diff --git a/src/builtin.jq b/src/builtin.jq
index e74e9771dc..1e23a2ed66 100644
--- a/src/builtin.jq
+++ b/src/builtin.jq
@@ -246,13 +246,14 @@ def bsearch($target):
 
 # Apply f to composite entities recursively, and to atoms
 def walk(f):
-  . as $in
-  | if type == "object" then
-      reduce keys_unsorted[] as $key
-        ( {}; . + { ($key):  ($in[$key] | walk(f)) } ) | f
-  elif type == "array" then map( walk(f) ) | f
-  else f
-  end;
+  def w:
+    if type == "object"
+    then map_values(w)
+    elif type == "array" then map(w)
+    else .
+    end
+    | f;
+  w;
 
 # pathexps could be a stream of dot-paths
 def pick(pathexps):
diff --git a/tests/jq.test b/tests/jq.test
index 55630a5a43..de92a8b91c 100644
--- a/tests/jq.test
+++ b/tests/jq.test
@@ -1968,3 +1968,22 @@ implode|explode
 map(try implode catch .)
 [123,["a"],[nan]]
 ["implode input must be an array","string (\"a\") can't be imploded, unicode codepoint needs to be numeric","number (null) can't be imploded, unicode codepoint needs to be numeric"]
+
+# walk
+walk(.)
+{"x":0}
+{"x":0}
+
+walk(1)
+{"x":0}
+1
+
+# The following is a regression test, not a requirement:
+[walk(.,1)]
+{"x":0}
+[{"x":0},1]
+
+# Issue #2584
+walk(select(IN({}, []) | not))
+{"a":1,"b":[]}
+{"a":1}