!(
+    rule!(http_raw<URL<ParsedSubExpr>>; children!(
         [scheme(sch), authority(auth), path(p)] => URL {
             scheme: sch,
             authority: auth,
@@ -619,10 +619,10 @@ make_parser! {
 
     rule!(query<String>; captured_str!(s) => s.to_owned());
 
-    rule!(http<URL>; children!(
+    rule!(http<URL<ParsedSubExpr>>; children!(
         [http_raw(url)] => url,
-        [http_raw(url), import_hashed(ih)] =>
-            URL { headers: Some(Box::new(ih)), ..url },
+        [http_raw(url), expression(e)] =>
+            URL { headers: Some(e), ..url },
     ));
 
     rule!(env<String>; children!(
@@ -654,7 +654,7 @@ make_parser! {
 
     token_rule!(missing<()>);
 
-    rule!(import_type<ImportLocation>; children!(
+    rule!(import_type<ImportLocation<ParsedSubExpr>>; children!(
         [missing(_)] => {
             ImportLocation::Missing
         },
@@ -679,33 +679,33 @@ make_parser! {
         Hash::SHA256(hex::decode(hash).unwrap())
     });
 
-    rule!(import_hashed<ImportHashed>; children!(
+    rule!(import_hashed<crate::Import<ParsedSubExpr>>; children!(
         [import_type(location)] =>
-            ImportHashed { location, hash: None },
+            crate::Import {mode: ImportMode::Code, location, hash: None },
         [import_type(location), hash(h)] =>
-            ImportHashed { location, hash: Some(h) },
+            crate::Import {mode: ImportMode::Code, location, hash: Some(h) },
     ));
 
     token_rule!(Text<()>);
     token_rule!(Location<()>);
 
     rule!(import<ParsedSubExpr> as expression; span; children!(
-        [import_hashed(location_hashed)] => {
-            spanned(span, Embed(Import {
+        [import_hashed(imp)] => {
+            spanned(span, Import(crate::Import {
                 mode: ImportMode::Code,
-                location_hashed
+                ..imp
             }))
         },
-        [import_hashed(location_hashed), Text(_)] => {
-            spanned(span, Embed(Import {
+        [import_hashed(imp), Text(_)] => {
+            spanned(span, Import(crate::Import {
                 mode: ImportMode::RawText,
-                location_hashed
+                ..imp
             }))
         },
-        [import_hashed(location_hashed), Location(_)] => {
-            spanned(span, Embed(Import {
+        [import_hashed(imp), Location(_)] => {
+            spanned(span, Import(crate::Import {
                 mode: ImportMode::Location,
-                location_hashed
+                ..imp
             }))
         },
     ));
diff --git a/dhall_syntax/src/printer.rs b/dhall_syntax/src/printer.rs
index 95eafe5..256ea65 100644
--- a/dhall_syntax/src/printer.rs
+++ b/dhall_syntax/src/printer.rs
@@ -88,6 +88,7 @@ impl<SE: Display + Clone, E: Display> Display for ExprF<SE, E> {
                 }
                 Ok(())
             })?,
+            Import(a) => a.fmt(f)?,
             Embed(a) => a.fmt(f)?,
         }
         Ok(())
@@ -151,12 +152,14 @@ impl<A: Display + Clone> Expr<A> {
             // Precedence is magically handled by the ordering of BinOps.
             ExprF::BinOp(op, _, _) if phase > PrintPhase::BinOp(*op) => true,
             ExprF::App(_, _) if phase > PrintPhase::App => true,
-            Field(_, _) | Projection(_, _) if phase > Import => true,
+            Field(_, _) | Projection(_, _) if phase > PrintPhase::Import => {
+                true
+            }
             _ => false,
         };
 
         // Annotate subexpressions with the appropriate phase, defaulting to Base
-        let phased_self = match self.map_ref_simple(|e| PhasedExpr(e, Base)) {
+        let phased_self = match self.map_ref(|e| PhasedExpr(e, Base)) {
             Pi(a, b, c) => {
                 if &String::from(&a) == "_" {
                     Pi(a, b.phase(Operator), c)
@@ -165,8 +168,8 @@ impl<A: Display + Clone> Expr<A> {
                 }
             }
             Merge(a, b, c) => Merge(
-                a.phase(Import),
-                b.phase(Import),
+                a.phase(PrintPhase::Import),
+                b.phase(PrintPhase::Import),
                 c.map(|x| x.phase(PrintPhase::App)),
             ),
             Annot(a, b) => Annot(a.phase(Operator), b),
@@ -175,8 +178,11 @@ impl<A: Display + Clone> Expr<A> {
                 a.phase(PrintPhase::BinOp(op)),
                 b.phase(PrintPhase::BinOp(op)),
             ),
-            SomeLit(e) => SomeLit(e.phase(Import)),
-            ExprF::App(f, a) => ExprF::App(f.phase(Import), a.phase(Import)),
+            SomeLit(e) => SomeLit(e.phase(PrintPhase::Import)),
+            ExprF::App(f, a) => ExprF::App(
+                f.phase(PrintPhase::Import),
+                a.phase(PrintPhase::Import),
+            ),
             Field(a, b) => Field(a.phase(Primitive), b),
             Projection(e, ls) => Projection(e.phase(Primitive), ls),
             e => e,
@@ -224,7 +230,7 @@ where
     f.write_str(close)
 }
 
-impl<SubExpr: Display + Clone> Display for InterpolatedText<SubExpr> {
+impl<SubExpr: Display> Display for InterpolatedText<SubExpr> {
     fn fmt(&self, f: &mut fmt::Formatter) -> Result<(), fmt::Error> {
         f.write_str("\"")?;
         for x in self.iter() {
@@ -338,10 +344,11 @@ impl Display for Hash {
         }
     }
 }
-impl Display for ImportHashed {
+impl<SubExpr: Display> Display for Import<SubExpr> {
     fn fmt(&self, f: &mut fmt::Formatter) -> Result<(), fmt::Error> {
         use FilePrefix::*;
         use ImportLocation::*;
+        use ImportMode::*;
         let fmt_remote_path_component = |s: &str| -> String {
             use percent_encoding::{
                 utf8_percent_encode, PATH_SEGMENT_ENCODE_SET,
@@ -417,14 +424,6 @@ impl Display for ImportHashed {
             write!(f, " ")?;
             hash.fmt(f)?;
         }
-        Ok(())
-    }
-}
-
-impl Display for Import {
-    fn fmt(&self, f: &mut fmt::Formatter) -> Result<(), fmt::Error> {
-        self.location_hashed.fmt(f)?;
-        use ImportMode::*;
         match self.mode {
             Code => {}
             RawText => write!(f, " as Text")?,
@@ -491,9 +490,3 @@ impl<Label: Display> Display for V<Label> {
         Ok(())
     }
 }
-
-impl Display for X {
-    fn fmt(&self, _: &mut fmt::Formatter) -> Result<(), fmt::Error> {
-        match *self {}
-    }
-}