diff --git a/tamer/src/asg/air.rs b/tamer/src/asg/air.rs
index 4e529b78..7373a362 100644
--- a/tamer/src/asg/air.rs
+++ b/tamer/src/asg/air.rs
@@ -36,7 +36,7 @@ use super::{
 use crate::{
     diagnose::Annotate,
     diagnostic_unreachable,
-    f::Functor,
+    f::Map,
     parse::{prelude::*, StateStack},
     span::Span,
     sym::SymbolId,
@@ -1310,7 +1310,7 @@ impl<T> AsRef<T> for EnvScopeKind<T> {
     }
 }
 
-impl<T, U> Functor<T, U> for EnvScopeKind<T> {
+impl<T, U> Map<T, U> for EnvScopeKind<T> {
     type Target = EnvScopeKind<U>;
 
     fn map(self, f: impl FnOnce(T) -> U) -> Self::Target {
diff --git a/tamer/src/asg/air/expr.rs b/tamer/src/asg/air/expr.rs
index 11b29ecd..5759e281 100644
--- a/tamer/src/asg/air/expr.rs
+++ b/tamer/src/asg/air/expr.rs
@@ -31,7 +31,7 @@ use super::{
 };
 use crate::{
     asg::{graph::object::ObjectIndexTo, ObjectKind},
-    f::Functor,
+    f::Map,
     parse::prelude::*,
 };
 
diff --git a/tamer/src/asg/graph.rs b/tamer/src/asg/graph.rs
index 2dc7e9d6..62bd7c36 100644
--- a/tamer/src/asg/graph.rs
+++ b/tamer/src/asg/graph.rs
@@ -29,7 +29,7 @@ use self::object::{
 use super::{AsgError, Object, ObjectIndex, ObjectKind};
 use crate::{
     diagnose::{panic::DiagnosticPanic, Annotate, AnnotatedSpan},
-    f::Functor,
+    f::Map,
     global,
     span::Span,
 };
diff --git a/tamer/src/asg/graph/object.rs b/tamer/src/asg/graph/object.rs
index 74199a18..32131fdb 100644
--- a/tamer/src/asg/graph/object.rs
+++ b/tamer/src/asg/graph/object.rs
@@ -123,7 +123,7 @@ use super::{Asg, AsgError};
 use crate::{
     diagnose::{panic::DiagnosticPanic, Annotate, AnnotatedSpan},
     diagnostic_panic,
-    f::Functor,
+    f::Map,
     parse::util::SPair,
     span::{Span, UNKNOWN_SPAN},
 };
@@ -924,7 +924,7 @@ impl ObjectIndex<Object> {
     }
 }
 
-impl<O: ObjectKind> Functor<Span> for ObjectIndex<O> {
+impl<O: ObjectKind> Map<Span> for ObjectIndex<O> {
     fn map(self, f: impl FnOnce(Span) -> Span) -> Self {
         match self {
             Self(index, span, ph) => Self(index, f(span), ph),
diff --git a/tamer/src/asg/graph/object/expr.rs b/tamer/src/asg/graph/object/expr.rs
index b2d1e86b..58a9f6fe 100644
--- a/tamer/src/asg/graph/object/expr.rs
+++ b/tamer/src/asg/graph/object/expr.rs
@@ -20,7 +20,7 @@
 //! Expressions on the ASG.
 
 use super::{prelude::*, Doc, Ident, ObjectIndexTo, Tpl};
-use crate::{f::Functor, num::Dim, span::Span};
+use crate::{f::Map, num::Dim, span::Span};
 use std::fmt::Display;
 
 #[cfg(doc)]
@@ -52,7 +52,7 @@ impl Expr {
     }
 }
 
-impl Functor<Span> for Expr {
+impl Map<Span> for Expr {
     fn map(self, f: impl FnOnce(Span) -> Span) -> Self {
         match self {
             Self(op, dim, span) => Self(op, dim, f(span)),
diff --git a/tamer/src/asg/graph/object/ident.rs b/tamer/src/asg/graph/object/ident.rs
index 6ec4a6c8..bc4270a9 100644
--- a/tamer/src/asg/graph/object/ident.rs
+++ b/tamer/src/asg/graph/object/ident.rs
@@ -23,7 +23,7 @@ use super::{prelude::*, Expr, Meta, Pkg, Tpl};
 use crate::{
     diagnose::{panic::DiagnosticPanic, Annotate, Diagnostic},
     diagnostic_todo,
-    f::Functor,
+    f::Map,
     fmt::{DisplayWrapper, TtQuote},
     num::{Dim, Dtype},
     parse::{util::SPair, Token},
diff --git a/tamer/src/asg/graph/object/meta.rs b/tamer/src/asg/graph/object/meta.rs
index 15db6c60..5e56090c 100644
--- a/tamer/src/asg/graph/object/meta.rs
+++ b/tamer/src/asg/graph/object/meta.rs
@@ -36,7 +36,7 @@ use super::{prelude::*, Doc, Ident};
 use crate::{
     diagnose::Annotate,
     diagnostic_todo,
-    f::Functor,
+    f::Map,
     fmt::{DisplayWrapper, TtQuote},
     parse::{util::SPair, Token},
     span::Span,
@@ -156,7 +156,7 @@ impl Display for Meta {
     }
 }
 
-impl Functor<Span> for Meta {
+impl Map<Span> for Meta {
     fn map(self, f: impl FnOnce(Span) -> Span) -> Self::Target {
         match self {
             Self::Required(span) => Self::Required(f(span)),
diff --git a/tamer/src/asg/graph/object/pkg.rs b/tamer/src/asg/graph/object/pkg.rs
index c07f5242..f64291a6 100644
--- a/tamer/src/asg/graph/object/pkg.rs
+++ b/tamer/src/asg/graph/object/pkg.rs
@@ -21,7 +21,7 @@
 
 use super::{prelude::*, Doc, Ident, Tpl};
 use crate::{
-    f::Functor,
+    f::Map,
     fmt::{DisplayWrapper, TtQuote},
     parse::{util::SPair, Token},
     span::Span,
@@ -87,7 +87,7 @@ impl Display for Pkg {
     }
 }
 
-impl Functor<Span> for Pkg {
+impl Map<Span> for Pkg {
     fn map(self, f: impl FnOnce(Span) -> Span) -> Self::Target {
         match self {
             Self(span, path) => Self(f(span), path),
diff --git a/tamer/src/asg/graph/object/rel.rs b/tamer/src/asg/graph/object/rel.rs
index 6a789422..41a7b2a8 100644
--- a/tamer/src/asg/graph/object/rel.rs
+++ b/tamer/src/asg/graph/object/rel.rs
@@ -30,7 +30,7 @@ use crate::{
         graph::{object::Tpl, AsgRelMut},
         Asg, AsgError,
     },
-    f::Functor,
+    f::Map,
     span::Span,
 };
 use std::{fmt::Display, marker::PhantomData};
@@ -481,7 +481,7 @@ impl DynObjectRel<ObjectIndex<Object>, ObjectIndex<Object>> {
     }
 }
 
-impl<S, T, U, V> Functor<(S, T), (U, V)> for DynObjectRel<S, T> {
+impl<S, T, U, V> Map<(S, T), (U, V)> for DynObjectRel<S, T> {
     type Target = DynObjectRel<U, V>;
 
     fn map(self, f: impl FnOnce((S, T)) -> (U, V)) -> Self::Target {
diff --git a/tamer/src/asg/graph/object/tpl.rs b/tamer/src/asg/graph/object/tpl.rs
index 1e631ee5..b977e0b3 100644
--- a/tamer/src/asg/graph/object/tpl.rs
+++ b/tamer/src/asg/graph/object/tpl.rs
@@ -22,7 +22,7 @@
 use std::fmt::Display;
 
 use super::{prelude::*, Doc, Expr, Ident};
-use crate::{f::Functor, parse::util::SPair, span::Span};
+use crate::{f::Map, parse::util::SPair, span::Span};
 
 /// Template with associated name.
 #[derive(Debug, PartialEq, Eq)]
@@ -46,7 +46,7 @@ impl Tpl {
     }
 }
 
-impl Functor<Span> for Tpl {
+impl Map<Span> for Tpl {
     fn map(self, f: impl FnOnce(Span) -> Span) -> Self::Target {
         match self {
             Self(span, shape) => Self(f(span), shape),
@@ -54,7 +54,7 @@ impl Functor<Span> for Tpl {
     }
 }
 
-impl Functor<TplShape> for Tpl {
+impl Map<TplShape> for Tpl {
     fn map(self, f: impl FnOnce(TplShape) -> TplShape) -> Self::Target {
         match self {
             Self(span, shape) => Self(span, f(shape)),
diff --git a/tamer/src/asg/graph/visit/ontree/test.rs b/tamer/src/asg/graph/visit/ontree/test.rs
index 4b0443d3..f5dec397 100644
--- a/tamer/src/asg/graph/visit/ontree/test.rs
+++ b/tamer/src/asg/graph/visit/ontree/test.rs
@@ -24,7 +24,7 @@ use crate::{
         graph::object::ObjectRelTy,
         ExprOp,
     },
-    f::Functor,
+    f::Map,
     parse::{
         util::{spair, SPair},
         ParseState,
diff --git a/tamer/src/f.rs b/tamer/src/f.rs
index 7f82588c..be6d60a8 100644
--- a/tamer/src/f.rs
+++ b/tamer/src/f.rs
@@ -33,11 +33,12 @@
 
 /// A type providing a `map` function from inner type `T` to `U`.
 ///
-/// In an abuse of terminology,
-///   this functor is polymorphic over the entire trait,
+/// This used to be called `Functor`,
+///   but was renamed because it was an abuse of terminology;
+///   this is polymorphic over the entire trait,
 ///     rather than just the definition of `map`,
-///   allowing implementations to provide multiple specialized `map`s
-///     without having to define individual `map_*` methods.
+///     allowing implementations to provide multiple specialized `map`s
+///       without having to define individual `map_*` methods.
 /// Rust will often be able to infer the proper types and invoke the
 ///   intended `map` function within a given context,
 ///     but methods may still be explicitly disambiguated using the
@@ -46,16 +47,13 @@
 ///   if a functor requires a monomorphic function
 ///     (so `T = U`),
 ///   then it's not really a functor.
-/// We'll refer to these structures informally as monomorphic functors,
-///   since they provide the same type of API as a functor,
-///   but cannot change the underlying type.
 ///
 /// This trait also provides a number of convenience methods that can be
-///   implemented in terms of [`Functor::map`].
+///   implemented in terms of [`Map::map`].
 ///
 /// Why a primitive `map` instead of `fmap`?
 /// ========================================
-/// One of the methods of this trait is [`Functor::fmap`],
+/// One of the methods of this trait is [`Map::fmap`],
 ///   which [is motivated by Haskell][haskell-functor].
 /// This trait implements methods in terms of [`map`](Self::map) rather than
 ///   [`fmap`](Self::fmap) because `map` is a familiar idiom in Rust and
@@ -66,8 +64,8 @@
 ///   which is additional boilerplate relative to `map`.
 ///
 /// [haskell-functor]: https://hackage.haskell.org/package/base/docs/Data-Functor.html
-pub trait Functor<T, U = T>: Sized {
-    /// Type of object resulting from [`Functor::map`] operation.
+pub trait Map<T, U = T>: Sized {
+    /// Type of object resulting from [`Map::map`] operation.
     ///
     /// The term "target" originates from category theory,
     ///   representing the codomain of the functor.
@@ -83,7 +81,7 @@ pub trait Functor<T, U = T>: Sized {
     ///   all others are implemented in terms of it.
     fn map(self, f: impl FnOnce(T) -> U) -> Self::Target;
 
-    /// Curried form of [`Functor::map`],
+    /// Curried form of [`Map::map`],
     ///   with arguments reversed.
     ///
     /// `fmap` returns a unary closure that accepts an object of type
@@ -106,22 +104,22 @@ pub trait Functor<T, U = T>: Sized {
     ///
     /// This is intended for cases where there's a single element that will
     ///   be replaced,
-    ///     taking advantage of [`Functor`]'s trait-level polymorphism.
+    ///     taking advantage of [`Map`]'s trait-level polymorphism.
     fn overwrite(self, value: U) -> Self::Target {
         self.map(|_| value)
     }
 
-    /// Curried form of [`Functor::overwrite`],
+    /// Curried form of [`Map::overwrite`],
     ///   with arguments reversed.
     fn foverwrite(value: U) -> impl FnOnce(Self) -> Self::Target {
         move |x| x.overwrite(value)
     }
 }
 
-impl<T, U> Functor<T, U> for Option<T> {
+impl<T, U> Map<T, U> for Option<T> {
     type Target = Option<U>;
 
-    fn map(self, f: impl FnOnce(T) -> U) -> <Self as Functor<T, U>>::Target {
+    fn map(self, f: impl FnOnce(T) -> U) -> <Self as Map<T, U>>::Target {
         Option::map(self, f)
     }
 }
diff --git a/tamer/src/nir.rs b/tamer/src/nir.rs
index 4040a008..50f165ef 100644
--- a/tamer/src/nir.rs
+++ b/tamer/src/nir.rs
@@ -57,7 +57,7 @@ mod tplshort;
 
 use crate::{
     diagnose::{Annotate, Diagnostic},
-    f::Functor,
+    f::Map,
     fmt::{DisplayWrapper, TtQuote},
     parse::{util::SPair, Object, Token},
     span::Span,
@@ -228,7 +228,7 @@ impl Nir {
     }
 }
 
-impl Functor<SymbolId> for Nir {
+impl Map<SymbolId> for Nir {
     /// Map over a token's [`SymbolId`].
     ///
     /// This allows modifying a token's [`SymbolId`] while retaining the
diff --git a/tamer/src/nir/interp.rs b/tamer/src/nir/interp.rs
index cc8d6bc8..0f476df8 100644
--- a/tamer/src/nir/interp.rs
+++ b/tamer/src/nir/interp.rs
@@ -108,7 +108,7 @@ use memchr::memchr2;
 use super::{Nir, NirEntity};
 use crate::{
     diagnose::{panic::DiagnosticPanic, Annotate, AnnotatedSpan, Diagnostic},
-    f::Functor,
+    f::Map,
     fmt::{DisplayWrapper, TtQuote},
     parse::{prelude::*, util::SPair, NoContext},
     span::Span,
diff --git a/tamer/src/parse/util.rs b/tamer/src/parse/util.rs
index d22bda37..1aa53db5 100644
--- a/tamer/src/parse/util.rs
+++ b/tamer/src/parse/util.rs
@@ -26,7 +26,7 @@
 //!     to use outside of the domain of the parsing system itself.
 
 use super::{prelude::*, state::TransitionData};
-use crate::{f::Functor, span::Span, sym::SymbolId};
+use crate::{f::Map, span::Span, sym::SymbolId};
 use std::fmt::Display;
 
 /// A [`SymbolId`] with a corresponding [`Span`].
@@ -83,7 +83,7 @@ impl SPair {
     }
 }
 
-impl Functor<SymbolId> for SPair {
+impl Map<SymbolId> for SPair {
     /// Map over the [`SymbolId`] of the pair while retaining the original
     ///   associated [`Span`].
     ///
@@ -98,7 +98,7 @@ impl Functor<SymbolId> for SPair {
     }
 }
 
-impl Functor<Span> for SPair {
+impl Map<Span> for SPair {
     /// Map over the [`Span`] of the pair while retaining the associated
     ///   [`SymbolId`].
     ///
diff --git a/tamer/src/xir/autoclose.rs b/tamer/src/xir/autoclose.rs
index f08dc6c8..08421ff7 100644
--- a/tamer/src/xir/autoclose.rs
+++ b/tamer/src/xir/autoclose.rs
@@ -101,7 +101,7 @@ use super::{
     CloseSpan, OpenSpan, QName,
 };
 use crate::{
-    f::Functor,
+    f::Map,
     parse::prelude::*,
     span::{Span, UNKNOWN_SPAN},
     xir::EleSpan,
diff --git a/tamer/src/xir/flat.rs b/tamer/src/xir/flat.rs
index ec01f04f..1b2ec2e4 100644
--- a/tamer/src/xir/flat.rs
+++ b/tamer/src/xir/flat.rs
@@ -46,7 +46,7 @@ use super::{
     CloseSpan, OpenSpan, QName, Token as XirToken, TokenStream,
 };
 use crate::{
-    f::Functor,
+    f::Map,
     parse::prelude::*,
     span::Span,
     sym::{st::is_common_whitespace, GlobalSymbolResolve, SymbolId},
@@ -248,7 +248,7 @@ impl<T: TextType> From<Attr> for XirfToken<T> {
     }
 }
 
-impl<T: TextType> Functor<Depth> for XirfToken<T> {
+impl<T: TextType> Map<Depth> for XirfToken<T> {
     fn map(self, f: impl FnOnce(Depth) -> Depth) -> Self::Target {
         use XirfToken::*;