Ordinary higher-order types,
such as ‘pred(T1, T2)’ and ‘func(T1, T2) = T’,
represent only pure predicates or pure functions.
But for each ordinary higher-order type Foo,
there are two corresponding types
‘semipure Foo’ and ‘impure Foo’.
These types can be used for higher-order code
that needs to manipulate impure or semipure procedures.
For example the type ‘impure func(int) = int’
represents impure functions from int to int.
There are no implicit conversions and no subtyping relationship between ordinary higher-order types and the corresponding impure or semipure higher-order types. However, a value of an ordinary higher-order type can be explicitly “converted” to a value of an impure (or semipure) higher-order type by wrapping it in an impure (or semipure) lambda expression that just calls the pure higher-order term.