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(g1(x), h0())

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. class table subtype query type checker Y/N/? Turing machine input tape

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

applies to Java!

eof