TypeSystem.txt

Type System

0.1 Basic Types
	There are eight primitive types: byte, short, int, long, float, double, char, boolean. Additionally, every class represents a type.
	
	assignment Rules:
		- A is assignable to C if A is a subclass of C.
	
0.2 Intersection Types
	An intersection type is a type which represents the intersection of multiple types. For example, intersect<X, Y> represents anything that is instanceof both X and Y.
	
	assignment Rules:
		- A is assignable to intersect<X1, X2... Xn> if A is assignable to all X.
		- intersect<X1, X2... Xn> is assignable to A if any X is assignable to A.
		
0.3 Union Types
	A union type is a type which represents the union of multiple types. For example, union<X, Y> represents a value which is either of type X or of type Y.
	
	assignment Rules:
		- A is assignable to union<X1, X2... Xn> if A is instanceof any X.
		- union<X1, X2... Xn> is an assignable to A if all X are assignable to A.
		
0.4 Function Types
	A function type is a type which represents a function. It contains a list of argument types and a single return type. For example, Function<X : Y> represents a function which has one parameter which is instanceof X, and returns something which is instanceof Y.
	
	assignment Rules:
		- A is assignable to function<X1, X2... Xn : R> if A is a function type, A has the same number of parametes, all parametes of A are instanceof the corresponding X, and the return value of A is instanceof R.
		- function<X1, X2... xn : R> is assignable to A if A is a function type, A has the same number of parameter, all X are instanceof the corresponding A parameter, and R is instanceof the return value of A.
		
0.5 The Null Type
	There is a Null type, Null.
	
	assignment Rules:
		- A is assignable to Null if A is the null value
		
	a note:
		- Nullabe types can thus be implemented as union<Null, A>