Day 7: Type Operators

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TypeOperators

Day 8: Recursive do

I understand the usefulness of the type operator GHC extension, but I don't like it. For value identifiers any operator not starting with a '' is treated the same way as identifiers starting with a lower case letter. This is how it used to be on the type level too. But with the latest version of theextension these operators now behave like upper case identifiers and can be used to name types. An ugly wart, IMO.This extension stems from Levent Erkök's PhD thesis Value Recursion in Monadic Computations . The motivation was to be able to describe circuits with feedback using monadic notation.

There's actually two way to get recursive do -notation. You can either use the rec keyword inside the do or you can use the keyword mdo instead of do . Why mdo , you ask? It should really be μdo , where μ is the recursion operator. But people at GHC HQ are scared of Unicode, so instead we got mdo .





Day 9: Nullary Type Classes

Once you have accepted multi-parameter type classes then nullary type classes are a natural consequence; zero is also a number, after all.

In 1994 I worked on the pH language when I visited MIT. The acronym pH stands for "parallel Haskell", which is what it is. It had some imperative features that were not in a monad. This was in 1994, and the ST monad was just being invented, so we were trying out other things. To keep track of what parts of the program used imperative features I used a nullary type class Imperative that tainted any code that used assignment et al. (As far as I know, this is the earliest use of a nullary type class.) When mixing imperative code and pure code it is important to not be too polymorphic. ML-like languages use the value restriction to accomplish this. Since Haskell's monomorphism restriction is essentially the same as the value restriction, having the Imperative type class neatly accomplished the value restriction for pH.





Day 10: Implicit Parameters

The implicit parameter started as an attempt to simplify Haskell overloading. Haskell overloading, when implemented by dictionary passing, really has two parts: first there is a way to implicitly pass dictionaries around, and second, dictionaries are constructed automatically by using the instance declarations as a logical inference system.

The implicit parameters do the automagic passing of parameters, and is thus half of what is needed for overloading. But they were never used for overloading, instead it was discovered that they can be made to behave like dynamic binding, but with static types. This is quite cool! Even if one doesn't like dynamic binding (I don't).



There idea is presented Erik Meijer et al's paper Implicit Parameters: Dynamic Scoping with Static Types. It's worth reading.





Day 11: Type Families

Type families grew out of the need to have type classes with associated types. The latter is not strictly necessary since it can be emulated with multi-parameter type classes, but it gives a much nicer notation in many cases. The same is true for type families; they can also be emulated by multi-parameter type classes. But MPTC gives a very logic programming style of doing type computation; whereas type families (which are just type functions that can pattern match on the arguments) is like functional programming.

Using closed type families adds some extra strength that cannot be achieved by type classes. To get the same power from type classes we would need to add closed type classes. Which would be quite useful; this is what instance chains gives you.





Day 12: Multi-Parameter Type Classes

Even the original paper on Haskell type classes mentions multiple parameters, so this idea has been with us from the start. But it's not present in Stefan Kaes original work on type classes

Unfortunately, multiple type class parameters very quickly lead to type ambiguities in the code, and we are forced to add type signatures. So MPTC was not really useful until Mark Jones introduced functional dependencies. Mark got the idea from database theory where the same idea is used to limit the relations in the database.





Labels: Haskell