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Add dump to other rules in compiler posts

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Danila Fedorin 2019-09-04 00:27:58 -07:00
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content/blog/05_compiler_execution.md
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@ -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.
@ -284,10 +290,10 @@ 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 +314,10 @@ 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 +339,10 @@ 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 +354,10 @@ 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 +392,10 @@ 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 +408,10 @@ 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 +434,10 @@ 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 +457,10 @@ 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 +479,10 @@ 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 +503,6 @@ 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 -