hello, type systems! - introduction to featherweight java
TRANSCRIPT
Hello, Type Systems!Introduction to Featherweight Java
Cheshire Cat (@y_taka_23)Shibuya Java #12 (Aug. 1, 2015)
Who Am I?
● HN: Cheshire Cat● Twitter: @y_taka_23● GitHub: y-taka-23● Favorites
○ Formal methods○ Functional programming
In the Era of Java 1.4
The following is compilable, but ...
public static void main(String[] args) {
List list = new ArrayList();
list.add(23);
String str = (String) list.get(0);
}
In the Era of Java 1.4
Implicite upcast from int to Object
public static void main(String[] args) {
List list = new ArrayList();
list.add(23);
String str = (String) list.get(0);
}
In the Era of Java 1.4
Downcast from Object to String
public static void main(String[] args) {
List list = new ArrayList();
list.add(23);
String str = (String) list.get(0);
}
In the Era of Java 1.4
Run-time exception!!
public static void main(String[] args) {
List list = new ArrayList();
list.add(23);
String str = (String) list.get(0);
}
What is the “Type Safety”?
Featherweight Java (FJ)
● Introduced by IGARASHI et al. (2002)● Formalized & minimalized model● Many features are omitted, e.g.
○ Assignment○ Interfaces○ Exceptions
● “Functional” fragment of Java
Three Points to Understand FJ
1. Expressions: What is the “programs”?
2. Typing: What is the “type check”?
3. Reduction: What is the “execution”?
Expressions
● Variables
● Constructors
● Field accesses
● Method invocations
● Casts
x1, x2, ...
new C(e1, ..., en)
e.f
e.m(x1, ..., xn)
(C)e
Typing Rules
Example: Rule for field accesses
Gamma |- e0 : C0
fields(C0) = C1 f1, ..., Cn fn
--------------------------------
Gamma |- e0.fi : Ci
Typing Rules
Premise
Gamma |- e0 : C0
fields(C0) = C1 f1, ..., Cn fn
--------------------------------
Gamma |- e0.fi : Ci
Typing Rules
Conclusion
Gamma |- e0 : C0
fields(C0) = C1 f1, ..., Cn fn
--------------------------------
Gamma |- e0.fi : Ci
Typing Rules
Type env: Map from variable names to types
Gamma |- e0 : C0
fields(C0) = C1 f1, ..., Cn fn
--------------------------------
Gamma |- e0.fi : Ci
Typing Rules
If e0 has type C0 under Gamma,
Gamma |- e0 : C0
fields(C0) = C1 f1, ..., Cn fn
--------------------------------
Gamma |- e0.fi : Ci
Typing Rules
and fields of class C0 are
Gamma |- e0 : C0
fields(C0) = C1 f1, ..., Cn fn
--------------------------------
Gamma |- e0.fi : Ci
Typing Rules
f1, ..., fn of classes C1, ..., Cn,
Gamma |- e0 : C0
fields(C0) = C1 f1, ..., Cn fn
--------------------------------
Gamma |- e0.fi : Ci
Typing Rules
then e0.fi has type Ci under Gamma
Gamma |- e0 : C0
fields(C0) = C1 f1, ..., Cn fn
--------------------------------
Gamma |- e0.fi : Ci
Reduction Rules
Example: Rule for field accesses
fields(C) = C1 f1, ..., Cn fn
--------------------------------
(new C(e1, ..., en)).fi -> ei
Reduction Rules
Premise
fields(C) = C1 f1, ..., Cn fn
--------------------------------
(new C(e1, ..., en)).fi -> ei
Reduction Rules
Conclusion
fields(C) = C1 f1, ..., Cn fn
--------------------------------
(new C(e1, ..., en)).fi -> ei
Reduction Rules
If fields of class C are ...
fields(C) = C1 f1, ..., Cn fn
--------------------------------
(new C(e1, ..., en)).fi -> ei
Reduction Rules
f1, ..., fn of classes C1, ..., Cn,
fields(C) = C1 f1, ..., Cn fn
--------------------------------
(new C(e1, ..., en)).fi -> ei
Reduction Rules
then(new ...).fi reduces to ei
fields(C) = C1 f1, ..., Cn fn
--------------------------------
(new C(e1, ..., en)).fi -> ei
“Type Safety” in FJ
If an expression e satisfies:● e has a type without the two “impolite” rules● e -> ... -> e’● No expression e’’ such that e’ -> e’’
Then e’ must be “completely reduced”, i.e.● e consists of only constructors
Summary
● FJ is the “minimum” model of Java● “Type safety” is the consistency of
○ Typing rules○ Reduction rules
● We can discuss properties ofprogramming languages by formalization
Have a Nice Typing!
Presented byCheshire Cat (@y_taka_23)