From 29a80854a4bd117b92897fe5b306964a8a71ccb1 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?=E3=83=AA=E3=82=AD=E8=90=8C?= <commits@liquidev.net>
Date: Tue, 2 Sep 2025 18:44:38 +0200
Subject: [PATCH 01/13] fix parsing prefix operators in calls

---
 crates/haku-wasm/src/lib.rs | 31 +++++++--------
 crates/haku/src/parser.rs   | 75 ++++++++++++++++++++++++-------------
 crates/haku/src/token.rs    |  4 ++
 static/brush-box.js         |  2 +-
 4 files changed, 69 insertions(+), 43 deletions(-)

diff --git a/crates/haku-wasm/src/lib.rs b/crates/haku-wasm/src/lib.rs
index 8459dc6..85c0635 100644
--- a/crates/haku-wasm/src/lib.rs
+++ b/crates/haku-wasm/src/lib.rs
@@ -401,6 +401,7 @@ unsafe extern "C" fn haku_compile_brush(
         "compiling: parsed successfully into {} AST nodes",
         ast.len()
     );
+    // debug!("ast: {}", ast::dump::dump(&ast, root, Some(code)));
 
     let src = Source { code, ast: &ast };
 
@@ -431,21 +432,21 @@ unsafe extern "C" fn haku_compile_brush(
     );
     debug!("compiling: {closure_spec:?}");
 
-    debug!("bytecode: {:?}", chunk.bytecode);
-    {
-        let mut cursor = 0_usize;
-        for info in &chunk.span_info {
-            let slice = &chunk.bytecode[cursor..cursor + info.len as usize];
-            debug!(
-                "{:?} | 0x{:x} {:?} | {:?}",
-                info.span,
-                cursor,
-                slice,
-                info.span.slice(src.code),
-            );
-            cursor += info.len as usize;
-        }
-    }
+    // debug!("bytecode: {:?}", chunk.bytecode);
+    // {
+    //     let mut cursor = 0_usize;
+    //     for info in &chunk.span_info {
+    //         let slice = &chunk.bytecode[cursor..cursor + info.len as usize];
+    //         debug!(
+    //             "{:?} | 0x{:x} {:?} | {:?}",
+    //             info.span,
+    //             cursor,
+    //             slice,
+    //             info.span.slice(src.code),
+    //         );
+    //         cursor += info.len as usize;
+    //     }
+    // }
 
     instance.compile_result2 = Some(CompileResult {
         defs_string: instance.defs.serialize_defs(),
diff --git a/crates/haku/src/parser.rs b/crates/haku/src/parser.rs
index a8e0cee..5d02a5a 100644
--- a/crates/haku/src/parser.rs
+++ b/crates/haku/src/parser.rs
@@ -311,31 +311,13 @@ enum Tighter {
 
 fn tighter(left: (TokenKind, Spaces), right: (TokenKind, Spaces)) -> Tighter {
     #[derive(Debug, Clone, Copy, PartialEq, Eq, PartialOrd, Ord)]
-    enum Spacing {
-        Loose,
+    enum Tightness {
+        Loose(usize),
         Call,
-        Tight,
+        Tight(usize),
     }
 
-    fn tightness((kind, spaces): (TokenKind, Spaces)) -> Option<(Spacing, usize)> {
-        let spacing = match kind {
-            // There are a few types of operators which are independent of tightness.
-
-            // For : and =, it does not matter if they're spelled one way or the other, because
-            // there is only one way to use them (at the beginning of the expression).
-            TokenKind::Colon | TokenKind::Equal => Spacing::Loose,
-
-            // For calls, there is a special intermediate level, such that they can sit between
-            // loose operators and tight operators.
-            _ if PREFIX_TOKENS.contains(kind) => Spacing::Call,
-
-            // For everything else, the usual rules apply.
-            _ => match spaces.pair() {
-                (false, false) => Spacing::Tight,
-                (true, true) => Spacing::Loose,
-                _ => return None, // not a valid infix operator
-            },
-        };
+    fn tightness((kind, spaces): (TokenKind, Spaces)) -> Option<Tightness> {
         let index = match kind {
             TokenKind::Equal | TokenKind::Colon => 0,
             // 1: reserved for `and` and `or`
@@ -350,7 +332,28 @@ fn tighter(left: (TokenKind, Spaces), right: (TokenKind, Spaces)) -> Tighter {
             _ if PREFIX_TOKENS.contains(kind) => 5,
             _ => return None, // not an infix operator
         };
-        Some((spacing, index))
+        Some(match kind {
+            // There are a few types of operators which are independent of tightness.
+
+            // For : and =, it does not matter if they're spelled one way or the other, because
+            // there is only one way to use them (at the beginning of the expression).
+            TokenKind::Colon | TokenKind::Equal => Tightness::Loose(index),
+
+            // For unary -, we treat it as having Tight spacing rather than Call, else it would
+            // be allowed to begin function calls.
+            TokenKind::Minus if spaces.pair() == (true, false) => Tightness::Tight(index),
+
+            // For calls, there is a special intermediate level, such that they can sit between
+            // loose operators and tight operators.
+            _ if PREFIX_TOKENS.contains(kind) => Tightness::Call,
+
+            // For everything else, the usual rules apply.
+            _ => match spaces.pair() {
+                (false, false) => Tightness::Tight(index),
+                (true, true) => Tightness::Loose(index),
+                _ => return None, // not a valid infix operator
+            },
+        })
     }
 
     let Some(right_tightness) = tightness(right) else {
@@ -361,6 +364,12 @@ fn tighter(left: (TokenKind, Spaces), right: (TokenKind, Spaces)) -> Tighter {
         return Tighter::Right;
     };
 
+    // When we're inside a call, subsequent arguments must not be slurped into the current
+    // expression, as it would result in calls being parsed as (vec (1 (-1))), which is not correct.
+    if left_tightness == Tightness::Call {
+        return Tighter::Left;
+    }
+
     if right_tightness > left_tightness {
         Tighter::Right
     } else {
@@ -585,18 +594,29 @@ const PREFIX_TOKENS: TokenKindSet = TokenKindSet::new(&[
 ]);
 
 fn prefix(p: &mut Parser) -> Closed {
-    match p.peek() {
+    let (kind, spaces) = p.peek_with_spaces();
+    match kind {
         TokenKind::Ident => one(p, NodeKind::Ident),
         TokenKind::Tag => one(p, NodeKind::Tag),
         TokenKind::Number => one(p, NodeKind::Number),
         TokenKind::Color => one(p, NodeKind::Color),
         TokenKind::LBrack => list(p),
 
-        TokenKind::Minus | TokenKind::Not => unary(p),
+        TokenKind::Minus if !spaces.right() => unary(p),
+        TokenKind::Not => unary(p),
         TokenKind::LParen => paren(p),
         TokenKind::Backslash => lambda(p),
         TokenKind::If => if_expr(p),
 
+        TokenKind::Minus if spaces.pair() == (false, true) => {
+            let span = p.span();
+            p.emit(Diagnostic::error(
+                span,
+                "`-` operator must be surrounded by an equal amount of spaces",
+            ));
+            p.advance_with_error()
+        }
+
         _ => {
             assert!(
                 !PREFIX_TOKENS.contains(p.peek()),
@@ -615,9 +635,9 @@ fn prefix(p: &mut Parser) -> Closed {
 }
 
 fn infix(p: &mut Parser, op: (TokenKind, Spaces)) -> NodeKind {
-    match op.0 {
+    let (kind, spaces) = op;
+    match kind {
         TokenKind::Plus
-        | TokenKind::Minus
         | TokenKind::Star
         | TokenKind::Slash
         | TokenKind::EqualEqual
@@ -627,6 +647,7 @@ fn infix(p: &mut Parser, op: (TokenKind, Spaces)) -> NodeKind {
         | TokenKind::Greater
         | TokenKind::GreaterEqual
         | TokenKind::Colon => infix_binary(p, op),
+        TokenKind::Minus if spaces.are_balanced() => infix_binary(p, op),
 
         TokenKind::Equal => infix_let(p, op),
 
diff --git a/crates/haku/src/token.rs b/crates/haku/src/token.rs
index c613408..047caf0 100644
--- a/crates/haku/src/token.rs
+++ b/crates/haku/src/token.rs
@@ -135,6 +135,10 @@ impl Spaces {
     pub fn pair(self) -> (bool, bool) {
         (self.left(), self.right())
     }
+
+    pub fn are_balanced(self) -> bool {
+        matches!(self.pair(), (true, true) | (false, false))
+    }
 }
 
 impl fmt::Debug for Spaces {
diff --git a/static/brush-box.js b/static/brush-box.js
index dfcc850..27750af 100644
--- a/static/brush-box.js
+++ b/static/brush-box.js
@@ -100,7 +100,7 @@ norm: \\u ->
   u / vec l l
 
 perpClockwise: \\v ->
-  vec (vecY v) (-(vecX v))
+  vec (vecY v) -(vecX v)
 
 withDotter \\d ->
   pi = 3.14159265

From 9808d3227f5831fe2898f3a40ea0c6aae175a429 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?=E3=83=AA=E3=82=AD=E8=90=8C?= <commits@liquidev.net>
Date: Tue, 2 Sep 2025 20:02:48 +0200
Subject: [PATCH 02/13] fix a few bugs with the new precedence rules

---
 crates/haku-wasm/src/lib.rs |  33 +++++------
 crates/haku/src/parser.rs   |  28 +++++----
 docs/rkgk.dj                | 111 +++++++++++++++++++++++++-----------
 3 files changed, 113 insertions(+), 59 deletions(-)

diff --git a/crates/haku-wasm/src/lib.rs b/crates/haku-wasm/src/lib.rs
index 85c0635..5030c58 100644
--- a/crates/haku-wasm/src/lib.rs
+++ b/crates/haku-wasm/src/lib.rs
@@ -432,22 +432,23 @@ unsafe extern "C" fn haku_compile_brush(
     );
     debug!("compiling: {closure_spec:?}");
 
-    // debug!("bytecode: {:?}", chunk.bytecode);
-    // {
-    //     let mut cursor = 0_usize;
-    //     for info in &chunk.span_info {
-    //         let slice = &chunk.bytecode[cursor..cursor + info.len as usize];
-    //         debug!(
-    //             "{:?} | 0x{:x} {:?} | {:?}",
-    //             info.span,
-    //             cursor,
-    //             slice,
-    //             info.span.slice(src.code),
-    //         );
-    //         cursor += info.len as usize;
-    //     }
-    // }
-
+    /*
+    debug!("bytecode: {:?}", chunk.bytecode);
+    {
+        let mut cursor = 0_usize;
+        for info in &chunk.span_info {
+            let slice = &chunk.bytecode[cursor..cursor + info.len as usize];
+            debug!(
+                "{:?} | 0x{:x} {:?} | {:?}",
+                info.span,
+                cursor,
+                slice,
+                info.span.slice(src.code),
+            );
+            cursor += info.len as usize;
+        }
+    }
+    // */
     instance.compile_result2 = Some(CompileResult {
         defs_string: instance.defs.serialize_defs(),
         tags_string: instance.defs.serialize_tags(),
diff --git a/crates/haku/src/parser.rs b/crates/haku/src/parser.rs
index 5d02a5a..3a99adf 100644
--- a/crates/haku/src/parser.rs
+++ b/crates/haku/src/parser.rs
@@ -329,7 +329,7 @@ fn tighter(left: (TokenKind, Spaces), right: (TokenKind, Spaces)) -> Tighter {
             | TokenKind::GreaterEqual => 2,
             TokenKind::Plus | TokenKind::Minus | TokenKind::Star | TokenKind::Slash => 3,
             // 4: reserve for `.`
-            _ if PREFIX_TOKENS.contains(kind) => 5,
+            _ if is_prefix_token((kind, spaces)) => 5,
             _ => return None, // not an infix operator
         };
         Some(match kind {
@@ -341,11 +341,11 @@ fn tighter(left: (TokenKind, Spaces), right: (TokenKind, Spaces)) -> Tighter {
 
             // For unary -, we treat it as having Tight spacing rather than Call, else it would
             // be allowed to begin function calls.
-            TokenKind::Minus if spaces.pair() == (true, false) => Tightness::Tight(index),
+            TokenKind::Minus if !spaces.are_balanced() => Tightness::Tight(index),
 
             // For calls, there is a special intermediate level, such that they can sit between
             // loose operators and tight operators.
-            _ if PREFIX_TOKENS.contains(kind) => Tightness::Call,
+            _ if is_prefix_token((kind, spaces)) => Tightness::Call,
 
             // For everything else, the usual rules apply.
             _ => match spaces.pair() {
@@ -366,7 +366,7 @@ fn tighter(left: (TokenKind, Spaces), right: (TokenKind, Spaces)) -> Tighter {
 
     // When we're inside a call, subsequent arguments must not be slurped into the current
     // expression, as it would result in calls being parsed as (vec (1 (-1))), which is not correct.
-    if left_tightness == Tightness::Call {
+    if left_tightness == Tightness::Call && right.0 == TokenKind::Minus && !right.1.are_balanced() {
         return Tighter::Left;
     }
 
@@ -579,13 +579,15 @@ fn if_expr(p: &mut Parser) -> Closed {
     p.close(o, NodeKind::If)
 }
 
+// TODO: There is a lot of special casing around `-` being both a prefix and an infix token.
+// Maybe there's a way to simplify it?
+
 // NOTE: This must be synchronised with the match expression in prefix().
 const PREFIX_TOKENS: TokenKindSet = TokenKindSet::new(&[
     TokenKind::Ident,
     TokenKind::Tag,
     TokenKind::Number,
     TokenKind::Color,
-    TokenKind::Minus,
     TokenKind::Not,
     TokenKind::LParen,
     TokenKind::Backslash,
@@ -593,6 +595,10 @@ const PREFIX_TOKENS: TokenKindSet = TokenKindSet::new(&[
     TokenKind::LBrack,
 ]);
 
+fn is_prefix_token((kind, spaces): (TokenKind, Spaces)) -> bool {
+    PREFIX_TOKENS.contains(kind) || (kind == TokenKind::Minus && !spaces.are_balanced())
+}
+
 fn prefix(p: &mut Parser) -> Closed {
     let (kind, spaces) = p.peek_with_spaces();
     match kind {
@@ -602,7 +608,7 @@ fn prefix(p: &mut Parser) -> Closed {
         TokenKind::Color => one(p, NodeKind::Color),
         TokenKind::LBrack => list(p),
 
-        TokenKind::Minus if !spaces.right() => unary(p),
+        TokenKind::Minus if spaces.pair() == (true, false) => unary(p),
         TokenKind::Not => unary(p),
         TokenKind::LParen => paren(p),
         TokenKind::Backslash => lambda(p),
@@ -619,9 +625,9 @@ fn prefix(p: &mut Parser) -> Closed {
 
         _ => {
             assert!(
-                !PREFIX_TOKENS.contains(p.peek()),
-                "{:?} found in PREFIX_TOKENS",
-                p.peek()
+                !is_prefix_token(p.peek_with_spaces()),
+                "{:?} is not a prefix token",
+                p.peek_with_spaces()
             );
 
             let span = p.span();
@@ -651,7 +657,7 @@ fn infix(p: &mut Parser, op: (TokenKind, Spaces)) -> NodeKind {
 
         TokenKind::Equal => infix_let(p, op),
 
-        _ if PREFIX_TOKENS.contains(op.0) => infix_call(p, op),
+        _ if is_prefix_token(op) => infix_call(p, op),
 
         _ => panic!("unhandled infix operator {op:?}"),
     }
@@ -671,7 +677,7 @@ fn infix_binary(p: &mut Parser, op: (TokenKind, Spaces)) -> NodeKind {
 }
 
 fn infix_call(p: &mut Parser, mut arg: (TokenKind, Spaces)) -> NodeKind {
-    while PREFIX_TOKENS.contains(p.peek()) {
+    while is_prefix_token(p.peek_with_spaces()) {
         precedence_parse(p, arg);
         arg = p.peek_with_spaces();
     }
diff --git a/docs/rkgk.dj b/docs/rkgk.dj
index 7335554..e91e98c 100644
--- a/docs/rkgk.dj
+++ b/docs/rkgk.dj
@@ -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
     []

From 449f2b59dfe62fc70f4f96d2f01553e833832f06 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?=E3=83=AA=E3=82=AD=E8=90=8C?= <commits@liquidev.net>
Date: Tue, 2 Sep 2025 20:02:48 +0200
Subject: [PATCH 03/13] disable ligatures in code

it can be hard for first-time users to understand what these ligatures mean or how to type them
---
 static/base.css | 1 +
 1 file changed, 1 insertion(+)

diff --git a/static/base.css b/static/base.css
index 6fc9acd..bf170d6 100644
--- a/static/base.css
+++ b/static/base.css
@@ -53,6 +53,7 @@ code,
 textarea {
     font-family: var(--font-monospace);
     line-height: var(--line-height);
+    font-variant-ligatures: none;
 }
 
 /* Buttons */

From 45099916fe6b4fc7211dc081ff3d16adf8ea4121 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?=E3=83=AA=E3=82=AD=E8=90=8C?= <commits@liquidev.net>
Date: Tue, 2 Sep 2025 20:15:35 +0200
Subject: [PATCH 04/13] update Zig code to 0.15.0

---
 crates/haku2/build.rs      |  1 +
 crates/haku2/src/haku2.zig |  3 ++-
 crates/haku2/src/value.zig | 24 ++++++++++++------------
 crates/haku2/src/vm.zig    |  4 ++--
 4 files changed, 17 insertions(+), 15 deletions(-)

diff --git a/crates/haku2/build.rs b/crates/haku2/build.rs
index a68dc93..3d49a8b 100644
--- a/crates/haku2/build.rs
+++ b/crates/haku2/build.rs
@@ -46,6 +46,7 @@ fn main() -> Result<(), Box<dyn Error>> {
         .arg("--prominent-compile-errors")
         .arg("--color")
         .arg(color)
+        .arg("-freference-trace")
         // Build output
         .arg("--cache-dir")
         .arg(out_path.join("zig-cache"))
diff --git a/crates/haku2/src/haku2.zig b/crates/haku2/src/haku2.zig
index ec428fc..cfadabe 100644
--- a/crates/haku2/src/haku2.zig
+++ b/crates/haku2/src/haku2.zig
@@ -22,8 +22,9 @@ pub const std_options: std.Options = .{
 };
 
 pub fn enableLogScope(scope: @TypeOf(.enum_literal)) bool {
+    // Replace any of the false returns below to enable log scopes for the build.
     if (scope == .vm)
-        return false
+        return true
     else
         return true;
 }
diff --git a/crates/haku2/src/value.zig b/crates/haku2/src/value.zig
index d1498ff..e34bc24 100644
--- a/crates/haku2/src/value.zig
+++ b/crates/haku2/src/value.zig
@@ -69,24 +69,24 @@ pub const Value = union(enum) {
         };
     }
 
-    pub fn format(value: Value, comptime fmt: []const u8, options: std.fmt.FormatOptions, writer: anytype) !void {
+    pub fn format(value: Value, writer: *std.Io.Writer) !void {
         switch (value) {
-            .nil => try std.fmt.formatBuf("Nil", options, writer),
-            .false => try std.fmt.formatBuf("False", options, writer),
-            .true => try std.fmt.formatBuf("True", options, writer),
-            inline .tag, .number => |x| try std.fmt.format(writer, "{d}", .{x}),
-            inline .vec4, .rgba => |x| try std.fmt.format(writer, "{s}{d}", .{ @tagName(value), x }),
+            .nil => try writer.writeAll("Nil"),
+            .false => try writer.writeAll("False"),
+            .true => try writer.writeAll("True"),
+            inline .tag, .number => |x| try writer.print("{d}", .{x}),
+            inline .vec4, .rgba => |x| try writer.print("{s}{d}", .{ @tagName(value), x }),
             .ref => |ref| switch (ref.*) {
-                .closure => |c| try std.fmt.format(writer, "function {s}", .{c.name}),
+                .closure => |c| try writer.print("function {s}", .{c.name}),
                 .list => |l| {
-                    try std.fmt.formatBuf("[", options, writer);
+                    try writer.writeAll("[");
                     for (l, 0..) |elem, i| {
-                        if (i != 0) try std.fmt.formatBuf(", ", options, writer);
-                        try elem.format(fmt, options, writer);
+                        if (i != 0) try writer.writeAll(", ");
+                        try elem.format(writer);
                     }
-                    try std.fmt.formatBuf("]", options, writer);
+                    try writer.writeAll("]");
                 },
-                inline .shape, .scribble, .reticle => |x| try std.fmt.format(writer, "{}", .{x}),
+                inline .shape, .scribble, .reticle => |x| try writer.print("{}", .{x}),
             },
         }
     }
diff --git a/crates/haku2/src/vm.zig b/crates/haku2/src/vm.zig
index 9f90953..910cb13 100644
--- a/crates/haku2/src/vm.zig
+++ b/crates/haku2/src/vm.zig
@@ -167,7 +167,7 @@ pub fn push(vm: *Vm, val: Value) Error!void {
     if (vm.stack_top >= vm.stack.len) {
         return vm.throw("too many live temporary values (local variables and expression operands)", .{});
     }
-    log.debug("PUSH {any} <- {}", .{ vm.stack[0..vm.stack_top], val });
+    log.debug("PUSH {any} <- {f}", .{ vm.stack[0..vm.stack_top], val });
     vm.stack[vm.stack_top] = val;
     vm.stack_top += 1;
 }
@@ -176,7 +176,7 @@ pub fn pop(vm: *Vm) Error!Value {
     try vm.validateBytecode(vm.stack_top > 0, "value stack underflow", .{});
     vm.stack_top -= 1;
     const result = vm.stack[vm.stack_top];
-    log.debug("POP  {any} -> {}", .{ vm.stack[0..vm.stack_top], result });
+    log.debug("POP  {any} -> {f}", .{ vm.stack[0..vm.stack_top], result });
     return vm.stack[vm.stack_top];
 }
 

From 2eea1f201f4ff7829b8b17b192d3a2aeec7c9e9f Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?=E3=83=AA=E3=82=AD=E8=90=8C?= <commits@liquidev.net>
Date: Tue, 2 Sep 2025 20:30:47 +0200
Subject: [PATCH 05/13] h2: add better VM value stack tracing

---
 crates/haku2/src/vm.zig | 22 ++++++++++++++++++++--
 1 file changed, 20 insertions(+), 2 deletions(-)

diff --git a/crates/haku2/src/vm.zig b/crates/haku2/src/vm.zig
index 910cb13..7bec9a1 100644
--- a/crates/haku2/src/vm.zig
+++ b/crates/haku2/src/vm.zig
@@ -147,6 +147,24 @@ pub fn stackFrame(vm: *const Vm, index: usize) StackFrame {
     }
 }
 
+const StackFmt = struct {
+    stack: []const Value,
+
+    pub fn format(f: *const StackFmt, writer: *std.Io.Writer) !void {
+        try writer.writeAll("[");
+        for (f.stack, 0..) |val, i| {
+            if (i != 0)
+                try writer.writeAll(", ");
+            try val.format(writer);
+        }
+        try writer.writeAll("]");
+    }
+};
+
+fn stackFmt(stack: []const Value) StackFmt {
+    return .{ .stack = stack };
+}
+
 /// Debug assertion for bytecode validity.
 /// In future versions, this may become disabled in release builds.
 fn validateBytecode(vm: *Vm, ok: bool, comptime fmt: []const u8, args: anytype) Error!void {
@@ -167,7 +185,7 @@ pub fn push(vm: *Vm, val: Value) Error!void {
     if (vm.stack_top >= vm.stack.len) {
         return vm.throw("too many live temporary values (local variables and expression operands)", .{});
     }
-    log.debug("PUSH {any} <- {f}", .{ vm.stack[0..vm.stack_top], val });
+    log.debug("PUSH {f} <- {f}", .{ stackFmt(vm.stack[0..vm.stack_top]), val });
     vm.stack[vm.stack_top] = val;
     vm.stack_top += 1;
 }
@@ -176,7 +194,7 @@ pub fn pop(vm: *Vm) Error!Value {
     try vm.validateBytecode(vm.stack_top > 0, "value stack underflow", .{});
     vm.stack_top -= 1;
     const result = vm.stack[vm.stack_top];
-    log.debug("POP  {any} -> {f}", .{ vm.stack[0..vm.stack_top], result });
+    log.debug("POP  {f} -> {f}", .{ stackFmt(vm.stack[0..vm.stack_top]), result });
     return vm.stack[vm.stack_top];
 }
 

From 958201cd18809447a5cb82931adc7f7d69626704 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?=E3=83=AA=E3=82=AD=E8=90=8C?= <commits@liquidev.net>
Date: Tue, 2 Sep 2025 20:30:47 +0200
Subject: [PATCH 06/13] h2: add better comment about how to use
 root.enableLogScope

---
 crates/haku2/src/haku2.zig | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/crates/haku2/src/haku2.zig b/crates/haku2/src/haku2.zig
index cfadabe..136f21f 100644
--- a/crates/haku2/src/haku2.zig
+++ b/crates/haku2/src/haku2.zig
@@ -24,7 +24,7 @@ pub const std_options: std.Options = .{
 pub fn enableLogScope(scope: @TypeOf(.enum_literal)) bool {
     // Replace any of the false returns below to enable log scopes for the build.
     if (scope == .vm)
-        return true
+        return false
     else
         return true;
 }

From c4ad609717b734e756359b705055635b6bb63768 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?=E3=83=AA=E3=82=AD=E8=90=8C?= <commits@liquidev.net>
Date: Tue, 2 Sep 2025 20:30:47 +0200
Subject: [PATCH 07/13] h2: fix implementation of Value.gt not actually being a
 greater-than operation

how did I miss that (a < b) is the same as (b > a) is beyond me
---
 crates/haku2/src/value.zig | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/crates/haku2/src/value.zig b/crates/haku2/src/value.zig
index e34bc24..3269a60 100644
--- a/crates/haku2/src/value.zig
+++ b/crates/haku2/src/value.zig
@@ -48,7 +48,7 @@ pub const Value = union(enum) {
     }
 
     pub fn gt(a: Value, b: Value) ?bool {
-        return !a.eql(b) and !(a.lt(b) orelse return null);
+        return b.lt(a);
     }
 
     pub fn typeName(value: Value) []const u8 {

From e31dde10487951c2767ca5d4c9e7bbecc188c9b0 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?=E3=83=AA=E3=82=AD=E8=90=8C?= <commits@liquidev.net>
Date: Tue, 2 Sep 2025 20:30:47 +0200
Subject: [PATCH 08/13] add .ignore file

---
 .ignore | 3 +++
 1 file changed, 3 insertions(+)
 create mode 100644 .ignore

diff --git a/.ignore b/.ignore
new file mode 100644
index 0000000..be8298c
--- /dev/null
+++ b/.ignore
@@ -0,0 +1,3 @@
+*.ttf
+*.woff2
+*.png

From 69cc34d07e2837eb473c49085c08ea905f7752b7 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?=E3=83=AA=E3=82=AD=E8=90=8C?= <commits@liquidev.net>
Date: Tue, 2 Sep 2025 20:30:47 +0200
Subject: [PATCH 09/13] h1: make ' and ? only allowed as suffixes in
 identifiers

---
 crates/haku/src/lexer.rs | 9 ++++++++-
 1 file changed, 8 insertions(+), 1 deletion(-)

diff --git a/crates/haku/src/lexer.rs b/crates/haku/src/lexer.rs
index f3e4ce2..3ebff7f 100644
--- a/crates/haku/src/lexer.rs
+++ b/crates/haku/src/lexer.rs
@@ -57,7 +57,11 @@ fn one_or_two(l: &mut Lexer<'_>, kind1: TokenKind, c2: char, kind2: TokenKind) -
 }
 
 fn is_ident_char(c: char) -> bool {
-    matches!(c, 'a'..='z' | 'A'..='Z' | '0'..='9' | '_' | '\'' | '?')
+    matches!(c, 'a'..='z' | 'A'..='Z' | '0'..='9' | '_')
+}
+
+fn is_ident_extra_char(c: char) -> bool {
+    matches!(c, '\'' | '?')
 }
 
 fn ident(l: &mut Lexer<'_>) -> TokenKind {
@@ -65,6 +69,9 @@ fn ident(l: &mut Lexer<'_>) -> TokenKind {
     while is_ident_char(l.current()) {
         l.advance();
     }
+    while is_ident_extra_char(l.current()) {
+        l.advance();
+    }
     let end = l.position;
 
     match Span::new(start, end).slice(l.input) {

From ec7ee9626fc394661074aa2ecb0625c72a048ad4 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?=E3=83=AA=E3=82=AD=E8=90=8C?= <commits@liquidev.net>
Date: Tue, 2 Sep 2025 22:03:42 +0200
Subject: [PATCH 10/13] implement `.` and `|` operators

`f . x` is the same as `f x`, and is mostly useful when used as an argument to another function call.
this allows us to simulate record field syntax very well: `d.Num` is the same as `d Num`, but with high precedence

`a |f b` is the same as `f a b` and effectively allows you to turn any function into an arithmetic operator.
it's the main reason behind + - * / having the same precedence---they now chain very nicely with pipes

closes #126 (`|` operator)
closes #127 (`.` operator)
---
 crates/haku/src/compiler.rs | 150 ++++++++++++++++++++++++++----------
 crates/haku/src/lexer.rs    |   2 +
 crates/haku/src/parser.rs   |  21 +++--
 crates/haku/src/token.rs    |   2 +
 4 files changed, 125 insertions(+), 50 deletions(-)

diff --git a/crates/haku/src/compiler.rs b/crates/haku/src/compiler.rs
index a458c5e..c60fb11 100644
--- a/crates/haku/src/compiler.rs
+++ b/crates/haku/src/compiler.rs
@@ -361,52 +361,43 @@ fn compile_binary<'a>(c: &mut Compiler<'a>, src: &Source<'a>, node_id: NodeId) -
     }
     let name = src.ast.span(op).slice(src.code);
 
-    if name == "=" {
-        c.emit(Diagnostic::error(
-            src.ast.span(op),
-            "defs `a = b` may only appear at the top level",
-        ));
-        return Ok(());
+    match name {
+        ":" => {
+            // Invalid use of a def inside an expression.
+            c.emit(Diagnostic::error(
+                src.ast.span(op),
+                "defs `a: b` may only appear at the top level",
+            ));
+            Ok(())
+        }
+        "." => compile_dot_call(c, src, left, right),
+        "|" => compile_pipe_call(c, src, left, right),
+        _ => {
+            compile_expr(c, src, left)?;
+            compile_expr(c, src, right)?;
+            if let Some(index) = system::resolve(SystemFnArity::Binary, name) {
+                let argument_count = 2;
+                c.chunk.emit_opcode(Opcode::System)?;
+                c.chunk.emit_u8(index)?;
+                c.chunk.emit_u8(argument_count)?;
+            } else {
+                c.emit(Diagnostic::error(
+                    src.ast.span(op),
+                    "this binary operator is currently unimplemented",
+                ));
+            }
+            Ok(())
+        }
     }
-
-    compile_expr(c, src, left)?;
-    compile_expr(c, src, right)?;
-    if let Some(index) = system::resolve(SystemFnArity::Binary, name) {
-        let argument_count = 2;
-        c.chunk.emit_opcode(Opcode::System)?;
-        c.chunk.emit_u8(index)?;
-        c.chunk.emit_u8(argument_count)?;
-    } else {
-        c.emit(Diagnostic::error(
-            src.ast.span(op),
-            "this unary operator is currently unimplemented",
-        ));
-    }
-
-    Ok(())
 }
 
-fn compile_call<'a>(c: &mut Compiler<'a>, src: &Source<'a>, node_id: NodeId) -> CompileResult {
-    let mut walk = src.ast.walk(node_id);
-    let Some(func) = walk.node() else {
-        return Ok(());
-    };
+fn emit_nary_call<'a>(
+    c: &mut Compiler<'a>,
+    src: &Source<'a>,
+    func: NodeId,
+    argument_count: u8,
+) -> CompileResult {
     let name = src.ast.span(func).slice(src.code);
-
-    let mut argument_count = 0;
-    while let Some(arg) = walk.node() {
-        compile_expr(c, src, arg)?;
-        argument_count += 1;
-    }
-
-    let argument_count = u8::try_from(argument_count).unwrap_or_else(|_| {
-        c.emit(Diagnostic::error(
-            src.ast.span(node_id),
-            "function call has too many arguments",
-        ));
-        0
-    });
-
     if let (NodeKind::Ident, Some(index)) = (
         src.ast.kind(func),
         system::resolve(SystemFnArity::Nary, name),
@@ -423,6 +414,81 @@ fn compile_call<'a>(c: &mut Compiler<'a>, src: &Source<'a>, node_id: NodeId) ->
         c.chunk.emit_opcode(Opcode::Call)?;
         c.chunk.emit_u8(argument_count)?;
     }
+    Ok(())
+}
+
+fn compile_call<'a>(c: &mut Compiler<'a>, src: &Source<'a>, node_id: NodeId) -> CompileResult {
+    let mut walk = src.ast.walk(node_id);
+    let Some(func) = walk.node() else {
+        return Ok(());
+    };
+
+    let mut argument_count = 0;
+    while let Some(arg) = walk.node() {
+        compile_expr(c, src, arg)?;
+        argument_count += 1;
+    }
+
+    let argument_count = u8::try_from(argument_count).unwrap_or_else(|_| {
+        c.emit(Diagnostic::error(
+            src.ast.span(node_id),
+            "function call has too many arguments",
+        ));
+        0
+    });
+
+    emit_nary_call(c, src, func, argument_count)?;
+
+    Ok(())
+}
+
+fn compile_dot_call<'a>(
+    c: &mut Compiler<'a>,
+    src: &Source<'a>,
+    func: NodeId,
+    right: NodeId,
+) -> CompileResult {
+    compile_expr(c, src, right)?;
+    emit_nary_call(c, src, func, 1)?;
+
+    Ok(())
+}
+
+fn compile_pipe_call<'a>(
+    c: &mut Compiler<'a>,
+    src: &Source<'a>,
+    left: NodeId,
+    call: NodeId,
+) -> CompileResult {
+    if src.ast.kind(call) != NodeKind::Call {
+        c.emit(Diagnostic::error(
+            src.ast.span(call),
+            "the right side of a pipe `|` must be a function call",
+        ));
+        return Ok(());
+    }
+
+    let mut walk = src.ast.walk(call);
+    let Some(func) = walk.node() else {
+        return Ok(());
+    };
+
+    compile_expr(c, src, left)?;
+    let mut argument_count = 1;
+    while let Some(arg) = walk.node() {
+        compile_expr(c, src, arg)?;
+        argument_count += 1;
+    }
+
+    let argument_count = u8::try_from(argument_count).unwrap_or_else(|_| {
+        c.emit(Diagnostic::error(
+            src.ast.span(call),
+            "function call has too many arguments",
+        ));
+        0
+    });
+
+    emit_nary_call(c, src, func, argument_count)?;
 
     Ok(())
 }
diff --git a/crates/haku/src/lexer.rs b/crates/haku/src/lexer.rs
index 3ebff7f..781d7d4 100644
--- a/crates/haku/src/lexer.rs
+++ b/crates/haku/src/lexer.rs
@@ -215,6 +215,8 @@ fn token(l: &mut Lexer<'_>) -> (TokenKind, Span, bool) {
         '!' => one_or_two(l, TokenKind::Not, '=', TokenKind::NotEqual),
         '<' => one_or_two(l, TokenKind::Less, '=', TokenKind::LessEqual),
         '>' => one_or_two(l, TokenKind::Greater, '=', TokenKind::GreaterEqual),
+        '.' => one(l, TokenKind::Dot),
+        '|' => one(l, TokenKind::Pipe),
 
         '\n' => return newline(l, has_left_space),
         '(' => one(l, TokenKind::LParen),
diff --git a/crates/haku/src/parser.rs b/crates/haku/src/parser.rs
index 3a99adf..fa1af6d 100644
--- a/crates/haku/src/parser.rs
+++ b/crates/haku/src/parser.rs
@@ -327,17 +327,20 @@ fn tighter(left: (TokenKind, Spaces), right: (TokenKind, Spaces)) -> Tighter {
             | TokenKind::LessEqual
             | TokenKind::Greater
             | TokenKind::GreaterEqual => 2,
-            TokenKind::Plus | TokenKind::Minus | TokenKind::Star | TokenKind::Slash => 3,
-            // 4: reserve for `.`
+
+            TokenKind::Plus
+            | TokenKind::Minus
+            | TokenKind::Star
+            | TokenKind::Slash
+            | TokenKind::Pipe => 3,
+
+            TokenKind::Dot => 4,
             _ if is_prefix_token((kind, spaces)) => 5,
             _ => return None, // not an infix operator
         };
         Some(match kind {
-            // There are a few types of operators which are independent of tightness.
-
-            // For : and =, it does not matter if they're spelled one way or the other, because
-            // there is only one way to use them (at the beginning of the expression).
-            TokenKind::Colon | TokenKind::Equal => Tightness::Loose(index),
+            // There are a few types of operators which work independent of tightness.
+            TokenKind::Colon | TokenKind::Equal | TokenKind::Pipe => Tightness::Loose(index),
 
             // For unary -, we treat it as having Tight spacing rather than Call, else it would
             // be allowed to begin function calls.
@@ -652,7 +655,9 @@ fn infix(p: &mut Parser, op: (TokenKind, Spaces)) -> NodeKind {
         | TokenKind::LessEqual
         | TokenKind::Greater
         | TokenKind::GreaterEqual
-        | TokenKind::Colon => infix_binary(p, op),
+        | TokenKind::Colon
+        | TokenKind::Dot
+        | TokenKind::Pipe => infix_binary(p, op),
         TokenKind::Minus if spaces.are_balanced() => infix_binary(p, op),
 
         TokenKind::Equal => infix_let(p, op),
diff --git a/crates/haku/src/token.rs b/crates/haku/src/token.rs
index 047caf0..96c8282 100644
--- a/crates/haku/src/token.rs
+++ b/crates/haku/src/token.rs
@@ -28,6 +28,8 @@ pub enum TokenKind {
     Greater,
     GreaterEqual,
     Not,
+    Dot,
+    Pipe,
 
     // Punctuation
     Newline,

From a4c18c37dc1abb1228251741edc37cfd9735f3bb Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?=E3=83=AA=E3=82=AD=E8=90=8C?= <commits@liquidev.net>
Date: Wed, 3 Sep 2025 16:57:10 +0200
Subject: [PATCH 11/13] h1: make `|` operator work with anything other than
 syntactic calls (in which case it just calls the value)

in case you call a function to get a function, parenthesise it

    1 | getFunction ()   -- getFunction 1 ()
    1 | (getFunction ()) -- (getFunction ()) 1
---
 crates/haku/src/compiler.rs | 56 ++++++++++++++++++-------------------
 1 file changed, 28 insertions(+), 28 deletions(-)

diff --git a/crates/haku/src/compiler.rs b/crates/haku/src/compiler.rs
index c60fb11..f3f8f3d 100644
--- a/crates/haku/src/compiler.rs
+++ b/crates/haku/src/compiler.rs
@@ -460,36 +460,36 @@ fn compile_pipe_call<'a>(
     left: NodeId,
     call: NodeId,
 ) -> CompileResult {
-    if src.ast.kind(call) != NodeKind::Call {
-        c.emit(Diagnostic::error(
-            src.ast.span(call),
-            "the right side of a pipe `|` must be a function call",
-        ));
-        return Ok(());
+    match src.ast.kind(call) {
+        NodeKind::Call => {
+            let mut walk = src.ast.walk(call);
+            let Some(func) = walk.node() else {
+                return Ok(());
+            };
+
+            compile_expr(c, src, left)?;
+            let mut argument_count = 1;
+            while let Some(arg) = walk.node() {
+                compile_expr(c, src, arg)?;
+                argument_count += 1;
+            }
+
+            let argument_count = u8::try_from(argument_count).unwrap_or_else(|_| {
+                c.emit(Diagnostic::error(
+                    src.ast.span(call),
+                    "function call has too many arguments",
+                ));
+                0
+            });
+
+            emit_nary_call(c, src, func, argument_count)?;
+        }
+        _ => {
+            compile_expr(c, src, left)?;
+            emit_nary_call(c, src, call, 1)?;
+        }
     }
 
-    let mut walk = src.ast.walk(call);
-    let Some(func) = walk.node() else {
-        return Ok(());
-    };
-
-    compile_expr(c, src, left)?;
-    let mut argument_count = 1;
-    while let Some(arg) = walk.node() {
-        compile_expr(c, src, arg)?;
-        argument_count += 1;
-    }
-
-    let argument_count = u8::try_from(argument_count).unwrap_or_else(|_| {
-        c.emit(Diagnostic::error(
-            src.ast.span(call),
-            "function call has too many arguments",
-        ));
-        0
-    });
-
-    emit_nary_call(c, src, func, argument_count)?;
-
     Ok(())
 }
 

From b5cdfdb1b6a79d01f8eceb3b03a42f1048829afd Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?=E3=83=AA=E3=82=AD=E8=90=8C?= <commits@liquidev.net>
Date: Wed, 3 Sep 2025 16:57:10 +0200
Subject: [PATCH 12/13] introduce haku reference docs

---
 docs/haku.dj | 520 +++++++++++++++++++++++++++++++++++++++++++++++++++
 rkgk.toml    |   1 +
 2 files changed, 521 insertions(+)
 create mode 100644 docs/haku.dj

diff --git a/docs/haku.dj b/docs/haku.dj
new file mode 100644
index 0000000..aa93e43
--- /dev/null
+++ b/docs/haku.dj
@@ -0,0 +1,520 @@
+# haku reference manual
+
+haku is a dynamically typed, pure functional programming language, used for programming brushes in rakugaki.
+
+For the layperson, it can be thought of a beefed up calculator.
+It has roots in ordinary school algebra, but has a much more powerful set of features, with the special ability of being able to edit images.
+
+
+## Overview
+
+haku programs are called _brushes_.
+The purpose of a brush is to produce instructions for rakugaki on how the user may interact with the wall (via _reticles_), and what things should be drawn on the wall as a result of those interactions (via _scribbles_).
+Collectively, reticles and scribbles are what we call _effects_.
+
+A brush's task is to compute (or in simpler terms, calculate) an effect that rakugaki will then _perform_.
+
+In case of reticles, rakugaki will allow the user to interact with the wall, and then ask haku for another effect to perform afterwards (a _continuation_).
+
+In case of scribbles, rakugaki will draw the scribble onto the wall, without asking haku for more.
+
+Once rakugaki runs through all effects, we say that the brush has _finished executing_.
+
+
+## Lexical elements
+
+
+### Comments
+
+haku's most basic lexical element is the _comment_.
+
+```
+-- This is a comment.
+-- こんにちは！
+```
+
+Comments introduce human-readable remarks into a brush's code.
+Their only purpose is documentation.
+They serve no semantic meaning, and thus do not affect the result of the brush whatsoever.
+
+Comments begin with `--`, and span until the end of the current line of text.
+Once the line ends, the comment does, too.
+
+Comments do not necessarily have to appear at the beginning of a line.
+
+```haku
+magnitude: \v ->  -- calculate the magnitude of a vector
+  hypot vecX.v vecY.v
+```
+
+
+### Literals
+
+Literals represent _literal values_ that are input into the brush.
+
+haku has a few types of literals, but not all literals are purely lexical elements (some of them can nest)---which is why the different types of literals are covered under the [Expressions](#Expressions) section.
+
+
+### Identifiers
+
+Identifiers are used for naming values inside a brush.
+New names are introduced using [defs](#Structure-of-a-brush) and [lets](#Let-expression).
+Once a name is introduced, it may be referenced using its identifier in its corresponding scope---the whole brush for defs, and the following expression in lets.
+
+An identifier starts with a *lowercase* ASCII letter---`a`--`z` or an underscore---`_`, and is followed by zero or more ASCII letters of any case---`a`--`z`, `A`--`Z`, digits---`0`--`9`, and underscores---`_`.
+This then may be followed by an arbitrary number of _suffix characters_ prime symbols---`'` and question marks---`?`.
+
+By convention, prime symbols are used in the same way they are used in math notation---for introducing a distinct variable of the same name as another variable, usually derived from the previous.
+For example, given a variable named `position`, an _updated_ position may be named `position'`.
+
+The question mark suffix is conventionally used for [boolean](#Boolean-type) variables, as well as boolean-returning functions.
+By convention, only one question mark is always used.
+
+Identifiers starting with *uppercase* ASCII letters---`A`--`Z` are not identifiers, but rather [tags](#tag-literal), and therefore cannot be used as def and let names.
+
+The following identifiers are reserved as _keywords_, and have special meaning assigned within the language syntax.
+
+- `if` --- Introduces an [`if` expression](#if-expression).
+- `else` --- Introduces the `else` clause in an [`if` expression](#if-expression).
+
+Additionally, the following identifiers are reserved for future use, and may not be used for naming defs and lets.
+
+- `and`
+- `or`
+
+By convention, a prime symbol `'` suffix can be used to work around this restriction.
+For example, instead of naming a variable `if`, try naming it `if'` (read as _if prime_, "_the other if_").
+
+
+### Operators and punctuation
+
+Operators and punctuation share a section in this part of the reference due to their lexical similarity.
+
+[Operators](#operators) serve as a terse syntax for calling a small set of built-in functions within the program (described in detail in the [system reference documentation](system.html)), while punctuation serves the purpose of syntactic delimiters.
+
+The following symbols are operators:
+
+```
++ - * /
+== != < <= > >= !
+```
+
+And the following symbols are punctuation:
+
+```
+<newline>
+( ) [ ] ,
+= :
+. |
+\ ->
+```
+
+`<newline>` is literally written down as a line break in programs, which would be invisible in this reference.
+
+
+## Structure of a brush
+
+A brush is structured like so:
+
+```haku
+def1: expr1
+def2: expr2
+def3: expr3
+-- ...
+effectExpr
+```
+
+That is, there are two parts to a brush: its _defs_, followed by the resulting effect [expression](#Expressions).
+The effect produced by this expression is the effect performed by rakugaki when the user interacts with the wall (clicks on it, touches it, starts a pen stroke).
+
+Defs introduce names for values that are available across the entire program.
+They are most commonly used to name constants and functions.
+
+Example:
+
+```haku
+-- Constant definition
+pi: 3.14159265
+
+-- Function definition
+magnitude: \v ->
+  hypot vecX.v vecY.v
+```
+
+
+## Expressions
+
+haku is a strictly expression-oriented language.
+There is no idea of statements, as would be the case in lower-level languages like C++ or JavaScript.
+This comes from the fact that haku is a _pure_ functional language, which means there aren't any expressions whose result you would want to discard, only for their side effects.
+
+
+### Nil
+
+An empty parenthesis represents a _nil_ value---that is, literally a value that means "no value."
+
+```haku
+()
+```
+
+It is one of the only values considered [_false_](#Truth) by the language, other than the [`False` boolean](#Tags).
+
+
+### Numbers
+
+Numbers in haku are written down as a sequence of ASCII digits---`0`--`9`, followed by an optional decimal point `.` with a decimal part.
+
+```haku
+0
+123
+3.14159265
+```
+
+Internally, they are represented by 32-bit floating point numbers.
+This means that they have [fairly limited precision](https://float.exposed/0x42f60000), and do not always behave exactly like math on real numbers.
+For example, there are magical values for ∞ and -∞ (which _can_ exist and can be operated upon), as well as a value called NaN (not a number), which are produced as results of certain operations that aren't well-defined in math (most commonly division by zero).
+
+
+### Tags
+
+Tags are similar to [identifiers](#Identifiers), but start with an *uppercase* rather than a lowercase ASCII letter (that is, `A`--`Z`).
+They are values which represent _names_.
+
+This concept may feel a bit alien.
+As an example, consider how haku implements record types.
+From the perspective of the user, a record type acts like a [function](#Functions) which accepts a tag as an argument---with the tag being the name of the record field.
+
+```haku
+withDotter \d ->
+  stroke 8 #000 (line d.From d.To)
+                        ----   --  these are tags
+```
+
+There are also two special tags, `True` and `False`, which are used to represent Boolean logic.
+
+The boolean `False` is the only [_false_](#Truth) value in the language, other than [nil](#Nil).
+
+
+### Colors
+
+haku has a literal for representing RGBA colors.
+It takes one of the following four forms, from most explicit to least explicit:
+
+```haku
+#RRGGBBAA
+#RRGGBB
+#RGBA
+#RGB
+```
+
+Each character in a color literal is a hexadecimal digit, with the digits `0`--`9` representing digits 0 to 9, and letters `a`--`f` representing digits 10 to 16 (case insensitive.)
+
+For `#RGB` and `#RGBA`, the digits are repeated twice implicitly---that is, `#1234` is the same as `#11223344`.
+
+This syntax is designed to be convenient for working with colors coming from external programs.
+For example, you may pick a color from an online palette, and paste its hex code straight into your brush code.
+
+Example (rakugaki logo colors):
+
+```haku
+white: #FFF
+peach: #FFA6A6
+raspberry: #F44096
+```
+
+
+### Lists
+
+Lists are fixed-length sequences of values.
+They are written down by listing out a sequence of comma `,` or newline-separated items, enclosed in square brackets `[]`.
+
+```haku
+six: [1, 2, 3, 4, 5, 6]
+four: [
+    1
+    2
+    3
+    4
+]
+```
+
+Lists are allowed to nest, as the values may be of any type---including lists themselves.
+
+Lists are most commonly used to compose scribbles.
+A list is also a scribble, which draws the scribbles it contains within itself, from first to last.
+
+
+### Operators
+
+Operators in haku are used mostly for basic mathematical operations.
+They are either unary, written in prefix form `!x`, or binary, written in infix form `a + b`.
+
+While order of operations in case of unary operators is unambiguous (innermost to outermost), infix operators are not as simple.
+Certain infix operators have _precedence_ over others.
+
+This precedence depends on the operator used, as well as the spacing around it.
+Spacing _only_ matters for infix operators; prefix operators may have any amount of spaces around them, though conventionally they are glued to the expression on the right, like `(-1)`, or `vec -1 0`.
+
+Infix operators with spaces around them are classified as _loose_, and those without spaces around them are _tight_.
+An unequal amount of spaces around an infix operator is considered an error (or is parsed as a prefix operator, depending on context).
+
+Based on these two groups, the precedence of operators is defined as follows:
+
+1. Prefix operators: `-a`, `!a`
+1. Tight
+
+    1. Dot: `a.b`
+    1. Arithmetic: `a+b`, `a-b`, `a*b`, `a/b`
+    1. Comparisons: `a==b`, `a!=b`, `a<b`, `a<=b`, `a>b`, `a>=b`
+
+1. Function calls: `a b`
+1. Loose
+
+    1. Dot: `a . b`
+    1. Arithmetic: `a + b`, `a - b`, `a * b`, `a / b`, `a |b`
+    1. Comparisons: `a == b`, `a != b`
+    1. Variables: `a: b`, `a = b`
+
+The operators `+`, `-`, `*`, `/`, `==`, `!=`, `<`, `<=`, `>`, `>=`, `!`, are used for calling functions built into the haku [system library](system.html).
+
+Other infix tokens listed above have other semantic meaning.
+
+- `a b`, `.`, and `|` --- Used for calling [functions](#Functions).
+- `:` --- Used for introducing [defs](#Structure-of-a-brush).
+- `=` --- Used for introducing [lets](#Let-expression).
+
+Examples of how these precedence rules work in practice:
+
+```haku
+2 + 2 * 2 == 8  -- left to right
+2 + 2*2   == 6  -- 2*2 goes first
+2+2 * 2   == 8  -- 2+2 goes first
+2+2*2     == 8  -- left to right
+
+sin 2 * pi * x == (sin 2) * pi * x  -- function call goes first
+sin 2*pi*x     == sin (2 * pi * x)  -- argument goes first
+
+-- unintuitive for users of C-likes:
+-- prefix `-` has higher precedence than `.`
+-vecX.v == (-vecX).v
+```
+
+One thing that should be noted about haku's operator precedence is that, unlike math notation and most other programming languages, `+`, `-`, `*`, and `/`, are evaluated from left to right.
+This is because otherwise they would interact unintuitively with the pipe `|` operator, which is effectively used as an operator that turns any function infix.
+
+It is not obvious where `|` would sit in the precedence hierarchy if arithmetic was split into separate precedence levels for `+` and `-`, and `*` and `/`, whereas with haku's solution, all arithmetic expressions are simply read from left to right.
+
+
+### Parentheses
+
+In case the tight-loose system is not expressive enough, parentheses can be used as an escape hatch for grouping expressions.
+
+```haku
+2 + (2 * 2) == 2 + 2*2
+```
+
+
+### Functions
+
+Functions in haku follow the definition of mathematical functions: given a set of _arguments_, the arguments are substituted into the function's _parameter variables_, and a result is computed from the resulting expression.
+
+A function literal is written down like `\params -> result`, where `params` is a comma-separated list of parameters, and `result` is the function's resulting expression.
+
+```haku
+square: \x -> x * x
+```
+
+A newline is permitted after the arrow `->`, which should be preferred for most functions.
+
+```haku
+magnitude: \v ->
+  hypot vecX.v vecY.v
+
+normalize: \v ->
+  l = magnitude v
+  v / vec l l
+```
+
+Note that there must be at least one parameter.
+In case you need a function with no parameters, you almost always want a constant value instead.
+
+Functions can be used by _calling_ them with space-separated arguments.
+Note that space-separated function calls have higher precedence than most arithmetic operators, which means you have to use parentheses or tighten the expression to pass more complicated expressions.
+
+```haku
+normalize (vec 4 4)
+```
+
+Note that a call must pass in _exactly_ the amount of arguments defined by the function.
+Calling the above-defined `normalize` with more than one argument will not work:
+
+```haku
+normalize (vec 4 4) (vec 5 5)
+```
+
+In places where a call with space-separated arguments is inconvenient, there are two alternative syntaxes for calling a function.
+
+The first is by using the `.` operator, which, when used tightly, can be used to do a function call with higher operator precedence than an ordinary space-separated call would have.
+
+```haku
+f x == f.x
+```
+
+Combined with [records](#Records) and [tags](#Tags), it mimics the record field access syntax found in C-like programming languages.
+
+```haku
+withDotter \d ->
+  stroke 8 #000 (line d.From d.To)
+                      ------ ----
+```
+
+The other alternative syntax is the _pipe_ `|` operator.
+It calls the function on the right with the argument on the left.
+
+```haku
+2 |sqrt
+```
+
+When a space-separated function call is found on the right, the `|` operator instead inserts the value from the left as the first argument of the function call.
+
+```haku
+x |mod 2 == mod x 2
+```
+
+The spacing convention around `|` is a bit unusual, but the above example demonstrates why: the `|` operator effectively turns an arbitrary function into an infix operator on par with built-in arithmetic operators.
+Therefore, the function name is glued to the pipe, like `|mod`, to appear as one word visually.
+
+Certain functions are _built-in_, and implement core functionality that cannot be implemented in haku alone (at all, or in a performant manner).
+The [haku system library](system.html) is what defines all the built-in functions.
+
+Due to temporary limitations of the implementation, built-in functions cannot be referenced like regular functions.
+They always have to appear in a call.
+
+If you'd like to reference a built-in function to e.g. pass it to a list-transforming function, you will have to wrap it in a function of your own:
+
+```haku
+add: \x, y -> x + y
+sum: [1, 2, 3] |reduce 0 sum
+
+sin': \x -> sin x
+sines: [0, pi*1/2, pi*2/2, pi*3/2] |map sin'
+```
+
+
+### `if` expressions
+
+`if` expressions allow for choosing between two different results based on a condition.
+
+```haku
+if (cond)
+  a
+else
+  b
+```
+
+When `cond` is [_true_](#Truth), `a` will be computed and returned as the result.
+Otherwise, `b` will be computed and returned as the result.
+
+Note that in both cases, only one of the two expressions is computed.
+This allows for implementing bounded recursion to achieve repetition.
+
+```haku
+-- Fibonacci sequence
+fib: \x ->
+  if (x > 1)
+    fib n-1 + fib n-2
+  else
+    x
+```
+
+
+### Let expressions
+
+Let expressions introduce a new _variable_, or _let_, that can be referenced in the expression on the next line.
+
+```haku
+x = y
+expr
+```
+
+The difference between lets and [defs](#Structure-of-a-brush) is that the value of a let can change, because it can depend on non-def values, such as function arguments (therefore making it _variable_.)
+
+This however means that lets have reduced _scope_.
+The name introduced by a def can be used in the entire program---even before the line it's introduced on---while the name introduced by a let can only be used in the expression that immediately follows the let.
+
+```haku
+x: 1
+
+f: \y ->
+  z = x + 1
+  x + y + z  -- ok
+
+z  -- not ok
+```
+
+This also means that lets cannot be used to create recursive functions, because the name introduced by a let only becomes visible in its following expression.
+
+```haku
+-- This is okay:
+defib: \x ->
+  if (x > 1)
+    defib n-1 + defib n-2
+  else
+    x
+
+-- This will not work:
+letfib = \x ->
+  if (x > 1)
+    -- Because letfib is not yet defined at this point.
+    letfib n-1 + letfib n-2
+  else
+    x
+
+defib 5 + letfib 5  -- It is only defined in this expression.
+```
+
+Since a let can be followed up by any other expression, multiple lets can be chained together.
+
+```
+x = 4
+y = x + 3
+x + y
+```
+
+Note however that `x + y` finishes the chain of lets, which means we cannot introduce additional ones after that line.
+That would begin another expression!
+
+
+## Types
+
+haku distinguishes values between a few different types.
+
+- [*nil*](#Nil)
+- [*tag*](#Tags)
+
+  - [*boolean*]{id="Boolean-type"} - either [`False` or `True`](#Tags). Indicates truth or falsehood, used in [`if` conditions](#if-expression).
+
+- [*number*](#Numbers)
+- *vec* - a 4-dimensional vector, composed of four `number`s.
+- [*rgba*](#Colors) - an RGBA color, composed of four `number`s. This is the type of color literals.
+- [*function*](#Functions)
+- [*list*](#Lists)
+- *shape* - a mathematical shape.
+- _*effect*_ - an action that can be performed by rakugaki.
+
+  - *scribble* - something that can be drawn on the wall.
+  - *reticle* - an interaction the user can make with the wall.
+
+These types are incompatible with each other.
+If you pass in a *tag* to a value that expects a *number*, you will get an error.
+
+You can refer to the [system library documentation](system.html) for more information on the types accepted by functions.
+Note that it has a more precise notation for describing types, which explicitly documents the types of values that will be found in more nuanced situations, such as the `map` function.
+
+
+### Truth
+
+Conditions in `if` expressions, as well as the `!` operator, consider certain types of values _truthy_, and others _falsy_.
+
+Falsy values include *nil* and the boolean `False`.
+All other values are considered truthy.
diff --git a/rkgk.toml b/rkgk.toml
index 5cd488c..21bc332 100644
--- a/rkgk.toml
+++ b/rkgk.toml
@@ -23,6 +23,7 @@ import_roots = [
 
 "docs/rkgk.dj" = "Introduction to rakugaki"
 "docs/system.dj" = "System library"
+"docs/haku.dj" = "haku language reference"
 
 [wall_broker.default_wall_settings]
 

From 914da923f7b5e5aee0d7a703a676a201a3e594b7 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?=E3=83=AA=E3=82=AD=E8=90=8C?= <commits@liquidev.net>
Date: Wed, 3 Sep 2025 16:57:10 +0200
Subject: [PATCH 13/13] update built-in examples to use newly introduced syntax

---
 crates/haku/src/parser.rs | 14 ++---------
 crates/haku/src/token.rs  |  4 ++--
 docs/rkgk.dj              | 49 +++++++++++++++++++++++++--------------
 static/brush-box.js       | 41 ++++++++++++++------------------
 4 files changed, 53 insertions(+), 55 deletions(-)

diff --git a/crates/haku/src/parser.rs b/crates/haku/src/parser.rs
index fa1af6d..dd2884e 100644
--- a/crates/haku/src/parser.rs
+++ b/crates/haku/src/parser.rs
@@ -603,29 +603,19 @@ fn is_prefix_token((kind, spaces): (TokenKind, Spaces)) -> bool {
 }
 
 fn prefix(p: &mut Parser) -> Closed {
-    let (kind, spaces) = p.peek_with_spaces();
-    match kind {
+    match p.peek() {
         TokenKind::Ident => one(p, NodeKind::Ident),
         TokenKind::Tag => one(p, NodeKind::Tag),
         TokenKind::Number => one(p, NodeKind::Number),
         TokenKind::Color => one(p, NodeKind::Color),
         TokenKind::LBrack => list(p),
 
-        TokenKind::Minus if spaces.pair() == (true, false) => unary(p),
+        TokenKind::Minus => unary(p),
         TokenKind::Not => unary(p),
         TokenKind::LParen => paren(p),
         TokenKind::Backslash => lambda(p),
         TokenKind::If => if_expr(p),
 
-        TokenKind::Minus if spaces.pair() == (false, true) => {
-            let span = p.span();
-            p.emit(Diagnostic::error(
-                span,
-                "`-` operator must be surrounded by an equal amount of spaces",
-            ));
-            p.advance_with_error()
-        }
-
         _ => {
             assert!(
                 !is_prefix_token(p.peek_with_spaces()),
diff --git a/crates/haku/src/token.rs b/crates/haku/src/token.rs
index 96c8282..a005630 100644
--- a/crates/haku/src/token.rs
+++ b/crates/haku/src/token.rs
@@ -28,8 +28,6 @@ pub enum TokenKind {
     Greater,
     GreaterEqual,
     Not,
-    Dot,
-    Pipe,
 
     // Punctuation
     Newline,
@@ -42,6 +40,8 @@ pub enum TokenKind {
     Colon,
     Backslash,
     RArrow,
+    Dot,
+    Pipe,
 
     // Keywords
     Underscore,
diff --git a/docs/rkgk.dj b/docs/rkgk.dj
index e91e98c..6c89a89 100644
--- a/docs/rkgk.dj
+++ b/docs/rkgk.dj
@@ -1,5 +1,15 @@
 # Introduction to rakugaki
 
+*Warning: Neither rakugaki, nor this introductory manual is finished.*
+While it will always use the most up-to-date and recommended syntax, there are things it does cover, and it will probably be rebuilt to improve coverage of features once the app stabilises a bit.
+
+For now, I recommend cross-referencing it with the following documents:
+
+- [haku language reference](haku.html)
+- [System library](system.html)
+
+---
+
 Welcome to rakugaki!
 
 I hope you've been having fun fiddling with the app so far.
@@ -28,7 +38,7 @@ In case you edited anything in the input box on the right, paste the following t
 -- and see what happens!
 
 withDotter \d ->
-  stroke 8 #000 (d To)
+  stroke 8 #000 d.To
 ```
 
 rakugaki is a drawing program for digital scribbles and other pieces of art.
@@ -86,8 +96,8 @@ If you want to draw multiple scribbles, you can wrap them into a list, which we
 -- Draw two colorful dots instead of one!
 withDotter \d ->
   [
-    stroke 8 #F00 (d To + vec 4 0)
-    stroke 8 #00F (d To + vec -4 0)
+    stroke 8 #F00 (d.To + vec 4 0)
+    stroke 8 #00F (d.To + vec -4 0)
   ]
 ```
 
@@ -108,12 +118,12 @@ It'll draw the first inner list, which contains two scribbles, and then it'll dr
 withDotter \d ->
   [
     [
-      stroke 8 #F00 (d To + vec 4 0)
-      stroke 8 #00F (d To + vec -4 0)
+      stroke 8 #F00 (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 #FF0 (d.To + vec 0 4)
+      stroke 8 #0FF (d.To + vec 0 -4)
     ]
   ]
 ```
@@ -136,7 +146,7 @@ Recall that super simple brush from before...
 
 ```haku
 withDotter \d ->
-  stroke 8 #000 (d To)
+  stroke 8 #000 d.To
 ```
 
 This reads as "given a dotter, output a stroke that's 8 pixels wide, has the color `#000`, and is drawn at the dotter's `To` coordinates."
@@ -169,6 +179,7 @@ If you reorder or remove any one of them, your brush isn't going to work!
   You can also specify an alpha channel, for transparent colors---`#RRGGBBAA`, or `#RGBA`.
 
 - The third ingredient is the stroke's _position_.
+  `d.To` is the position of your mouse cursor.
 
 Positions in haku are represented using mathematical _vectors_, which, when broken down into pieces, are just lists of some numbers.
 
@@ -187,22 +198,22 @@ Likewise, negative X coordinates go leftwards, and negative Y coordinates go upw
 
 ---
 
-Vectors in haku are obtained with another function---`vec`---though we don't use it in the basic example, because `d To` already is a vector.
-Vectors support all the usual math operators though, so if we wanted to, we could, for example, add a vector to `d To`, thus moving the position of the dot relative to the mouse cursor:
+Vectors in haku are obtained with another function---`vec`---though we don't use it in the basic example, because `d.To` already is a vector.
+Vectors support all the usual math operators though, so if we wanted to, we could, for example, add a vector to `d.To`, thus moving the position of the dot relative to the mouse cursor:
 
 ```haku
 withDotter \d ->
-  stroke 8 #000 (d To + vec 10 0) -- moved 10 pixels rightwards
+  stroke 8 #000 (d.To + vec 10 0) -- moved 10 pixels rightwards
 ```
 
-Also note how the `d To + vec 10 0` 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.
 
 ```haku
 withDotter \d ->
-  stroke 8 #000 (d To)
+  stroke 8 #000 d.To
 ```
 
 Nice!
@@ -221,10 +232,10 @@ Let's fix that by drawing a `line` instead!
 
 ```haku
 withDotter \d ->
-  stroke 8 #000 (line (d From) (d To))
+  stroke 8 #000 (line d.From d.To)
 ```
 
-We replace the singular position `d To` with a `line`. `line` expects two arguments, which are vectors defining the line's start and end points.
+We replace the singular position `d.To` with a `line`. `line` expects two arguments, which are vectors defining the line's start and end points.
 For the starting position we use a _different_ property of `d`, which is `From`---this is the _previous_ value of `To`, which allows us to draw a continuous line.
 
 ::: aside
@@ -239,8 +250,8 @@ 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) (vec 32 32))
+    stroke 8 #F00 (circle (d.To + vec -16 0) 16)
+    stroke 8 #00F (rect (d.To + vec 0 -16) (vec 32 32))
   ]
 ```
 
@@ -292,13 +303,15 @@ In fact, here's the full order of operations in haku for reference:
 
 1. Tight
 
+    1. Function applications: `.`
     1. Arithmetic: `+`, `-`, `*`, `/`
     1. Comparisons: `==`, `!=`, `<`, `<=`, `>`, `>=`
 
 1. Function calls
 1. Loose
 
-    1. Arithmetic
+    1. Function applications: `.`
+    1. Arithmetic and pipelines `|`
     1. Comparisons
     1. Variables: `:`, `=`
 
diff --git a/static/brush-box.js b/static/brush-box.js
index 27750af..bee6be6 100644
--- a/static/brush-box.js
+++ b/static/brush-box.js
@@ -15,7 +15,7 @@ color: #000
 thickness: 8
 
 withDotter \\d ->
-  stroke thickness color (line (d From) (d To))
+  stroke thickness color (line d.From d.To)
         `.trim(),
     },
 
@@ -27,7 +27,7 @@ color: #000
 thickness: 48
 
 withDotter \\d ->
-  stroke thickness color (line (d From) (d To))
+  stroke thickness color (line d.From d.To)
         `.trim(),
     },
 
@@ -40,14 +40,10 @@ thickness: 4
 length: 5
 duty: 0.5
 
-or_: \\a, b ->
-  if (a) a
-  else b
-
 withDotter \\d ->
-  visible? = mod (d Num) length < length * duty
+  visible? = d.Num |mod length < length * duty
   if (visible?)
-    stroke thickness color (line (d From) (d To))
+    stroke thickness color (line d.From d.To)
   else
     ()
         `.trim(),
@@ -61,7 +57,7 @@ color: #0003
 thickness: 6
 
 withDotter \\d ->
-  stroke thickness color (line (d From) (d To))
+  stroke thickness color (line d.From d.To)
         `.trim(),
     },
 
@@ -76,10 +72,10 @@ wavelength: 1
 
 withDotter \\d ->
   pi = 3.14159265
-  a = sin (d Num * wavelength / pi) + 1 / 2
+  a = sin (d.Num * wavelength / pi) + 1 / 2
   range = maxThickness - minThickness
   thickness = a * range + minThickness
-  stroke thickness color (line (d From) (d To))
+  stroke thickness color (line d.From d.To)
         `.trim(),
     },
 
@@ -93,22 +89,21 @@ amplitude: 50
 wavelength: 1
 
 mag: \\v ->
-  hypot (vecX v) (vecY v)
+  hypot vecX.v vecY.v
 
 norm: \\u ->
   l = mag u
   u / vec l l
 
 perpClockwise: \\v ->
-  vec (vecY v) -(vecX v)
+  vec vecY.v -(vecX.v)
 
 withDotter \\d ->
   pi = 3.14159265
-  a = sin (d Num * wavelength / pi) * amplitude
-  direction = (d To) - (d From)
-  clockwise = norm (perpClockwise direction) * vec a a
-  from = d From + clockwise
-  to = d To + clockwise
+  a = sin (d.Num * wavelength / pi) * amplitude
+  clockwise = norm (perpClockwise d.To-d.From) * vec a a
+  from = d.From + clockwise
+  to = d.To + clockwise
   stroke thickness color (line from to)
         `.trim(),
     },
@@ -121,16 +116,16 @@ wavelength: 0.1
 thickness: 8
 
 colorCurve: \\n ->
-  abs (cos n)
+  n |cos |abs
 
 withDotter \\d ->
   pi = 3.14159265
   l = wavelength
-  r = colorCurve (d Num * l)
-  g = colorCurve (d Num * l + pi/3)
-  b = colorCurve (d Num * l + 2*pi/3)
+  r = colorCurve (d.Num * l)
+  g = colorCurve (d.Num * l + pi/3)
+  b = colorCurve (d.Num * l + 2*pi/3)
   color = rgba r g b 1
-  stroke thickness color (line (d From) (d To))
+  stroke thickness color (line d.From d.To)
         `.trim(),
     },