Java Generics Are Turing Complete Radu Grigore September 2017 - PowerPoint PPT Presentation

Java Generics Are Turing Complete Radu Grigore September 2017 Highlights

Why do we care?

. . . . . .

distinguished at ECOOP 2016

But . . . Java is messy!

FOOL 2007

Problem Input infinite directed graph two distinguished vertices t and t ′ Output Is there a finite path t � t ′ in the given graph?

Vertices: Types f ( g ( x ) , h ())

Vertices: Types f 2 ( g 1 ( x ) , h 0 ())

Vertices: Types f gxh

Vertices: Types x , y , ...are variables C , D , ...have arity 1 Z has arity 0 Example vertex/type: CDCCDEZ s , t , ...are meta-variables, ranging over types

Arcs: Inheritance Rules the inheritance rule Cx < :: t ( x ) means that, for all ground types s , there is an arc Cs → t ( s )

Arcs: Inheritance Rules the inheritance rule Cx < :: t ( x ) means that, for all ground types s , there is an arc Cs → t ( s ) class table � set of inheritance rules

Arcs: Contravariance if s � t then Ct → Cs

Theorem It is undecidable whether t � t ′ according to a given unambiguous class table.

Theorem It is undecidable whether t � t ′ according to a given unambiguous class table. Turing machine input tape subtype query class table type checker Y/N/?

Theorem It is undecidable whether t � t ′ according to a given unambiguous class table. applies to Java! Turing machine input tape subtype query class table type checker Y/N/?

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