S u p p o r t i n g S u p p o r t i n g C o v - - PowerPoint PPT Presentation

SLIDE 1

S u p p

• r

t i n g S u p p

• r

t i n g C

• v

a r i a n t R e t u r n T y p e s C

• v

a r i a n t R e t u r n T y p e s & G e n e r i c s & G e n e r i c s i n i n T y p e R e l a x e d We a v i n g T y p e R e l a x e d We a v i n g

T

• mo

y u k i A

• t

a n i T

• mo

y u k i A

• t

a n i J a p a n A d v a n c e d I n s t i t u t e

• f

S c i e n c e a n d T e c h n

• l
• g

y J a p a n A d v a n c e d I n s t i t u t e

• f

S c i e n c e a n d T e c h n

• l
• g

y J

• i

n t w

• r

k w / J

• i

n t w

• r

k w / H i d e h i k

• Ma

s u h a r a & Ma n a b u T

• y

a ma H i d e h i k

• Ma

s u h a r a & Ma n a b u T

• y

a ma U n i v e r s i t y

• f

T

• k

y

• U

n i v e r s i t y

• f

T

• k

y

SLIDE 2

B a c k g r

• u

n d : B a c k g r

• u

n d : A s p e c t J , R e l a x A J a n d G e n t l e A J A s p e c t J , R e l a x A J a n d G e n t l e A J

+ T y p e r e l a x e d w e a v i n g

[ Ma s u h a r a 1 ]

+ S u p p

• r

t f

• r

* G e n e r i c s * C

• v

a r i a n t r e t u r n t y p e s * proceed > mu l t i p l e r e t u r n t y p e s > a r g u me n t t y p e r e l a x a t i

• n

G e n t l e A J R e l a x A J

[ Ma s u h a r a 1 ]

A s p e c t J

SLIDE 3

B a c k g r

• u

n d : B a c k g r

• u

n d : A s p e c t J , R e l a x A J a n d G e n t l e A J A s p e c t J , R e l a x A J a n d G e n t l e A J

+ T y p e r e l a x e d w e a v i n g

[ Ma s u h a r a 1 ]

+ S u p p

• r

t f

• r

* G e n e r i c s * C

• v

a r i a n t r e t u r n t y p e s

* proceed > mu l t i p l e r e t u r n t y p e s > a r g u me n t t y p e r e l a x a t i

• n

G e n t l e A J R e l a x A J

[ Ma s u h a r a 1 ]

A s p e c t J

SLIDE 4

T y p e r e l a x e d w e a v i n g ( T R W) T y p e r e l a x e d w e a v i n g ( T R W)

[ Ma s u h a r a 1 ] [ Ma s u h a r a 1 ]

: : D i f f e r e n c e f r

• m

A s p e c t J ' s w e a v i n g D i f f e r e n c e f r

• m

A s p e c t J ' s w e a v i n g

Int around():call(BigInt *.*(...)){...} Int around():call(Object *.*(...)){...}

• S

u p p

• s

e w e h a v e

• A

s p e c t J a n d R e l a x A J ( = T R W) a c c e p t

• R

e l a x A J c

• n

d i t i

• n

a l l y a c c e p t b u t A s p e c t J r e j e c t s

class Object{...} class BigInt extends Object{...} class Int extends Object{...} s u p e r t y p e s i b l i n g

SLIDE 5

T y p e r e l a x e d w e a v i n g T y p e r e l a x e d w e a v i n g

[ Ma s u h a r a 1 ] [ Ma s u h a r a 1 ]

• B

y t e c

• d

e

• l

e v e l w e a v i n g

• T

y p i n g p r i n c i p l e f

• r

w e a v i n g a d v i c e :

– jp:

a j

• i

n p

• i

n t

– adv:

a p i e c e

• f

a r

• u

n d a d v i c e a p p l i e d t

• jp

P r i n c i p l e .

T h e r e t u r n t y p e

• f

adv mu s t b e c

• n

s i s t e n t w i t h t h e

• p

e r a t i

• n

s t h a t u s e t h e r e t u r n v a l u e f r

• m

jp.

a me t h

• d

T around(): p(){...} adv jp a p p l i e d u s e a s T1 u s e a s T2 u s e a s T3 T mu s t b e a s u b t y p e

• f

T1, T2 a n d T3

SLIDE 6

T y p e r e l a x e d w e a v i n g : T y p e r e l a x e d w e a v i n g :

• p

e r a t i

• n

s t h a t

• p

e r a t i

• n

s t h a t u s e u s e t h e r e t u r n v a l u e t h e r e t u r n v a l u e

• I

n v

• k

i n g a me t h

• d

:

• .m(a)

– R

e c e i v e r : u s e t y p e i s t h e mo s t g e n e r a l t y p e t h a t d e f i n e s m

– A

r g u me n t : u s e t y p e i s t h e t y p e a p p e a r i n t h e s i g n a t u r e

• R

e t u r n n i n g f r

• m

t h e me t h

• d

: return v

• A

c c e s s i n g a f i e l d :

• .

f = v

• T

h r

• w

i n g a n e x c e p t i

• n

: throw v

• A

c c e s s i n g a n a r r a y : a[i]=v

SLIDE 7

E x a m p l e

• f

R e l a x A J a d v i c e : E x a m p l e

• f

R e l a x A J a d v i c e : R e p l a c i n g B i g I n t S t r e a m w / I n t S t r e a m R e p l a c i n g B i g I n t S t r e a m w / I n t S t r e a m

interface Stream{ Object get(); } class BigIntStream implements Stream{ Object get(){ /*return a BigInt*/ } } class IntStream implements Stream{ Object get(){ /*return an Int*/ } } bs = new BigIntStream();

• = bs.get();

s = o.toString(); /* bs is no longer used*/ IntStream around(): call(BigIntStream.new()){ return new IntStream(); } C h e c k IntStream i s c

• n

s i s t e n t w i t h Stream.get() invokevirtual BigIntStream.get() invokeinterface Stream.get()

→

S i b l i n g

• f

BigIntStream A c c e p t e d t r u e

SLIDE 8

T y p e r e l a x e d w e a v i n g T y p e r e l a x e d w e a v i n g

[ Ma s u h a r a 1 ] [ Ma s u h a r a 1 ]

• B

y t e c

• d

e w e a v i n g me c h a n i s m

• T

y p i n g r u l e f

• r

a r

• u

n d a d v i c e :

– jp:

a j

• i

n p

• i

n t

– adv:

a p i e c e

• f

a r

• u

n d a d v i c e a p p l i e d t

• jp
• F
• r

ma l mo d e l : b a s e d

• n

F J

[ I g a r a s h i 1 ]

w / u n i

• n

t y p e

• S

u p p

• r

t f

• r

J a v a 5 f e a t u r e s i s n

• t

c

• n

s i d e r e d

– G

e n e r i c s a n d c

• v

a r i a n t r e t u r n t y p e s

P r i n c i p l e .

T h e r e t u r n t y p e

• f

adv mu s t b e c

• n

s i s t e n t w i t h t h e

• p

e r a t i

• n

s t h a t u s e t h e r e t u r n v a l u e f r

• m

jp.

SLIDE 9

G

• f
• r

w a r d i n t

• J

a v a 5 : G

• f
• r

w a r d i n t

• J

a v a 5 : w h a t a r e n e e d e d ? w h a t a r e n e e d e d ?

• S

u p p

• r

t f

• r

c

• v

a r i a n t r e t u r n t y p e s

– C

h a n g i n g t h e r e l a x a t i

• n

r u l e f

• r

s i g n a t u r e s

• f

me t h

• d

i n v

• c

a t i

• n

s

• S

u p p

• r

t f

• r

g e n e r i c s

– I

n f e r r i n g e r a s e d t y p e s

We a r e a t b y t e c

• d

e

• l

e v e l !

SLIDE 10

E x a m p l e

• f

R e l a x A J a d v i c e : E x a m p l e

• f

R e l a x A J a d v i c e : R e p l a c i n g B i g I n t S t r e a m w / I n t S t r e a m R e p l a c i n g B i g I n t S t r e a m w / I n t S t r e a m

interface Stream{ Object get(); } class BigIntStream implements Stream{ Object get(){ /*return a BigInt*/ } } class IntStream implements Stream{ Object get(){ /*return an Int*/ } } bs = new BigIntStream();

• = bs.get();

s = o.toString(); /* bs is no longer used*/ IntStream around(): call(BigIntStream.new()){ return new IntStream(); } C h e c k IntStream i s c

• n

s i s t e n t w i t h Stream.get() invokevirtual BigIntStream.get() invokeinterface Stream.get() t r u e

SLIDE 11

G

• f
• r

w a r d i n t

• J

a v a 5 : G

• f
• r

w a r d i n t

• J

a v a 5 : w h a t a r e n e e d e d ? w h a t a r e n e e d e d ?

• S

u p p

• r

t f

• r

c

• v

a r i a n t r e t u r n t y p e s

– C

h a n g i n g t h e r e l a x a t i

• n

r u l e f

• r

s i g n a t u r e s

• f

me t h

• d

i n v

• c

a t i

• n

s

• S

u p p

• r

t f

• r

g e n e r i c s

– I

n f e r r i n g e r a s e d t y p e s

SLIDE 12

G

• f
• r

w a r d i n t

• J

a v a 5 : G

• f
• r

w a r d i n t

• J

a v a 5 : w h a t a r e n e e d e d ? w h a t a r e n e e d e d ?

• S

u p p

• r

t f

• r

c

• v

a r i a n t r e t u r n t y p e s

– C

h a n g i n g t h e r e l a x a t i

• n

r u l e f

• r

s i g n a t u r e s

• f

me t h

• d

i n v

• c

a t i

• n

s

– C

h e c k i n g c

• n

s i s t e n c y

• f

v a l u e s d e r i v e d f r

• m

t h e r e t u r n v a l u e f r

• m

t h e j

• i

n p

• i

n t

• S

u p p

• r

t f

• r

g e n e r i c s

– I

n f e r r i n g e r a s e d t y p e s

– C

h e c k i n g c

• n

s i s t e n c y

• f

v a l u e s d e r i v e d f r

• m

t h e r e t u r n v a l u e f r

• m

t h e j

• i

n p

• i

n t

D e r i v e d v a l u e s : L e t v a n d u a r e v a l u e s . v i s d e r i v e d f r

• m

u i f v i s t h e r e t u r n v a l u e f r

• m

x.m w h e r e x i s u

• r

s

• me

d e r i v e d v a l u e f r

• m

u

SLIDE 13

S i m p l e s u p p

• r

t f

• r

S i m p l e s u p p

• r

t f

• r

c

• v

a r i a n t r e t u r n t y p e s c

• v

a r i a n t r e t u r n t y p e s g

• e

s w r

• n

g g

• e

s w r

• n

g

class Int{ Object toString(){...} } class BigInt{ Object toString(){...} BigInt abs(){...} } interface Stream{ Object get(); } class BigIntStream implements Stream{ BigInt get(){...} } class IntStream implements Stream{ Int get(){...} } bs = new BigIntStream();

• = bs.get();

s = o.abs(); /* no bs, o and s*/ IntStream around(): call(BigIntStream.new()){ return new IntStream(); } C h e c k IntStream i s c

• n

s i s t e n t w i t h Stream.get() BigInt BigIntStream.get() Object Stream.get() Not defined in Object

SLIDE 14

S i m p l e s u p p

• r

t f

• r

S i m p l e s u p p

• r

t f

• r

c

• v

a r i a n t r e t u r n t y p e s c

• v

a r i a n t r e t u r n t y p e s g

• e

s w r

• n

g g

• e

s w r

• n

g

class Int{ Object toString(){...} } class BigInt{ Object toString(){...} BigInt abs(){...} } interface Stream{ Object get(); } class BigIntStream implements Stream{ BigInt get(){...} } class IntStream implements Stream{ Int get(){...} } bs = new IntStream();

• = bs.get();

s = o.abs(); /* no bs, o and s*/ IntStream around(): call(BigIntStream.new()){ return new IntStream(); }

V e r i f y E r r

• r

Not defined in Object

SLIDE 15

S i m p l e s u p p

• r

t f

• r

S i m p l e s u p p

• r

t f

• r

c

• v

a r i a n t r e t u r n t y p e s c

• v

a r i a n t r e t u r n t y p e s g

• e

s w r

• n

g g

• e

s w r

• n

g

class Int{ Object toString(){...} } class BigInt{ Object toString(){...} BigInt abs(){...} } interface Stream{ Object get(); } class BigIntStream implements Stream{ BigInt get(){...} } class IntStream implements Stream{ Int get(){...} } bs = new IntStream();

• = bs.get();

s = o.abs(); /* no bs, o and s*/ IntStream around(): call(BigIntStream.new()){ return new IntStream(); } Object Stream.get() BigInt BigInt.abs()

V e r i f y E r r

• r

Not defined in Object O b j e c t i s u s e d a s B i g I n t = > E r r

• r

!

SLIDE 16

S i m p l e s u p p

• r

t f

• r

S i m p l e s u p p

• r

t f

• r

g e n e r i c s g

• e

s w r

• n

g g e n e r i c s g

• e

s w r

• n

g

class Int{ Object toString(){...} } class BigInt{ Object toString(){...} BigInt abs(){...} } class Stream<X>{ X val; Stream(X v){val=v;} X get(){...} } bs=new Stream<BigInt>(...);

• =bs.get();

s=o.abs(); /* no bs, o and s */ Stream<Int> around(): call(Stream<BigInt>.new(*)){ return new Stream<Int>(...); } C h e c k Stream<Int> i s c

• n

s i s t e n t w i t h Stream<?Obj>.get() BigInt Stream<BigInt>.get() ?Obj Stream<?Obj>.get() ?Obj=? extends Object

SLIDE 17

S i m p l e s u p p

• r

t f

• r

S i m p l e s u p p

• r

t f

• r

g e n e r i c s g

• e

s w r

• n

g g e n e r i c s g

• e

s w r

• n

g

class Int{ Object toString(){...} } class BigInt{ Object toString(){...} BigInt abs(){...} } class Stream<X>{ X val; Stream(X v){val=v;} X get(){...} } bs=new Stream<Int>(...);

• =bs.get();

s=o.abs(); /* no bs, o and s */ Stream<Int> around(): call(Stream<BigInt>.new(*)){ return new Stream<Int>(...); } ?Obj=? extends Object

Wr

• n

g c

• d

e

SLIDE 18

S i m p l e s u p p

• r

t f

• r

S i m p l e s u p p

• r

t f

• r

g e n e r i c s g

• e

s w r

• n

g g e n e r i c s g

• e

s w r

• n

g

class Int{ Object toString(){...} } class BigInt{ Object toString(){...} BigInt abs(){...} } class Stream<X>{ X val; Stream(X v){val=v;} X get(){...} } bs=new Stream<Int>(...);

• =bs.get();

s=o.abs(); /* no bs, o and s */ ?Obj Stream<?Obj>.get() ?Obj=? extends Object BigInt BigInt.abs() ? O b j i s u s e d a s B i g I n t = > E r r

• r

Stream<Int> around(): call(Stream<BigInt>.new(*)){ return new Stream<Int>(...); }

Wr

• n

g c

• d

e

SLIDE 19

O u r s

• l

u t i

• n

: c h e c k i n g c

• n

s i s t e n c y O u r s

• l

u t i

• n

: c h e c k i n g c

• n

s i s t e n c y

• f
• f

d e r i v e d d e r i v e d v a l u e s v a l u e s

• Mo

d i f i e d t y p i n g p r i n c i p l e ( T R Wc ) : L e t adv b e a d v i c e a n d jp b e a j

• i

n p

• i

n t . adv c a n b e a p p l i e d t

• jp

i f t h e r e t u r n t y p e

• f

adv i s c

• n

s i s t e n t w /

• p

e r a t i

• n

s

– u

s i n g retjp

– u

s i n g t h e d e r i v e d v a l u e s f r

• m

retjp

t h e r e t u r n v a l u e f r

• m

jp D e r i v e d v a l u e s : L e t v a n d u a r e v a l u e s . v i s d e r i v e d f r

• m

u i f v i s t h e r e t u r n v a l u e f r

• m

x.m w h e r e x i s u

• r

s

• me

d e r i v e d v a l u e f r

• m

u

SLIDE 20

E x a m p l e : c h e c k i n g E x a m p l e : c h e c k i n g c

• n

s i s t e n c y

• f

c

• n

s i s t e n c y

• f

d e r i v e d v a l u e s d e r i v e d v a l u e s

class Int{ Object toString(){...} } class BigInt{ Object toString(){...} BigInt abs(){...} } interface Stream{ Object get(); } class BigIntStream implements Stream{ BigInt get(){...} } class IntStream implements Stream{ Int get(){...} } bs = new BigIntStream();

• = bs.get();

s = o.abs(); /* no bs, o and s */ IntStream around(): call(BigIntStream.new()){ return new IntStream(); } C h e c k * IntStream<:Stream * Object<:BigInt BigInt BigIntStream.get() Object Stream.get() BigInt BigInt.abs() = > S u c c e s s f u l l y r e j e c t !

SLIDE 21

E x a m p l e : c h e c k i n g E x a m p l e : c h e c k i n g c

• n

s i s t e n c y

• f

c

• n

s i s t e n c y

• f

d e r i v e d v a l u e s d e r i v e d v a l u e s

class Int{ Object toString(){...} } class BigInt{ Object toString(){...} BigInt abs(){...} } interface Stream{ Object get(); } class BigIntStream implements Stream{ BigInt get(){...} } class IntStream implements Stream{ Int get(){...} } bs = new BigIntStream();

• = bs.get();

s = o.toString(); /* no bs, o and s */ IntStream around(): call(BigIntStream.new()){ return new IntStream(); } C h e c k * IntStream <:Stream * Object<:Object BigInt BigIntStream.get() Object Stream.get() Objet BigInt.toString() = > S u c c e s s f u l l y a c c e p t ! Object Object.toString()

SLIDE 22

F

• r

m a l i z a t i

• n

:

• v

e r v i e w F

• r

m a l i z a t i

• n

:

• v

e r v i e w

• F

e a t h e r w e i g h t J a v a f

• r

R e l a x a t i

• n

w / c

• v

a r i a n t r e t u r n t y p e s ( F J R c )

– S

i mp l e e x t e n s i

• n

t

• F

e a t h e r w e i g h t J a v a f

• r

R e l a x a t i

• n

( F J R )

[ Ma s u h a r a 1 ]

• C

h e c k i n g c

• n

s i s t e n c y : c

• n

s t r a i n t s a t i s f a c t i

• n

– G

e n e r a t e s u b t y p i n g c

• n

s t r a i n t s f

• r

e a c h F J R c e x p r e s s i

• n

– I

f a s

• l

u t i

• n

i s f

• u

n d , t h e w

• v

e n c

• d

e i s ( h

• p

e f u l l y ) t y p e s a f e – p r

• f

: f u t u r e w

• r

k

SLIDE 23

F e a t h e r w e i g h t J a v a f

• r

R e l a x a t i

• n

w / F e a t h e r w e i g h t J a v a f

• r

R e l a x a t i

• n

w / C

• v

a r i a n t R e t u r n T y p e s ( F J R c ) C

• v

a r i a n t R e t u r n T y p e s ( F J R c )

• S

y n t a x : s a me t

• F

J R

• T

y p i n g r u l e s s u p p

• r

t c

• v

a r i a n t r e t u r n t y p e s

– P

r e d i c a t e

• verride(m,C,T T0)

→

– C

l a s s t y p i n g r u l e

CL ::= class C extends C implements I { M } M ::= T m(T x){ return e; } IF ::= interface I { N } N ::= T m (T x); e ::= x | e.m(e) | new C() | let x = e in e | (?e:e) T ::= C | I U ::= T | U U ∪ n

• n
• d

e t e r mi n i s t i c c h

• i

c e w

• v

e n a d v i c e

SLIDE 24

C

• n

s t r a i n t g e n e r a t i

• n

:

• v

e r v i e w C

• n

s t r a i n t g e n e r a t i

• n

:

• v

e r v i e w

• C
• n

s t r a i n t g e n e r a t i

• n

a l g

• r

i t h m c ::(G,e) (P,U) →

– T

y p i n g e n v i r

• n

me n t G ::= x:T,G | .

– E

x p r e s s i

• n

e

– S

u b t y p i n g c

• n

s t r a i n t P={p} w h e r e p ::= S <: S | retT<:(m,S,S) S ::= C | I | X

– T

y p e U ::= S | U

∪ U

• S
• l

u t i

• n

t

• a

s u b t y p i n g c

• n

s t r a i n t P: s u b s t i t u t i

• n

[S/X] s . t . f

• r

a l l p∈P. [S/X]p

t h e r e t u r n t y p e

• f

S 1 . m i s a s u b t y p e

• f

S 2

P1∪P2 P1∪P2

v a r i a b l e

SLIDE 25

C

• n

s t r a i n t g e n e r a t i

• n

: C

• n

s t r a i n t g e n e r a t i

• n

: i n t e r e s t i n g c a s e i n t e r e s t i n g c a s e

• Me

t h

• d

i n v

• c

a t i

• n

e . m( e )

c(G,e0.m(e1,...,en))= let (P0,U0) = c(G,e0) in let (P,U) = c(G,e) in let T T = mtype(m,typeOf(e →

0)) in

let V = mdeftypes(m,typeOf(e ∪

0)) in

(P0∪ P { ∪ U<:T} {U ∪

0<:X1,X1<:V,retT<:(m,X1,X2)}

,X2) n

• n
• r

e l a x e d t y p e

• f

e0 l e a s t u p p e r b

• u

n d

• f

t h e t y p e s t h a t d e f i n e m r e c e i v e r ' s t y p e c a n b e r e l a x e d c h e c k i n g d e r i v e d v a l u e s

SLIDE 26

E x a m p l e : c

• n

t r a d i c t i

• n

s f

• u

n d

• n

E x a m p l e : c

• n

t r a d i c t i

• n

s f

• u

n d

• n

t y p e

• u

n s a f e c

• d

e t y p e

• u

n s a f e c

• d

e

Object m(){return let s = (?new BigIntStrm() :x) in let i = s.get() in let iabs = i.abs() in new Object(); }

SLIDE 27

E x a m p l e : c

• n

t r a d i c t i

• n

s f

• u

n d

• n

E x a m p l e : c

• n

t r a d i c t i

• n

s f

• u

n d

• n

t y p e

• u

n s a f e c

• d

e t y p e

• u

n s a f e c

• d

e

Object m(){return let s = (?new BigIntStrm() :x) in let i = s.get() in let iabs = i.abs() in new Object(); } c(x:IntStream,BigIntStrm)= (x:IntStream,BigIntStrm) c(x:IntStream,IntStrm)= (x:IntStream,IntStrm) c(x:IntStream,(?BigIntStrm:x))= ({} {} ∪ , BigIntStrm IntStrm ∪ ) {}

SLIDE 28

E x a m p l e : c

• n

t r a d i c t i

• n

s f

• u

n d

• n

E x a m p l e : c

• n

t r a d i c t i

• n

s f

• u

n d

• n

t y p e

• u

n s a f e c

• d

e t y p e

• u

n s a f e c

• d

e

Object m(){return let s = (?new BigIntStrm() :x) in let i = s.get() in let iabs = i.abs() in new Object(); } c((x:IntStrm,s:BigIntStrm IntStrm) ∪ ,s)= ({},BigIntStrm IntStrm ∪ ) mtype(get,typeOf(s))=() BigInt → ∪ mdeftypes(get,BigIntStrm)=Strm c((x:IntStrm,s:BigIntStrm IntStrm) ∪ ,s.get())= ({BigIntStrm IntStrm ∪ <:X1,X1<:Strm,retT<:(get,X1,X2} ,X2) {} {BigIntStrm IntStrm ∪ <:X1, X1<:Strm,retT<:(get,X1,X2)}

SLIDE 29

E x a m p l e : c

• n

t r a d i c t i

• n

s f

• u

n d

• n

E x a m p l e : c

• n

t r a d i c t i

• n

s f

• u

n d

• n

t y p e

• u

n s a f e c

• d

e t y p e

• u

n s a f e c

• d

e

Object m(){return let s = (?new BigIntStrm() :x) in let i = s.get() in let iabs = i.abs() in new Object(); } c((x:IntStrm,s:BigIntStrm IntStrm,i: ∪ X2),i)= ({},X2) mtype(abs,typeOf(s))=() BigInt → ∪ mdeftypes(abs,BigInt)=BigInt c((x:IntStrm,s:BigIntStrm IntStrm,i: ∪ X2),i.abs())= ({X2<:X3,X3<:BigInt,retT<:(abs,X3,X4)} ,X4) {} {BigIntStrm IntStrm ∪ <:X1, X1<:Strm,retT<:(get,X1,X2)} {X2<:X3,X3<:BigInt, retT<:(abs,X3,X4)}

SLIDE 30

E x a m p l e : c

• n

t r a d i c t i

• n

s f

• u

n d

• n

E x a m p l e : c

• n

t r a d i c t i

• n

s f

• u

n d

• n

t y p e

• u

n s a f e c

• d

e t y p e

• u

n s a f e c

• d

e

Object m(){return let s = (?new BigIntStrm() :x) in let i = s.get() in let iabs = i.abs() in new Object(); } {} {BigIntStrm IntStrm ∪ <:X1, X1<:Strm,retT<:(get,X1,X2)} {X2<:X3,X3<:BigInt, retT<:(abs,X3,X4)} BigIntStrm IntStrm ∪ <:X1<:Strm => X1=Strm retT<:(get,X1,X2) = retT<:(get,Strm,X2) => X2=Object X2<:X3<:BigInt = Object<:X3<:BigInt => False

SLIDE 31

C

• n

c l u s i

• n

s a n d f u t u r e w

• r

k C

• n

c l u s i

• n

s a n d f u t u r e w

• r

k

• T

y p e r e l a x e d w e a v i n g w / c

• v

a r i a n t r e t u r n t y p e s ( a n d g e n e r i c s )

– C

h e c k i n g d e r i v e d v a l u e s i s n e c e s s a r y

• C
• n

s t r a i n t g e n e r a t i

• n

a l g

• r

i t h m f

• r

F J R c

– C

h a n g e s f r

• m

F J R : j u s t a b

• u

t r e t u r n t y p e s

• F

u t u r e w

• r

k

– P

r

• v

i n g t y p e s a f e t y

• f

F J R c a n d s

• u

n d n e s s

• f

t h e a l g

• r

i t h m

– I

mp l e me n t a t i

• n

SLIDE 32

E x a m p l e : c h e c k i n g E x a m p l e : c h e c k i n g c

• n

s i s t e n c y

• f

c

• n

s i s t e n c y

• f

d e r i v e d v a l u e s d e r i v e d v a l u e s

class Int{ Object toString(){...} } class BigInt{ Object toString(){...} BigInt abs(){...} } interface Stream{ Object get(); } class BigIntStream implements Stream{ BigInt get(){...} } class IntStream implements Stream{ Int get(){...} } bs = new BigIntStream();

• = bs.get();

s = o.abs(); /* no bs, o and s */ IntStream around(): call(BigIntStream.new()){ return new IntStream(); } C h e c k * IntStream<: BigIntStream * BigInt<:BigInt BigInt BigIntStream.get() BigInt BigInt.abs() = > S u c c e s s f u l l y r e j e c t !

SLIDE 33

E x a m p l e : c

• n

t r a d i c t i

• n

s f

• u

n d

• n

E x a m p l e : c

• n

t r a d i c t i

• n

s f

• u

n d

• n

t y p e

• s

a f e c

• d

e t y p e

• s

a f e c

• d

e

Object m(){return let s = (?new BigIntStrm() :x) in let i = s.get() in let t = i.toStr() in new Object(); } {} {BigIntStrm IntStrm ∪ <:X1, X1<:Strm,retT<:(get,X1,X2)} {X2<:X3,X3<:Object, retT<:(toStr,X3,X4)} BigIntStrm IntStrm ∪ <:X1<:Strm => X1=Strm retT<:(get,X1,X2) = retT<:(get,Strm,X2) => X2=Object X2<:X3<:Object = Object<:X3<:Object => X3=Object retT<:(toStr,X3,X4) = retT<:(toStr,Object,X4) => X4=Str