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Clarify place expressions vs place objects
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@ -20,27 +20,34 @@
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//! # Correctness
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//!
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//! Warning: This is a semi-formal attempt to argue for the correctness of this analysis. If you
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//! find any weak spots, let me know! Recommended reading: Abstract Interpretation.
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//! find any weak spots, let me know! Recommended reading: Abstract Interpretation. We will use the
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//! term "place" to refer to a place expression (like `mir::Place`), and we will call the
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//! underlying entity "object". For instance, `*_1` and `*_2` are not the same place, but depending
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//! on the value of `_1` and `_2`, they could refer to the same object. Also, the same place can
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//! refer to different objects during execution. If `_1` is reassigned, then `*_1` may refer to
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//! different objects before and after assignment. Additionally, when saying "access to a place",
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//! what we really mean is "access to an object denoted by arbitrary projections of that place".
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//!
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//! In the following, we will assume a constant propagation analysis. Our analysis is correct if
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//! every transfer function is correct. This is the case if for every pair (f, f#) and abstract
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//! state s, we have f(y(s)) <= y(f#(s)), where s is a mapping from tracked place to top, bottom or
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//! a constant. Since pointers (and mutable references) are not tracked, but can be used to change
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//! values in the concrete domain, f# must assume that all places that can be affected in this way
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//! for a given program point are marked with top (otherwise many assignments and function calls
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//! would have no choice but to mark all tracked places with top). This leads us to an invariant:
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//! For all possible program points where there could possibly exist a mutable reference or pointer
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//! to a tracked place (in the concrete domain), this place must be assigned to top (in the
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//! for a given program point are already marked with top in s (otherwise many assignments and
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//! function calls would have no choice but to mark all tracked places with top). This leads us to
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//! an invariant: For all possible program points where there could possibly exist means of mutable
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//! access to a tracked place (in the concrete domain), this place must be assigned to top (in the
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//! abstract domain). The concretization function y can be defined as expected for the constant
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//! propagation analysis, although the concrete state of course contains all kinds of non-tracked
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//! data. However, by the invariant above, no mutable references or pointers to tracked places that
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//! are not marked with top may be introduced.
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//! data. However, by the invariant above, no mutable access to tracked places that are not marked
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//! with top may be introduced.
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//!
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//! Note that we (at least currently) do not differentiate between "this place may assume different
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//! values" and "a pointer to this place escaped the analysis". However, we still want to handle
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//! assignments to constants as usual for f#. This adds an assumption: Whenever we have an
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//! assignment, all mutable access to the underlying place (which is not observed by the analysis)
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//! must be invalidated. This is (hopefully) covered by Stacked Borrows.
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//! assignment that is captured by the analysis, all mutable access to the underlying place (which
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//! is not observable by the analysis) must be invalidated. This is (hopefully) covered by Stacked
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//! Borrows.
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//!
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//! To be continued...
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