Stop using images and use HTML/CSS to render stacks
18
assets/scss/stack.scss
Normal file
|
@ -0,0 +1,18 @@
|
|||
@import "style.scss";
|
||||
|
||||
.stack {
|
||||
display: flex;
|
||||
flex-direction: column;
|
||||
max-width: 10rem;
|
||||
margin: auto;
|
||||
@include bordered-block;
|
||||
}
|
||||
|
||||
.stack-element {
|
||||
text-align: center;
|
||||
height: 1.5rem;
|
||||
|
||||
&:not(:last-child) {
|
||||
border-bottom: $standard-border;
|
||||
}
|
||||
}
|
|
@ -4,6 +4,8 @@ date: 2020-03-06T17:56:55-08:00
|
|||
tags: ["Programming Languages"]
|
||||
---
|
||||
|
||||
{{< stack_css >}}
|
||||
|
||||
In CS 381, Programming Language Fundamentals, many students chose to
|
||||
implement a stack based language. Such languages are very neat,
|
||||
but two of the requirements for such languages may, at first,
|
||||
|
@ -132,16 +134,31 @@ However, to stick by convention 4, we pretend that the stack is empty, and that
|
|||
trying to manipulate it will result in an error. So, we can start by imagining
|
||||
an empty stack, with an integer \\(x\\) on top:
|
||||
|
||||
{{< stack_image "if_999_1_part1.png" >}}
|
||||
{{< stack >}}
|
||||
{{< stack_element >}}{{< /stack_element >}}
|
||||
{{< stack_element >}}{{< /stack_element >}}
|
||||
{{< stack_element >}}{{< /stack_element >}}
|
||||
{{< stack_element >}}\(x\){{< /stack_element >}}
|
||||
{{< /stack >}}
|
||||
|
||||
Then, \\(\\text{PushI} \\; 0\\) will push 0 onto the stack:
|
||||
|
||||
{{< stack_image "if_999_1_part2.png" >}}
|
||||
{{< stack >}}
|
||||
{{< stack_element >}}{{< /stack_element >}}
|
||||
{{< stack_element >}}{{< /stack_element >}}
|
||||
{{< stack_element >}}0{{< /stack_element >}}
|
||||
{{< stack_element >}}\(x\){{< /stack_element >}}
|
||||
{{< /stack >}}
|
||||
|
||||
\\(\\text{Slide} \\; 1\\) will then remove the 1 element after the top element: \\(x\\).
|
||||
We end up with the following stack:
|
||||
|
||||
{{< stack_image "slide_example_part3.png" >}}
|
||||
{{< stack >}}
|
||||
{{< stack_element >}}{{< /stack_element >}}
|
||||
{{< stack_element >}}{{< /stack_element >}}
|
||||
{{< stack_element >}}{{< /stack_element >}}
|
||||
{{< stack_element >}}0{{< /stack_element >}}
|
||||
{{< /stack >}}
|
||||
|
||||
The function has finished running, and we maintain convention 3: the function's
|
||||
return value is in place of its argument on the stack.
|
||||
|
@ -194,20 +211,40 @@ Eq
|
|||
Let's walk through this. We start with only the arguments
|
||||
on the stack:
|
||||
|
||||
{{< stack_image "recursion_all_part1.png" >}}
|
||||
{{< stack >}}
|
||||
{{< stack_element >}}{{< /stack_element >}}
|
||||
{{< stack_element >}}{{< /stack_element >}}
|
||||
{{< stack_element >}}\(n\){{< /stack_element >}}
|
||||
{{< stack_element >}}factorial{{< /stack_element >}}
|
||||
{{< /stack >}}
|
||||
|
||||
Then, \\(\\text{Offset} \\; 0\\) duplicates the first argument
|
||||
(the number):
|
||||
|
||||
{{< stack_image "recursion_all_part2.png" >}}
|
||||
{{< stack >}}
|
||||
{{< stack_element >}}{{< /stack_element >}}
|
||||
{{< stack_element >}}\(n\){{< /stack_element >}}
|
||||
{{< stack_element >}}\(n\){{< /stack_element >}}
|
||||
{{< stack_element >}}factorial{{< /stack_element >}}
|
||||
{{< /stack >}}
|
||||
|
||||
Next, 0 is pushed onto the stack:
|
||||
|
||||
{{< stack_image "recursion_all_part3.png" >}}
|
||||
{{< stack >}}
|
||||
{{< stack_element >}}0{{< /stack_element >}}
|
||||
{{< stack_element >}}\(n\){{< /stack_element >}}
|
||||
{{< stack_element >}}\(n\){{< /stack_element >}}
|
||||
{{< stack_element >}}factorial{{< /stack_element >}}
|
||||
{{< /stack >}}
|
||||
|
||||
Finally, \\(\\text{Eq}\\) performs the equality check:
|
||||
|
||||
{{< stack_image "recursion_all_part4.png" >}}
|
||||
{{< stack >}}
|
||||
{{< stack_element >}}{{< /stack_element >}}
|
||||
{{< stack_element >}}true/false{{< /stack_element >}}
|
||||
{{< stack_element >}}\(n\){{< /stack_element >}}
|
||||
{{< stack_element >}}factorial{{< /stack_element >}}
|
||||
{{< /stack >}}
|
||||
|
||||
Great! Now, it's time to branch. What happens if "true" is on top of
|
||||
the stack? In that case, we no longer need any more information.
|
||||
|
@ -221,11 +258,21 @@ Slide 2
|
|||
|
||||
As before, we push the desired answer onto the stack:
|
||||
|
||||
{{< stack_image "recursion_base_part2.png" >}}
|
||||
{{< stack >}}
|
||||
{{< stack_element >}}{{< /stack_element >}}
|
||||
{{< stack_element >}}1{{< /stack_element >}}
|
||||
{{< stack_element >}}\(n\){{< /stack_element >}}
|
||||
{{< stack_element >}}factorial{{< /stack_element >}}
|
||||
{{< /stack >}}
|
||||
|
||||
Then, to follow convention 3, we must get rid of the arguments. We do this by using \\(\\text{Slide}\\):
|
||||
|
||||
{{< stack_image "recursion_base_part3.png" >}}
|
||||
{{< stack >}}
|
||||
{{< stack_element >}}{{< /stack_element >}}
|
||||
{{< stack_element >}}{{< /stack_element >}}
|
||||
{{< stack_element >}}{{< /stack_element >}}
|
||||
{{< stack_element >}}1{{< /stack_element >}}
|
||||
{{< /stack >}}
|
||||
|
||||
Great! The \\(\\textbf{if}\\) branch is now done, and we're left with the correct answer on the stack.
|
||||
Excellent!
|
||||
|
@ -240,7 +287,12 @@ Offset 1
|
|||
|
||||
The result is as follows:
|
||||
|
||||
{{< stack_image "recursion_rec_part1.png" >}}
|
||||
{{< stack >}}
|
||||
{{< stack_element >}}{{< /stack_element >}}
|
||||
{{< stack_element >}}factorial{{< /stack_element >}}
|
||||
{{< stack_element >}}\(n\){{< /stack_element >}}
|
||||
{{< stack_element >}}factorial{{< /stack_element >}}
|
||||
{{< /stack >}}
|
||||
|
||||
Next, we must compute \\(n-1\\). This is pretty standard stuff:
|
||||
|
||||
|
@ -253,11 +305,21 @@ Add
|
|||
Why these three instructions? Well, with the function now on the top of the stack, the number argument is somewhat
|
||||
buried, and thus, we need to use \\(\\text{Offset} \\; 1\\) to get to it:
|
||||
|
||||
{{< stack_image "recursion_rec_part2.png" >}}
|
||||
{{< stack >}}
|
||||
{{< stack_element >}}\(n\){{< /stack_element >}}
|
||||
{{< stack_element >}}factorial{{< /stack_element >}}
|
||||
{{< stack_element >}}\(n\){{< /stack_element >}}
|
||||
{{< stack_element >}}factorial{{< /stack_element >}}
|
||||
{{< /stack >}}
|
||||
|
||||
Then, we push a negative number, and add it to to the number on top. We end up with:
|
||||
|
||||
{{< stack_image "recursion_rec_part3.png" >}}
|
||||
{{< stack >}}
|
||||
{{< stack_element >}}\(n-1\){{< /stack_element >}}
|
||||
{{< stack_element >}}factorial{{< /stack_element >}}
|
||||
{{< stack_element >}}\(n\){{< /stack_element >}}
|
||||
{{< stack_element >}}factorial{{< /stack_element >}}
|
||||
{{< /stack >}}
|
||||
|
||||
Finally, we have our arguments in order as per convention 2. To follow convention 1, we must
|
||||
now push the function onto the top of the stack:
|
||||
|
@ -268,7 +330,13 @@ Offset 1
|
|||
|
||||
The stack is now as follows:
|
||||
|
||||
{{< stack_image "recursion_rec_part4.png" >}}
|
||||
{{< stack >}}
|
||||
{{< stack_element >}}factorial{{< /stack_element >}}
|
||||
{{< stack_element >}}\(n-1\){{< /stack_element >}}
|
||||
{{< stack_element >}}factorial{{< /stack_element >}}
|
||||
{{< stack_element >}}\(n\){{< /stack_element >}}
|
||||
{{< stack_element >}}factorial{{< /stack_element >}}
|
||||
{{< /stack >}}
|
||||
|
||||
Good! With the preparations for the function call now complete, we take
|
||||
the leap:
|
||||
|
@ -284,7 +352,12 @@ will be removed from the stack and replaced with the result of the function
|
|||
as per convention 2. The rest of the stack will remain untouched as
|
||||
per convention 4. We thus expect the stack to look as follows:
|
||||
|
||||
{{< stack_image "recursion_rec_part5.png" >}}
|
||||
{{< stack >}}
|
||||
{{< stack_element >}}{{< /stack_element >}}
|
||||
{{< stack_element >}}\((n-1)!\){{< /stack_element >}}
|
||||
{{< stack_element >}}\(n\){{< /stack_element >}}
|
||||
{{< stack_element >}}factorial{{< /stack_element >}}
|
||||
{{< /stack >}}
|
||||
|
||||
We're almost there! What's left is to perform the multiplication (we're
|
||||
safe to destroy the argument now, since we will not be needing it after
|
||||
|
@ -298,12 +371,22 @@ Slide 1
|
|||
The multiplication leaves us with \\(n(n-1)! = n!\\) on top of the stack,
|
||||
and the function argument below it:
|
||||
|
||||
{{< stack_image "recursion_rec_part6.png" >}}
|
||||
{{< stack >}}
|
||||
{{< stack_element >}}{{< /stack_element >}}
|
||||
{{< stack_element >}}{{< /stack_element >}}
|
||||
{{< stack_element >}}\(n!\){{< /stack_element >}}
|
||||
{{< stack_element >}}factorial{{< /stack_element >}}
|
||||
{{< /stack >}}
|
||||
|
||||
We then use \\(\\text{Slide}\\) so that only the factorial is on the
|
||||
stack, satisfying convention 3:
|
||||
|
||||
{{< stack_image "recursion_rec_part7.png" >}}
|
||||
{{< stack >}}
|
||||
{{< stack_element >}}{{< /stack_element >}}
|
||||
{{< stack_element >}}{{< /stack_element >}}
|
||||
{{< stack_element >}}{{< /stack_element >}}
|
||||
{{< stack_element >}}\(n!\){{< /stack_element >}}
|
||||
{{< /stack >}}
|
||||
|
||||
That's it! We have successfully executed the recursive case. The whole
|
||||
function is now as follows:
|
Before Width: | Height: | Size: 30 KiB |
Before Width: | Height: | Size: 34 KiB |
Before Width: | Height: | Size: 36 KiB |
Before Width: | Height: | Size: 35 KiB |
Before Width: | Height: | Size: 38 KiB |
Before Width: | Height: | Size: 41 KiB |
Before Width: | Height: | Size: 58 KiB |
Before Width: | Height: | Size: 36 KiB |
Before Width: | Height: | Size: 38 KiB |
Before Width: | Height: | Size: 26 KiB |
Before Width: | Height: | Size: 42 KiB |
Before Width: | Height: | Size: 45 KiB |
Before Width: | Height: | Size: 45 KiB |
Before Width: | Height: | Size: 52 KiB |
Before Width: | Height: | Size: 41 KiB |
Before Width: | Height: | Size: 35 KiB |
Before Width: | Height: | Size: 28 KiB |
Before Width: | Height: | Size: 30 KiB |
3
layouts/shortcodes/stack.html
Normal file
|
@ -0,0 +1,3 @@
|
|||
<div class="stack">
|
||||
{{ .Inner }}
|
||||
</div>
|
2
layouts/shortcodes/stack_css.html
Normal file
|
@ -0,0 +1,2 @@
|
|||
{{ $style := resources.Get "scss/stack.scss" | resources.ToCSS | resources.Minify }}
|
||||
<link rel="stylesheet" href="{{ $style.Permalink }}">
|
3
layouts/shortcodes/stack_element.html
Normal file
|
@ -0,0 +1,3 @@
|
|||
<div class="stack-element">
|
||||
{{ .Inner }}
|
||||
</div>
|