A Practical, Typed Variant Object Model Or, How to Stand On Your - PowerPoint PPT Presentation

Typing the Onion ( ❵❞❜❧ x -> x + x) & 1 ( ❵♦❞❞ y -> y ♠♦❞ 2 == 1) 2 ( ❵❞❜❧ ✐♥t ∪ ❵♦❞❞ ✐♥t ) -> ( ✐♥t ∪ ❜♦♦❧ ) Simple union type loses alignment

Typing the Onion ( ❵❞❜❧ x -> x + x) & 1 ( ❵♦❞❞ y -> y ♠♦❞ 2 == 1) 2 ( ❵❞❜❧ ✐♥t -> ✐♥t ) & ( ❵♦❞❞ ✐♥t -> ❜♦♦❧ ) Simple union type loses alignment Onion type does not

Typing the Onion ( ❵❞❜❧ x -> x + x) & 1 ( ❵♦❞❞ y -> y ♠♦❞ 2 == 1) 2 ( ❵❞❜❧ ✐♥t -> ✐♥t ) & ( ❵♦❞❞ ✐♥t -> ❜♦♦❧ ) Simple union type loses alignment Onion type does not Weakly dependent type

Typing the Onion ( ❵❞❜❧ x -> x + x) & 1 ( ❵♦❞❞ y -> y ♠♦❞ 2 == 1) 2 ( ❵❞❜❧ ✐♥t -> ✐♥t ) & ( ❵♦❞❞ ✐♥t -> ❜♦♦❧ ) Simple union type loses alignment Onion type does not Weakly dependent type Relies heavily on polymorphism

Fields Pure variant model: get/set messages

Fields ( ❵❞❜❧ x -> x + x) & 1 ( ❵♦❞❞ y -> y ♠♦❞ 2 == 1) & 2 ❵❩ 5 3 Pure variant model: get/set messages Hybrid model: variant methods, record fields

Fields ( ❵❞❜❧ x -> x + x) & 1 ( ❵♦❞❞ y -> y ♠♦❞ 2 == 1) & 2 ❵❩ 5 3 Pure variant model: get/set messages Hybrid model: variant methods, record fields Similar to type-indexed rows [Shields, Meijer ’01]

Fields ( ❵❞❜❧ x -> x + x) & 1 ( ❵♦❞❞ y -> y ♠♦❞ 2 == 1) & 2 ❵❩ 5 3 Pure variant model: get/set messages Hybrid model: variant methods, record fields Similar to type-indexed rows [Shields, Meijer ’01] Labels implicitly create cells

Fields 1 ❞❡❢ o = ( ❵❞❜❧ x -> x + x) & ( ❵♦❞❞ y -> y ♠♦❞ 2 == 1) & 2 ❵❩ 5 3 4 ✐♥ o. ❩ Pure variant model: get/set messages Hybrid model: variant methods, record fields Similar to type-indexed rows [Shields, Meijer ’01] Labels implicitly create cells Field access by projection

Fields 1 ❞❡❢ o = ( ❵❞❜❧ x -> x + x) & ( ❵♦❞❞ y -> y ♠♦❞ 2 == 1) & 2 ❵❩ 5 3 4 ✐♥ ( ❵❩ z -> z) o Pure variant model: get/set messages Hybrid model: variant methods, record fields Similar to type-indexed rows [Shields, Meijer ’01] Labels implicitly create cells Field access by projection/pattern match

Fields 1 ❞❡❢ o = ( ❵❞❜❧ x -> x + x) & ( ❵♦❞❞ y -> y ♠♦❞ 2 == 1) & 2 ❵❩ 5 3 4 ✐♥ ( ❵❩ z -> z) o Pure variant model: get/set messages Hybrid model: variant methods, record fields Similar to type-indexed rows [Shields, Meijer ’01] Labels implicitly create cells Field access by projection/pattern match But what about self?

❵s❡❧❢ ❵s❡❧❢ Na¨ ıve Self 1 ❞❡❢ ticker = ❵① 0 & 2 ( ❵✐♥❝ _ -> 3 s❡❧❢ . ① = s❡❧❢ . ① + 1 ✐♥ s❡❧❢ . ① ) 4 5 ✐♥ ticker ❵✐♥❝ ✭✮

❵s❡❧❢ Na¨ ıve Self 1 ❞❡❢ ticker = ❵① 0 & 2 ( ❵✐♥❝ _ & ❵s❡❧❢ s❡❧❢ -> 3 s❡❧❢ . ① = s❡❧❢ . ① + 1 ✐♥ s❡❧❢ . ① ) 4 5 ✐♥ ticker ❵✐♥❝ ✭✮ Add ❵s❡❧❢ to all parameters

❵s❡❧❢ Na¨ ıve Self 1 ❞❡❢ ticker = ❵① 0 & 2 ( ❵✐♥❝ _ & ❵s❡❧❢ s❡❧❢ -> 3 s❡❧❢ . ① = s❡❧❢ . ① + 1 ✐♥ s❡❧❢ . ① ) 4 5 ✐♥ ticker ❵✐♥❝ ✭✮ Add ❵s❡❧❢ to all parameters & is pattern conjunction

Na¨ ıve Self 1 ❞❡❢ ticker = ❵① 0 & 2 ( ❵✐♥❝ _ & ❵s❡❧❢ s❡❧❢ -> 3 s❡❧❢ . ① = s❡❧❢ . ① + 1 ✐♥ s❡❧❢ . ① ) 4 5 ✐♥ ticker ( ❵✐♥❝ ✭✮ & ❵s❡❧❢ ticker) Add ❵s❡❧❢ to all parameters & is pattern conjunction Add ❵s❡❧❢ to all call sites

Na¨ ıve Self 1 ❞❡❢ ticker = ❵① 0 & 2 ( ❵✐♥❝ _ & ❵s❡❧❢ s❡❧❢ -> 3 s❡❧❢ . ① = s❡❧❢ . ① + 1 ✐♥ s❡❧❢ . ① ) 4 5 ✐♥ ticker ( ❵✐♥❝ ✭✮ & ❵s❡❧❢ ticker) Add ❵s❡❧❢ to all parameters & is pattern conjunction Add ❵s❡❧❢ to all call sites Be happy?

Na¨ ıve Self: Type Problems 1 ❞❡❢ obj = ✐❢ something t❤❡♥ 2 ( ❵❢♦♦ _ & ❵s❡❧❢ s -> s ❵❜❛r ✭✮ ) & 3 ( ❵❜❛r _ -> 1) 4 ❡❧s❡ 5 ( ❵❢♦♦ _ & ❵s❡❧❢ s -> s ❵❜❛③ ✭✮ ) & 6 ( ❵❜❛③ _ -> 2) 7 8 ✐♥ obj ❵❢♦♦ ✭✮

Na¨ ıve Self: Problems α Self = ( ❵❢♦♦ _ & ❵s❡❧❢ α 1 -> ✐♥t ) & ( ❵❜❛r _ -> ✐♥t ) where α 1 has ❵❜❛r � ( ❵❢♦♦ _ & ❵s❡❧❢ α 2 -> ✐♥t ) & ( ❵❜❛③ _ -> ✐♥t ) where α 2 has ❵❜❛③

Na¨ ıve Self: Problems ( ❵❢♦♦ _ & ❵s❡❧❢ α 1 -> ✐♥t ) & < : ( ❵❜❛r _ -> ✐♥t ) α Self where α 1 has ❵❜❛r ( ❵❢♦♦ _ & ❵s❡❧❢ α 2 -> ✐♥t ) & < : ( ❵❜❛③ _ -> ✐♥t ) α Self where α 2 has ❵❜❛③

Self Solutions Classic object encodings [Bruce et. al. ’98]

Self Solutions Classic object encodings [Bruce et. al. ’98] Type of self is fixed at instantiation

Self Solutions Classic object encodings [Bruce et. al. ’98] Type of self is fixed at instantiation No object extensibility

Self Solutions Classic object encodings [Bruce et. al. ’98] Type of self is fixed at instantiation No object extensibility Extensible Object Calculus [Fisher et. al. ’98]

Self Solutions Classic object encodings [Bruce et. al. ’98] Type of self is fixed at instantiation No object extensibility Extensible Object Calculus [Fisher et. al. ’98] Prototype objects: extensible but not callable

Self Solutions Classic object encodings [Bruce et. al. ’98] Type of self is fixed at instantiation No object extensibility Extensible Object Calculus [Fisher et. al. ’98] Prototype objects: extensible but not callable Proper objects: callable but not extensible

Self Solutions Classic object encodings [Bruce et. al. ’98] Type of self is fixed at instantiation No object extensibility Extensible Object Calculus [Fisher et. al. ’98] Prototype objects: extensible but not callable Proper objects: callable but not extensible Prototypes can be sealed into proper objects

Self Solutions Classic object encodings [Bruce et. al. ’98] Type of self is fixed at instantiation No object extensibility Extensible Object Calculus [Fisher et. al. ’98] Prototype objects: extensible but not callable Proper objects: callable but not extensible Prototypes can be sealed into proper objects Sealing is permanent

Self Solutions Classic object encodings [Bruce et. al. ’98] Type of self is fixed at instantiation No object extensibility Extensible Object Calculus [Fisher et. al. ’98] Prototype objects: extensible but not callable Proper objects: callable but not extensible Prototypes can be sealed into proper objects Sealing is permanent Sealing is meta-theoretic

Self Solutions Classic object encodings [Bruce et. al. ’98] Type of self is fixed at instantiation No object extensibility Extensible Object Calculus [Fisher et. al. ’98] Prototype objects: extensible but not callable Proper objects: callable but not extensible Prototypes can be sealed into proper objects Sealing is permanent Sealing is meta-theoretic TinyBang

Self Solutions Classic object encodings [Bruce et. al. ’98] Type of self is fixed at instantiation No object extensibility Extensible Object Calculus [Fisher et. al. ’98] Prototype objects: extensible but not callable Proper objects: callable but not extensible Prototypes can be sealed into proper objects Sealing is permanent Sealing is meta-theoretic TinyBang Sealing is encodable (no meta-theory)

Self Solutions Classic object encodings [Bruce et. al. ’98] Type of self is fixed at instantiation No object extensibility Extensible Object Calculus [Fisher et. al. ’98] Prototype objects: extensible but not callable Proper objects: callable but not extensible Prototypes can be sealed into proper objects Sealing is permanent Sealing is meta-theoretic TinyBang Sealing is encodable (no meta-theory) Sealed objects can be extended and resealed

Sealing in TinyBang 1 ❞❡❢ r❡❝ seal = obj -> obj & 2 (msg -> obj ( ❵s❡❧❢ (seal obj) & msg)) ✐♥ 3 4 ❞❡❢ point = ❵① 2 & ❵② 4 & 5 ( ❵❧✶ _ & ❵s❡❧❢ s❡❧❢ -> s❡❧❢ . ① + s❡❧❢ . ② ) ✐♥ 6 7 ❞❡❢ sealedPoint = seal point ✐♥ 8 sealedPoint ❵❧✶ ✭✮ 9 . . .

Resealing Objects 1 . . . 2 ❞❡❢ obj = seal ( ❵① 0 & 3 ( ❵✐♥❝ _ & ❵s❡❧❢ s❡❧❢ -> 4 s❡❧❢ . ① = s❡❧❢ . ① + 1 ✐♥ s❡❧❢ . ① )) ✐♥ 5 6 obj ❵✐♥❝ ✭✮ ; obj ❵✐♥❝ ✭✮ ; 7 ❞❡❢ extobj = seal ( obj & 8 ( ❵❞❜❧ _ & ❵s❡❧❢ s❡❧❢ -> 9 s❡❧❢ . ① = s❡❧❢ . ① + s❡❧❢ . ① ✐♥ s❡❧❢ . ① )) ✐♥ 10 11 extobj ❵❞❜❧ ✭✮ ; extobj ❵✐♥❝ ✭✮ x =0

Resealing Objects 1 . . . 2 ❞❡❢ obj = seal ( ❵① 0 & 3 ( ❵✐♥❝ _ & ❵s❡❧❢ s❡❧❢ -> 4 s❡❧❢ . ① = s❡❧❢ . ① + 1 ✐♥ s❡❧❢ . ① )) ✐♥ 5 6 obj ❵✐♥❝ ✭✮ ; obj ❵✐♥❝ ✭✮ ; 7 ❞❡❢ extobj = seal ( obj & 8 ( ❵❞❜❧ _ & ❵s❡❧❢ s❡❧❢ -> 9 s❡❧❢ . ① = s❡❧❢ . ① + s❡❧❢ . ① ✐♥ s❡❧❢ . ① )) ✐♥ 10 11 extobj ❵❞❜❧ ✭✮ ; extobj ❵✐♥❝ ✭✮ x =1

Resealing Objects 1 . . . 2 ❞❡❢ obj = seal ( ❵① 0 & 3 ( ❵✐♥❝ _ & ❵s❡❧❢ s❡❧❢ -> 4 s❡❧❢ . ① = s❡❧❢ . ① + 1 ✐♥ s❡❧❢ . ① )) ✐♥ 5 6 obj ❵✐♥❝ ✭✮ ; obj ❵✐♥❝ ✭✮ ; 7 ❞❡❢ extobj = seal ( obj & 8 ( ❵❞❜❧ _ & ❵s❡❧❢ s❡❧❢ -> 9 s❡❧❢ . ① = s❡❧❢ . ① + s❡❧❢ . ① ✐♥ s❡❧❢ . ① )) ✐♥ 10 11 extobj ❵❞❜❧ ✭✮ ; extobj ❵✐♥❝ ✭✮ x =2

Resealing Objects 1 . . . 2 ❞❡❢ obj = seal ( ❵① 0 & 3 ( ❵✐♥❝ _ & ❵s❡❧❢ s❡❧❢ -> 4 s❡❧❢ . ① = s❡❧❢ . ① + 1 ✐♥ s❡❧❢ . ① )) ✐♥ 5 6 obj ❵✐♥❝ ✭✮ ; obj ❵✐♥❝ ✭✮ ; 7 ❞❡❢ extobj = seal ( obj & 8 ( ❵❞❜❧ _ & ❵s❡❧❢ s❡❧❢ -> 9 s❡❧❢ . ① = s❡❧❢ . ① + s❡❧❢ . ① ✐♥ s❡❧❢ . ① )) ✐♥ 10 11 extobj ❵❞❜❧ ✭✮ ; extobj ❵✐♥❝ ✭✮ x =4

Resealing Objects 1 . . . 2 ❞❡❢ obj = seal ( ❵① 0 & 3 ( ❵✐♥❝ _ & ❵s❡❧❢ s❡❧❢ -> 4 s❡❧❢ . ① = s❡❧❢ . ① + 1 ✐♥ s❡❧❢ . ① )) ✐♥ 5 6 obj ❵✐♥❝ ✭✮ ; obj ❵✐♥❝ ✭✮ ; 7 ❞❡❢ extobj = seal ( obj & 8 ( ❵❞❜❧ _ & ❵s❡❧❢ s❡❧❢ -> 9 s❡❧❢ . ① = s❡❧❢ . ① + s❡❧❢ . ① ✐♥ s❡❧❢ . ① )) ✐♥ 10 11 extobj ❵❞❜❧ ✭✮ ; extobj ❵✐♥❝ ✭✮ x =5

Resealing Objects 1 . . . 2 ❞❡❢ obj = seal ( . . . ) ✐♥ 3 obj ❵✐♥❝ ✭✮ ; obj ❵✐♥❝ ✭✮ ; 4 ❞❡❢ extobj = seal ( . . . ) ✐♥ 5 extobj ❵❞❜❧ ✭✮ ; extobj ❵✐♥❝ ✭✮

Resealing Objects 1 . . . 2 ❞❡❢ obj = seal ( . . . ) ✐♥ 3 obj ❵✐♥❝ ✭✮ ; obj ❵✐♥❝ ✭✮ ; 4 ❞❡❢ extobj = seal ( . . . ) ✐♥ 5 extobj ❵❞❜❧ ✭✮ ; extobj ❵✐♥❝ ✭✮ ❵✐♥❝ ✭✮

Resealing Objects 1 . . . 2 ❞❡❢ obj = seal ( . . . ) ✐♥ 3 obj ❵✐♥❝ ✭✮ ; obj ❵✐♥❝ ✭✮ ; 4 ❞❡❢ extobj = seal ( . . . ) ✐♥ 5 extobj ❵❞❜❧ ✭✮ ; extobj ❵✐♥❝ ✭✮ ❵s❡❧❢ extobj & ❵✐♥❝ ✭✮

Resealing Objects 1 . . . 2 ❞❡❢ obj = seal ( . . . ) ✐♥ 3 obj ❵✐♥❝ ✭✮ ; obj ❵✐♥❝ ✭✮ ; 4 ❞❡❢ extobj = seal ( . . . ) ✐♥ 5 extobj ❵❞❜❧ ✭✮ ; extobj ❵✐♥❝ ✭✮ ❵s❡❧❢ obj & ❵s❡❧❢ extobj & ❵✐♥❝ ✭✮

Resealing Objects 1 . . . 2 ❞❡❢ obj = seal ( . . . ) ✐♥ 3 obj ❵✐♥❝ ✭✮ ; obj ❵✐♥❝ ✭✮ ; 4 ❞❡❢ extobj = seal ( . . . ) ✐♥ 5 extobj ❵❞❜❧ ✭✮ ; extobj ❵✐♥❝ ✭✮ ❵s❡❧❢ obj & ❵s❡❧❢ extobj & ❵✐♥❝ ✭✮

Other Features 1 ❞❡❢ point = seal ( ❵① 0 & ❵② 0 & ( ❵❧✶ _ & ❵s❡❧❢ s❡❧❢ -> 2 s❡❧❢ . ① + s❡❧❢ . ② )) ✐♥ 3 4 ❞❡❢ mixin = ( ❵♥❡❛r❩❡r♦ _ & ❵s❡❧❢ s❡❧❢ -> ( s❡❧❢ ❵❧✶ ✭✮ ) <= 4) ✐♥ 5 6 ❞❡❢ mixedPoint = seal (point & mixin) ✐♥ 7 mixedPoint ❵♥❡❛r❩❡r♦ ✭✮ Mixins

Other Features 1 ❞❡❢ point = . . . ✐♥ 2 ❞❡❢ mixin = (( ❵♥❡❛r❩❡r♦ _ & ❵s❡❧❢ s❡❧❢ -> ( s❡❧❢ ❵❧✶ ✭✮ ) <= 4)) ✐♥ 3 4 ❞❡❢ mixedPoint = seal (point & mixin) ✐♥ 5 mixedPoint ❵♥❡❛r❩❡r♦ ✭✮ Mixins Higher-order object extension

Other Features 1 ❞❡❢ obj = seal ( ❵① 0 & ( ❵✐♥❝ _ & ❵s❡❧❢ s❡❧❢ -> 2 s❡❧❢ . ① = s❡❧❢ . ① + 1 ✐♥ s❡❧❢ . ① )) ✐♥ 3 4 ❞❡❢ obj2 = seal ( (obj &. ❵① ) & ❵② 0 & 5 ( ❵✐♥❝ _ & ❵s❡❧❢ s❡❧❢ -> 6 s❡❧❢ . ② = s❡❧❢ . ② + s❡❧❢ . ① ✐♥ s❡❧❢ . ② )) ✐♥ 7 8 . . . Mixins Higher-order object extension Data sharing

Other Features 1 ❞❡❢ obj = seal ( ❵① 0 & 2 ( ❵✐♥❝ n: ✐♥t & ❵s❡❧❢ s❡❧❢ -> 3 s❡❧❢ . ① = s❡❧❢ . ① + n ✐♥ s❡❧❢ . ① ) & 4 ( ❵✐♥❝ n: ✉♥✐t & ❵s❡❧❢ s❡❧❢ -> 5 s❡❧❢ ❵✐♥❝ 1) ✐♥ 6 7 obj ( ❵✐♥❝ ✭✮ ); obj ( ❵✐♥❝ 4) Mixins Higher-order object extension Data sharing Overloading

Other Features etc. Mixins Higher-order object extension Data sharing Overloading Classes, inheritance, etc.

Type Inference

Type Inference Subtype constraint system

Type Inference Subtype constraint system Assign each subexpression a type variable

Type Inference Subtype constraint system Assign each subexpression a type variable Derive initial constraint set over expression

Type Inference Subtype constraint system Assign each subexpression a type variable Derive initial constraint set over expression Perform knowledge closure on constraints

Type Inference Subtype constraint system Assign each subexpression a type variable Derive initial constraint set over expression Perform knowledge closure on constraints Check resulting closure for consistency

Type Inference Subtype constraint system Assign each subexpression a type variable Derive initial constraint set over expression Perform knowledge closure on constraints Check resulting closure for consistency Soundness is proven over inference system

Constraint Types int ∪ unit

Constraint Types int ∪ unit � α \{ int < : α, unit < : α }