Update "compiler: execution" to new math delimiters

Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>

content/blog/05_compiler_execution.md

@@ -147,19 +147,19 @@ We will follow the same notation as Simon Peyton Jones in
 [his book](https://www.microsoft.com/en-us/research/wp-content/uploads/1992/01/student.pdf)
 , which was my source of truth when implementing my compiler. The machine
 will be executing instructions that we give it, and as such, it must have
-an instruction queue, which we will reference as \\(i\\). We will write
-\\(x:i\\) to mean "an instruction queue that starts with
-an instruction x and ends with instructions \\(i\\)". A stack machine
-obviously needs to have a stack - we will call it \\(s\\), and will
-adopt a similar notation to the instruction queue: \\(a\_1, a\_2, a\_3 : s\\)
-will mean "a stack with the top values \\(a\_1\\), \\(a\_2\\), and \\(a\_3\\),
-and remaining instructions \\(s\\)". Finally, as we said, our stack
-machine has a dump, which we will write as \\(d\\). On this dump,
+an instruction queue, which we will reference as \(i\). We will write
+\(x:i\) to mean "an instruction queue that starts with
+an instruction x and ends with instructions \(i\)". A stack machine
+obviously needs to have a stack - we will call it \(s\), and will
+adopt a similar notation to the instruction queue: \(a_1, a_2, a_3 : s\)
+will mean "a stack with the top values \(a_1\), \(a_2\), and \(a_3\),
+and remaining instructions \(s\)". Finally, as we said, our stack
+machine has a dump, which we will write as \(d\). On this dump,
 we will push not only the current stack, but also the current
 instructions that we are executing, so we may resume execution
-later. We will write \\(\\langle i, s \\rangle : d\\) to mean
-"a dump with instructions \\(i\\) and stack \\(s\\) on top,
-followed by instructions and stacks in \\(d\\)".
+later. We will write \(\langle i, s \rangle : d\) to mean
+"a dump with instructions \(i\) and stack \(s\) on top,
+followed by instructions and stacks in \(d\)".
 
 There's one more thing the G-machine will have that we've not yet discussed at all,
 and it's needed because of the following quip earlier in the post:
@@ -179,14 +179,14 @@ its address the same, but change the value on the heap.
 This way, all trees that reference the node we change become updated,
 without us having to change them - their child address remains the same,
 but the child has now been updated. We represent the heap
-using \\(h\\). We write \\(h[a : v]\\) to say "the address \\(a\\) points
-to value \\(v\\) in the heap \\(h\\)". Now you also know why we used
-the letter \\(a\\) when describing values on the stack - the stack contains
+using \(h\). We write \(h[a : v]\) to say "the address \(a\) points
+to value \(v\) in the heap \(h\)". Now you also know why we used
+the letter \(a\) when describing values on the stack - the stack contains
 addresses of (or pointers to) tree nodes.
 
 _Compiling Functional Languages: a tutorial_ also keeps another component
 of the G-machine, the __global map__, which maps function names to addresses of nodes
-that represent them. We'll stick with this, and call this global map \\(m\\).
+that represent them. We'll stick with this, and call this global map \(m\).
 
 Finally, let's talk about what kind of nodes our trees will be made of.
 We don't have to include every node that we've defined as a subclass of
@@ -218,7 +218,7 @@ First up is __PushInt__:
 
 Let's go through this. We start with an instruction queue
 with `PushInt n` on top. We allocate a new `NInt` with the
-number `n` on the heap at address \\(a\\). We then push
+number `n` on the heap at address \(a\). We then push
 the address of the `NInt` node on top of the stack. Next,
 __PushGlobal__:
 
@@ -251,7 +251,7 @@ __Push__:
 {{< /gmachine >}}
 
 We define this instruction to work if and only if there exists an address
-on the stack at offset \\(n\\). We take the value at that offset, and
+on the stack at offset \(n\). We take the value at that offset, and
 push it onto the stack again. This can be helpful for something like
 `f x x`, where we use the same tree twice. Speaking of that - let's
 define an instruction to combine two nodes into an application:
@@ -274,11 +274,11 @@ that is an `NApp` node, with its two children being the nodes we popped off.
 Finally, we push it onto the stack.
 
 Let's try use these instructions to get a feel for it. In
-order to conserve space, let's use \\(\\text{G}\\) for PushGlobal,
-\\(\\text{I}\\) for PushInt, and \\(\\text{A}\\) for PushApp.
+order to conserve space, let's use \(\text{G}\) for PushGlobal,
+\(\text{I}\) for PushInt, and \(\text{A}\) for PushApp.
 Let's say we want to construct a graph for `double 326`. We'll
-use the instructions \\(\\text{I} \; 326\\), \\(\\text{G} \; \\text{double}\\),
-and \\(\\text{A}\\). Let's watch these instructions play out:
+use the instructions \(\text{I} \; 326\), \(\text{G} \; \text{double}\),
+and \(\text{A}\). Let's watch these instructions play out:
 {{< latex >}}
 \begin{aligned}
 [\text{I} \; 326, \text{G} \; \text{double}, \text{A}] & \quad s \quad & d \quad & h \quad & m[\text{double} : a_d] \\
@@ -346,13 +346,13 @@ code for the global function:
     {{< /gmachine_inner >}}
 {{< /gmachine >}}
 
-In this rule, we used a general rule for \\(a\_k\\), in which \\(k\\) is any number
-between 1 and \\(n-1\\). We also expect the `NGlobal` node to contain two parameters,
-\\(n\\) and \\(c\\). \\(n\\) is the arity of the function (the number of arguments
-it expects), and \\(c\\) are the instructions to construct the function's tree.
+In this rule, we used a general rule for \(a_k\), in which \(k\) is any number
+between 1 and \(n-1\). We also expect the `NGlobal` node to contain two parameters,
+\(n\) and \(c\). \(n\) is the arity of the function (the number of arguments
+it expects), and \(c\) are the instructions to construct the function's tree.
 
-The attentive reader will have noticed a catch: we kept \\(a\_{n-1}\\) on the stack!
-This once again goes back to replacing a node in-place. \\(a\_{n-1}\\) is the address of the "root" of the
+The attentive reader will have noticed a catch: we kept \(a_{n-1}\) on the stack!
+This once again goes back to replacing a node in-place. \(a_{n-1}\) is the address of the "root" of the
 whole expression we're simplifying. Thus, to replace the value at this address, we need to keep
 the address until we have something to replace it with.
 
@@ -451,7 +451,7 @@ and define it to contain a mapping from tags to instructions
 to be executed for a value of that tag. For instance,
 if the constructor `Nil` has tag 0, and `Cons` has tag 1,
 the mapping for the case expression of a length function
-could be written as \\([0 \\rightarrow [\\text{PushInt} \; 0], 1 \\rightarrow [\\text{PushGlobal} \; \\text{length}, ...] ]\\).
+could be written as \([0 \rightarrow [\text{PushInt} \; 0], 1 \rightarrow [\text{PushGlobal} \; \text{length}, ...] ]\).
 Let's define the rule for it:
 
 {{< gmachine "Jump" >}}
@@ -475,7 +475,7 @@ creating a final graph. We then continue to reduce this final
 graph. But we've left the function parameters on the stack!
 This is untidy. We define a __Slide__ instruction,
 which keeps the address at the top of the stack, but gets
-rid of the next \\(n\\) addresses:
+rid of the next \(n\) addresses:
 
 {{< gmachine "Slide" >}}
     {{< gmachine_inner "Before">}}