diff --git a/src/eval/state.rs b/src/eval/state.rs
index d90096140..295a106c9 100644
--- a/src/eval/state.rs
+++ b/src/eval/state.rs
@@ -4,7 +4,7 @@ use fontdock::{fallback, FallbackTree, FontStretch, FontStyle, FontVariant, Font
 
 use super::Scope;
 use crate::geom::{Insets, Linear, Size};
-use crate::layout::{Dir, GenAlign, LayoutAlign, LayoutSystem, Sides};
+use crate::layout::{Dir, Gen2, GenAlign, Sides};
 use crate::length::Length;
 use crate::paper::{Paper, PaperClass, PAPER_A4};
 
@@ -17,10 +17,10 @@ pub struct State {
     pub text: TextState,
     /// The page state.
     pub page: PageState,
-    /// The active layouting system.
-    pub sys: LayoutSystem,
+    /// The active layouting directions.
+    pub dirs: Gen2<Dir>,
     /// The active alignments.
-    pub align: LayoutAlign,
+    pub aligns: Gen2<GenAlign>,
 }
 
 impl Default for State {
@@ -29,8 +29,8 @@ impl Default for State {
             scope: crate::library::_std(),
             text: TextState::default(),
             page: PageState::default(),
-            sys: LayoutSystem::new(Dir::LTR, Dir::TTB),
-            align: LayoutAlign::new(GenAlign::Start, GenAlign::Start),
+            dirs: Gen2::new(Dir::TTB, Dir::LTR),
+            aligns: Gen2::new(GenAlign::Start, GenAlign::Start),
         }
     }
 }
diff --git a/src/geom.rs b/src/geom.rs
index d38d6fe74..0089aa4af 100644
--- a/src/geom.rs
+++ b/src/geom.rs
@@ -6,7 +6,7 @@ pub use kurbo::*;
 use std::fmt::{self, Debug, Formatter};
 use std::ops::*;
 
-use crate::layout::primitive::{Dir, GenAlign, LayoutAlign, LayoutSystem, SpecAxis};
+use crate::layout::primitive::{Dir, Gen2, GenAlign, Side, SpecAxis};
 
 /// Additional methods for [sizes].
 ///
@@ -18,26 +18,28 @@ pub trait SizeExt {
     /// Borrow the component for the specified axis mutably.
     fn get_mut(&mut self, axis: SpecAxis) -> &mut f64;
 
-    /// Returns the generalized version of a `Size` based on the layouting
-    /// system, that is:
-    /// - `x` describes the primary axis instead of the horizontal one.
-    /// - `y` describes the secondary axis instead of the vertical one.
-    fn generalized(self, sys: LayoutSystem) -> Self;
+    /// Returns the generalized version of a `Size` based on the current
+    /// directions.
+    ///
+    /// In the generalized version:
+    /// - `x` describes the cross axis instead of the horizontal one.
+    /// - `y` describes the main axis instead of the vertical one.
+    fn generalized(self, dirs: Gen2<Dir>) -> Self;
 
-    /// Returns the specialized version of this generalized Size2D (inverse to
+    /// Returns the specialized version of this generalized `Size` (inverse to
     /// `generalized`).
-    fn specialized(self, sys: LayoutSystem) -> Self;
+    fn specialized(self, dirs: Gen2<Dir>) -> Self;
 
     /// Whether the given size fits into this one, that is, both coordinate
     /// values are smaller or equal.
     fn fits(self, other: Self) -> bool;
 
-    /// The anchor position for an object to be aligned according to `align` in
-    /// a container with this size.
+    /// The anchor position for an object to be aligned in a container with this
+    /// size and the given directions.
     ///
     /// This assumes the size to be generalized such that `width` corresponds to
-    /// the primary and `height` to the secondary axis.
-    fn anchor(self, align: LayoutAlign, sys: LayoutSystem) -> Point;
+    /// the cross and `height` to the main axis.
+    fn anchor(self, dirs: Gen2<Dir>, aligns: Gen2<GenAlign>) -> Point;
 }
 
 impl SizeExt for Size {
@@ -55,25 +57,25 @@ impl SizeExt for Size {
         }
     }
 
-    fn generalized(self, sys: LayoutSystem) -> Self {
-        match sys.primary.axis() {
-            SpecAxis::Horizontal => self,
-            SpecAxis::Vertical => Self::new(self.height, self.width),
+    fn generalized(self, dirs: Gen2<Dir>) -> Self {
+        match dirs.main.axis() {
+            SpecAxis::Horizontal => Self::new(self.height, self.width),
+            SpecAxis::Vertical => self,
         }
     }
 
-    fn specialized(self, sys: LayoutSystem) -> Self {
+    fn specialized(self, dirs: Gen2<Dir>) -> Self {
         // Even though generalized is its own inverse, we still have this second
         // function, for clarity at the call-site.
-        self.generalized(sys)
+        self.generalized(dirs)
     }
 
     fn fits(self, other: Self) -> bool {
         self.width >= other.width && self.height >= other.height
     }
 
-    fn anchor(self, align: LayoutAlign, sys: LayoutSystem) -> Point {
-        fn anchor(length: f64, align: GenAlign, dir: Dir) -> f64 {
+    fn anchor(self, dirs: Gen2<Dir>, aligns: Gen2<GenAlign>) -> Point {
+        fn anchor(length: f64, dir: Dir, align: GenAlign) -> f64 {
             match (dir.is_positive(), align) {
                 (true, GenAlign::Start) | (false, GenAlign::End) => 0.0,
                 (_, GenAlign::Center) => length / 2.0,
@@ -82,8 +84,8 @@ impl SizeExt for Size {
         }
 
         Point::new(
-            anchor(self.width, align.primary, sys.primary),
-            anchor(self.height, align.secondary, sys.secondary),
+            anchor(self.width, dirs.cross, aligns.cross),
+            anchor(self.height, dirs.main, aligns.main),
         )
     }
 }
@@ -92,34 +94,29 @@ impl SizeExt for Size {
 ///
 /// [rectangles]: ../../kurbo/struct.Rect.html
 pub trait RectExt {
-    /// Return the side identified by direction and alignment.
-    ///
-    /// Center alignment is treated the same as origin alignment.
-    fn get(&mut self, dir: Dir, align: GenAlign) -> f64;
+    /// Return the value for the given side.
+    fn get(self, side: Side) -> f64;
 
-    /// Get a mutable reference to the side identified by direction and
-    /// alignment.
-    ///
-    /// Center alignment is treated the same as origin alignment.
-    fn get_mut(&mut self, dir: Dir, align: GenAlign) -> &mut f64;
+    /// Borrow the value for the given side mutably.
+    fn get_mut(&mut self, side: Side) -> &mut f64;
 }
 
 impl RectExt for Rect {
-    fn get(&mut self, dir: Dir, align: GenAlign) -> f64 {
-        match if align == GenAlign::End { dir.inv() } else { dir } {
-            Dir::LTR => self.x0,
-            Dir::TTB => self.y0,
-            Dir::RTL => self.x1,
-            Dir::BTT => self.y1,
+    fn get(self, side: Side) -> f64 {
+        match side {
+            Side::Left => self.x0,
+            Side::Top => self.y0,
+            Side::Right => self.x1,
+            Side::Bottom => self.y1,
         }
     }
 
-    fn get_mut(&mut self, dir: Dir, align: GenAlign) -> &mut f64 {
-        match if align == GenAlign::End { dir.inv() } else { dir } {
-            Dir::LTR => &mut self.x0,
-            Dir::TTB => &mut self.y0,
-            Dir::RTL => &mut self.x1,
-            Dir::BTT => &mut self.y1,
+    fn get_mut(&mut self, side: Side) -> &mut f64 {
+        match side {
+            Side::Left => &mut self.x0,
+            Side::Top => &mut self.y0,
+            Side::Right => &mut self.x1,
+            Side::Bottom => &mut self.y1,
         }
     }
 }
diff --git a/src/layout/line.rs b/src/layout/line.rs
index 745a0d144..acf143c0c 100644
--- a/src/layout/line.rs
+++ b/src/layout/line.rs
@@ -1,9 +1,8 @@
 //! Arranging boxes into lines.
 //!
-//! Along the primary axis, the boxes are laid out next to each other as long as
-//! they fit into a line. When necessary, a line break is inserted and the new
-//! line is offset along the secondary axis by the height of the previous line
-//! plus extra line spacing.
+//! The boxes are laid out along the cross axis as long as they fit into a line.
+//! When necessary, a line break is inserted and the new line is offset along
+//! the main axis by the height of the previous line plus extra line spacing.
 //!
 //! Internally, the line layouter uses a stack layouter to stack the finished
 //! lines on top of each.
@@ -23,8 +22,8 @@ pub struct LineLayouter {
 /// The context for line layouting.
 #[derive(Debug, Clone)]
 pub struct LineContext {
-    /// The initial layouting system, which can be updated through `set_sys`.
-    pub sys: LayoutSystem,
+    /// The layout directions.
+    pub dirs: Gen2<Dir>,
     /// The spaces to layout into.
     pub spaces: Vec<LayoutSpace>,
     /// Whether to spill over into copies of the last space or finish layouting
@@ -40,7 +39,7 @@ impl LineLayouter {
         Self {
             stack: StackLayouter::new(StackContext {
                 spaces: ctx.spaces.clone(),
-                sys: ctx.sys,
+                dirs: ctx.dirs,
                 repeat: ctx.repeat,
             }),
             ctx,
@@ -49,26 +48,24 @@ impl LineLayouter {
     }
 
     /// Add a layout.
-    pub fn add(&mut self, layout: BoxLayout, align: LayoutAlign) {
-        let sys = self.ctx.sys;
-
-        if let Some(prev) = self.run.align {
-            if align.secondary != prev.secondary {
+    pub fn add(&mut self, layout: BoxLayout, aligns: Gen2<GenAlign>) {
+        if let Some(prev) = self.run.aligns {
+            if aligns.main != prev.main {
                 // TODO: Issue warning for non-fitting alignment in
                 // non-repeating context.
-                let fitting = self.stack.is_fitting_alignment(align);
+                let fitting = self.stack.is_fitting_alignment(aligns);
                 if !fitting && self.ctx.repeat {
                     self.finish_space(true);
                 } else {
                     self.finish_line();
                 }
-            } else if align.primary < prev.primary {
+            } else if aligns.cross < prev.cross {
                 self.finish_line();
-            } else if align.primary > prev.primary {
+            } else if aligns.cross > prev.cross {
                 let mut rest_run = LineRun::new();
 
-                let usable = self.stack.usable().get(sys.primary.axis());
-                rest_run.usable = Some(match align.primary {
+                let usable = self.stack.usable().get(self.ctx.dirs.cross.axis());
+                rest_run.usable = Some(match aligns.cross {
                     GenAlign::Start => unreachable!("start > x"),
                     GenAlign::Center => usable - 2.0 * self.run.size.width,
                     GenAlign::End => usable - self.run.size.width,
@@ -84,10 +81,10 @@ impl LineLayouter {
         }
 
         if let LastSpacing::Soft(spacing, _) = self.run.last_spacing {
-            self.add_primary_spacing(spacing, SpacingKind::Hard);
+            self.add_cross_spacing(spacing, SpacingKind::Hard);
         }
 
-        let size = layout.size.generalized(sys);
+        let size = layout.size.generalized(self.ctx.dirs);
 
         if !self.usable().fits(size) {
             if !self.line_is_empty() {
@@ -100,7 +97,7 @@ impl LineLayouter {
             }
         }
 
-        self.run.align = Some(align);
+        self.run.aligns = Some(aligns);
         self.run.layouts.push((self.run.size.width, layout));
 
         self.run.size.width += size.width;
@@ -114,19 +111,25 @@ impl LineLayouter {
     /// needed.
     fn usable(&self) -> Size {
         // The base is the usable space of the stack layouter.
-        let mut usable = self.stack.usable().generalized(self.ctx.sys);
+        let mut usable = self.stack.usable().generalized(self.ctx.dirs);
 
         // If there was another run already, override the stack's size.
-        if let Some(primary) = self.run.usable {
-            usable.width = primary;
+        if let Some(cross) = self.run.usable {
+            usable.width = cross;
         }
 
         usable.width -= self.run.size.width;
         usable
     }
 
+    /// Finish the line and add spacing to the underlying stack.
+    pub fn add_main_spacing(&mut self, spacing: f64, kind: SpacingKind) {
+        self.finish_line_if_not_empty();
+        self.stack.add_spacing(spacing, kind)
+    }
+
     /// Add spacing to the line.
-    pub fn add_primary_spacing(&mut self, mut spacing: f64, kind: SpacingKind) {
+    pub fn add_cross_spacing(&mut self, mut spacing: f64, kind: SpacingKind) {
         match kind {
             SpacingKind::Hard => {
                 spacing = spacing.min(self.usable().width);
@@ -150,19 +153,6 @@ impl LineLayouter {
         }
     }
 
-    /// Finish the line and add spacing to the underlying stack.
-    pub fn add_secondary_spacing(&mut self, spacing: f64, kind: SpacingKind) {
-        self.finish_line_if_not_empty();
-        self.stack.add_spacing(spacing, kind)
-    }
-
-    /// Update the layouting system.
-    pub fn set_sys(&mut self, sys: LayoutSystem) {
-        self.finish_line_if_not_empty();
-        self.ctx.sys = sys;
-        self.stack.set_sys(sys)
-    }
-
     /// Update the layouting spaces.
     ///
     /// If `replace_empty` is true, the current space is replaced if there are
@@ -181,7 +171,7 @@ impl LineLayouter {
     /// it will fit into this layouter's underlying stack.
     pub fn remaining(&self) -> Vec<LayoutSpace> {
         let mut spaces = self.stack.remaining();
-        *spaces[0].size.get_mut(self.ctx.sys.secondary.axis()) -= self.run.size.height;
+        *spaces[0].size.get_mut(self.ctx.dirs.main.axis()) -= self.run.size.height;
         spaces
     }
 
@@ -206,17 +196,17 @@ impl LineLayouter {
 
     /// Finish the active line and start a new one.
     pub fn finish_line(&mut self) {
-        let mut layout = BoxLayout::new(self.run.size.specialized(self.ctx.sys));
-        let align = self.run.align.unwrap_or_default();
+        let mut layout = BoxLayout::new(self.run.size.specialized(self.ctx.dirs));
+        let aligns = self.run.aligns.unwrap_or_default();
 
         let layouts = std::mem::take(&mut self.run.layouts);
         for (offset, child) in layouts {
-            let x = match self.ctx.sys.primary.is_positive() {
+            let x = match self.ctx.dirs.cross.is_positive() {
                 true => offset,
                 false => {
                     self.run.size.width
                         - offset
-                        - child.size.get(self.ctx.sys.primary.axis())
+                        - child.size.get(self.ctx.dirs.cross.axis())
                 }
             };
 
@@ -224,7 +214,7 @@ impl LineLayouter {
             layout.push_layout(pos, child);
         }
 
-        self.stack.add(layout, align);
+        self.stack.add(layout, aligns);
 
         self.run = LineRun::new();
         self.stack.add_spacing(self.ctx.line_spacing, SpacingKind::LINE);
@@ -249,7 +239,7 @@ struct LineRun {
     /// When a new run is created the alignment is yet to be determined and
     /// `None` as such. Once a layout is added, its alignment decides the
     /// alignment for the whole run.
-    align: Option<LayoutAlign>,
+    aligns: Option<Gen2<GenAlign>>,
     /// The amount of space left by another run on the same line or `None` if
     /// this is the only run so far.
     usable: Option<f64>,
@@ -263,7 +253,7 @@ impl LineRun {
         Self {
             layouts: vec![],
             size: Size::ZERO,
-            align: None,
+            aligns: None,
             usable: None,
             last_spacing: LastSpacing::Hard,
         }
diff --git a/src/layout/mod.rs b/src/layout/mod.rs
index 2ba1b0de5..f9372e506 100644
--- a/src/layout/mod.rs
+++ b/src/layout/mod.rs
@@ -11,11 +11,10 @@ pub use primitive::*;
 pub use stack::*;
 pub use tree::*;
 
-use crate::geom::{Insets, Point, Rect, RectExt, Size, SizeExt};
-
 use crate::diag::Diag;
 use crate::eval::{PageState, State, TextState};
 use crate::font::SharedFontLoader;
+use crate::geom::{Insets, Point, Rect, RectExt, Size, SizeExt};
 use crate::shaping::Shaped;
 use crate::syntax::{Deco, Spanned, SynTree};
 use crate::{Feedback, Pass};
@@ -29,7 +28,7 @@ pub async fn layout(
     let space = LayoutSpace {
         size: state.page.size,
         insets: state.page.insets(),
-        expansion: LayoutExpansion::new(true, true),
+        expansion: Spec2::new(true, true),
     };
 
     let constraints = LayoutConstraints {
@@ -134,7 +133,7 @@ pub struct LayoutSpace {
     pub insets: Insets,
     /// Whether to expand the size of the resulting layout to the full size of
     /// this space or to shrink it to fit the content.
-    pub expansion: LayoutExpansion,
+    pub expansion: Spec2<bool>,
 }
 
 impl LayoutSpace {
@@ -154,7 +153,7 @@ impl LayoutSpace {
         Self {
             size: self.usable(),
             insets: Insets::ZERO,
-            expansion: LayoutExpansion::new(false, false),
+            expansion: Spec2::new(false, false),
         }
     }
 }
@@ -172,8 +171,8 @@ pub enum Command {
     LayoutSyntaxTree(SynTree),
 
     /// Add a finished layout.
-    Add(BoxLayout, LayoutAlign),
-    /// Add spacing of the given kind along the primary or secondary axis. The
+    Add(BoxLayout, Gen2<GenAlign>),
+    /// Add spacing of the given kind along the given axis. The
     /// kind defines how the spacing interacts with surrounding spacing.
     AddSpacing(f64, SpacingKind, GenAxis),
 
@@ -187,11 +186,8 @@ pub enum Command {
     SetTextState(TextState),
     /// Update the page style.
     SetPageState(PageState),
-    /// Update the layouting system along which future boxes will be laid
-    /// out. This ends the current line.
-    SetSystem(LayoutSystem),
     /// Update the alignment for future boxes added to this layouting process.
-    SetAlignment(LayoutAlign),
+    SetAlignment(Gen2<GenAlign>),
 }
 
 /// Defines how spacing interacts with surrounding spacing.
diff --git a/src/layout/primitive.rs b/src/layout/primitive.rs
index 64cd1dff5..9070c9727 100644
--- a/src/layout/primitive.rs
+++ b/src/layout/primitive.rs
@@ -2,30 +2,6 @@
 
 use std::fmt::{self, Display, Formatter};
 
-/// Specifies the directions into which content is laid out.
-///
-/// The primary component defines into which direction text and lines flow and the
-/// secondary into which paragraphs and pages grow.
-pub type LayoutSystem = Gen2<Dir>;
-
-impl Default for LayoutSystem {
-    fn default() -> Self {
-        Self::new(Dir::LTR, Dir::TTB)
-    }
-}
-
-/// Specifies where to align a layout in a parent container.
-pub type LayoutAlign = Gen2<GenAlign>;
-
-impl Default for LayoutAlign {
-    fn default() -> Self {
-        Self::new(GenAlign::Start, GenAlign::Start)
-    }
-}
-
-/// Whether to expand a layout to an area's full size or shrink it to fit its content.
-pub type LayoutExpansion = Spec2<bool>;
-
 /// The four directions into which content can be laid out.
 #[derive(Debug, Copy, Clone, Eq, PartialEq)]
 pub enum Dir {
@@ -66,6 +42,23 @@ impl Dir {
         if self.is_positive() { 1.0 } else { -1.0 }
     }
 
+    /// The side of this direction the alignment identifies.
+    ///
+    /// `Center` alignment is treated the same as `Start` alignment.
+    pub fn side(self, align: GenAlign) -> Side {
+        let start = match self {
+            Self::LTR => Side::Left,
+            Self::RTL => Side::Right,
+            Self::TTB => Side::Top,
+            Self::BTT => Side::Bottom,
+        };
+
+        match align {
+            GenAlign::Start | GenAlign::Center => start,
+            GenAlign::End => start.inv(),
+        }
+    }
+
     /// The inverse direction.
     pub fn inv(self) -> Self {
         match self {
@@ -75,18 +68,6 @@ impl Dir {
             Self::BTT => Self::TTB,
         }
     }
-
-    /// The side of this direction the alignment identifies.
-    ///
-    /// `Center` alignment is treated the same as `Start` alignment.
-    pub fn side(self, align: GenAlign) -> Side {
-        match if align == GenAlign::End { self.inv() } else { self } {
-            Self::LTR => Side::Left,
-            Self::RTL => Side::Right,
-            Self::TTB => Side::Top,
-            Self::BTT => Side::Bottom,
-        }
-    }
 }
 
 impl Display for Dir {
@@ -100,27 +81,159 @@ impl Display for Dir {
     }
 }
 
+/// Convert a type into its generic representation.
+///
+/// The generic representation deals with main and cross axes while the specific
+/// representation deals with horizontal and vertical axes.
+///
+/// See also [`ToSpec`] for the inverse conversion.
+///
+/// [`ToSpec`]: trait.ToSpec.html
+pub trait ToGen {
+    /// The generic version of this type.
+    type Output;
+
+    /// The generic version of this type based on the current directions.
+    fn to_gen(self, dirs: Gen2<Dir>) -> Self::Output;
+}
+
+/// Convert a type into its specific representation.
+///
+/// The specific representation deals with horizontal and vertical axes while
+/// the generic representation deals with main and cross axes.
+///
+/// See also [`ToGen`] for the inverse conversion.
+///
+/// [`ToGen`]: trait.ToGen.html
+pub trait ToSpec {
+    /// The specific version of this type.
+    type Output;
+
+    /// The specific version of this type based on the current directions.
+    fn to_spec(self, dirs: Gen2<Dir>) -> Self::Output;
+}
+
+/// A generic container with two components for the two generic axes.
+#[derive(Debug, Default, Copy, Clone, Eq, PartialEq)]
+pub struct Gen2<T> {
+    /// The main component.
+    pub main: T,
+    /// The cross component.
+    pub cross: T,
+}
+
+impl<T> Gen2<T> {
+    /// Create a new instance from the two components.
+    pub fn new(main: T, cross: T) -> Self {
+        Self { main, cross }
+    }
+
+    /// Return the component for the specified generic axis.
+    pub fn get(self, axis: GenAxis) -> T {
+        match axis {
+            GenAxis::Main => self.main,
+            GenAxis::Cross => self.cross,
+        }
+    }
+
+    /// Borrow the component for the specified generic axis mutably.
+    pub fn get_mut(&mut self, axis: GenAxis) -> &mut T {
+        match axis {
+            GenAxis::Main => &mut self.main,
+            GenAxis::Cross => &mut self.cross,
+        }
+    }
+}
+
+impl<T> ToSpec for Gen2<T> {
+    type Output = Spec2<T>;
+
+    fn to_spec(self, dirs: Gen2<Dir>) -> Self::Output {
+        match dirs.main.axis() {
+            SpecAxis::Horizontal => Spec2::new(self.main, self.cross),
+            SpecAxis::Vertical => Spec2::new(self.cross, self.main),
+        }
+    }
+}
+
+/// A generic container with two components for the two specific axes.
+#[derive(Debug, Default, Copy, Clone, Eq, PartialEq)]
+pub struct Spec2<T> {
+    /// The horizontal component.
+    pub horizontal: T,
+    /// The vertical component.
+    pub vertical: T,
+}
+
+impl<T> Spec2<T> {
+    /// Create a new instance from the two components.
+    pub fn new(horizontal: T, vertical: T) -> Self {
+        Self { horizontal, vertical }
+    }
+
+    /// Return the component for the given specific axis.
+    pub fn get(self, axis: SpecAxis) -> T {
+        match axis {
+            SpecAxis::Horizontal => self.horizontal,
+            SpecAxis::Vertical => self.vertical,
+        }
+    }
+
+    /// Borrow the component for the given specific axis mutably.
+    pub fn get_mut(&mut self, axis: SpecAxis) -> &mut T {
+        match axis {
+            SpecAxis::Horizontal => &mut self.horizontal,
+            SpecAxis::Vertical => &mut self.vertical,
+        }
+    }
+}
+
+impl<T> ToGen for Spec2<T> {
+    type Output = Gen2<T>;
+
+    fn to_gen(self, dirs: Gen2<Dir>) -> Self::Output {
+        match dirs.main.axis() {
+            SpecAxis::Horizontal => Gen2::new(self.horizontal, self.vertical),
+            SpecAxis::Vertical => Gen2::new(self.vertical, self.horizontal),
+        }
+    }
+}
+
 /// The two generic layouting axes.
 #[derive(Debug, Copy, Clone, Eq, PartialEq)]
 pub enum GenAxis {
-    /// The primary layouting direction into which text and lines flow.
-    Primary,
-    /// The secondary layouting direction into which paragraphs grow.
-    Secondary,
+    /// The axis pages and paragraphs are set along.
+    Main,
+    /// The axis words and lines are set along.
+    Cross,
 }
 
 impl GenAxis {
-    /// The specific version of this axis in the given layout system.
-    pub fn to_spec(self, sys: LayoutSystem) -> SpecAxis {
-        sys.get(self).axis()
+    /// The other axis.
+    pub fn other(self) -> Self {
+        match self {
+            Self::Main => Self::Cross,
+            Self::Cross => Self::Main,
+        }
+    }
+}
+
+impl ToSpec for GenAxis {
+    type Output = SpecAxis;
+
+    fn to_spec(self, dirs: Gen2<Dir>) -> Self::Output {
+        match self {
+            Self::Main => dirs.main.axis(),
+            Self::Cross => dirs.cross.axis(),
+        }
     }
 }
 
 impl Display for GenAxis {
     fn fmt(&self, f: &mut Formatter) -> fmt::Result {
         f.pad(match self {
-            Self::Primary => "primary",
-            Self::Secondary => "secondary",
+            Self::Main => "main",
+            Self::Cross => "cross",
         })
     }
 }
@@ -128,19 +241,31 @@ impl Display for GenAxis {
 /// The two specific layouting axes.
 #[derive(Debug, Copy, Clone, Eq, PartialEq)]
 pub enum SpecAxis {
-    /// The horizontal layouting axis.
-    Horizontal,
     /// The vertical layouting axis.
     Vertical,
+    /// The horizontal layouting axis.
+    Horizontal,
 }
 
 impl SpecAxis {
-    /// The generic version of this axis in the given layout system.
-    pub fn to_gen(self, sys: LayoutSystem) -> GenAxis {
-        if self == sys.primary.axis() {
-            GenAxis::Primary
+    /// The other axis.
+    pub fn other(self) -> Self {
+        match self {
+            Self::Horizontal => Self::Vertical,
+            Self::Vertical => Self::Horizontal,
+        }
+    }
+}
+
+impl ToGen for SpecAxis {
+    type Output = GenAxis;
+
+    fn to_gen(self, dirs: Gen2<Dir>) -> Self::Output {
+        if self == dirs.main.axis() {
+            GenAxis::Main
         } else {
-            GenAxis::Secondary
+            debug_assert_eq!(self, dirs.cross.axis());
+            GenAxis::Cross
         }
     }
 }
@@ -148,8 +273,8 @@ impl SpecAxis {
 impl Display for SpecAxis {
     fn fmt(&self, f: &mut Formatter) -> fmt::Result {
         f.pad(match self {
-            Self::Horizontal => "horizontal",
             Self::Vertical => "vertical",
+            Self::Horizontal => "horizontal",
         })
     }
 }
@@ -173,6 +298,12 @@ impl GenAlign {
     }
 }
 
+impl Default for GenAlign {
+    fn default() -> Self {
+        Self::Start
+    }
+}
+
 impl Display for GenAlign {
     fn fmt(&self, f: &mut Formatter) -> fmt::Result {
         f.pad(match self {
@@ -207,21 +338,36 @@ impl SpecAlign {
         }
     }
 
-    /// The generic version of this alignment in the given layout system.
-    pub fn to_gen(self, sys: LayoutSystem) -> GenAlign {
-        let get = |spec: SpecAxis, positive: GenAlign| {
-            if sys.get(spec.to_gen(sys)).is_positive() {
-                positive
+    /// The inverse alignment.
+    pub fn inv(self) -> Self {
+        match self {
+            Self::Left => Self::Right,
+            Self::Right => Self::Left,
+            Self::Top => Self::Bottom,
+            Self::Bottom => Self::Top,
+            Self::Center => Self::Center,
+        }
+    }
+}
+
+impl ToGen for SpecAlign {
+    type Output = GenAlign;
+
+    fn to_gen(self, dirs: Gen2<Dir>) -> Self::Output {
+        let dirs = dirs.to_spec(dirs);
+        let get = |dir: Dir, at_positive_start| {
+            if dir.is_positive() == at_positive_start {
+                GenAlign::Start
             } else {
-                positive.inv()
+                GenAlign::End
             }
         };
 
         match self {
-            Self::Left => get(SpecAxis::Horizontal, GenAlign::Start),
-            Self::Right => get(SpecAxis::Horizontal, GenAlign::End),
-            Self::Top => get(SpecAxis::Vertical, GenAlign::Start),
-            Self::Bottom => get(SpecAxis::Vertical, GenAlign::End),
+            Self::Left => get(dirs.horizontal, true),
+            Self::Right => get(dirs.horizontal, false),
+            Self::Top => get(dirs.vertical, true),
+            Self::Bottom => get(dirs.vertical, false),
             Self::Center => GenAlign::Center,
         }
     }
@@ -239,91 +385,6 @@ impl Display for SpecAlign {
     }
 }
 
-/// A side of a container.
-#[derive(Debug, Copy, Clone, Eq, PartialEq)]
-pub enum Side {
-    Left,
-    Top,
-    Right,
-    Bottom,
-}
-
-impl Side {
-    /// The opposite side.
-    pub fn inv(self) -> Self {
-        match self {
-            Self::Left => Self::Right,
-            Self::Top => Self::Bottom,
-            Self::Right => Self::Left,
-            Self::Bottom => Self::Top,
-        }
-    }
-}
-
-/// A generic container with two components for the two generic axes.
-#[derive(Debug, Default, Copy, Clone, Eq, PartialEq)]
-pub struct Gen2<T> {
-    /// The primary component.
-    pub primary: T,
-    /// The secondary component.
-    pub secondary: T,
-}
-
-impl<T> Gen2<T> {
-    /// Create a new instance from the two components.
-    pub fn new(primary: T, secondary: T) -> Self {
-        Self { primary, secondary }
-    }
-
-    /// Return the component for the specified generic axis.
-    pub fn get(self, axis: GenAxis) -> T {
-        match axis {
-            GenAxis::Primary => self.primary,
-            GenAxis::Secondary => self.secondary,
-        }
-    }
-
-    /// Borrow the component for the specified generic axis mutably.
-    pub fn get_mut(&mut self, axis: GenAxis) -> &mut T {
-        match axis {
-            GenAxis::Primary => &mut self.primary,
-            GenAxis::Secondary => &mut self.secondary,
-        }
-    }
-}
-
-/// A generic container with two components for the two specific axes.
-#[derive(Debug, Default, Copy, Clone, Eq, PartialEq)]
-pub struct Spec2<T> {
-    /// The horizontal component.
-    pub horizontal: T,
-    /// The vertical component.
-    pub vertical: T,
-}
-
-impl<T> Spec2<T> {
-    /// Create a new instance from the two components.
-    pub fn new(horizontal: T, vertical: T) -> Self {
-        Self { horizontal, vertical }
-    }
-
-    /// Return the component for the given specific axis.
-    pub fn get(self, axis: SpecAxis) -> T {
-        match axis {
-            SpecAxis::Horizontal => self.horizontal,
-            SpecAxis::Vertical => self.vertical,
-        }
-    }
-
-    /// Borrow the component for the given specific axis mutably.
-    pub fn get_mut(&mut self, axis: SpecAxis) -> &mut T {
-        match axis {
-            SpecAxis::Horizontal => &mut self.horizontal,
-            SpecAxis::Vertical => &mut self.vertical,
-        }
-    }
-}
-
 /// A generic container with left, top, right and bottom components.
 #[derive(Debug, Default, Copy, Clone, Eq, PartialEq)]
 pub struct Sides<T> {
@@ -360,8 +421,8 @@ impl<T> Sides<T> {
     pub fn get(self, side: Side) -> T {
         match side {
             Side::Left => self.left,
-            Side::Right => self.right,
             Side::Top => self.top,
+            Side::Right => self.right,
             Side::Bottom => self.bottom,
         }
     }
@@ -370,9 +431,30 @@ impl<T> Sides<T> {
     pub fn get_mut(&mut self, side: Side) -> &mut T {
         match side {
             Side::Left => &mut self.left,
-            Side::Right => &mut self.right,
             Side::Top => &mut self.top,
+            Side::Right => &mut self.right,
             Side::Bottom => &mut self.bottom,
         }
     }
 }
+
+/// A side of a container.
+#[derive(Debug, Copy, Clone, Eq, PartialEq)]
+pub enum Side {
+    Left,
+    Top,
+    Right,
+    Bottom,
+}
+
+impl Side {
+    /// The opposite side.
+    pub fn inv(self) -> Self {
+        match self {
+            Self::Left => Self::Right,
+            Self::Top => Self::Bottom,
+            Self::Right => Self::Left,
+            Self::Bottom => Self::Top,
+        }
+    }
+}
diff --git a/src/layout/stack.rs b/src/layout/stack.rs
index de933fbf2..a98e4f52a 100644
--- a/src/layout/stack.rs
+++ b/src/layout/stack.rs
@@ -1,4 +1,4 @@
-//! Arranging boxes into a stack along the secondary axis.
+//! Arranging boxes into a stack along the main axis.
 //!
 //! Individual layouts can be aligned at `Start`, `Center` or  `End` along both
 //! axes. These alignments are with respect to the size of the finished layout
@@ -34,8 +34,8 @@ pub struct StackLayouter {
 /// The context for stack layouting.
 #[derive(Debug, Clone)]
 pub struct StackContext {
-    /// The initial layouting system, which can be updated through `set_sys`.
-    pub sys: LayoutSystem,
+    /// The layouting directions.
+    pub dirs: Gen2<Dir>,
     /// The spaces to layout into.
     pub spaces: Vec<LayoutSpace>,
     /// Whether to spill over into copies of the last space or finish layouting
@@ -55,15 +55,15 @@ impl StackLayouter {
     }
 
     /// Add a layout to the stack.
-    pub fn add(&mut self, layout: BoxLayout, align: LayoutAlign) {
+    pub fn add(&mut self, layout: BoxLayout, aligns: Gen2<GenAlign>) {
         // If the alignment cannot be fitted in this space, finish it.
         // TODO: Issue warning for non-fitting alignment in non-repeating
         // context.
-        if !self.update_rulers(align) && self.ctx.repeat {
+        if !self.update_rulers(aligns) && self.ctx.repeat {
             self.finish_space(true);
         }
 
-        // Now, we add a possibly cached soft space. If the secondary alignment
+        // Now, we add a possibly cached soft space. If the main alignment
         // changed before, a possibly cached space would have already been
         // discarded.
         if let LastSpacing::Soft(spacing, _) = self.space.last_spacing {
@@ -76,11 +76,11 @@ impl StackLayouter {
         }
 
         // Change the usable space and size of the space.
-        self.update_metrics(layout.size.generalized(self.ctx.sys));
+        self.update_metrics(layout.size.generalized(self.ctx.dirs));
 
         // Add the box to the vector and remember that spacings are allowed
         // again.
-        self.space.layouts.push((self.ctx.sys, align, layout));
+        self.space.layouts.push((self.ctx.dirs, aligns, layout));
         self.space.last_spacing = LastSpacing::None;
     }
 
@@ -90,15 +90,15 @@ impl StackLayouter {
             // A hard space is simply an empty box.
             SpacingKind::Hard => {
                 // Reduce the spacing such that it definitely fits.
-                let axis = self.ctx.sys.secondary.axis();
+                let axis = self.ctx.dirs.main.axis();
                 spacing = spacing.min(self.space.usable.get(axis));
 
                 let size = Size::new(0.0, spacing);
                 self.update_metrics(size);
                 self.space.layouts.push((
-                    self.ctx.sys,
-                    LayoutAlign::default(),
-                    BoxLayout::new(size.specialized(self.ctx.sys)),
+                    self.ctx.dirs,
+                    Gen2::default(),
+                    BoxLayout::new(size.specialized(self.ctx.dirs)),
                 ));
 
                 self.space.last_spacing = LastSpacing::Hard;
@@ -121,37 +121,34 @@ impl StackLayouter {
     }
 
     fn update_metrics(&mut self, added: Size) {
-        let sys = self.ctx.sys;
-
-        let mut size = self.space.size.generalized(sys);
-        let mut extra = self.space.extra.generalized(sys);
+        let mut size = self.space.size.generalized(self.ctx.dirs);
+        let mut extra = self.space.extra.generalized(self.ctx.dirs);
 
         size.width += (added.width - extra.width).max(0.0);
         size.height += (added.height - extra.height).max(0.0);
-
         extra.width = extra.width.max(added.width);
         extra.height = (extra.height - added.height).max(0.0);
 
-        self.space.size = size.specialized(sys);
-        self.space.extra = extra.specialized(sys);
-        *self.space.usable.get_mut(sys.secondary.axis()) -= added.height;
+        self.space.size = size.specialized(self.ctx.dirs);
+        self.space.extra = extra.specialized(self.ctx.dirs);
+        *self.space.usable.get_mut(self.ctx.dirs.main.axis()) -= added.height;
     }
 
     /// Returns true if a space break is necessary.
-    fn update_rulers(&mut self, align: LayoutAlign) -> bool {
-        let allowed = self.is_fitting_alignment(align);
+    fn update_rulers(&mut self, aligns: Gen2<GenAlign>) -> bool {
+        let allowed = self.is_fitting_alignment(aligns);
         if allowed {
-            let side = self.ctx.sys.secondary.side(GenAlign::Start);
-            *self.space.rulers.get_mut(side) = align.secondary;
+            let side = self.ctx.dirs.main.side(GenAlign::Start);
+            *self.space.rulers.get_mut(side) = aligns.main;
         }
         allowed
     }
 
     /// Whether a layout with the given alignment can still be layouted into the
     /// active space or a space break is necessary.
-    pub(crate) fn is_fitting_alignment(&self, align: LayoutAlign) -> bool {
-        self.is_fitting_axis(self.ctx.sys.primary, align.primary)
-            && self.is_fitting_axis(self.ctx.sys.secondary, align.secondary)
+    pub(crate) fn is_fitting_alignment(&self, aligns: Gen2<GenAlign>) -> bool {
+        self.is_fitting_axis(self.ctx.dirs.main, aligns.main)
+            && self.is_fitting_axis(self.ctx.dirs.cross, aligns.cross)
     }
 
     fn is_fitting_axis(&self, dir: Dir, align: GenAlign) -> bool {
@@ -159,16 +156,6 @@ impl StackLayouter {
             && align <= self.space.rulers.get(dir.side(GenAlign::End)).inv()
     }
 
-    /// Update the layouting system.
-    pub fn set_sys(&mut self, sys: LayoutSystem) {
-        // Forget the spacing because it is not relevant anymore.
-        if sys.secondary != self.ctx.sys.secondary {
-            self.space.last_spacing = LastSpacing::Hard;
-        }
-
-        self.ctx.sys = sys;
-    }
-
     /// Update the layouting spaces.
     ///
     /// If `replace_empty` is true, the current space is replaced if there are
@@ -200,12 +187,10 @@ impl StackLayouter {
     /// The remaining inner spaces. If something is laid out into these spaces,
     /// it will fit into this stack.
     pub fn remaining(&self) -> Vec<LayoutSpace> {
-        let size = self.usable();
-
         let mut spaces = vec![LayoutSpace {
-            size,
+            size: self.usable(),
             insets: Insets::ZERO,
-            expansion: LayoutExpansion::new(false, false),
+            expansion: Spec2::new(false, false),
         }];
 
         for space in &self.ctx.spaces[self.next_space() ..] {
@@ -219,7 +204,7 @@ impl StackLayouter {
     pub fn usable(&self) -> Size {
         self.space.usable
             - Size::new(0.0, self.space.last_spacing.soft_or_zero())
-                .specialized(self.ctx.sys)
+                .specialized(self.ctx.dirs)
     }
 
     /// Whether the current layout space is empty.
@@ -274,7 +259,7 @@ impl StackLayouter {
             y1: start.y + self.space.size.height,
         };
 
-        for (sys, _, layout) in &self.space.layouts {
+        for &(dirs, _, ref layout) in &self.space.layouts {
             // First, we store the bounds calculated so far (which were reduced
             // by the predecessors of this layout) as the initial bounding box
             // of this layout.
@@ -283,41 +268,42 @@ impl StackLayouter {
             // Then, we reduce the bounding box for the following layouts. This
             // layout uses up space from the origin to the end. Thus, it reduces
             // the usable space for following layouts at its origin by its
-            // extent along the secondary axis.
-            *bound.get_mut(sys.secondary, GenAlign::Start) +=
-                sys.secondary.factor() * layout.size.get(sys.secondary.axis());
+            // main-axis extent.
+            *bound.get_mut(dirs.main.side(GenAlign::Start)) +=
+                dirs.main.factor() * layout.size.get(dirs.main.axis());
         }
 
         // ------------------------------------------------------------------ //
         // Step 3: Backward pass. Reduce the bounding boxes from the previous
         // layouts by what is taken by the following ones.
 
-        // The `x` field stores the maximal primary extent in one axis-aligned
-        // run, while the `y` fields stores the accumulated secondary extent.
+        // The `x` field stores the maximal cross-axis extent in one
+        // axis-aligned run, while the `y` fields stores the accumulated
+        // main-axis extent.
         let mut extent = Size::ZERO;
         let mut rotation = SpecAxis::Vertical;
 
         for (bound, entry) in bounds.iter_mut().zip(&self.space.layouts).rev() {
-            let (sys, _, layout) = entry;
+            let &(dirs, _, ref layout) = entry;
 
-            // When the axes are rotated, the maximal primary size (`extent.x`)
-            // dictates how much secondary extent the whole run had. This value
-            // is thus stored in `extent.y`. The primary extent is reset for
-            // this new axis-aligned run.
-            if rotation != sys.secondary.axis() {
+            // When the axes are rotated, the maximal cross-axis size
+            // (`extent.x`) dictates how much main-axis extent the whole run
+            // had. This value is thus stored in `extent.y`. The cross-axis
+            // extent is reset for this new axis-aligned run.
+            if rotation != dirs.main.axis() {
                 extent.height = extent.width;
                 extent.width = 0.0;
-                rotation = sys.secondary.axis();
+                rotation = dirs.main.axis();
             }
 
             // We reduce the bounding box of this layout at its end by the
-            // accumulated secondary extent of all layouts we have seen so far,
+            // accumulated main-axis extent of all layouts we have seen so far,
             // which are the layouts after this one since we iterate reversed.
-            *bound.get_mut(sys.secondary, GenAlign::End) -=
-                sys.secondary.factor() * extent.height;
+            *bound.get_mut(dirs.main.side(GenAlign::End)) -=
+                dirs.main.factor() * extent.height;
 
-            // Then, we add this layout's secondary extent to the accumulator.
-            let size = layout.size.generalized(*sys);
+            // Then, we add this layout's main-axis extent to the accumulator.
+            let size = layout.size.generalized(dirs);
             extent.width = extent.width.max(size.width);
             extent.height += size.height;
         }
@@ -329,14 +315,14 @@ impl StackLayouter {
         let mut layout = BoxLayout::new(size);
 
         let layouts = std::mem::take(&mut self.space.layouts);
-        for ((sys, align, child), bound) in layouts.into_iter().zip(bounds) {
-            let size = child.size.specialized(sys);
+        for ((dirs, aligns, child), bound) in layouts.into_iter().zip(bounds) {
+            let size = child.size.specialized(dirs);
 
             // The space in which this layout is aligned is given by the
             // distances between the borders of its bounding box.
-            let usable = bound.size().generalized(sys);
-            let local = usable.anchor(align, sys) - size.anchor(align, sys);
-            let pos = bound.origin() + local.to_size().specialized(sys).to_vec2();
+            let usable = bound.size().generalized(dirs);
+            let local = usable.anchor(dirs, aligns) - size.anchor(dirs, aligns);
+            let pos = bound.origin() + local.to_size().specialized(dirs).to_vec2();
 
             layout.push_layout(pos, child);
         }
@@ -359,7 +345,7 @@ impl StackLayouter {
     }
 }
 
-/// A layout space composed of subspaces which can have different systems and
+/// A layout space composed of subspaces which can have different directions and
 /// alignments.
 struct Space {
     /// The index of this space in `ctx.spaces`.
@@ -367,7 +353,7 @@ struct Space {
     /// Whether to include a layout for this space even if it would be empty.
     hard: bool,
     /// The so-far accumulated layouts.
-    layouts: Vec<(LayoutSystem, LayoutAlign, BoxLayout)>,
+    layouts: Vec<(Gen2<Dir>, Gen2<GenAlign>, BoxLayout)>,
     /// The specialized size of this space.
     size: Size,
     /// The specialized remaining space.
diff --git a/src/layout/tree.rs b/src/layout/tree.rs
index 435b7109e..4e53cedca 100644
--- a/src/layout/tree.rs
+++ b/src/layout/tree.rs
@@ -26,7 +26,7 @@ impl<'a> TreeLayouter<'a> {
     fn new(ctx: &'a mut LayoutContext) -> Self {
         let layouter = LineLayouter::new(LineContext {
             spaces: ctx.constraints.spaces.clone(),
-            sys: ctx.state.sys,
+            dirs: ctx.state.dirs,
             repeat: ctx.constraints.repeat,
             line_spacing: ctx.state.text.line_spacing(),
         });
@@ -89,14 +89,12 @@ impl<'a> TreeLayouter<'a> {
 
     fn layout_space(&mut self) {
         self.layouter
-            .add_primary_spacing(self.ctx.state.text.word_spacing(), SpacingKind::WORD);
+            .add_cross_spacing(self.ctx.state.text.word_spacing(), SpacingKind::WORD);
     }
 
     fn layout_parbreak(&mut self) {
-        self.layouter.add_secondary_spacing(
-            self.ctx.state.text.par_spacing(),
-            SpacingKind::PARAGRAPH,
-        );
+        self.layouter
+            .add_main_spacing(self.ctx.state.text.par_spacing(), SpacingKind::PARAGRAPH);
     }
 
     async fn layout_text(&mut self, text: &str) {
@@ -117,14 +115,14 @@ impl<'a> TreeLayouter<'a> {
         let boxed = shaping::shape(
             text,
             self.ctx.state.text.font_size(),
-            self.ctx.state.sys.primary,
+            self.ctx.state.dirs.cross,
             &mut self.ctx.loader.borrow_mut(),
             &self.ctx.state.text.fallback,
             variant,
         )
         .await;
 
-        self.layouter.add(boxed, self.ctx.state.align);
+        self.layouter.add(boxed, self.ctx.state.aligns);
     }
 
     async fn layout_heading(&mut self, heading: &NodeHeading) {
@@ -187,10 +185,10 @@ impl<'a> TreeLayouter<'a> {
         match command {
             LayoutSyntaxTree(tree) => self.layout_tree(&tree).await,
 
-            Add(layout, align) => self.layouter.add(layout, align),
+            Add(layout, aligns) => self.layouter.add(layout, aligns),
             AddSpacing(space, kind, axis) => match axis {
-                GenAxis::Primary => self.layouter.add_primary_spacing(space, kind),
-                GenAxis::Secondary => self.layouter.add_secondary_spacing(space, kind),
+                GenAxis::Main => self.layouter.add_main_spacing(space, kind),
+                GenAxis::Cross => self.layouter.add_cross_spacing(space, kind),
             },
 
             BreakLine => self.layouter.finish_line(),
@@ -219,7 +217,7 @@ impl<'a> TreeLayouter<'a> {
                     let space = LayoutSpace {
                         size: style.size,
                         insets: style.insets(),
-                        expansion: LayoutExpansion::new(true, true),
+                        expansion: Spec2::new(true, true),
                     };
                     self.constraints.base = space.usable();
                     self.layouter.set_spaces(vec![space], true);
@@ -230,12 +228,7 @@ impl<'a> TreeLayouter<'a> {
                     ));
                 }
             }
-
-            SetAlignment(align) => self.ctx.state.align = align,
-            SetSystem(sys) => {
-                self.layouter.set_sys(sys);
-                self.ctx.state.sys = sys;
-            }
+            SetAlignment(aligns) => self.ctx.state.aligns = aligns,
         }
     }
 }
diff --git a/src/library/align.rs b/src/library/align.rs
index e7a8eb77d..6c9c675f8 100644
--- a/src/library/align.rs
+++ b/src/library/align.rs
@@ -35,7 +35,7 @@ pub async fn align(mut args: Args, ctx: &mut LayoutContext) -> Value {
         Some(tree) => vec![
             SetAlignment(aligns),
             LayoutSyntaxTree(tree),
-            SetAlignment(ctx.state.align),
+            SetAlignment(ctx.state.aligns),
         ],
         None => vec![SetAlignment(aligns)],
     })
@@ -45,8 +45,8 @@ pub async fn align(mut args: Args, ctx: &mut LayoutContext) -> Value {
 fn dedup_aligns(
     ctx: &mut LayoutContext,
     iter: impl Iterator<Item = (Option<SpecAxis>, Spanned<SpecAlign>)>,
-) -> LayoutAlign {
-    let mut aligns = ctx.state.align;
+) -> Gen2<GenAlign> {
+    let mut aligns = ctx.state.aligns;
     let mut had = Gen2::new(false, false);
     let mut had_center = false;
 
@@ -54,8 +54,8 @@ fn dedup_aligns(
         // Check whether we know which axis this alignment belongs to.
         if let Some(axis) = axis {
             // We know the axis.
-            let gen_axis = axis.to_gen(ctx.state.sys);
-            let gen_align = align.to_gen(ctx.state.sys);
+            let gen_axis = axis.to_gen(ctx.state.dirs);
+            let gen_align = align.to_gen(ctx.state.dirs);
 
             if align.axis().map_or(false, |a| a != axis) {
                 ctx.diag(error!(
@@ -73,14 +73,13 @@ fn dedup_aligns(
             // positional argument.
             debug_assert_eq!(align, SpecAlign::Center);
 
-            if had.primary && had.secondary {
+            if had.main && had.cross {
                 ctx.diag(error!(span, "duplicate alignment"));
             } else if had_center {
                 // Both this and the previous one are unspecified `center`
                 // alignments. Both axes should be centered.
-                aligns = LayoutAlign::new(GenAlign::Center, GenAlign::Center);
-                had.primary = true;
-                had.secondary = true;
+                aligns = Gen2::new(GenAlign::Center, GenAlign::Center);
+                had = Gen2::new(true, true);
             } else {
                 had_center = true;
             }
@@ -88,22 +87,22 @@ fn dedup_aligns(
 
         // If we we know one alignment, we can handle the unspecified `center`
         // alignment.
-        if had_center && (had.primary || had.secondary) {
-            if had.primary {
-                aligns.secondary = GenAlign::Center;
-                had.secondary = true;
+        if had_center && (had.main || had.cross) {
+            if had.main {
+                aligns.cross = GenAlign::Center;
+                had.cross = true;
             } else {
-                aligns.primary = GenAlign::Center;
-                had.primary = true;
+                aligns.main = GenAlign::Center;
+                had.main = true;
             }
             had_center = false;
         }
     }
 
     // If center has not been flushed by now, it is the only argument and then
-    // we default to applying it to the primary axis.
+    // we default to applying it to the cross axis.
     if had_center {
-        aligns.primary = GenAlign::Center;
+        aligns.cross = GenAlign::Center;
     }
 
     aligns
diff --git a/src/library/boxed.rs b/src/library/boxed.rs
index caeb206e2..b88f5b7ce 100644
--- a/src/library/boxed.rs
+++ b/src/library/boxed.rs
@@ -12,7 +12,7 @@ pub async fn boxed(mut args: Args, ctx: &mut LayoutContext) -> Value {
     let height = args.get::<_, Linear>(ctx, "height");
     args.done(ctx);
 
-    let align = ctx.state.align;
+    let aligns = ctx.state.aligns;
     let constraints = &mut ctx.constraints;
     constraints.base = constraints.spaces[0].size;
     constraints.spaces.truncate(1);
@@ -35,5 +35,5 @@ pub async fn boxed(mut args: Args, ctx: &mut LayoutContext) -> Value {
     let layouted = layout_tree(&body, ctx).await;
     let layout = layouted.into_iter().next().unwrap();
 
-    Value::Commands(vec![Add(layout, align)])
+    Value::Commands(vec![Add(layout, aligns)])
 }
diff --git a/src/library/spacing.rs b/src/library/spacing.rs
index b38f06070..7a55ff98e 100644
--- a/src/library/spacing.rs
+++ b/src/library/spacing.rs
@@ -24,7 +24,7 @@ fn spacing(mut args: Args, ctx: &mut LayoutContext, axis: SpecAxis) -> Value {
 
     Value::Commands(if let Some(spacing) = spacing {
         let spacing = spacing.eval(ctx.state.text.font_size());
-        let axis = axis.to_gen(ctx.state.sys);
+        let axis = axis.to_gen(ctx.state.dirs);
         vec![AddSpacing(spacing, SpacingKind::Hard, axis)]
     } else {
         vec![]