We can also define these properties for data types that we do not control, for example providing a custom way of hashing a data type implemented by someone else

The distinction in computer programming between classes and objects is related, though in this context, "class" sometimes refers to a set of objects (with class-level attribute or operations) rather than a description of an object in the set, as "type" would.

a class is an implementation‍—‌a concrete data structure and collection of subroutines‍—‌while a type is an interface

“There is very little incentive for Microsoft to make a significant change to features that are used extremely widely by the rest of the massive community of Excel users.”

Now you can easily spot them! The rule is: if you see a Result it means that this function can throw an exception. And you even know its type in advance.

Make your functions return something meaningful, typed, and safe!

To emphasize how Just acts on the underlying value by wrapping it, it can be redefined as a function too, called eta for now

Informative data about objects that are considered prototypes for the role. Base concept is similar to type, but without inheritance of limitations and properties. Base concepts are designed as a substitute for inheritance for external concepts. A base concept is like a related concept except that the base concept is almost identical to the role definition.

In 1980 Joachim Lambek showed that the types and programs used in computerscience form a specific kind of category. This provided a new semantics for talking aboutprograms, allowing people to investigate how programs combine and compose to createother programs, without caring about the specifics of implementation. Eugenio Moggibrought the category theoretic notion of monads into computer science to encapsulateideas that up to that point were considered outside the realm of such theory.