# Class extensions

A class extension is an expression of the form C { | f_1 => e_1 … | f_n => e_n }, where C is a record, f_1, … f_n are its fields of types A_1, … A_n respectively, and e_1, … e_n are expressions such that e_i : A_i[e_1/f_1, … e_n/f_n]. Note that A_i cannot depend on any field except for f_1, … f_n. An expression of the form C e_1 … e_n is equivalent to C { | f_1 => e_1 … | f_n => e_n }, where f_1, … f_n is the list of not implemented fields of C in the order of their definition.

The expression C {} is equivalent to C. An expression of the form C { I } is a subtype of C’ { I’ } if and only if C is a subclass of C’ and I’ is a subset of I. The expression \new C { I } is an instance of type C { I }, which is a subtype C. Thus, you can use this expression to create an element of type C.

## New expression

The expression \new C { I } is correct only if all fields of C are implemented in C { I }, but the typechecker can infer some implementations from the expected type of the expression. For example, in the following code we do not have to implement field x in the \new expression explicitly since f expects an element of R 0, so the typechecker knows that x must be equal to 0.

```
\record R (x y : Nat)
\func f (r : R 0) => r.y
\func g => f (\new R { | y => 1 })
```

If c is an instance of a record C with fields f_1, … f_n, then the expression \new c is equivalent to \new C { | f_1 => c.f_1 … | f_n => c.f_n }. More generally, the expression \new c { | f_{i_1} => e_1 … | f_{i_k} => e_k } is equivalent to \new c in which c.f_{i_j} is replaced with e_j.