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fix a few bugs with the new precedence rules

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りき萌 2025-09-02 20:02:48 +02:00
parent 29a80854a4
commit 9808d3227f
3 changed files with 113 additions and 59 deletions
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111
docs/rkgk.dj
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@ -87,7 +87,7 @@ If you want to draw multiple scribbles, you can wrap them into a list, which we
withDotter \d ->
[
stroke 8 #F00 (d To + vec 4 0)
stroke 8 #00F (d To + vec (-4) 0)
stroke 8 #00F (d To + vec -4 0)
]
```
@ -109,25 +109,15 @@ withDotter \d ->
[
[
stroke 8 #F00 (d To + vec 4 0)
stroke 8 #00F (d To + vec (-4) 0)
stroke 8 #00F (d To + vec -4 0)
]
[
stroke 8 #FF0 (d To + vec 0 4)
stroke 8 #0FF (d To + vec 0 (-4))
stroke 8 #0FF (d To + vec 0 -4)
]
]
```
::: aside
Another weird thing: when negating a number, you have to put it in parentheses.
This is because haku does not see your spaces---`vec -4`, `vec - 4`, and `vec-4` all mean the same thing!
In this case, it will always choose the 2nd interpretation---vec minus four.
So to make it interpret our minus four as, well, _minus four_, we need to enclose it in parentheses.
:::
This might seem useless, but it's a really useful property in computer programs.
It essentially means you can snap pieces together like Lego bricks!
@ -186,7 +176,7 @@ haku vectors however are a little more constrained, because they always contain
We call these four numbers X, Y, Z, and W respectively.
Four is a useful number of dimensions to have, because it lets us do 3D math---which technically isn't built into haku, but if you want it, it's there.
For most practical purposes, we'll only be using the first _two_ of the four dimensions though---X and Y.
For most practical purposes, we'll only be using the first _two_ of the four dimensions though---X and Y.
This is because the wall is a 2D space---it's a flat surface with no depth.
It's important to know though that vectors don't mean much _by themselves_---rakugaki just chooses them to represent points on the wall, but in a flat 2D space, all points need to be relative to some _origin_---the vector `(0, 0)`.
@ -205,7 +195,7 @@ withDotter \d ->
stroke 8 #000 (d To + vec 10 0) -- moved 10 pixels rightwards
```
Also note how the `d To` expression is parenthesized.
Also note how the `d To + vec 10 0` expression is parenthesized.
This is because otherwise, its individual parts would be interpreted as separate arguments to `stroke`, which is not what we want!
Anyways, with all that, we let haku mix all the ingredients together, and get a black dot under the cursor.
@ -249,16 +239,72 @@ haku also supports other kinds of shapes: circles and rectangles.
```haku
withDotter \d ->
[
stroke 8 #F00 (circle (d To + vec (-16) 0) 16)
stroke 8 #00F (rect (d To + vec 0 (-16)) 32 32)
stroke 8 #F00 (circle (d To + vec -16 0) 16)
stroke 8 #00F (rect (d To + vec 0 -16) (vec 32 32))
]
```
- `circle`s are made up of an X position, Y position, and radius.
- `rect`s are made up of the (X and Y) position of their top-left corner, and a size (width and height).\
Our example produces a square, because the rectangle's width and height are equal!
## Math in haku
While haku is based entirely in pure math, it is important to note that haku is _not_ math notation!
It is a textual programming language, and has different rules concerning order of operations than math.
::: aside
If you've programmed in any other language, you might find those rules alien.
But I promise you, they make sense in the context of the rest of the language!
:::
In traditional math notation, the conventional order of operations is:
1. Parentheses
2. Exponentiation
3. Multiplication and division
4. Addition and subtraction
haku does not have an exponentiation operator.
That purpose is served by the function `pow`.
It does however have parentheses, multiplication, division, addition, and subtraction.
Unlike in math notation, addition, subtraction, multiplication, and division, are _all_ calculated from left to right---multiplication and division does not take precedence over addition and subtraction.
So for the expression `2 + 2 * 2`, the result is `8`, and not `6`!
Since this can be inconvenient at times, there is a way to work around that.
haku has a distinction between _tight_ and _loose_ operators, where tight operators always take precedence over loose ones in the order of operations.
Remove the spaces around the `*` multiplication operator, like `2 + 2*2`, and the result is now `6` again---because we made `*` tight!
This is convenient when representing fractions.
If you want a constant like half-π, the way to write it is `1/2*pi`---and order of operations will never mess you up, as long as you keep it tight without spaces!
The same thing happens with functions.
For example, if you wanted to calculate the sine of `1/2*pi*x`, as long as you write that as `sin 1/2*pi*x`, with the whole argument without spaces, you won't have to wrap it in parentheses.
Inside a single whole tight or loose expression, there is still an order of operations.
In fact, here's the full order of operations in haku for reference:
1. Tight
1. Arithmetic: `+`, `-`, `*`, `/`
1. Comparisons: `==`, `!=`, `<`, `<=`, `>`, `>=`
1. Function calls
1. Loose
1. Arithmetic
1. Comparisons
1. Variables: `:`, `=`
Naturally, you can still use parentheses when the loose-tight distinction is not enough.
## Programming in haku
So far we've been using haku solely to describe data.
@ -270,7 +316,7 @@ Remember that example from before?
withDotter \d ->
[
stroke 8 #F00 (d To + vec 4 0)
stroke 8 #00F (d To + vec (-4) 0)
stroke 8 #00F (d To + vec -4 0)
]
```
@ -281,7 +327,7 @@ If we wanted to change the size of the points, we'd need to first update the str
withDotter \d ->
[
stroke 4 #F00 (d To + vec 4 0)
stroke 4 #00F (d To + vec (-4) 0)
stroke 4 #00F (d To + vec -4 0)
---
]
```
@ -294,8 +340,8 @@ So we also have to update their positions.
[
stroke 4 #F00 (d To + vec 2 0)
---
stroke 4 #00F (d To + vec (-2) 0)
--
stroke 4 #00F (d To + vec -2 0)
--
]
```
@ -322,7 +368,7 @@ thickness: 4
withDotter \d ->
[
stroke thickness #F00 (d To + vec 2 0)
stroke thickness #00F (d To + vec (-2) 0)
stroke thickness #00F (d To + vec -2 0)
---------
]
```
@ -355,7 +401,7 @@ xOffset: 2
withDotter \d ->
[
stroke thickness #F00 (d To + vec xOffset 0)
stroke thickness #00F (d To + vec (-xOffset) 0)
stroke thickness #00F (d To + vec -xOffset 0)
---------
]
```
@ -371,7 +417,7 @@ Uppercase names are special values we call _tags_.
Tags are values which represent names.
For example, the `To` in `d To` is a tag.
It represents the name of the piece of data we're extracting from `d`.
It is the name of the piece of data we're extracting from `d`.
There are also two special tags, `True` and `False`, which represent [Boolean](https://en.wikipedia.org/wiki/Boolean_algebra) truth and falsehood.
@ -388,7 +434,7 @@ xOffset: 2
withDotter \d ->
[
stroke thickness #F00 (d To + vec xOffset 0)
stroke thickness #00F (d To + vec (-xOffset) 0)
stroke thickness #00F (d To + vec -xOffset 0)
]
```
@ -402,7 +448,7 @@ xOffset: thickness / 2
withDotter \d ->
[
stroke thickness #F00 (d To + vec xOffset 0)
stroke thickness #00F (d To + vec (-xOffset) 0)
stroke thickness #00F (d To + vec -xOffset 0)
]
```
@ -564,6 +610,7 @@ Seriously, 64 is my limit.
I wonder if there's any way we could automate this?
### The Ouroboros
You know the drill by now.
@ -587,7 +634,7 @@ splat: \d, radius ->
airbrush: \d, size ->
[
splat d size
airbrush d (size - 8)
airbrush d size-8
]
withDotter \d ->
@ -649,7 +696,7 @@ airbrush: \d, size ->
if (size > 0)
[
splat d size
airbrush d (size - 8)
airbrush d size-8
]
else
[]
@ -675,8 +722,8 @@ airbrush: \d, size ->
if (size > 0)
[
splat d size
airbrush d (size - 1)
---
airbrush d size-1
---
]
else
[]
@ -696,7 +743,7 @@ airbrush: \d, size ->
if (size > 0)
[
splat d size
airbrush d (size - 1)
airbrush d size-1
]
else
[]