Allow constraining an explicit requirement

src/pip/_internal/resolution/resolvelib/base.py

@@ -58,6 +58,13 @@ class Constraint(object):
         hashes = self.hashes & other.hashes(trust_internet=False)
         return Constraint(specifier, hashes)
 
+    def is_satisfied_by(self, candidate):
+        # type: (Candidate) -> bool
+        # We can safely always allow prereleases here since PackageFinder
+        # already implements the prerelease logic, and would have filtered out
+        # prerelease candidates if the user does not expect them.
+        return self.specifier.contains(candidate.version, prereleases=True)
+
 
 class Requirement(object):
     @property

src/pip/_internal/resolution/resolvelib/factory.py

@@ -235,16 +235,10 @@ class Factory(object):
                 prefers_installed,
             )
 
-        if constraint:
-            name = explicit_candidates.pop().name
-            raise InstallationError(
-                "Could not satisfy constraints for {!r}: installation from "
-                "path or url cannot be constrained to a version".format(name)
-            )
-
         return (
             c for c in explicit_candidates
-            if all(req.is_satisfied_by(c) for req in requirements)
+            if constraint.is_satisfied_by(c)
+            and all(req.is_satisfied_by(c) for req in requirements)
         )
 
     def make_requirement_from_install_req(self, ireq, requested_extras):