Existential Types - Special Topics - Lecture Slides | ECEN 5023, Study notes of Electrical and Electronics Engineering

Download Existential Types - Special Topics - Lecture Slides | ECEN 5023 and more Study notes Electrical and Electronics Engineering in PDF only on Docsity! Existential Types I Provide a form of first-class information hiding (abstract data types) I Example: p = pack {Nat, (5, λx:Nat. succ x)} as ∃α. α× (α → α) open p as {β,x} in ((snd x) (fst x)) Existential Types Syntax: T ::= . . . | ∃α. T e ::= pack {T , e} as T | open e as {α, x} in e Evaluation contexts: E ::= . . . | pack {T ,E} as T | open E as {α, x} in e Reduction rule: open (pack {T1, v} as T2) as {α, x} in e −→ [α 7→ T1][x 7→ v ]e Type rules: Γ ` e : [α 7→ U]T Γ ` pack {U, e} as ∃α.T Γ ` e1 : ∃α. T1 Γ, α, x : T1 ` e2 : T2 Γ ` open e1 as {α, x} in e2 : T2