* avoid traversing functions multiple times

* condense function cache setup

* pass function cache to CombineMapper.__init__ too

* use Never instead of None as the function result type for mappers that don't support functions

* remove multiple inheritance for TransformMapperWithExtraArgs

doesn't appear to be needed

* add _verify_is_array to avoid the need for rec_ary

the latter inflates recursion depth

* remove map_foreign from Mapper

* use Never as FunctionResultT for NumpyCodegenMapper and FancyDotWriter too

* make PlaceholderSubstitutor explicit about not supporting functions

* tweak types in rec/rec_function_definition

* use P.args/P.kwargs in CachedWalkMapper

* use a more specific type than Any for cache key in CachedWalkMapper

* remove some more Anys

* do not pickle cached hash of arrays

* no clue why this works

* remove unneeded changes

* add an explanation

* add simple test

* add another test

* copy getstate/setstate implementation from dataclasses

* typo?

* DictOfNamedArrays: better repr, keys

* add tags to repr

* make keys() abstract

* add to doc

* fix lint

* remove invalid requirements.txt pytools version specification

---------

Co-authored-by: Andreas Klöckner <inform@tiker.net>

* change attrs to dataclasses

* post-merge fix

* more fixes

* switch to array_dataclass

* use _augment_array_dataclass

* restore attribute validation

* mypy?

* Disable pylint invalid-field-call

---------

Co-authored-by: Andreas Kloeckner <inform@tiker.net>

This reverts commit 3c90e784.

This reverts commit a0da6dc9.