diff --git a/lib/spack/spack/solver/asp.py b/lib/spack/spack/solver/asp.py
index 53783e7f1cc..143b27910b1 100644
--- a/lib/spack/spack/solver/asp.py
+++ b/lib/spack/spack/solver/asp.py
@@ -1452,7 +1452,9 @@ def external_packages(self):
             for local_idx, spec in enumerate(external_specs):
                 msg = "%s available as external when satisfying %s" % (spec.name, spec)
                 condition_id = self.condition(spec, msg=msg)
-                self.gen.fact(fn.possible_external(condition_id, pkg_name, local_idx))
+                self.gen.fact(fn.imposed_constraint(
+                    condition_id, "external_conditions_hold", pkg_name, local_idx
+                ))
                 self.possible_versions[spec.name].add(spec.version)
                 self.gen.newline()
 
@@ -2399,6 +2401,7 @@ class SpecBuilder(object):
                 r"^root$",
                 r"^virtual_node$",
                 r"^virtual_root$",
+                r"^.*holds?$",
             ]
         )
     )
diff --git a/lib/spack/spack/solver/concretize.lp b/lib/spack/spack/solver/concretize.lp
index 2d9e390992b..40fcaf66b4e 100644
--- a/lib/spack/spack/solver/concretize.lp
+++ b/lib/spack/spack/solver/concretize.lp
@@ -425,25 +425,15 @@ external(Package) :- attr("external_spec_selected", Package, _).
 
 % determine if an external spec has been selected
 attr("external_spec_selected", Package, LocalIndex) :-
-    external_conditions_hold(Package, LocalIndex),
+    attr("external_conditions_hold", Package, LocalIndex),
     attr("node", Package),
     not attr("hash", Package, _).
 
-external_conditions_hold(Package, LocalIndex) :-
-    possible_external(ID, Package, LocalIndex), condition_holds(ID).
-
 % it cannot happen that a spec is external, but none of the external specs
 % conditions hold.
 error(100, "Attempted to use external for '{0}' which does not satisfy any configured external spec", Package)
  :- external(Package),
-    not external_conditions_hold(Package, _).
-
-#defined possible_external/3.
-#defined external_spec_index/3.
-#defined external_spec_condition/3.
-#defined external_spec_condition/4.
-#defined external_spec_condition/5.
-#defined external_spec_condition/6.
+    not attr("external_conditions_hold", Package, _).
 
 %-----------------------------------------------------------------------------
 % Config required semantics
@@ -653,7 +643,7 @@ variant_default_not_used(Package, Variant, Value)
 external_with_variant_set(Package, Variant, Value)
  :- attr("variant_value", Package, Variant, Value),
     condition_requirement(ID, "variant_value", Package, Variant, Value),
-    possible_external(ID, Package, _),
+    imposed_constraint(ID, "external_conditions_hold", Package, _),
     external(Package),
     attr("node", Package).