remove a footnote again

diff --git a/personal/_posts/2018-07-24-pointers-and-bytes.md b/personal/_posts/2018-07-24-pointers-and-bytes.md
index 26afca56a93966db7560fff576f60cd6f285d988..4a9406fac3ad37d9089a48f5469274667dd9c09e 100644 (file)
--- a/personal/_posts/2018-07-24-pointers-and-bytes.md
+++ b/personal/_posts/2018-07-24-pointers-and-bytes.md
@@ -134,11 +134,9 @@ That's how miri can detect that our second example (with `&x[8]`) is UB.
 
 In this model, pointers are not integers, but they are at least simple.
 However, this simple model starts to fall apart once you consider pointer-integer casts.
 
 In this model, pointers are not integers, but they are at least simple.
 However, this simple model starts to fall apart once you consider pointer-integer casts.

-In miri, casting a pointer to an integer does not actually do anything, we now just have an integer variable (i.e., its *type* says it is an integer) whose *value* is a pointer (i.e., an allocation-offset pair).[^3]
+In miri, casting a pointer to an integer does not actually do anything, we now just have an integer variable (i.e., its *type* says it is an integer) whose *value* is a pointer (i.e., an allocation-offset pair).

 However, multiplying that "integer" by 2 leads to an error, because it is entirely unclear what it means to multiply such an abstract pointer by 2.
 
 However, multiplying that "integer" by 2 leads to an error, because it is entirely unclear what it means to multiply such an abstract pointer by 2.
 

-[^3]: This disconnect between the type and the value may seem somewhat strange, but we are actually not very concerned with *types* at this point.  Types serve to classify values with the goal of establishing certain guarantees about a program, so we can only really start talking about types once we are done defining our set of values and program behaviors.  Still, this means there are safe programs that miri cannot execute, such as `(Box::new(0).into_raw() as usize) * 2`.  To avoid trouble with multiplication, I proposed to only allow "normal" integer values for integer types when doing [compile-time function evaluation]({{ site.baseurl }}{% post_url 2018-07-19-const %}).  However, this makes pointer-integer casts a "const-unsafe" operation, because they do not actually produce a "fully operational" integer.
-

 This is the most lazy thing to do, and we do it because it is not clear what else to do -- in our abstract machine, there is no single coherent "address space" that all allocations live in, that we could use to map every pointer to a distinct integer.
 Every allocation is just identified by a (unobservable) ID.
 We could now start to enrich this model with extra data like a base address for each allocation, and somehow use that when casting an integer back to a pointer... but that's where it gets really complicated, and anyway discussing such a model is not the point of this post.
 This is the most lazy thing to do, and we do it because it is not clear what else to do -- in our abstract machine, there is no single coherent "address space" that all allocations live in, that we could use to map every pointer to a distinct integer.
 Every allocation is just identified by a (unobservable) ID.
 We could now start to enrich this model with extra data like a base address for each allocation, and somehow use that when casting an integer back to a pointer... but that's where it gets really complicated, and anyway discussing such a model is not the point of this post.


@@ -218,9 +216,9 @@ int test() {
 }
 {% endhighlight %}
 With `Uninit`, we can easily argue that `x` is either `Uninit` or `1`, and since replacing `Uninit` by `1` is okay, the optimization is easily justified.
 }
 {% endhighlight %}
 With `Uninit`, we can easily argue that `x` is either `Uninit` or `1`, and since replacing `Uninit` by `1` is okay, the optimization is easily justified.

-Without `Uninit`, however, `x` is either "some arbitrary bit pattern" or `1`, and doing the same optimization becomes much harder to justify.[^4]
+Without `Uninit`, however, `x` is either "some arbitrary bit pattern" or `1`, and doing the same optimization becomes much harder to justify.[^3]

 
 

-[^4]: We could argue that we can reorder when the non-deterministic choice is made, but then we have to prove that the hard to analyze code does not observe `x`.  `Uninit` avoids that unnecessary extra proof burden.
+[^3]: We could argue that we can reorder when the non-deterministic choice is made, but then we have to prove that the hard to analyze code does not observe `x`.  `Uninit` avoids that unnecessary extra proof burden.

 
 Finally, `Uninit` is also a better choice for interpreters like miri.
 Such interpreters have a hard time dealing with operations of the form "just choose any of these values" (i.e., non-deterministic operations), because if they want to fully explore all possible program executions, that means they have to try every possible value.
 
 Finally, `Uninit` is also a better choice for interpreters like miri.
 Such interpreters have a hard time dealing with operations of the form "just choose any of these values" (i.e., non-deterministic operations), because if they want to fully explore all possible program executions, that means they have to try every possible value.