diff --git a/lib/check.ml b/lib/check.ml
index fb5aa531..7a1199d7 100644
--- a/lib/check.ml
+++ b/lib/check.ml
@@ -7371,6 +7371,60 @@ and named_call ?(qualified = false) ctx ~want loc name args =
     expect ctx loc ~want
       (List.fold_left (fun acc arg -> pick acc (check ctx ~want:ty arg))
          (pick a b) rest)
+  (* (max-of T) and (min-of T): the type-limit constants, by type, so a
+     generic body can name its own type's. Odin's max(T) and min(T), and the
+     same answer for a float: the largest finite value and its negation, not
+     the smallest positive one. Given a value rather than a type, the name is
+     the prelude's reduction of a slice, and the call is an ordinary one —
+     the same split [vec-new] makes between a type and an allocator. *)
+  | ("max-of" | "min-of")
+    when (match args with
+          | [ a ] ->
+            type_of_expr a <> None
+            || (match a.Ast.e with
+                | Ast.Var n ->
+                  lookup ctx n = None
+                  && (not (Hashtbl.mem ctx.env.globals n))
+                  && type_named ctx n
+                | _ -> false)
+          | _ -> false) ->
+    let a = List.hd args in
+    let ty =
+      match type_of_expr a, a.Ast.e with
+      | Some t, _ -> resolve ctx.env t
+      | _, Ast.Var n -> resolve_name ctx.env ~seen:[] a.Ast.loc n
+      | _ -> fail a.Ast.loc "internal: max-of's type argument is not a type"
+    in
+    let max = String.equal name "max-of" in
+    let v =
+      match ty with
+      | Types.Int k ->
+        let b = Types.bits k in
+        let n =
+          if Types.signed k then
+            let top = Int64.shift_left 1L (b - 1) in
+            if max then Int64.sub top 1L else Int64.neg top
+          else if not max then 0L
+          else if b = 64 then -1L
+          else Int64.sub (Int64.shift_left 1L b) 1L
+        in
+        mk loc ty (Tast.Int (n, k))
+      | Types.Float k ->
+        let m =
+          match k with
+          | Types.F32 -> Int32.float_of_bits 0x7f7fffffl
+          | Types.F64 -> Float.max_float
+        in
+        mk loc ty (Tast.Float ((if max then m else -.m), k))
+      | Types.Var _ ->
+        unconstrained ctx.env loc name ~needs:"numeric?" ty;
+        int_literal loc ~want:(Some ty) ~preds:ctx.env.tvpreds 0L
+      | _ ->
+        fail a.Ast.loc
+          "%s takes a numeric? type, and %s is not one — as in (%s i32)" name
+          (Types.to_string ty) name
+    in
+    expect ctx loc ~want v
   (* (zeroed) is the all-bytes-zero value of whatever it is being stored into,
      so it only means anything where a type is expected of it. *)
   | "zeroed" ->
diff --git a/lib/prelude.ml b/lib/prelude.ml
index ff520d4b..4cab01aa 100644
--- a/lib/prelude.ml
+++ b/lib/prelude.ml
@@ -406,6 +406,8 @@ let source = {flan|
 ;; or more numbers, and a defn cannot shadow a builtin: nothing shadows [+]
 ;; either. These reduce a slice, which is a different operation with a
 ;; different arity, so the different name is honest rather than a workaround.
+;; Given a type instead of a slice, (min-of i8) and (max-of $t) are the type's
+;; limits, and the checker answers those itself.
 (defn min-of [s [$t]] (Option $t)
   {:where (ordered? $t)}
   (if (= (length s) 0)
diff --git a/test/programs/max-of.flan b/test/programs/max-of.flan
new file mode 100644
index 00000000..2b5f5e76
--- /dev/null
+++ b/test/programs/max-of.flan
@@ -0,0 +1,54 @@
+;;;; (max-of T) and (min-of T): a numeric type's limits, named by the type, at
+;;;; a concrete type and inside a generic whose bound admits numbers.
+
+;; A selection sort, descending, whose running best starts at the least value
+;; of the element type, so any element beats it.
+(defn sort-desc [s [$t]] ()
+  {:where (numeric? $t)}
+  (dotimes [i (length s)]
+    (let [best (min-of $t)
+          at-best i]
+      (dotimes [j (- (length s) i)]
+        (let [k (+ i j)]
+          (when (> (at s k) best)
+            (set best (at s k))
+            (set at-best k))))
+      (swap s i at-best))))
+
+(defn largest [s [$t]] $t
+  {:where (numeric? $t)}
+  (let [best (min-of t)]
+    (dotimes [i (length s)]
+      (when (> (at s i) best) (set best (at s i))))
+    best))
+
+(defn show-i32 [s [i32]] ()
+  (dotimes [i (length s)] (print (at s i)) (print " "))
+  (println ""))
+
+(defn show-f64 [s [f64]] ()
+  (dotimes [i (length s)] (print (at s i)) (print " "))
+  (println ""))
+
+(defn main [] i32
+  (println (max-of u8))
+  (println (min-of u8))
+  (println (max-of i8))
+  (println (min-of i8))
+  (println (max-of i32))
+  (println (min-of i64))
+  (println (max-of u64))
+  (println (= (max-of f32) f32-max))
+  (println (= (min-of f64) (- f64-max)))
+  (println (= (max-of i16) i16-max))
+  (let [a [(i32 3) -7 12 0 -2147483648 5]
+        b [2.5 -1.0 1e300 -1e308]
+        c [(u8 4) 0 200 9]]
+    (sort-desc (slice a))
+    (show-i32 (slice a))
+    (sort-desc (slice b))
+    (show-f64 (slice b))
+    (println (largest (slice c)))
+    (println (let [d [(i64 -5) -9]] (largest (slice d))))
+    (println (let [e [(f32 -1.0) -3.0]] (= (largest (slice e)) (f32 -1.0)))))
+  0)
diff --git a/test/test_acceptance.ml b/test/test_acceptance.ml
index c6660228..2dd063da 100644
--- a/test/test_acceptance.ml
+++ b/test/test_acceptance.ml
@@ -573,6 +573,14 @@ let () =
     outputs "a prelude function shadowed" "programs/shadow-prelude.flan" sp_out;
     outputs ~x86:true "a prelude function shadowed, x86"
       "programs/shadow-prelude.flan" sp_out;
+    (* (max-of T) and (min-of T), concrete and inside a generic. *)
+    let maxof_out =
+      "255\n0\n127\n-128\n2147483647\n-9223372036854775808\n\
+       18446744073709551615\ntrue\ntrue\ntrue\n\
+       12 5 3 0 -7 -2147483648 \n1e+300 2.5 -1 -1e+308 \n200\n-5\ntrue\n" in
+    outputs "max-of and min-of" "programs/max-of.flan" maxof_out;
+    outputs ~opt:"-O0" "max-of and min-of, -O0" "programs/max-of.flan" maxof_out;
+    outputs ~x86:true "max-of and min-of, x86" "programs/max-of.flan" maxof_out;
     (* (- x) negates, on every numeric type, a type variable and a dyn. *)
     let neg_out =
       "-3\n7\n-2.5\n-inf\n-1.5\n255\n-4\n-2.5\n-inf\n-9000000000\n\
diff --git a/test/test_flan.ml b/test/test_flan.ml
index 636c1f36..759b7bbd 100644
--- a/test/test_flan.ml
+++ b/test/test_flan.ml
@@ -6399,6 +6399,19 @@ let () =
     "(defn main [] i32 (let [a [None None]] 0))"
     ~needle:"what None is an Option of";
 
+  (* ── (max-of T) and (min-of T) ──────────────────────────────────── *)
+  infers "max-of carries its type" "(max-of u16)" "u16";
+  infers "min-of at a float" "(min-of f32)" "f32";
+  rejects_check "max-of at an unbounded type variable names the bound"
+    "(defn f [x $t] $t (max-of $t))" ~needle:"{:where (numeric? $t)}";
+  accepts "max-of at a type variable the bound admits"
+    "(defn f [x $t] $t {:where (integer? $t)} (max-of t))";
+  rejects_check "max-of at a type that is not a number names the bound"
+    "(defn f [] string (max-of string))"
+    ~needle:"max-of takes a numeric? type, and string is not one";
+  accepts "max-of of a slice is still the prelude's reduction"
+    "(defn f [xs [i32]] (Option i32) (max-of xs))";
+
   (* ── (the T e) ─────────────────────────────────────────────────── *)
   infers "the gives a literal its type" "(the u8 200)" "u8";
   infers "the widens as an annotation does" "(the i64 (the i32 1))" "i64";