Bazel use tensorflow ( or only use tbb) as a external dependency has a "Make" Variables not defined error - tensorflow

Question

I have a c++ project that use bazel as build tools and use tensorflow as a external dependency, bazel version is 0.24.1 and tensorflow version is 1.14.0, it works fine (In my project I use tbb in the tensorflow as a deps in bazel's rule).
But when I update bazel to 3.1.0 and update tensorflow to 2.3.0, I have the error：
ERROR: external/tbb/BUILD.bazel:11:1: in cmd attribute of genrule rule #tbb//:build_tbb: $(AR) not defined
My WOKSPACE file:
http_archive(
name = "org_tensorflow",
strip_prefix = "tensorflow-2.3.0",
sha256 = "2595a5c401521f20a2734c4e5d54120996f8391f00bb62a57267d930bce95350",
urls = ["https://github.com/tensorflow/tensorflow/archive/tensorflow-2.3.0.tar.gz"]
)
My BUILD file:
cc_library(
name = "tf_utils",
srcs = ["tf_utils.cpp"],
hdrs = ["tf_utils.h"],
deps = ["#org_tensorflow//tensorflow/cc/saved_model:loader", "utils"],
visibility = ["//visibility:public"]
)
cc_library(
name = "utils",
hdrs = ["utils.h"],
srcs = ["utils.cpp"],
deps = ["#boost//:filesystem",
"#eigen_archive//:eigen",
"#tbb//:tbb",], # I use the tbb in the tensorflow
visibility = ["//visibility:public"]
)
Firts, I test tbb in the tensorflow project itself, it has the same error.
The way of my test is, write the follow c++ rule in the tensorflow/BUILD:
cc_library(
name = "test-tbb",
srcs = ["test.cpp"],
deps = ["#ngraph_tf//:ngraph_tf"] # ngraph_tf's deps has tbb
)
and then excute bazel build //tensorflow:test-tbb, it has the same error:
#tbb//:build_tbb: $(AR) not defined
second, I think the problem may be in tbb. I test tbb in two ways:
I download tbb sources, and in the root dir of the tbb, make a WORKSPACE(empty) and a BUILD (only rename tbb.BUILD to BUILD), then excute bazel build //:build_tbb, when bazel version is 0.24.1, all is right, but has the above error when change bazel version to 3.1.0.
I only use tbb as a external dependency in a miniproject, which WORKSPACE has a http_archive named tbb, and it's build_file point to a tbb.BUILD. I write a cc_library in BUILD flie and it's deps = ["#tbb:build_tbb"], the test result is the same as 1), when bazel version is 0.24.1 is ok, 3.1.0 is broken.
tbb.BUILD I used: https://github.com/tensorflow/tensorflow/blob/r2.3/third_party/ngraph/tbb.BUILD
Third, I follow the document of bazel (https://docs.bazel.build/versions/master/be/make-variables.html#custom_variables), sets toolchains = ["#bazel_tools//tools/cpp:current_cc_toolchain"] in the rule "build_tbb" in tbb.BUILD, than the error message is "in cmd attribute of genrule rule //:build_tbb: $(CC_FLAGS) not defined".
Fourth, I follow the solution of the issue：https://github.com/rnburn/satyr/issues/2, update the tbb.BUILD file, than retry and the error message is "in cmd attribute of genrule rule #tbb//:build_tbb: $(C_COMPILER) not defined".
I just want use use tensorflow as an external dependency and use the bazel target "tbb" statement in tensorflow (Since it is in tensorflow, I don’t want to recompile multiple times)
Does anyone know how to correctly use tensorflow and tbb as an external dependency that use bazel 3.0.0+? Thanks!