diff --git a/Package.resolved b/Package.resolved
index 2afd825..ef2bf29 100644
--- a/Package.resolved
+++ b/Package.resolved
@@ -1,6 +1,15 @@
 {
-  "originHash" : "a37ab791b028e91ba927aed2f01979a802c12b4164919a272b77af2d9e021dbb",
+  "originHash" : "00743848cbb91a47eb19084a5d4a354ab430ceab782cdee3f3c57556b13f019f",
   "pins" : [
+    {
+      "identity" : "keycodes",
+      "kind" : "remoteSourceControl",
+      "location" : "https://github.com/ChimeHQ/KeyCodes",
+      "state" : {
+        "revision" : "93ba759d2bfd7b5233294188bc685fd09dce2729",
+        "version" : "1.0.3"
+      }
+    },
     {
       "identity" : "ligature",
       "kind" : "remoteSourceControl",
diff --git a/Package.swift b/Package.swift
index 88c35e2..7bdd7ff 100644
--- a/Package.swift
+++ b/Package.swift
@@ -14,11 +14,11 @@ let package = Package(
 		.library(name: "IBeam", targets: ["IBeam"]),
 	],
 	dependencies: [
-		.package(url: "https://github.com/ChimeHQ/Ligature", branch: "main"),
+		.package(url: "https://github.com/ChimeHQ/Ligature", revision: "b184b82dd4c68327ed37257d1b60fc9f41a50042"),
 		.package(url: "https://github.com/ChimeHQ/KeyCodes", from: "1.0.3"),
 	],
 	targets: [
 		.target(name: "IBeam", dependencies: ["KeyCodes", "Ligature"]),
-		.testTarget(name: "IBeamTests", dependencies: ["IBeam"]),
+		.testTarget(name: "IBeamTests", dependencies: ["IBeam", "Ligature"]),
 	]
 )
diff --git a/Sources/IBeam/Cursor.swift b/Sources/IBeam/Cursor.swift
index bd6085a..e9b8dd5 100644
--- a/Sources/IBeam/Cursor.swift
+++ b/Sources/IBeam/Cursor.swift
@@ -10,7 +10,7 @@ public struct Cursor<TextLocation: Comparable>: Identifiable {
 	public typealias TextRange = Range<TextLocation>
 
 	public let id: UUID
-	public let range: TextRange
+	public var range: TextRange
 
 	public init(range: TextRange) {
 		self.range = range
diff --git a/Sources/IBeam/MultiCursorState.swift b/Sources/IBeam/MultiCursorState.swift
index a6b494c..9296c2c 100644
--- a/Sources/IBeam/MultiCursorState.swift
+++ b/Sources/IBeam/MultiCursorState.swift
@@ -5,24 +5,26 @@ import UIKit
 #endif
 
 import KeyCodes
+import Ligature
 
 public enum SelectionAffinity: Hashable, Sendable, Codable {
 	case upstream
 	case downstream
 }
 
-public struct MultiCursorState<CoordinateProvider: TextCoordinateProvider> {
-	public typealias TextLocation = CoordinateProvider.TextLocation
-	public typealias Cursor = IBeam.Cursor<TextLocation>
+@MainActor
+public final class MultiCursorState<Tokenizer: TextTokenizer> where Tokenizer.Position: Comparable {
+	public typealias Position = Tokenizer.Position
+	public typealias Cursor = IBeam.Cursor<Position>
 
 	public var affinity: SelectionAffinity
     public var cursors: [Cursor]
-	public let coordinateProvider: CoordinateProvider
+	public let tokenizer: Tokenizer
 
-	public init(cursors: [Cursor] = [], affinity: SelectionAffinity = .upstream, coordinateProvider: CoordinateProvider) {
+	public init(cursors: [Cursor] = [], affinity: SelectionAffinity = .upstream, tokenizer: Tokenizer) {
         self.cursors = cursors
 		self.affinity = affinity
-		self.coordinateProvider = coordinateProvider
+		self.tokenizer = tokenizer
     }
 
     public var hasMultipleCursors: Bool {
@@ -35,15 +37,15 @@ extension MultiCursorState {
 
 	}
 
-	public mutating func addCursorBelow() {
+	public func addCursorBelow() {
 		guard let range = cursors.last?.range else {
 			assertionFailure("at least one cursor should be present")
 			return
 		}
 
 		guard
-			let start = coordinateProvider.closestMatchingVerticalLocation(to: range.lowerBound, above: false),
-			let end = coordinateProvider.closestMatchingVerticalLocation(to: range.upperBound, above: false)
+			let start = tokenizer.position(from: range.lowerBound, toBoundary: .character, inDirection: .layout(.down)),
+			let end = tokenizer.position(from: range.upperBound, toBoundary: .character, inDirection: .layout(.down))
 		else {
 			return
 		}
@@ -54,8 +56,8 @@ extension MultiCursorState {
 		self.cursors.sort()
 	}
 
-	public mutating func addCursor(at location: TextLocation) {
-		let newCursor = Cursor(range: location..<location)
+	public func addCursor(at position: Position) {
+		let newCursor = Cursor(range: position..<position)
 
 		self.cursors.append(newCursor)
 		self.cursors.sort()
@@ -63,10 +65,11 @@ extension MultiCursorState {
 }
 
 extension MultiCursorState {
+#if os(macOS)
     /// Process a keyDown event
     ///
     /// - Returns: true if the event was processed and should now be ignored.
-	public mutating func handleKeyDown(with event: NSEvent) -> Bool {
+	public func handleKeyDown(with event: NSEvent) -> Bool {
 		let flags = event.keyModifierFlags?.subtracting(.numericPad) ?? []
 		let key = event.keyboardHIDUsage
 
@@ -77,14 +80,36 @@ extension MultiCursorState {
 		case ([.control, .shift], .keyboardDownArrow):
 			addCursorBelow()
             return true
+		case ([], .keyboardLeftArrow):
+			moveLeft(self)
+			return true
 		default:
 			break
 		}
 
-        guard hasMultipleCursors else {
-            return false
-        }
-
 		return false
 	}
+#endif
+}
+
+extension MultiCursorState {
+	public func moveLeft(_ sender: Any?) {
+		self.cursors = cursors.compactMap { cursor in
+			let start = cursor.range.lowerBound
+			guard let newStart = tokenizer.position(from: start, toBoundary: .character, inDirection: .layout(.left)) else {
+				return nil
+			}
+
+			var cursor = cursor
+
+			switch affinity {
+			case .upstream:
+				cursor.range = newStart..<newStart
+			case .downstream:
+				cursor.range = newStart..<cursor.range.upperBound
+			}
+
+			return cursor
+		}
+	}
 }
diff --git a/Sources/IBeam/TextCoordinateProvider.swift b/Sources/IBeam/TextCoordinateProvider.swift
deleted file mode 100644
index 520873f..0000000
--- a/Sources/IBeam/TextCoordinateProvider.swift
+++ /dev/null
@@ -1,11 +0,0 @@
-#if os(macOS)
-import AppKit
-#elseif os(iOS) || os(visionOS)
-import UIKit
-#endif
-
-public protocol TextCoordinateProvider {
-	associatedtype TextLocation: Comparable
-
-	func closestMatchingVerticalLocation(to location: TextLocation, above: Bool) -> TextLocation?
-}
diff --git a/Tests/IBeamTests/MultiCursorStateTests.swift b/Tests/IBeamTests/MultiCursorStateTests.swift
index e4bc17e..87214fa 100644
--- a/Tests/IBeamTests/MultiCursorStateTests.swift
+++ b/Tests/IBeamTests/MultiCursorStateTests.swift
@@ -1,23 +1,32 @@
 import Testing
 import IBeam
 
-class MockCoordinateProvider: TextCoordinateProvider {
-	func closestMatchingVerticalLocation(to location: Int, above: Bool) -> Int? {
-		let offset = above ? -5 : 5
-
-		return location + offset
-	}
-}
+import Ligature
 
 final class MultiCursorStateTests {
-	@Test
-	func addCursorBelow() async throws {
+	@Test @MainActor
+	func addCursorBelow() throws {
 		let cursor = Cursor(range: 0..<10)
-		let provider = MockCoordinateProvider()
-		var state = MultiCursorState(cursors: [cursor], coordinateProvider: provider)
+		let tokenizer = MockTextTokenizer()
+		let state = MultiCursorState(cursors: [cursor], tokenizer: tokenizer)
 
+		tokenizer.responses = [.position(5), .position(15)]
 		state.addCursorBelow()
 
+		#expect(tokenizer.requests == [.position(0, .character, .layout(.down)), .position(10, .character, .layout(.down))])
 		#expect(state.cursors.map(\.range) == [0..<10, 5..<15])
 	}
+
+	@Test @MainActor
+	func handleLeftArrowWithSingleInsertion() throws {
+		let cursor = Cursor(range: 1..<1)
+		let tokenizer = MockTextTokenizer()
+		let state = MultiCursorState(cursors: [cursor], affinity: .upstream, tokenizer: tokenizer)
+
+		tokenizer.responses = [.position(0)]
+		state.moveLeft(nil)
+
+		#expect(tokenizer.requests == [.position(1, .character, .layout(.left))])
+		#expect(state.cursors.map(\.range) == [0..<0])
+	}
 }