diff --git a/loopy/kernel/function_interface.py b/loopy/kernel/function_interface.py
index 33dfd73f2..40d9969bf 100644
--- a/loopy/kernel/function_interface.py
+++ b/loopy/kernel/function_interface.py
@@ -23,8 +23,8 @@
 THE SOFTWARE.
 """
 from abc import ABC, abstractmethod
-from collections.abc import Mapping, Sequence
-from dataclasses import dataclass, replace
+from collections.abc import Collection, Mapping, Sequence
+from dataclasses import dataclass, fields, replace
 from typing import TYPE_CHECKING, Any, Callable, FrozenSet, TypeVar
 from warnings import warn
 
@@ -304,7 +304,9 @@ def get_kw_pos_association(kernel):
 
 # {{{ template class
 
-@dataclass(frozen=True, init=False)
+# not frozen for Firedrake compatibility
+# not eq to avoid having __hash__ set to None in subclasses
+@dataclass(init=False, eq=False)
 class InKernelCallable(ABC):
     """
     An abstract interface to define a callable encountered in a kernel.
@@ -368,9 +370,51 @@ def __init__(self,
         def name(self) -> str:
             raise NotImplementedError()
 
+    # {{{ hackery to avoid breaking Firedrake
+
+    def _all_attrs(self) -> Collection[str]:
+        dc_attrs = {
+            fld.name for fld in fields(self)
+        }
+        legacy_fields: Collection[str] = getattr(self, "fields", [])
+        return dc_attrs | set(legacy_fields)
+
     def copy(self, **kwargs: Any) -> Self:
+        present_kwargs = {
+            name: getattr(self, name)
+            for name in self._all_attrs()
+        }
+        kwargs = {
+            **present_kwargs,
+            **kwargs,
+        }
+
         return replace(self, **kwargs)
 
+    def update_persistent_hash(self, key_hash, key_builder) -> None:
+        for field_name in self._all_attrs():
+            key_builder.rec(key_hash, getattr(self, field_name))
+
+    def __eq__(self, other: object):
+        if type(self) is not type(other):
+            return False
+
+        for f in self._all_attrs():
+            if getattr(self, f) != getattr(other, f):
+                return False
+
+        return True
+
+    def __hash__(self):
+        import hashlib
+
+        from loopy.tools import LoopyKeyBuilder
+        key_hash = hashlib.sha256()
+        self.update_persistent_hash(key_hash, LoopyKeyBuilder())
+        return hash(key_hash.digest())
+
+    # }}}
+
     def with_types(self, arg_id_to_dtype, clbl_inf_ctx):
         """
         :arg arg_id_to_type: a mapping from argument identifiers (integers for
@@ -521,7 +565,8 @@ def is_type_specialized(self):
 
 # {{{ scalar callable
 
-@dataclass(frozen=True, init=False)
+# not frozen, not eq for Firedrake compatibility
+@dataclass(init=False, eq=False)
 class ScalarCallable(InKernelCallable):
     """
     An abstract interface to a scalar callable encountered in a kernel.
@@ -699,7 +744,8 @@ def is_type_specialized(self):
 
 # {{{ callable kernel
 
-@dataclass(frozen=True, init=False)
+# not frozen, not eq for Firedrake compatibility
+@dataclass(init=False, eq=False)
 class CallableKernel(InKernelCallable):
     """
     Records information about a callee kernel. Also provides interface through
diff --git a/loopy/library/random123.py b/loopy/library/random123.py
index 329770e05..786f4db31 100644
--- a/loopy/library/random123.py
+++ b/loopy/library/random123.py
@@ -176,7 +176,8 @@ def full_name(self) -> str:
 # }}}
 
 
-@dataclass(frozen=True, init=False)
+# non-frozen for compatibility with Firedrake
+@dataclass(init=False)
 class Random123Callable(ScalarCallable):
     """
     Records information about for the random123 functions.