diff --git a/src/eval/ops.rs b/src/eval/ops.rs
index c1dd726b6..53205ce89 100644
--- a/src/eval/ops.rs
+++ b/src/eval/ops.rs
@@ -1,8 +1,27 @@
-use std::cmp::Ordering::*;
+use std::cmp::Ordering;
 
 use super::Value;
 use Value::*;
 
+/// Join a value with another value.
+pub fn join(lhs: Value, rhs: Value) -> Result<Value, Value> {
+    Ok(match (lhs, rhs) {
+        (_, Error) => Error,
+        (Error, _) => Error,
+        (a, None) => a,
+        (None, b) => b,
+
+        (Str(a), Str(b)) => Str(a + &b),
+        (Array(a), Array(b)) => Array(a + &b),
+        (Dict(a), Dict(b)) => Dict(a + &b),
+        (Template(a), Template(b)) => Template(a + &b),
+        (Template(a), Str(b)) => Template(a + b),
+        (Str(a), Template(b)) => Template(a + b),
+
+        (lhs, _) => return Err(lhs),
+    })
+}
+
 /// Apply the plus operator to a value.
 pub fn pos(value: Value) -> Value {
     match value {
@@ -55,7 +74,14 @@ pub fn add(lhs: Value, rhs: Value) -> Value {
 
         (Fractional(a), Fractional(b)) => Fractional(a + b),
 
-        (a, b) => concat(a, b).unwrap_or(Value::Error),
+        (Str(a), Str(b)) => Str(a + &b),
+        (Array(a), Array(b)) => Array(a + &b),
+        (Dict(a), Dict(b)) => Dict(a + &b),
+        (Template(a), Template(b)) => Template(a + &b),
+        (Template(a), Str(b)) => Template(a + b),
+        (Str(a), Template(b)) => Template(a + b),
+
+        _ => Error,
     }
 }
 
@@ -184,30 +210,80 @@ pub fn or(lhs: Value, rhs: Value) -> Value {
     }
 }
 
+/// Determine whether two values are equal.
+pub fn equal(lhs: &Value, rhs: &Value) -> bool {
+    match (lhs, rhs) {
+        // Compare reflexively.
+        (None, None) => true,
+        (Auto, Auto) => true,
+        (Bool(a), Bool(b)) => a == b,
+        (Int(a), Int(b)) => a == b,
+        (Float(a), Float(b)) => a == b,
+        (Length(a), Length(b)) => a == b,
+        (Angle(a), Angle(b)) => a == b,
+        (Relative(a), Relative(b)) => a == b,
+        (Linear(a), Linear(b)) => a == b,
+        (Fractional(a), Fractional(b)) => a == b,
+        (Color(a), Color(b)) => a == b,
+        (Str(a), Str(b)) => a == b,
+        (Array(a), Array(b)) => a == b,
+        (Dict(a), Dict(b)) => a == b,
+        (Template(a), Template(b)) => a == b,
+        (Func(a), Func(b)) => a == b,
+        (Any(a), Any(b)) => a == b,
+        (Error, Error) => true,
+
+        // Some technically different things should compare equal.
+        (&Int(a), &Float(b)) => a as f64 == b,
+        (&Float(a), &Int(b)) => a == b as f64,
+        (&Length(a), &Linear(b)) => a == b.abs && b.rel.is_zero(),
+        (&Relative(a), &Linear(b)) => a == b.rel && b.abs.is_zero(),
+        (&Linear(a), &Length(b)) => a.abs == b && a.rel.is_zero(),
+        (&Linear(a), &Relative(b)) => a.rel == b && a.abs.is_zero(),
+
+        _ => false,
+    }
+}
+
 /// Compute whether two values are equal.
 pub fn eq(lhs: Value, rhs: Value) -> Value {
-    Bool(lhs.eq(&rhs))
+    Bool(equal(&lhs, &rhs))
 }
 
 /// Compute whether two values are equal.
 pub fn neq(lhs: Value, rhs: Value) -> Value {
-    Bool(!lhs.eq(&rhs))
+    Bool(!equal(&lhs, &rhs))
+}
+
+/// Compare two values.
+pub fn compare(lhs: &Value, rhs: &Value) -> Option<Ordering> {
+    match (lhs, rhs) {
+        (Bool(a), Bool(b)) => a.partial_cmp(b),
+        (Int(a), Int(b)) => a.partial_cmp(b),
+        (Int(a), Float(b)) => (*a as f64).partial_cmp(b),
+        (Float(a), Int(b)) => a.partial_cmp(&(*b as f64)),
+        (Float(a), Float(b)) => a.partial_cmp(b),
+        (Angle(a), Angle(b)) => a.partial_cmp(b),
+        (Length(a), Length(b)) => a.partial_cmp(b),
+        (Str(a), Str(b)) => a.partial_cmp(b),
+        _ => Option::None,
+    }
 }
 
 macro_rules! comparison {
     ($name:ident, $($pat:tt)*) => {
         /// Compute how a value compares with another value.
         pub fn $name(lhs: Value, rhs: Value) -> Value {
-            lhs.cmp(&rhs)
-                .map_or(Value::Error, |x| Value::Bool(matches!(x, $($pat)*)))
+            compare(&lhs, &rhs)
+                .map_or(Error, |x| Bool(matches!(x, $($pat)*)))
         }
     };
 }
 
-comparison!(lt, Less);
-comparison!(leq, Less | Equal);
-comparison!(gt, Greater);
-comparison!(geq, Greater | Equal);
+comparison!(lt, Ordering::Less);
+comparison!(leq, Ordering::Less | Ordering::Equal);
+comparison!(gt, Ordering::Greater);
+comparison!(geq, Ordering::Greater | Ordering::Equal);
 
 /// Compute the range from `lhs` to `rhs`.
 pub fn range(lhs: Value, rhs: Value) -> Value {
@@ -216,29 +292,3 @@ pub fn range(lhs: Value, rhs: Value) -> Value {
         _ => Error,
     }
 }
-
-/// Join a value with another value.
-pub fn join(lhs: Value, rhs: Value) -> Result<Value, Value> {
-    Ok(match (lhs, rhs) {
-        (_, Error) => Error,
-        (Error, _) => Error,
-
-        (a, None) => a,
-        (None, b) => b,
-
-        (a, b) => return concat(a, b),
-    })
-}
-
-/// Concatentate two values.
-fn concat(lhs: Value, rhs: Value) -> Result<Value, Value> {
-    Ok(match (lhs, rhs) {
-        (Str(a), Str(b)) => Str(a + &b),
-        (Array(a), Array(b)) => Array(a + &b),
-        (Dict(a), Dict(b)) => Dict(a + &b),
-        (Template(a), Template(b)) => Template(a + &b),
-        (Template(a), Str(b)) => Template(a + b),
-        (Str(a), Template(b)) => Template(a + b),
-        (a, _) => return Err(a),
-    })
-}
diff --git a/src/eval/value.rs b/src/eval/value.rs
index fe9494b1b..7c35fdbd8 100644
--- a/src/eval/value.rs
+++ b/src/eval/value.rs
@@ -10,7 +10,7 @@ use crate::geom::{Angle, Fractional, Length, Linear, Relative};
 use crate::syntax::{Span, Spanned};
 
 /// A computational value.
-#[derive(Debug, Clone, PartialEq)]
+#[derive(Debug, Clone)]
 pub enum Value {
     /// The value that indicates the absence of a meaningful value.
     None,
@@ -83,39 +83,6 @@ impl Value {
         }
     }
 
-    /// Recursively compute whether two values are equal.
-    pub fn eq(&self, rhs: &Self) -> bool {
-        match (self, rhs) {
-            (&Self::Int(a), &Self::Float(b)) => a as f64 == b,
-            (&Self::Float(a), &Self::Int(b)) => a == b as f64,
-            (&Self::Length(a), &Self::Linear(b)) => a == b.abs && b.rel.is_zero(),
-            (&Self::Relative(a), &Self::Linear(b)) => a == b.rel && b.abs.is_zero(),
-            (&Self::Linear(a), &Self::Length(b)) => a.abs == b && a.rel.is_zero(),
-            (&Self::Linear(a), &Self::Relative(b)) => a.rel == b && a.abs.is_zero(),
-            (Self::Array(a), Self::Array(b)) => {
-                a.len() == b.len() && a.iter().zip(b).all(|(x, y)| x.eq(y))
-            }
-            (Self::Dict(a), Self::Dict(b)) => {
-                a.len() == b.len()
-                    && a.iter().all(|(k, x)| b.get(k).map_or(false, |y| x.eq(y)))
-            }
-            (a, b) => a == b,
-        }
-    }
-
-    /// Compare a value with another value.
-    pub fn cmp(&self, rhs: &Self) -> Option<Ordering> {
-        match (self, rhs) {
-            (Self::Int(a), Self::Int(b)) => a.partial_cmp(b),
-            (Self::Int(a), Self::Float(b)) => (*a as f64).partial_cmp(b),
-            (Self::Float(a), Self::Int(b)) => a.partial_cmp(&(*b as f64)),
-            (Self::Float(a), Self::Float(b)) => a.partial_cmp(b),
-            (Self::Angle(a), Self::Angle(b)) => a.partial_cmp(b),
-            (Self::Length(a), Self::Length(b)) => a.partial_cmp(b),
-            _ => None,
-        }
-    }
-
     /// Try to cast the value into a specific type.
     pub fn cast<T>(self) -> CastResult<T, Self>
     where
@@ -143,6 +110,18 @@ impl Default for Value {
     }
 }
 
+impl PartialEq for Value {
+    fn eq(&self, other: &Self) -> bool {
+        ops::equal(self, other)
+    }
+}
+
+impl PartialOrd for Value {
+    fn partial_cmp(&self, other: &Self) -> Option<Ordering> {
+        ops::compare(self, other)
+    }
+}
+
 /// A wrapper around a dynamic value.
 pub struct AnyValue(Box<dyn Bounds>);
 
diff --git a/src/library/utility.rs b/src/library/utility.rs
index c1f20cc6d..eaa6146d4 100644
--- a/src/library/utility.rs
+++ b/src/library/utility.rs
@@ -82,7 +82,7 @@ fn minmax(ctx: &mut EvalContext, args: &mut FuncArgs, goal: Ordering) -> Value {
 
     while let Some(value) = args.eat::<Value>(ctx) {
         if let Some(prev) = &extremum {
-            match value.cmp(&prev) {
+            match value.partial_cmp(&prev) {
                 Some(ordering) if ordering == goal => extremum = Some(value),
                 Some(_) => {}
                 None => {