The purpose of eq is to represent type equalities that may not otherwise be known by the type checker (e.g. because they may depend on dynamic data).

A value of type (a, b) eq represents the fact that types a and b are equal.

If one has a value eq : (a, b) eq that proves types a and b are equal, one can use it to convert a value of type a to a value of type b by pattern matching on Equal:

      let cast (type a) (type b) (Equal : (a, b) Type.eq) (a : a) : b = a
    

At runtime, this function simply returns its second argument unchanged.