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Formal definition, metatheory, and tools for the Machine Independent Language using HOL4 and CakeML

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MIL

zenodo-DOI fmcad22-DOI

A formalization in HOL4 of a machine independent language for defining the semantics of microarchitectural features such as out-of-order execution.

Meta

Building

Requirements:

The hol Makefile task, which assumes Holmake is available on the system, builds all core HOL4 theories (i.e., excluding examples and theories related to HolBA and CakeML):

make hol

This can take up to a few minutes on a modern machine.

Files

Key definitions and results

  • semantics

    • milScript.sml: datatypes res, e, i, act, obs, l, State; functions sem_expr, translate_val, Completed, addr_of, str_may, str_act, sem_instr; relations out_of_order_step, in_order_step
    • milTracesScript.sml: relation step_execution; functions trace, commits, step_invariant
    • milMetaScript.sml: function well_formed_state; theorems well_formed_OoO_transition_well_formed, OoO_transition_deterministic, OoO_transitions_can_be_applied, OoO_transitions_exist
    • milMetaIOScript.sml: theorem IO_transition_deterministic
    • milReorderScript.sml: theorems OoO_IO_well_formed_memory_consistent, IO_OoO_memory_consistent
  • executable

    • milExecutableIOScript.sml: function IO_bounded_execution; theorems IO_bounded_execution_out_of_order_step_sound, IO_bounded_execution_in_order_step_sound
    • milExecutableIOTraceScript.sml: function IO_bounded_trace; theorems IO_bounded_trace_out_of_order_step_list_sound, IO_bounded_trace_in_order_step_list_sound
  • cakeml

    • milCakeScript.sml: functions IO_bounded_execution_cake, IO_bounded_trace_cake
    • milCakeProofScript.sml: theorems IO_bounded_execution_eq_cake, IO_bounded_trace_eq_cake

Analyzed MIL Programs

The directory examples contains definitions of MIL programs and corresponding information flow analysis theorems in HOL4. The theory for each example program has two parts:

  • milExample<Program>Script.sml: definition of the example and bisimulation proof
  • milMaxExeTraceExample<Program>Script.sml: generation of the information leakage relation for the example using the IO executor

To build all example theories, run the following command:

make examples

This can take around 15 minutes on a modern machine.

BIR-to-MIL Translator

The directory bir contains an (unverified) SML function that translates a BIR program to a MIL program, and some examples of using this function.

To build the translator, HolBA with the tag FMCAD2022_artifact must be present in a sibling directory named HolBA:

git clone https://github.com/kth-step/HolBA.git
cd HolBA
git checkout FMCAD2022_artifact

With the HolBA directory available as a sibling, the translator can be built by running:

make bir

This can take a few minutes on a modern machine (due to BIR and some long-running examples).

CakeML Library for MIL

The directory cakeml contains definitions and scripts for generating a (verified) CakeML library that can process MIL data and programs.

To build the library, CakeML with the tag v1469 must be present in a sibling directory named cakeml:

git clone https://github.com/CakeML/cakeml.git
cd cakeml
git checkout v1469

With the cakeml directory available as a sibling along with HolBA as above, the library can be built by running:

make cakeml

This can take more than an hour on a modern machine, due to that some key CakeML theories must be built.

Running code compiled by CakeML

For convenience, we pretty-printed the MIL CakeML code along with an example for trace generation in the file mil_reg_translate.cml in the cakeml directory. This file can be compiled and run as follows, on an x86-64 machine:

wget https://github.com/CakeML/cakeml/releases/download/v1469/cake-x64-64.tar.gz
tar xzvf cake-x64-64.tar.gz
cd cake-x64-64
cp path/to/MIL/cakeml/mil_reg_translate.cml .
make mil_reg_translate.cake
./mil_reg_translate.cake

On a modern machine, compilation can take a few minutes, but running the program should take only a few milliseconds to output the following MIL trace:

[il 0wx0, il 0wx4, il 0wx0, il 0wx4, il 0wx0, il 0wx4, il 0wx0,
 il 0wx4, il 0wx0, il 0wx4, il 0wx0, il 0wx4, il 0wx0, il 0wx4,
 il 0wx0, il 0wx4, il 0wx0, il 0wx4, il 0wx0, il 0wx4, il 0wx0,
 il 0wx4, il 0wx0, il 0wx4]

In comparison, the HOL4 EVAL_TAC call that proves the equivalent theorem ex_bir_prog_IO_bounded_trace_long in bir/bir_to_mil_test_basicScript.sml can take up to a minute.

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Formal definition, metatheory, and tools for the Machine Independent Language using HOL4 and CakeML

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