Add links to part 5 in compiler series

content/blog/00_compiler_intro.md

@@ -137,3 +137,4 @@ Here are the posts that I've written so far for this series:
 * [Parsing]({{< relref "02_compiler_parsing.md" >}})
 * [Typechecking]({{< relref "03_compiler_typechecking.md" >}})
 * [Small Improvements]({{< relref "04_compiler_improvements.md" >}})
+* [Execution]({{< relref "05_compiler_execution.md" >}})

content/blog/02_compiler_parsing.md

@@ -291,4 +291,4 @@ wrong:
 We are told an error occured. Excellent! We're not really sure what our tree looks like, though.
 We just know there's __stuff__ in the list of definitions. Having read our source code into
 a structure we're more equipped to handle, we can now try to verify that the code
-makes sense in [Part 3 - Type Checking]({{< relref "03_compiler_typechecking.md" >}})
+makes sense in [Part 3 - Type Checking]({{< relref "03_compiler_typechecking.md" >}}).

content/blog/03_compiler_typechecking.md

@@ -606,4 +606,4 @@ All of our examples print the number of declarations in the program,
 which means they don't throw 0. And so, we have typechecking!
 Before we look at how we will execute our source code,
 we will slow down and make quality of life improvements
-in our codebase in [Part 4 - Small Improvements]({{< relref "04_compiler_improvements.md" >}})
+in our codebase in [Part 4 - Small Improvements]({{< relref "04_compiler_improvements.md" >}}).

content/blog/04_compiler_improvements.md

@@ -234,3 +234,6 @@ cd build && make -j8
 We've made a lot of changes to the codebase, and I've only shown snippets of the code
 so far. If you'de like to see the whole codebase, you can go to my site's git repository
 and check out [the code so far](https://dev.danilafe.com/Web-Projects/blog-static/src/branch/master/code/compiler/04).
+
+Having taken this little break, it's time for our next push. We will define
+how our programs will be evaluated in [Part 5 - Execution]({{< relref "05_compiler_execution.md" >}}).

content/blog/05_compiler_execution.md

@@ -140,7 +140,7 @@ for a [G-machine](https://link.springer.com/chapter/10.1007/3-540-15975-4_50),
 an abstract architecture which we will use to reduce our graphs. The G-machine
 is stack-based - all operations push and pop items from a stack. The machine
 will also have a "dump", which is a stack of stacks; this will help with
-separating function calls.
+separating evaluation of various graphs.
 
 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)
@@ -152,7 +152,13 @@ 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\\)".
+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\\)".
 
 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:
@@ -199,10 +205,10 @@ First up is __PushInt__:
 
 {{< gmachine "PushInt" >}}
     {{< gmachine_inner "Before">}}
-    \( \text{PushInt} \; n : i \quad s \quad h \quad m \)
+    \( \text{PushInt} \; n : i \quad s \quad d \quad h \quad m \)
     {{< /gmachine_inner >}}
     {{< gmachine_inner "After" >}}
-    \( i \quad a : s \quad h[a : \text{NInt} \; n] \quad m \)
+    \( i \quad a : s \quad d \quad h[a : \text{NInt} \; n] \quad m \)
     {{< /gmachine_inner >}}
     {{< gmachine_inner "Description" >}}
     Push an integer \(n\) onto the stack.
@@ -217,10 +223,10 @@ __PushGlobal__:
 
 {{< gmachine "PushGlobal" >}}
     {{< gmachine_inner "Before">}}
-    \( \text{PushGlobal} \; f : i \quad s \quad h \quad m[f : a] \)
+    \( \text{PushGlobal} \; f : i \quad s \quad d \quad h \quad m[f : a] \)
     {{< /gmachine_inner >}}
     {{< gmachine_inner "After" >}}
-    \( i \quad a : s \quad h \quad m[f : a] \)
+    \( i \quad a : s \quad d \quad h \quad m[f : a] \)
     {{< /gmachine_inner >}}
     {{< gmachine_inner "Description" >}}
     Push a global function \(f\) onto the stack.
@@ -233,10 +239,10 @@ __Push__:
 
 {{< gmachine "Push" >}}
     {{< gmachine_inner "Before">}}
-    \( \text{Push} \; n : i \quad a_0, a_1, ..., a_n : s \quad h \quad m \)
+    \( \text{Push} \; n : i \quad a_0, a_1, ..., a_n : s \quad d \quad h \quad m \)
     {{< /gmachine_inner >}}
     {{< gmachine_inner "After" >}}
-    \( i \quad a_n, a_0, a_1, ..., a_n : s \quad h \quad m \)
+    \( i \quad a_n, a_0, a_1, ..., a_n : s \quad d \quad h \quad m \)
     {{< /gmachine_inner >}}
     {{< gmachine_inner "Description" >}}
     Push a value at offset \(n\) from the top of the stack onto the stack.
@@ -251,10 +257,10 @@ define an instruction to combine two nodes into an application:
 
 {{< gmachine "MkApp" >}}
     {{< gmachine_inner "Before">}}
-    \( \text{MkApp} : i \quad a_0, a_1 : s \quad h \quad m \)
+    \( \text{MkApp} : i \quad a_0, a_1 : s \quad d \quad h \quad m \)
     {{< /gmachine_inner >}}
     {{< gmachine_inner "After" >}}
-    \( i \quad a : s \quad h[ a : \text{NApp} \; a_0 \; a_1] \quad m \)
+    \( i \quad a : s \quad d \quad h[ a : \text{NApp} \; a_0 \; a_1] \quad m \)
     {{< /gmachine_inner >}}
     {{< gmachine_inner "Description" >}}
     Apply a function at the top of the stack to a value after it.
@@ -266,8 +272,29 @@ the thing we apply it to. We then create a new node on the heap
 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.
-{{< todo >}}Add an example, probably without notation.{{< /todo >}}
+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.
+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:
+$$
+\\begin{align}
+[\\text{I} \; 326, \\text{G} \; \text{double}, \\text{A}] & \\quad s \\quad & d \\quad & h \\quad & m[\\text{double} : a\_d] \\\\\\
+[\\text{G} \; \text{double}, \\text{A}] & \\quad a\_1 : s \\quad & d \\quad & h[a\_1 : \\text{NInt} \; 326] \\quad & m[\\text{double} : a\_d] \\\\\\
+[\\text{A}] & \\quad a\_d, a\_1 : s \\quad & d \\quad & h[a\_1 : \\text{NInt} \; 326] \\quad & m[\\text{double} : a\_d] \\\\\\
+[] & \\quad a\_2 : s \\quad & d \\quad & h[\\substack{\\begin{aligned}a\_1 & : \\text{NInt} \; 326 \\\\ a\_2 & : \\text{NApp} \; a\_d \; a\_1 \\end{aligned}}] \\quad & m[\\text{double} : a\_d] \\\\\\
+\\end{align}
+$$
+How did we come up with these instructions? We'll answer this question with
+more generality later, but let's take a look at this particular expression
+right now. We know it's an application, so we'll be using MkApp eventually.
+We also know that MkApp expects two values on top of the stack from
+which to make an application. The node on top has to be the function, and the next
+node is the value to be passed into that function. Since a stack is first-in-last-out,
+for the function (`double`, in our case) to be on top, we need
+to push it last. Thus, we push `double` first, then 326. Finally,
+we call MkApp now that the stack is in the right state.
 
 Having defined instructions to __build__ graphs, it's now time
 to move on to instructions to __reduce__ graphs - after all,
@@ -284,10 +311,10 @@ that __isn't__ an application. Let's write this rule as follows:
 
 {{< gmachine "Unwind-App" >}}
     {{< gmachine_inner "Before">}}
-    \( \text{Unwind} : i \quad a : s \quad h[a : \text{NApp} \; a_0 \; a_1] \quad m \)
+    \( \text{Unwind} : i \quad a : s \quad d \quad h[a : \text{NApp} \; a_0 \; a_1] \quad m \)
     {{< /gmachine_inner >}}
     {{< gmachine_inner "After" >}}
-    \( \text{Unwind} : i \quad a_0, a : s \quad h[ a : \text{NApp} \; a_0 \; a_1] \quad m \)
+    \( \text{Unwind} : i \quad a_0, a : s \quad d \quad h[ a : \text{NApp} \; a_0 \; a_1] \quad m \)
     {{< /gmachine_inner >}}
     {{< gmachine_inner "Description" >}}
     Unwind an application by pushing its left node.
@@ -308,10 +335,10 @@ code for the global function:
 
 {{< gmachine "Unwind-Global" >}}
     {{< gmachine_inner "Before">}}
-    \( \text{Unwind} : i \quad a, a_0, a_1, ..., a_n : s \quad h[\substack{a : \text{NGlobal} \; n \; c \\ a_k : \text{NApp} \; a_{k-1} \; a_k'}] \quad m \)
+    \( \text{Unwind} : i \quad a, a_0, a_1, ..., a_n : s \quad d \quad h[\substack{a : \text{NGlobal} \; n \; c \\ a_k : \text{NApp} \; a_{k-1} \; a_k'}] \quad m \)
     {{< /gmachine_inner >}}
     {{< gmachine_inner "After" >}}
-    \( c \quad a_0', a_1', ..., a_n', a_n : s \quad h[\substack{a : \text{NGlobal} \; n \; c \\ a_k : \text{NApp} \; a_{k-1} \; a_k'}] \quad m \)
+    \( c \quad a_0', a_1', ..., a_n', a_n : s \quad d \quad h[\substack{a : \text{NGlobal} \; n \; c \\ a_k : \text{NApp} \; a_{k-1} \; a_k'}] \quad m \)
     {{< /gmachine_inner >}}
     {{< gmachine_inner "Description" >}}
     Call a global function.
@@ -333,10 +360,10 @@ We simply replace `NInd` with the node it points to, and resume Unwind:
 
 {{< gmachine "Unwind-Ind" >}}
     {{< gmachine_inner "Before">}}
-    \( \text{Unwind} : i \quad a : s \quad h[a : \text{NInd} \; a' ] \quad m \)
+    \( \text{Unwind} : i \quad a : s \quad d \quad h[a : \text{NInd} \; a' ] \quad m \)
     {{< /gmachine_inner >}}
     {{< gmachine_inner "After" >}}
-    \( \text{Unwind} : i \quad a' : s \quad h[a : \text{NInd} \; a' ] \quad m \)
+    \( \text{Unwind} : i \quad a' : s \quad d \quad h[a : \text{NInd} \; a' ] \quad m \)
     {{< /gmachine_inner >}}
     {{< gmachine_inner "Description" >}}
     Replace indirection node with its target.
@@ -348,10 +375,10 @@ haven't yet an instruction to perform these actions. Let's do so now:
 
 {{< gmachine "Update" >}}
     {{< gmachine_inner "Before">}}
-    \( \text{Update} \; n : i \quad a,a_0,a_1,...a_n : s \quad h \quad m \)
+    \( \text{Update} \; n : i \quad a,a_0,a_1,...a_n : s \quad d \quad h \quad m \)
     {{< /gmachine_inner >}}
     {{< gmachine_inner "After" >}}
-    \( i \quad a_0,a_1,...,a_n : s \quad h[a_n : \text{NInd} \; a ] \quad m \)
+    \( i \quad a_0,a_1,...,a_n : s \quad d \quad h[a_n : \text{NInd} \; a ] \quad m \)
     {{< /gmachine_inner >}}
     {{< gmachine_inner "Description" >}}
     Transform node at offset into an indirection.
@@ -386,10 +413,10 @@ allocated array:
 
 {{< gmachine "Pack" >}}
     {{< gmachine_inner "Before">}}
-    \( \text{Pack} \; t \; n : i \quad a_1,a_2,...a_n : s \quad h \quad m \)
+    \( \text{Pack} \; t \; n : i \quad a_1,a_2,...a_n : s \quad d \quad h \quad m \)
     {{< /gmachine_inner >}}
     {{< gmachine_inner "After" >}}
-    \( i \quad a : s \quad h[a : \text{NData} \; t \; [a_1, a_2, ..., a_n] ] \quad m \)
+    \( i \quad a : s \quad d \quad h[a : \text{NData} \; t \; [a_1, a_2, ..., a_n] ] \quad m \)
     {{< /gmachine_inner >}}
     {{< gmachine_inner "Description" >}}
     Pack \(n\) nodes from the stack into a node with tag \(t\).
@@ -402,10 +429,10 @@ array onto the stack:
 
 {{< gmachine "Split" >}}
     {{< gmachine_inner "Before">}}
-    \( \text{Split} : i \quad a : s \quad h[a : \text{NData} \; t \; [a_1, a_2, ..., a_n] ] \quad m \)
+    \( \text{Split} : i \quad a : s \quad d \quad h[a : \text{NData} \; t \; [a_1, a_2, ..., a_n] ] \quad m \)
     {{< /gmachine_inner >}}
     {{< gmachine_inner "After" >}}
-    \( i \quad a_1, a_2, ...,a_n : s \quad h[a : \text{NData} \; t \; [a_1, a_2, ..., a_n] ] \quad m \)
+    \( i \quad a_1, a_2, ...,a_n : s \quad d \quad h[a : \text{NData} \; t \; [a_1, a_2, ..., a_n] ] \quad m \)
     {{< /gmachine_inner >}}
     {{< gmachine_inner "Description" >}}
     Unpack a data node on top of the stack.
@@ -428,10 +455,10 @@ Let's define the rule for it:
 
 {{< gmachine "Jump" >}}
     {{< gmachine_inner "Before">}}
-    \( \text{Jump} [..., t \rightarrow i_t, ...] : i \quad a : s \quad h[a : \text{NData} \; t \; as ] \quad m \)
+    \( \text{Jump} [..., t \rightarrow i_t, ...] : i \quad a : s \quad d \quad h[a : \text{NData} \; t \; as ] \quad m \)
     {{< /gmachine_inner >}}
     {{< gmachine_inner "After" >}}
-    \( i_t, i \quad a : s \quad h[a : \text{NData} \; t \; as ] \quad m \)
+    \( i_t, i \quad a : s \quad d \quad h[a : \text{NData} \; t \; as ] \quad m \)
     {{< /gmachine_inner >}}
     {{< gmachine_inner "Description" >}}
     Execute instructions corresponding to a tag.
@@ -451,10 +478,10 @@ rid of the next \\(n\\) addresses:
 
 {{< gmachine "Slide" >}}
     {{< gmachine_inner "Before">}}
-    \( \text{Slide} \; n : i \quad a_0, a_1, ..., a_n : s \quad h \quad m \)
+    \( \text{Slide} \; n : i \quad a_0, a_1, ..., a_n : s \quad d \quad h \quad m \)
     {{< /gmachine_inner >}}
     {{< gmachine_inner "After" >}}
-    \( i \quad a_0 : s \quad h \quad m \)
+    \( i \quad a_0 : s \quad d \quad h \quad m \)
     {{< /gmachine_inner >}}
     {{< gmachine_inner "Description" >}}
     Remove \(n\) addresses after the top from the stack.
@@ -473,10 +500,10 @@ them, called __BinOp__:
 
 {{< gmachine "BinOp" >}}
     {{< gmachine_inner "Before">}}
-    \( \text{BinOp} \; \text{op} : i \quad a_0, a_1 : s \quad h[\substack{a_0 : \text{NInt} \; n \\ a_1 : \text{NInt} \; m}] \quad m \)
+    \( \text{BinOp} \; \text{op} : i \quad a_0, a_1 : s \quad d \quad h[\substack{a_0 : \text{NInt} \; n \\ a_1 : \text{NInt} \; m}] \quad m \)
     {{< /gmachine_inner >}}
     {{< gmachine_inner "After" >}}
-    \( i \quad a : s \quad h[\substack{a_0 : \text{NInt} \; n \\ a_1 : \text{NInt} \; m \\ a : \text{NInt} \; (\text{op} \; n \; m)}] \quad m \)
+    \( i \quad a : s \quad d \quad h[\substack{a_0 : \text{NInt} \; n \\ a_1 : \text{NInt} \; m \\ a : \text{NInt} \; (\text{op} \; n \; m)}] \quad m \)
     {{< /gmachine_inner >}}
     {{< gmachine_inner "Description" >}}
     Apply a binary operator on integers.
@@ -497,8 +524,6 @@ reducing a graph, to say, "we need this value now".
 We call this instruction __Eval__. This is where
 the dump finally comes in!
 
-{{< todo >}}Actually show the dump in the previous evaluasion rules.{{< /todo >}}
-
 When we execute Eval, another graph becomes our "focus", and we switch
 to a new stack. We obviously want to return from this once we've finished
 evaluating what we "focused" on, so we must store the program state somewhere -
@@ -562,6 +587,9 @@ We can allocate an indirection on the stack, and call Update on it when
 we've constructed a node. While we're constructing the tree, we can
 refer to the indirection when a self-reference is required.
 
-That's it for the instructions. Next up, we have to convert our expression
-trees into such instructions. However, this has already gotten pretty long,
-so we'll do it in the next post.
+That's it for the instructions. Knowing them, however, doesn't
+tell us what to do with our `ast` structs. We'll need to define
+rules to translate trees into these instructions, and I've already
+alluded to this when we went over `double 326`.
+However, this has already gotten pretty long,
+so we'll do it in the next post: (link me!)