diff --git a/loki/batch/item.py b/loki/batch/item.py
index 1ce98917f..3ce14b39b 100644
--- a/loki/batch/item.py
+++ b/loki/batch/item.py
@@ -685,7 +685,7 @@ def _dependencies(self):
         inline_calls = tuple({
             call.function.name: call.function
             for call in FindInlineCalls().visit(self.ir.ir)
-            if isinstance(call.function, ProcedureSymbol)
+            if isinstance(call.function, ProcedureSymbol) and not call.function.type.is_intrinsic
         }.values())
         imports = tuple(
             imprt for imprt in self.ir.imports
diff --git a/loki/expression/mappers.py b/loki/expression/mappers.py
index 57083faa9..441965759 100644
--- a/loki/expression/mappers.py
+++ b/loki/expression/mappers.py
@@ -559,6 +559,7 @@ def map_variable_symbol(self, expr, *args, **kwargs):
         new_type = expr.type
         if recurse_to_declaration_attributes:
             old_type = expr.type
+            assert expr.type is not None
             kind = self.rec(old_type.kind, *args, **kwargs)
 
             if expr.scope and expr.name == old_type.initial:
diff --git a/loki/expression/tests/test_expression.py b/loki/expression/tests/test_expression.py
index b8f3b54b5..2722d455b 100644
--- a/loki/expression/tests/test_expression.py
+++ b/loki/expression/tests/test_expression.py
@@ -79,14 +79,53 @@ def test_math_intrinsics(tmp_path, frontend):
 """
     filepath = tmp_path/(f'expression_math_intrinsics_{frontend}.f90')
     routine = Subroutine.from_source(fcode, frontend=frontend)
-    function = jit_compile(routine, filepath=filepath, objname='math_intrinsics')
 
+    for assign in FindNodes(ir.Assignment).visit(routine.body):
+        assert isinstance(assign.rhs, sym.InlineCall)
+        assert isinstance(assign.rhs.function, sym.ProcedureSymbol)
+        assert assign.rhs.function.type.dtype.is_intrinsic
+
+    # Test full functionality via JIT example
+    function = jit_compile(routine, filepath=filepath, objname='math_intrinsics')
     vmin, vmax, vabs, vexp, vsqrt, vlog = function(2., 4.)
     assert vmin == 2. and vmax == 4. and vabs == 2.
     assert vexp == np.exp(6.) and vsqrt == np.sqrt(6.) and vlog == np.log(6.)
     clean_test(filepath)
 
 
+@pytest.mark.parametrize('frontend', available_frontends())
+def test_general_intrinsics(frontend):
+    """
+    Test general intrinsic functions (size, shape, ubound, lbound,
+    allocated, trim, kind)
+    """
+    fcode = """
+subroutine general_intrinsics(arr, ptr, name)
+  implicit none
+  real(kind=8), intent(inout) :: arr(:,:)
+  real(kind=8), pointer, intent(inout) :: ptr(:,:)
+  character(len=*), intent(inout) :: name
+  integer :: isize, ishape(:), ilower, iupper, mykind
+  logical :: alloc
+  character(len=*) :: myname
+
+  isize = size(arr)
+  ishape = shape(arr)
+  ilower = lbound(arr)
+  iupper = ubound(arr)
+  mykind = kind(arr)
+  alloc = allocated(ptr)
+  myname = trim(name)
+end subroutine general_intrinsics
+"""
+    routine = Subroutine.from_source(fcode, frontend=frontend)
+
+    for assign in FindNodes(ir.Assignment).visit(routine.body):
+        assert isinstance(assign.rhs, sym.InlineCall)
+        assert isinstance(assign.rhs.function, sym.ProcedureSymbol)
+        assert assign.rhs.function.type.dtype.is_intrinsic
+
+
 @pytest.mark.parametrize('frontend', available_frontends())
 def test_logicals(tmp_path, frontend):
     """
diff --git a/loki/frontend/fparser.py b/loki/frontend/fparser.py
index 865bcb8f8..693a89aa4 100644
--- a/loki/frontend/fparser.py
+++ b/loki/frontend/fparser.py
@@ -2547,7 +2547,20 @@ def visit_Function_Reference(self, o, **kwargs):
 
 
     def visit_Intrinsic_Function_Reference(self, o, **kwargs):
+
+        # Register the ProcedureType in the scope before the name lookup
+        pname = o.children[0].string
+        scope = kwargs['scope']
+        if not scope.get_symbol_scope(pname):
+            # No known alternative definition; register a true intrinsic procedure type
+            proc_type = ProcedureType(
+                name=pname, is_function=True, is_intrinsic=True, procedure=None
+            )
+            kwargs['scope'].symbol_attrs[pname] = SymbolAttributes(dtype=proc_type, is_intrinsic=True)
+
+        # Look up the function symbol
         name = self.visit(o.children[0], **kwargs)
+
         if o.children[1] is not None:
             arguments = self.visit(o.children[1], **kwargs)
             kwarguments = tuple(arg for arg in arguments if isinstance(arg, tuple))
diff --git a/loki/frontend/omni.py b/loki/frontend/omni.py
index 08c6cbf2b..833cb5ffa 100644
--- a/loki/frontend/omni.py
+++ b/loki/frontend/omni.py
@@ -1210,6 +1210,15 @@ def visit_FarrayConstructor(self, o, **kwargs):
         return sym.LiteralList(values=values, dtype=dtype)
 
     def visit_functionCall(self, o, **kwargs):
+
+        if 'is_intrinsic' in o.attrib:
+            # Register the ProcedureType in the scope before the name lookup
+            pname = o.find('name').text
+            proc_type = ProcedureType(
+                name=pname, is_function=True, is_intrinsic=True, procedure=None
+            )
+            kwargs['scope'].symbol_attrs[pname] = SymbolAttributes(dtype=proc_type, is_intrinsic=True)
+
         if o.find('name') is not None:
             name = self.visit(o.find('name'), **kwargs)
         elif o.find('FmemberRef') is not None:
diff --git a/loki/frontend/tests/test_frontends.py b/loki/frontend/tests/test_frontends.py
index 07f04982d..86ea0762b 100644
--- a/loki/frontend/tests/test_frontends.py
+++ b/loki/frontend/tests/test_frontends.py
@@ -2127,3 +2127,80 @@ def test_import_of_private_symbols(tmp_path, frontend):
     assert var.type.imported is True
     # Check if the symbol comes from the mod_public module
     assert var.type.module is mod_public
+
+
+@pytest.mark.parametrize('frontend', available_frontends(
+    xfail=[(OMNI, 'OMNI does not like intrinsic shading for member functions!')]
+))
+def test_intrinsic_shadowing(tmp_path, frontend):
+    """
+    Test that locally defined functions that shadow intrinsics are handled.
+    """
+    fcode_algebra = """
+module algebra_mod
+implicit none
+contains
+  function dot_product(a, b) result(c)
+    real(kind=8), intent(inout) :: a(:), b(:)
+    real(kind=8) :: c
+  end function dot_product
+
+  function min(x, y)
+    real(kind=8), intent(in) :: x, y
+    real(kind=8) :: min
+
+    min = y
+    if (x < y) min = x
+  end function min
+end module algebra_mod
+"""
+
+    fcode = """
+module test_intrinsics_mod
+use algebra_mod, only: dot_product
+implicit none
+
+contains
+
+  subroutine test_intrinsics(a, b, c, d)
+    use algebra_mod, only: min
+    implicit none
+    real(kind=8), intent(inout) :: a(:), b(:)
+    real(kind=8) :: c, d, e
+
+    c = dot_product(a, b)
+    d = max(c, a(1))
+    e = min(c, a(1))
+
+  contains
+
+    function max(x, y)
+      real(kind=8), intent(in) :: x, y
+      real(kind=8) :: max
+
+      max = y
+      if (x > y) max = x
+    end function max
+  end subroutine test_intrinsics
+end module test_intrinsics_mod
+"""
+    algebra = Module.from_source(fcode_algebra, frontend=frontend, xmods=[tmp_path])
+    module = Module.from_source(
+        fcode, definitions=algebra, frontend=frontend, xmods=[tmp_path]
+    )
+    routine = module['test_intrinsics']
+
+    assigns = FindNodes(ir.Assignment).visit(routine.body)
+    assert len(assigns) == 3
+
+    assert isinstance(assigns[0].rhs.function, sym.ProcedureSymbol)
+    assert not assigns[0].rhs.function.type.is_intrinsic
+    assert assigns[0].rhs.function.type.dtype.procedure == algebra['dot_product']
+
+    assert isinstance(assigns[1].rhs.function, sym.ProcedureSymbol)
+    assert not assigns[1].rhs.function.type.is_intrinsic
+    assert assigns[1].rhs.function.type.dtype.procedure == routine.members[0]
+
+    assert isinstance(assigns[2].rhs.function, sym.ProcedureSymbol)
+    assert not assigns[2].rhs.function.type.is_intrinsic
+    assert assigns[2].rhs.function.type.dtype.procedure == algebra['min']
diff --git a/loki/ir/tests/test_visitor.py b/loki/ir/tests/test_visitor.py
index c5a5a2e3a..f0056a406 100644
--- a/loki/ir/tests/test_visitor.py
+++ b/loki/ir/tests/test_visitor.py
@@ -369,7 +369,7 @@ def test_find_variables_associates(frontend):
     routine = Subroutine.from_source(fcode, frontend=frontend)
 
     variables = FindVariables(unique=False).visit(routine.body)
-    assert len(variables) == 29
+    assert len(variables) == 27 if frontend == OMNI else 28
     assert len([v for v in variables if v.name == 'v']) == 1
     assert len([v for v in variables if v.name == 'm']) == 2
 
diff --git a/loki/tests/test_modules.py b/loki/tests/test_modules.py
index 52dce2dc6..7914fd1cf 100644
--- a/loki/tests/test_modules.py
+++ b/loki/tests/test_modules.py
@@ -1330,11 +1330,11 @@ def test_module_enrichment_within_file(frontend, tmp_path):
   integer, parameter :: j = 16
 
   contains
-    integer function SUM(v)
+    integer function plus_one(v)
       implicit none
       integer, intent(in) :: v
-      SUM = v + 1
-    end function SUM
+      plus_one = v + 1
+    end function plus_one
 end module foo
 
 module test
@@ -1348,7 +1348,7 @@ def test_module_enrichment_within_file(frontend, tmp_path):
         real(kind=rk), intent(inout) :: res
         integer(kind=ik) :: i
         do i = 1, n
-            res = res + SUM(j)
+            res = res + plus_one(j)
         end do
     end subroutine calc
 end module test
@@ -1358,10 +1358,10 @@ def test_module_enrichment_within_file(frontend, tmp_path):
     routine = source['calc']
     calls = list(FindInlineCalls().visit(routine.body))
     assert len(calls) == 1
-    assert calls[0].function == 'sum'
+    assert calls[0].function == 'plus_one'
     assert calls[0].function.type.imported
     assert calls[0].function.type.module is source['foo']
-    assert calls[0].function.type.dtype.procedure is source['sum']
+    assert calls[0].function.type.dtype.procedure is source['plus_one']
     if frontend != OMNI:
         # OMNI inlines parameters
         assert calls[0].arguments[0].type.dtype == BasicType.INTEGER
diff --git a/loki/transformations/tests/test_raw_stack_allocator.py b/loki/transformations/tests/test_raw_stack_allocator.py
index 49e6f2346..d833f8d33 100644
--- a/loki/transformations/tests/test_raw_stack_allocator.py
+++ b/loki/transformations/tests/test_raw_stack_allocator.py
@@ -10,7 +10,7 @@
 from loki.backend import fgen
 from loki.batch import Scheduler, SchedulerConfig
 from loki.dimension import Dimension
-from loki.expression import DeferredTypeSymbol, InlineCall, IntLiteral
+from loki.expression import DeferredTypeSymbol, InlineCall, IntLiteral, ProcedureSymbol
 from loki.frontend import available_frontends, OMNI
 from loki.ir import FindNodes, CallStatement, Assignment, Pragma
 from loki.sourcefile import Sourcefile
@@ -282,7 +282,7 @@ def test_raw_stack_allocator_temporaries(frontend, block_dim, horizontal, direct
     real = BasicType.REAL
     logical = BasicType.LOGICAL
     jprb = DeferredTypeSymbol('JPRB')
-    srk = InlineCall(function = DeferredTypeSymbol(name = 'SELECTED_REAL_KIND'),
+    srk = InlineCall(function = ProcedureSymbol(name = 'SELECTED_REAL_KIND'),
                      parameters = (IntLiteral(13), IntLiteral(300)))
 
     stack_dict = kernel1_item.trafo_data[transformation._key]['stack_dict']
diff --git a/loki/types.py b/loki/types.py
index bf79766dc..73f80b6f6 100644
--- a/loki/types.py
+++ b/loki/types.py
@@ -168,16 +168,22 @@ class ProcedureType(DataType):
         Indicate that this is a function
     is_generic : bool, optional
         Indicate that this is a generic function
+    is_intrinsic : bool, optional
+        Indicate that this is an intrinsic function
     procedure : :any:`Subroutine` or :any:`StatementFunction` or :any:`LazyNodeLookup`, optional
         The procedure this type represents
     """
 
-    def __init__(self, name=None, is_function=None, is_generic=False, procedure=None, return_type=None):
+    def __init__(
+            self, name=None, is_function=None, is_generic=False,
+            is_intrinsic=False, procedure=None, return_type=None
+    ):
         from loki.subroutine import Subroutine  # pylint: disable=import-outside-toplevel,cyclic-import
         super().__init__()
         assert name or isinstance(procedure, Subroutine)
-        assert isinstance(return_type, SymbolAttributes) or procedure or not is_function
+        assert isinstance(return_type, SymbolAttributes) or procedure or not is_function or is_intrinsic
         self.is_generic = is_generic
+        self.is_intrinsic = is_intrinsic
         if procedure is None or isinstance(procedure, LazyNodeLookup):
             self._procedure = procedure
             self._name = name
diff --git a/pyproject.toml b/pyproject.toml
index 9ce538ce1..caac0c9c6 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -31,7 +31,7 @@ dependencies = [
   "coloredlogs",  # optional for loki-build utility
   "junit_xml",  # optional for JunitXML output in loki-lint
   "codetiming",  # essential for scheduler and sourcefile timings
-  "pydantic>=2.0",  # type checking for IR nodes
+  "pydantic>=2.0,<2.10.0",  # type checking for IR nodes
 ]
 
 [project.optional-dependencies]