Swift Concurrency Type System

Swift Concurrency Type System / try! Swift Tokyo 2026
Paper: https://github.com/inamiy/swift-concurrency-type-system/

1. Swift Concurrency Type System try! Swift Tokyo 2026 @inamiy
2. Swift Concurrency Keywords async await actor @globalActor @MainActor Task TaskGroup @TaskLocal AsyncSequence Continuation isolated nonisolated nonisolated(unsafe) nonisolated(nonsending) @isolated(any) @concurrent #isolation Sendable @Sendable sending 20+ concurrency-related types, keywords, and attributes
3. Swift Concurrency is Hard 😇
4. What makes Swift Concurrency Hard? Especially when closures are involved: Swift compiler knows. But do you know why?
5. The Question What are the core rules behind Swift Concurrency type system?
6. Closure Conversion Rules
7. Closure Conversion This is subtyping / coercion between concurrency annotations Given f: @A () -> Void , can we assign to / use in g: @B () -> Void ? N o t e : @ A a n d @ B c a n b e A N Y c o n c u r re n c y a t t r i b u t e s , n o t o n l y a b o u t g l o b a l a c t o r i s o l a t i o n
8. Sync closure conversion
9. Sync Conversion Matrix From ↓ \ To → ~iso @S @MA @MA @S @iso? @iso? @S iso(a) iso(a) @S ~iso ✅ ❌ ❌ ❌ ✅ ❌ ❌ ❌ @S ✅ ✅ ✅ ✅ ✅ ✅ ✅ ✅ @MA ❌ ❌ ✅ ✅ ✅ ✅ ❌ ❌ @MA @S ❌ ❌ ✅ ✅ ✅ ✅ ❌ ❌ @iso? ⚠️ ❌ ❌ ❌ ✅ ❌ ❌ ❌ @iso? @S ⚠️ ⚠️ ❌ ❌ ✅ ✅ ❌ ❌ iso(a) ❌ ❌ ❌ ❌ ❌ ❌ ✅ ❌ iso(a) @S ❌ ❌ ❌ ❌ ❌ ❌ ✅ ✅ ~ i s o = n o n i s o l a t e d , @ S = @ S e n d a b l e , @ M A = @ M a i n A c t o r, @ i s o ? = @ i s o l a t e d ( a n y ) , i s o ( a ) = i s o l a t e d Lo c a l A c t o r, ⚠️ = w a r n i n g ( f u t u re e r ro r )
10. Sync Conversion Sendable Sync nonisolated @Sendable sync @MainActor (@Sendable) sync @isolated(any) @Sendable sync isolated LocalActor @Sendable sync @isolated(any) sync nonisolated sync isolated LocalActor sync ⚠ deprecated
11. Async closure conversion
12. Async Conversion Matrix From ↓ \ To → ~iso @S @MA @MA @S @iso? @iso? @S @conc @conc @S ~iso ✅ ❌ ❌ ❌ ✅ ❌ ✅ ❌ @S ✅ ✅ ✅ ✅ ✅ ✅ ✅ ✅ @MA ✅ ✅ ✅ ✅ ✅ ✅ ✅ ✅ @MA @S ✅ ✅ ✅ ✅ ✅ ✅ ✅ ✅ @iso? ✅ ❌ ❌ ❌ ✅ ❌ ✅ ❌ @iso? @S ✅ ✅ ✅ ✅ ✅ ✅ ✅ ✅ @conc ✅ ❌ ❌ ❌ ✅ ❌ ✅ ❌ @conc @S ✅ ✅ ✅ ✅ ✅ ✅ ✅ ✅ @ c o n c = @ c o n c u r re n t . i s o ( a ) o m i t t e d i n t h i s t a b l e ( s a m e a s " s y n c " ) .
13. Async Conversion Sendable Async Non-Sendable Async nonisolated @Sendable async @MainActor (@Sendable) async @concurrent @Sendable async @isolated(any) @Sendable async isolated LocalActor @Sendable async nonisolated async @concurrent async @isolated(any) async isolated LocalActor async
14. Isolation Conversion Sync Conversion Async Conversion Sendable Sync Sendable Async Non-Sendable Async nonisolated @Sendable sync @MainActor (@Sendable) sync @isolated(any) @Sendable sync isolated LocalActor @Sendable sync @isolated(any) sync nonisolated sync isolated LocalActor sync nonisolated @Sendable async @MainActor (@Sendable) async @concurrent @Sendable async @isolated(any) @Sendable async isolated LocalActor @Sendable async nonisolated async @concurrent async @isolated(any) async isolated LocalActor async ⚠ deprecated Async Lift
15. Closure Conversion Rules @Sendable is stronger closure than non-@Sendable nonisolated is stronger closure than isolated @isolated(any) is the weakest closure (most generic) isolated LocalActor is tied to extra isolated param, which can be added but cannot be reduced for conversion Sync closure conversion is the most painful due to await being impossible Async closure conversion is easier to achieve via await (actor hop) Sync to Async conversion is always possible (but not vice-versa)
16. Capability & Region
17. Question Q. Which isolation does handler have?
18. Answer Where does the code run? → @BarActor Where does the value live? → @FooActor @MainActor is not used in handler 😛 Isolation Domain (capability, execution context) and Isolation Region (value isolation) are different!
19. Axis 1: Capability ( ) Where code runs — Actor's execution context Determines what values actor can access Controls whether await is needed for cross-isolation calls @κ
20. Function Annotation ( ) & Capability ( ) @φ ::= ​ ​ s e n d a b i l i t y ​ @σ i s o l a t i o n ​ @ι (Sendability) (Isolation Domain) (none) (none) ( @nonisolated ) @Sendable @isolated(a) (e.g. @MainActor ) @isolated(any) @concurrent (async only) Capability @nonisolated | @isolated(a) ( ) @φ @κ @σ @ι ⋅ ⋅ @κ ::= @κ ⊆ @ι
21. Axis 2: Region ( ) Where data lives — Actor's value isolation (SE-0414) ρ ​ ::= ns disconnected ∣ isolated(a) ∣ task ∣ invalid Meaning Free to travel (not yet bound) Bound to actor Bound to current async task Tracks which isolation a NonSendable value belongs to. ρ ρ ​ n s disconnected isolated(a) a task
22. Region in Action Region merge: Once bound, a value cannot be sent across isolation boundaries. disconnected ⊔ isolated(a) = isolated(a)
23. Region Merge ( ) invalid invalid ρ ​ ⊔ 1 ρ ​ 2 ρ ​ 1 ρ ​ 2 ρ ​ ⊔ 1 ρ ​ 2 disconnected disconnected disconnected disconnected isolated(a) isolated(a) disconnected task task isolated(a) isolated(a) isolated(a) isolated(a) isolated(b) (a =  b) isolated(a) task task task task S e e a l s o : S E - 0 4 1 4 : R e g i o n b a s e d I s o l a t i o n
24. Region Merge as Join Semilattice disconnected (⊥) isolated(a) task invalid (⊤) = bottom of = top (compile error) disconnected ρ ​ ns invalid
25. The Two Axes Together Aspect Capability Region What Execution context Value location Question Where does code run? Where does data live? Examples @nonisolated , @MainActor , Changes Fixed per scope Flow-sensitive Controls async / await sending @κ ρ disconnected isolated(a)
26. Affine Types
27. Swift Ownership Keyword Description Copyable Can be copied and used multiple times ~Copyable Cannot be implicitly copied (consume once) consuming param Takes ownership borrowing param Temporary read-only access
28. Affine Types A ⊬ A ⊗ A ← can NOT copy A ⊢ 1 ← can discard Linear Types: use exactly once (no copy, must use) Affine Types: use at most once (no copy, can skip use) No copy = Enforced consumption
29. Similarity: Consumption Ownership Concurrency Both consuming and sending enforces consumption of ~Copyable / ~Sendable value.
30. Region-based Isolation is like Ownership Sendable is like Copyable Value and reference can be copied and used in multiple isolation domains NonSendable is like ~Copyable Cannot be used after transferring to another isolation domain sending is like consuming (but not always) sending param may still not get consumed in the same region condition
31. sending param (in same isolation) non-sending binds to actor region sending keeps in same region
32. sending return sending -return guarantees the value is disconnected
33. Formalizing Swift Concurrency Type System D i s c l a i m e r : Th i s s e c t i o n i s a n A I v i b e - f o r m a l i z a t i o n .
34. Γ ⊢ e : T
35. Γ;@κ;α ⊢ e : T at ρ ⊣ Γ′
36. The Judgment Form ​ ; ​ ; ​ ​ ​ : env ​ in ​ Γ capability ​ @κ mode ​ α proves ​ ⊢ expr ​ e at ​ ​ type T region ​ ρ outputs ​ ⊣ env ​ out ​ Γ ′ / : what variables are available (input / output) e.g. Every expression transforms the type environment from to (Affinity) : current capability (where we're running) : (asynchrony) : which region the expression result lives in Γ Γ′ Γ = {e ​ : 1 T ​ at ρ ​ , e ​ : 1 1 2 T ​ at ρ ​ , …} 2 2 Γ Γ′ @κ α sync ∣ async ρ
37. Example 1 Γ; @nonisolated; sync ⊢ x : T at disconnected ⊣ Γ
38. Example 2 Γ; @MainActor; async ⊢ await f (x) : T at _ ⊣ ​ Γ ∖ {x}
39. Key Rules: Variables Access-only variable rule: ​ (var) Γ; @κ; α ⊢ x : T at ρ ⊣ Γ x : T at ρ ∈ Γ ​ ρ ∈ accessible(@κ) accessible(@κ) : P (Regions) accessible(@nonisolated) = {disconnected, task, _} accessible(@isolated(a)) = {disconnected, isolated(a), task, _} T : Sendable ⇔ (ρ = _) (normal form in Γ)
40. Key Rules: Transfer & Merge call-nonsendable-consume — cross-isolation consumption: ​ (call-nonsendable-consume) Γ; @κ; async ⊢ await f (arg) : B at _ ⊣ ​ Γ ​ ∖ {arg} 2 ​ f : @σ @ι (A) α → B arg : A at disconnected ∈ Γ ​ 2 A : ∼Sendable B : Sendable @κ = @ι  region-merge — e.g. binding via assignment: ​ (region-merge) Γ; @κ; α ⊢ (e ​ .field = e ​ ) : () at _ ⊣ ​ 1 2 Γ ​ [ρ ​ ↦ ρ, ρ ​ ↦ ρ] 2 1 2 ​ Γ; @κ; α ⊢ e ​ : T ​ at ρ ​ ⊣ Γ ​ Γ ​ ; @κ; α ⊢ e ​ : T ​ at ρ ​ ⊣ Γ ​ 1 1 1 1 1 2 2 2 2 T ​ , T ​ : ∼Sendable ρ ​ , ρ ​ ∈ ρ ​ ρ = ρ ​ ⊔ ρ ​ 1 2 1 2 ns 1 2 Cross-isolation shrinks . Region-merge refines it. Γ
41. Key Rules: Closures — Isolation Inference Non-@Sendable — closure inherits parent's capability : ​ (closure-inherit-parent) Γ; @κ; α ⊢ {e} : ​ at ρ ​ ⊣ Γ @κ () α → B ′ closure ​ Γ ⊆ Γ cap Γ ​ ; @κ; α ⊢ e : B at ρ ​ ⊣ Γ ​ cap ′ ret cl ′ @Sendable — No inheritance, uses instead: ​ (closure-no-inherit-parent) Γ; @κ; α ⊢ {e} : ​ at _ ⊣ Γ @Sendable @ι () α → B ′ ​ Γ ​ ⊆ Γ isAllSendable(Γ ​ ) cap cap @κ ​ = toCapability(@ι) cl Γ ​ ; @κ ​ ; α ⊢ e : B at ρ ​ ⊣ Γ ​ cap cl ′ ret cl ′ @κ @ι
42. Key Rules: Closures — sending Capture transfer case — consumes NonSendable captures: ​ (closure-sending-consume) Γ; @κ; α ⊢ f ({e}) : () at _ ⊣ Γ′ ​ f : (sending (@κ ​ () α → T )) → () Γ ​ ⊆ Γ cl ′ cap ¬(⋯ ∧ isActorIsolated(@κ) ∧ @κ ​ = @κ) ⋯ cl Γ ​ ; @κ ​ ; α ⊢ e : T at ρ ​ ⊣ Γ ​ cap cl ′ ret cl ′ Γ = Γ ∖ {x ∣ (x : U at disconnected) ∈ Γ ​ , U : ∼Sendable} ′ cap
43. https://github.com/inamiy/swift-concurrency-type-system
44. Recap (Formalization) Γ; @κ; α ⊢ e : T at ρ ⊣ Γ′ Component Role Details WHERE code runs @nonisolated , @MainActor , ... WHERE data lives Affine discipline Merge refines, transfer shrinks @κ ρ disconnected → isolated(a) Γ → Γ′
45. Wrap Up 1. Swift Concurrency = Capability × Region @κ : where code runs / ρ : where data lives Covers the mystery of closure conversion rules 2. sending = Affine transfer (in many cases) Precondition: x : T at disconnected Effect: (use-after-send is rejected) 3. Region Merge = Context refinement e.g. disconnected ⊔ isolated(a) = isolated(a) Γ = ′ Γ ∖ {x} Γ
46. References Swift Evolution SE-0414: Region-based Isolation SE-0430: sending parameter and result values SE-0431: @isolated(any) function types SE-0461: Run nonisolated async functions on the caller's actor Papers Tofte & Talpin (1994), Region-Based Memory Management Walker, Crary & Morrisett (2000), Typed Memory Management via Static Capabilities Walker & Watkins (2001), On Regions and Linear Types Grossman et al. (2002), Region-Based Memory Management in Cyclone Charguéraud & Pottier (2008), Functional Translation of a Calculus of Capabilities Milano, Turcotti & Myers (2022), A Flexible Type System for Fearless Concurrency