feat[next]: Infer as_fieldop type without domain

[SF-N]

This extends the GTIR type inference to infer the type of as_fieldop calls without a domain.

TODOs:

• Fix the unnecessary promotion in the domain inference by using the now available type information.
• as_fieldop with scan without domain, e.g., test_fieldop_from_scan:
  __field_operator_simple_scan_operator(out, __out_0_range) { out @ c⟨ KDimᵥ: [__out_0_range[0], __out_0_range[1][ ⟩ ← as_fieldop(scan(λ(carry) → carry + 1.0, True, 1.0), cartesian_domain())();
  has an empty domain. A special case is implemented for that, which ensures, that the vertical dimensions are kept.
• test_cse.py:test_scalar_extraction_inside_as_fieldop results in an Assertion Error for assert isinstance(subexpr.type, ts.TypeSpec) because subexpr.type = None when running it or debugging without breakpoints. There is however no error when setting a breakpoint in type_synthesizer.py:applied_as_fieldop.
• test_program.py::test_index_builtin[None] - TypeError: broadcast() missing 1 required positional argument: 'dimensions'
• test_icon_like_scan.py::test_solve_nonhydro_stencil_52_like_z_q_tup[gtfn.run_gtfn] - NotImplementedError: Tuple expressions with different domains is not supported yet.
• test_type_inference.py::test_function_definition - AssertionError: Node bar already has a type Field[[IDim], float64] which differs from (IteratorType(position_dims=[Dimension(value='IDim', kind=<DimensionKind.HORIZONTAL: 'horizontal'>)], defined_dims=[Dimension(value='IDim', kind=<DimensionKind.HORIZONTAL: 'horizontal'>)], element_type=ScalarType(kind=<ScalarKind.FLOAT64: 11>, shape=None))) -> float64.
• test_domain_inference.py::test_nested_let_arg_shadowed2 - TypeError: Error during coercion of given value 'in_field1' for field 'Sym.id'
• test_domain_inference.py everything with tuple_get
• test_execution.py::test_zero_dim_tuple_arg[simple_mesh-dace.run_dace_cpu] - TypeError: Expected an array of index expressions: got empty array or None
• test_execution.py::test_implicit_broadcast_mixed_dim[dace.run_dace_cpu] - ValueError: not enough values to unpack (expected 3, got 0)
• test_gt4py_builtins.py::test_reduction_expression_in_call[simple_mesh-dace.run_dace_cpu_noopt] - ValueError: not enough values to unpack (expected 3, got 0)
• test_collapse_tuple.py::test_flatten_as_fieldop_args (ant the two tests below) fail with: AssertionError: Node it already has a type IteratorType(position_dims=[Dimension(value='Vertex', kind=<DimensionKind.HORIZONTAL: 'horizontal'>)], defined_dims=[Dimension(value='Vertex', kind=<DimensionKind.HORIZONTAL: 'horizontal'>)], element_type=TupleType(types=[ScalarType(kind=<ScalarKind.INT32: 6>, shape=None), ScalarType(kind=<ScalarKind.INT32: 6>, shape=None)])) which differs from IteratorType(position_dims=[], defined_dims=[], element_type=TupleType(types=[ScalarType(kind=<ScalarKind.INT32: 6>, shape=None), ScalarType(kind=<ScalarKind.INT32: 6>, shape=None)])).
  It passes when removing Vertex from the position_dims and the defined_dims, i.e.,

it_type = it_ts.IteratorType(
        position_dims=[],
        defined_dims=[],
        element_type=ts.TupleType(types=[int_type, int_type]),
    )

[SF-N]

I think the subset requirement is not necessary anymore, e.g. in the case

itir.SetAt(
        domain=unstructured_domain,
        expr=im.as_fieldop(
            im.lambda_("it")(im.reduce("plus", 0.0)(im.deref("it"))),
            unstructured_domain,
        )(im.ref("inp")),
        target=im.ref("out"),
)

with
im.sym("inp", float_vertex_v2e_k_field) and im.sym("out", float_vertex_k_field)

the expr_type is

[Dimension(value='Vertex', kind=<DimensionKind.HORIZONTAL: 'horizontal'>), Dimension(value='KDim', kind=<DimensionKind.VERTICAL: 'vertical'>), Dimension(value='V2E', kind=<DimensionKind.LOCAL: 'local'>)]

and the target_type is

[Dimension(value='Vertex', kind=<DimensionKind.HORIZONTAL: 'horizontal'>), Dimension(value='KDim', kind=<DimensionKind.VERTICAL: 'vertical'>)]

which is correct in my opinion.

cf. test_fencil_with_nb_field_input

[SF-N]

Is ts.TupleType(types=[float_ij_field, float_ij_field] correct here?

[edopao]

I have fixed the lowering of empty domains in dace backend, so the tests should now pass after you rebase.

[SF-N]

I have fixed the lowering of empty domains in dace backend, so the tests should now pass after you rebase.

Thanks @edopao! Now the respective tests are passing.