diff --git a/core/src/main/scala/org/bykn/bosatsu/DefRecursionCheck.scala b/core/src/main/scala/org/bykn/bosatsu/DefRecursionCheck.scala
index 2214ae97e..1fce50450 100644
--- a/core/src/main/scala/org/bykn/bosatsu/DefRecursionCheck.scala
+++ b/core/src/main/scala/org/bykn/bosatsu/DefRecursionCheck.scala
@@ -109,7 +109,7 @@ object DefRecursionCheck {
           case Def(defn) =>
             // make this the same shape as a in declaration
             checkDef(TopLevel, defn.copy(result = (defn.result, ())))
-          case ExternalDef(_, _, _) =>
+          case ExternalDef(_, _, _, _) =>
             unitValid
         }
       case _ => unitValid
diff --git a/core/src/main/scala/org/bykn/bosatsu/Package.scala b/core/src/main/scala/org/bykn/bosatsu/Package.scala
index 5ed481ff1..a2b79b6d8 100644
--- a/core/src/main/scala/org/bykn/bosatsu/Package.scala
+++ b/core/src/main/scala/org/bykn/bosatsu/Package.scala
@@ -273,6 +273,11 @@ object Package {
         Type.Const.Defined(p, TypeName(tds.name)) -> tds.region
       }.toMap
 
+    lazy val extDefRegions: Map[Identifier.Bindable, Region] =
+      stmts.iterator.collect { case ed: Statement.ExternalDef =>
+        ed.name -> ed.region
+      }.toMap
+
     optProg.flatMap {
       case Program((importedTypeEnv, parsedTypeEnv), lets, extDefs, _) =>
         val inferVarianceParsed
@@ -336,8 +341,17 @@ object Package {
                 errs.map(PackageError.TotalityCheckError(p, _))
               }
 
+          val theseExternals =
+            parsedTypeEnv
+              .externalDefs
+              .collect { case (pack, b, t) if pack === p =>
+                // by construction this has to have all the regions
+                (b, (t, extDefRegions(b))) 
+              }
+              .toMap
+
           val inferenceEither = Infer
-            .typeCheckLets(p, lets)
+            .typeCheckLets(p, lets, theseExternals)
             .runFully(
               withFQN,
               Referant.typeConstructors(imps) ++ typeEnv.typeConstructors,
diff --git a/core/src/main/scala/org/bykn/bosatsu/PackageError.scala b/core/src/main/scala/org/bykn/bosatsu/PackageError.scala
index a029dd4f6..521cd6953 100644
--- a/core/src/main/scala/org/bykn/bosatsu/PackageError.scala
+++ b/core/src/main/scala/org/bykn/bosatsu/PackageError.scala
@@ -363,6 +363,20 @@ object PackageError {
               ) + Doc.hardLine +
               context
 
+            (doc, Some(region))
+          case Infer.Error.KindExpectedType(tpe, kind, region) =>
+            val tmap = showTypes(pack, tpe :: Nil)
+            val context =
+              lm.showRegion(region, 2, errColor)
+                .getOrElse(
+                  Doc.str(region)
+                ) // we should highlight the whole region
+            val doc = Doc.text("expected type ") +
+              tmap(tpe) + Doc.text(
+                " to have kind *, which is to say be a valid value, but it is kind "
+              ) + Kind.toDoc(kind) + Doc.hardLine +
+              context
+
             (doc, Some(region))
           case Infer.Error.KindInvalidApply(applied, leftK, rightK, region) =>
             val leftT = applied.on
diff --git a/core/src/main/scala/org/bykn/bosatsu/SourceConverter.scala b/core/src/main/scala/org/bykn/bosatsu/SourceConverter.scala
index a31c37ff1..428a5a383 100644
--- a/core/src/main/scala/org/bykn/bosatsu/SourceConverter.scala
+++ b/core/src/main/scala/org/bykn/bosatsu/SourceConverter.scala
@@ -157,7 +157,7 @@ final class SourceConverter(
                 SourceConverter.InvalidDefTypeParameters(
                   args,
                   freeVarsList,
-                  ds,
+                  Right(ds),
                   region
                 ),
                 gen
@@ -1227,7 +1227,7 @@ final class SourceConverter(
       values: List[Statement.ValueStatement]
   ): Result[Unit] = {
     val extDefNames =
-      values.collect { case ed @ Statement.ExternalDef(name, _, _) =>
+      values.collect { case ed @ Statement.ExternalDef(name, _, _, _) =>
         (name, ed.region)
       }
 
@@ -1259,7 +1259,7 @@ final class SourceConverter(
         s match {
           case b @ Statement.Bind(_)          => Some(Left(b))
           case d @ Statement.Def(_)           => Some(Right(d))
-          case Statement.ExternalDef(_, _, _) => None
+          case Statement.ExternalDef(_, _, _, _) => None
         }
 
       def checkDefBind(s: Statement.ValueStatement): Result[Unit] =
@@ -1391,7 +1391,7 @@ final class SourceConverter(
       stmts.toList.flatMap {
         case d @ Def(_) =>
           (d.defstatement.name, RecursionKind.Recursive, Left(d)) :: Nil
-        case ExternalDef(_, _, _) =>
+        case ExternalDef(_, _, _, _) =>
           // we don't allow external defs to shadow at all, so skip it here
           Nil
         case Bind(BindingStatement(bound, decl, _)) =>
@@ -1456,7 +1456,7 @@ final class SourceConverter(
       }
 
     val withEx: List[Either[ExternalDef, Flattened]] =
-      stmts.collect { case e @ ExternalDef(_, _, _) => Left(e) }.toList :::
+      stmts.collect { case e @ ExternalDef(_, _, _, _) => Left(e) }.toList :::
         flatIn.map {
           case (b, _, Left(d @ Def(dstmt))) =>
             Right(Left(Def(dstmt.copy(name = b))(d.region)))
@@ -1513,7 +1513,7 @@ final class SourceConverter(
             (boundName, rec, l1) :: Nil
           }
           (topBound1, r)
-        case Left(ExternalDef(n, _, _)) =>
+        case Left(ExternalDef(n, _, _, _)) =>
           (topBound + n, success(Nil))
       }
     }(SourceConverter.parallelIor)).map(_.flatten)
@@ -1526,7 +1526,7 @@ final class SourceConverter(
   ], List[Statement]]] = {
     val stmts = Statement.valuesOf(ss).toList
     stmts
-      .collect { case ed @ Statement.ExternalDef(name, params, result) =>
+      .collect { case ed @ Statement.ExternalDef(name, ta, params, result) =>
         (
           params.traverse(p => toType(p._2, ed.region)),
           toType(result, ed.region)
@@ -1547,7 +1547,7 @@ final class SourceConverter(
                 }
             }
           }
-          .map { (tpe: rankn.Type) =>
+          .flatMap { (tpe: rankn.Type) =>
             val freeVars = rankn.Type.freeTyVars(tpe :: Nil)
             // these vars were parsed so they are never skolem vars
             val freeBound = freeVars.map {
@@ -1557,10 +1557,34 @@ final class SourceConverter(
                 sys.error(s"invariant violation: parsed a skolem var: $s")
               // $COVERAGE-ON$
             }
-            // TODO: Kind support parsing kinds
-            val maybeForAll =
-              rankn.Type.forAll(freeBound.map(n => (n, Kind.Type)), tpe)
-            (name, maybeForAll)
+            val finalTpe = ta match {
+              case None =>
+                success(rankn.Type.forAll(freeBound.map(n => (n, Kind.Type)), tpe))
+              case Some(frees0) =>
+                val frees = frees0.map { case (ref, optK) => ref.toBoundVar -> optK }
+                if (frees.iterator.map(_._1).toSet === freeBound.toSet[rankn.Type.Var.Bound]) {
+                  success(rankn.Type.forAll(frees.map {
+                    case (v, None) => (v, Kind.Type)
+                    case (v, Some(k)) => (v, k)
+                  }, tpe))
+                }
+                else {
+                  val kindMap = frees.iterator.collect { case (v, Some(k)) => (v, k) }.toMap
+                  val vs = freeBound.map { v => (v, kindMap.getOrElse(v, Kind.Type)) }
+                  val t = rankn.Type.forAll(vs, tpe)
+                  SourceConverter.partial(
+                    SourceConverter.InvalidDefTypeParameters(
+                      frees0,
+                      freeBound,
+                      Left(ed),
+                      ed.region
+                    ),
+                    t
+                  )
+                }
+            }
+
+            finalTpe.map(name -> _)
           }
       }
       // TODO: we could implement Iterable[Ior[A, B]] => Ior[A, Iterble[B]]
@@ -1887,10 +1911,21 @@ object SourceConverter {
   final case class InvalidDefTypeParameters[B](
       declaredParams: NonEmptyList[(TypeRef.TypeVar, Option[Kind])],
       free: List[Type.Var.Bound],
-      defstmt: DefStatement[Pattern.Parsed, B],
+      defstmt: Either[Statement.ExternalDef, DefStatement[Pattern.Parsed, B]],
       region: Region
   ) extends Error {
 
+    def name: Identifier.Bindable = defstmt match {
+      case Right(ds) => ds.name
+      case Left(ed) => ed.name
+    }
+
+    def expectation: String = defstmt match {
+      case Right(_) => "a subset of"
+      case Left(_) => "the same as"
+    }
+
+
     def message = {
       def tstr(l: List[Type.Var.Bound]): String =
         l.iterator.map(_.name).mkString("[", ", ", "]")
@@ -1903,7 +1938,7 @@ object SourceConverter {
         .renderTrim(80)
 
       val freeStr = tstr(free)
-      s"${defstmt.name.asString} found declared types: $decl, not a subset of $freeStr"
+      s"${name.asString} found declared types: $decl, not $expectation $freeStr"
     }
   }
 
diff --git a/core/src/main/scala/org/bykn/bosatsu/Statement.scala b/core/src/main/scala/org/bykn/bosatsu/Statement.scala
index d22c1adda..f536cf985 100644
--- a/core/src/main/scala/org/bykn/bosatsu/Statement.scala
+++ b/core/src/main/scala/org/bykn/bosatsu/Statement.scala
@@ -34,8 +34,8 @@ sealed abstract class Statement {
         Struct(nm, typeArgs, args)(r)
       case Enum(nm, typeArgs, parts) =>
         Enum(nm, typeArgs, parts)(r)
-      case ExternalDef(name, args, res) =>
-        ExternalDef(name, args, res)(r)
+      case ExternalDef(name, ta, args, res) =>
+        ExternalDef(name, ta, args, res)(r)
       case ExternalStruct(nm, targs) =>
         ExternalStruct(nm, targs)(r)
     }
@@ -83,7 +83,7 @@ object Statement {
         case Bind(BindingStatement(bound, _, _)) =>
           bound.names // TODO Keep identifiers
         case Def(defstatement)       => defstatement.name :: Nil
-        case ExternalDef(name, _, _) => name :: Nil
+        case ExternalDef(name, _, _, _) => name :: Nil
       }
 
     /** These are all the free bindable names in the right hand side of this
@@ -98,7 +98,7 @@ object Statement {
           (innerFrees - defstatement.name) -- defstatement.args.toList.flatMap(
             _.patternNames
           )
-        case ExternalDef(_, _, _) => SortedSet.empty
+        case ExternalDef(_, _, _, _) => SortedSet.empty
       }
 
     /** These are all the bindings, free or not, in this Statement
@@ -109,7 +109,7 @@ object Statement {
         case Def(defstatement) =>
           (defstatement.result.get.allNames + defstatement.name) ++ defstatement.args.toList
             .flatMap(_.patternNames)
-        case ExternalDef(name, _, _) => SortedSet(name)
+        case ExternalDef(name, _, _, _) => SortedSet(name)
       }
   }
 
@@ -126,6 +126,7 @@ object Statement {
       extends ValueStatement
   case class ExternalDef(
       name: Bindable,
+      typeArgs: Option[NonEmptyList[(TypeRef.TypeVar, Option[Kind])]],
       params: List[(Bindable, TypeRef)],
       result: TypeRef
   )(val region: Region)
@@ -230,6 +231,10 @@ object Statement {
 
       val externalDef = {
 
+        val kindAnnot: P[Kind] =
+          (maybeSpace.soft.with1 *> (P.char(':') *> maybeSpace *> Kind.parser))
+        val typeParams = TypeRef.typeParams(kindAnnot.?).?
+
         val args =
           P.char('(') *> maybeSpace *> argParser.nonEmptyList <* maybeSpace <* P
             .char(')')
@@ -239,16 +244,16 @@ object Statement {
 
         (((keySpace(
           "def"
-        ) *> Identifier.bindableParser ~ args ~ result).region) <* toEOL)
-          .map { case (region, ((name, args), resType)) =>
-            ExternalDef(name, args.toList, resType)(region)
+        ) *> Identifier.bindableParser ~ typeParams ~ args ~ result).region) <* toEOL)
+          .map { case (region, (((name, tps), args), resType)) =>
+            ExternalDef(name, tps, args.toList, resType)(region)
           }
       }
 
       val externalVal =
         (argParser <* toEOL).region
           .map { case (region, (name, resType)) =>
-            ExternalDef(name, Nil, resType)(region)
+            ExternalDef(name, None, Nil, resType)(region)
           }
 
       keySpace("external") *> P.oneOf(
@@ -385,11 +390,19 @@ object Statement {
           .char(':') +
           colonSep +
           indentedCons + Doc.line
-      case ExternalDef(name, Nil, res) =>
+      case ExternalDef(name, None, Nil, res) =>
         Doc.text("external ") + Document[Bindable].document(name) + Doc.text(
           ": "
         ) + res.toDoc + Doc.line
-      case ExternalDef(name, args, res) =>
+      case ExternalDef(name, tps, args, res) =>
+        val taDoc = tps match {
+          case None => Doc.empty
+          case Some(ta) =>
+            TypeRef.docTypeArgs(ta.toList) {
+              case None    => Doc.empty
+              case Some(k) => colonSpace + Kind.toDoc(k)
+            }
+        }
         val argDoc = {
           val da = Doc.intercalate(
             Doc.text(", "),
@@ -401,7 +414,7 @@ object Statement {
         }
         Doc.text("external def ") + Document[Bindable].document(
           name
-        ) + argDoc + Doc.text(" -> ") + res.toDoc + Doc.line
+        ) + taDoc + argDoc + Doc.text(" -> ") + res.toDoc + Doc.line
       case ExternalStruct(nm, typeArgs) =>
         val taDoc =
           TypeRef.docTypeArgs(typeArgs.toList) {
diff --git a/core/src/main/scala/org/bykn/bosatsu/TypeRefConverter.scala b/core/src/main/scala/org/bykn/bosatsu/TypeRefConverter.scala
index 15abe8ebc..886c92dcd 100644
--- a/core/src/main/scala/org/bykn/bosatsu/TypeRefConverter.scala
+++ b/core/src/main/scala/org/bykn/bosatsu/TypeRefConverter.scala
@@ -21,7 +21,7 @@ object TypeRefConverter {
     import TypeRef._
 
     t match {
-      case TypeVar(v)  => Applicative[F].pure(TyVar(Type.Var.Bound(v)))
+      case tv @ TypeVar(_)  => Applicative[F].pure(TyVar(tv.toBoundVar))
       case TypeName(n) => nameToType(n.ident).map(TyConst(_))
       case TypeArrow(as, b) =>
         (as.traverse(toType(_)), toType(b)).mapN(Fun(_, _))
diff --git a/core/src/main/scala/org/bykn/bosatsu/rankn/Infer.scala b/core/src/main/scala/org/bykn/bosatsu/rankn/Infer.scala
index e305357a0..4a07e343b 100644
--- a/core/src/main/scala/org/bykn/bosatsu/rankn/Infer.scala
+++ b/core/src/main/scala/org/bykn/bosatsu/rankn/Infer.scala
@@ -182,6 +182,11 @@ object Infer {
         rightK: Kind,
         region: Region
     ) extends TypeError
+    case class KindExpectedType(
+      tpe: Type,
+      kind: Kind.Cons,
+      region: Region
+    ) extends TypeError
     case class KindMismatch(
         target: Type,
         targetKind: Kind,
@@ -2614,7 +2619,8 @@ object Infer {
     */
   def typeCheckLets[A: HasRegion](
       pack: PackageName,
-      ls: List[(Bindable, RecursionKind, Expr[A])]
+      ls: List[(Bindable, RecursionKind, Expr[A])],
+      externals: Map[Bindable, (Type, Region)]
   ): Infer[List[(Bindable, RecursionKind, TypedExpr[A])]] = {
     // Group together lets that don't include each other to get more type errors
     // if we can
@@ -2655,7 +2661,22 @@ object Infer {
           else Some(bs :+ item)
       }
 
-    run(groups)
+    val checkExternals =
+      GetEnv.flatMap { env =>
+        externals
+          .toList
+          .sortBy { case (_, (_, region)) => region }
+          .parTraverse_ { case (_, (t, region)) =>
+            env.getKind(t, region) match {
+              case Right(Kind.Type) => unit
+              case Right(cons @ Kind.Cons(_, _)) =>
+                fail(Error.KindExpectedType(t, cons, region))
+              case Left(err) => fail(err)
+            }
+          }
+      }
+
+    run(groups).parProductL(checkExternals)
   }
 
   /** This is useful to testing purposes.
diff --git a/core/src/test/scala/org/bykn/bosatsu/EvaluationTest.scala b/core/src/test/scala/org/bykn/bosatsu/EvaluationTest.scala
index 3eea45f7e..626a93ecd 100644
--- a/core/src/test/scala/org/bykn/bosatsu/EvaluationTest.scala
+++ b/core/src/test/scala/org/bykn/bosatsu/EvaluationTest.scala
@@ -3990,4 +3990,21 @@ test = TestSuite("bases",
       12
     )
   }
+
+  test("external defs with explicit type parameters exactly match") {
+    val testCode = """
+package ErrorCheck
+
+external def foo[b](lst: List[a]) -> a
+
+"""
+    evalFail(List(testCode)) {
+      case kie @ PackageError.SourceConverterErrorsIn(_, _, _) =>
+        val message = kie.message(Map.empty, Colorize.None)
+        assert(message.contains("Region(30,59)"))
+        assert(message.contains("[b], not the same as [a]"))
+        assert(testCode.substring(30, 59) == "def foo[b](lst: List[a]) -> a")
+        ()
+    }
+  }
 }
diff --git a/core/src/test/scala/org/bykn/bosatsu/Gen.scala b/core/src/test/scala/org/bykn/bosatsu/Gen.scala
index 363c4f32a..64b7a5887 100644
--- a/core/src/test/scala/org/bykn/bosatsu/Gen.scala
+++ b/core/src/test/scala/org/bykn/bosatsu/Gen.scala
@@ -1120,11 +1120,13 @@ object Generators {
   val genExternalDef: Gen[Statement] =
     for {
       name <- bindIdentGen
+      tas0 <- Gen.option(smallList(Gen.zip(typeRefVarGen, Gen.option(NTypeGen.genKind))))
       argc <- Gen.choose(0, 5)
       argG = Gen.zip(bindIdentGen, typeRefGen)
       args <- Gen.listOfN(argc, argG)
+      tas = if (args.isEmpty) None else tas0
       res <- typeRefGen
-    } yield Statement.ExternalDef(name, args, res)(emptyRegion)
+    } yield Statement.ExternalDef(name, tas.flatMap(NonEmptyList.fromList(_)), args, res)(emptyRegion)
 
   val genEnum: Gen[Statement] =
     for {
diff --git a/core/src/test/scala/org/bykn/bosatsu/ParserTest.scala b/core/src/test/scala/org/bykn/bosatsu/ParserTest.scala
index 4f0507613..7d1c0db24 100644
--- a/core/src/test/scala/org/bykn/bosatsu/ParserTest.scala
+++ b/core/src/test/scala/org/bykn/bosatsu/ParserTest.scala
@@ -1716,6 +1716,13 @@ external def foo(i: Integer, b: a) -> String
 external def foo2(i: Integer, b: a) -> String
 """
     )
+    roundTrip(
+      Statement.parser,
+      """# header
+external def foo[a](i: Integer, b: a) -> String
+external def foo_co[a: +* -> *](i: Integer, b: a) -> String
+""")
+
   }
 
   test("we can parse any package") {
diff --git a/core/src/test/scala/org/bykn/bosatsu/rankn/RankNInferTest.scala b/core/src/test/scala/org/bykn/bosatsu/rankn/RankNInferTest.scala
index 1fd7eb8b8..6a8da993a 100644
--- a/core/src/test/scala/org/bykn/bosatsu/rankn/RankNInferTest.scala
+++ b/core/src/test/scala/org/bykn/bosatsu/rankn/RankNInferTest.scala
@@ -126,7 +126,8 @@ class RankNInferTest extends AnyFunSuite {
         testPackage,
         terms.map { case (k, v, _) =>
           (Identifier.Name(k), RecursionKind.NonRecursive, v)
-        }
+        },
+        Map.empty
       )
       .runFully(withBools, boolTypes, Type.builtInKinds) match {
       case Left(err) => assert(false, err)
@@ -224,7 +225,7 @@ class RankNInferTest extends AnyFunSuite {
         fail(
           "expected an invalid program, but got:\n\n" + program.lets
             .map { case (b, r, t) =>
-              s"$b: $r = ${t.repr}"
+              s"$b: $r = ${t.repr.render(80)}"
             }
             .mkString("\n\n")
         )
@@ -1897,4 +1898,32 @@ ignore: exists a. a = Tup(refl_bottom, refl_bottom1, refl_Foo, refl_any)
       "exists a. a"
     )
   }
+
+  test("test external def with kinds") {
+    parseProgram("""
+struct Foo
+external def foo[f: * -> *](f: f[Foo]) -> Foo
+
+struct Box[a](item: a)
+
+f = foo(Box(Foo))
+    """, "Foo")
+  }
+
+  test("ill kinded external defs are not allowed") {
+    parseProgramIllTyped("""#
+struct Foo
+external def foo[f: * -> *](function: f) -> f
+
+f = Foo
+""")
+
+    parseProgramIllTyped("""#
+struct Box[a](item: a)
+external foo: Box
+
+struct Foo
+f = Foo
+""")
+  }
 }