This repository serves as a compilation of research, thoughts, and discussions into the topic of AFRP for use in an upcoming library tegami. Perhaps this resource can be useful for those looking to get into AFRP implementation in the future, giving them insight into implementation issues and helping them avoid common implementation pitfalls.
This compilation does not aim to be academically rigorous.
At its core, tegami aims to be an AFRP implementation designed around real-world practicality.
Most AFRP implementations use the same encoding. Yampa in particular uses a GADT, however if one were to simplify said GADT down to its bare bones it would ultimately be the same encoding:
newtype X a b = X { step :: a -> (b, X a b) }Notice that we are talking about encoding, not definition. From this encoding, a valid signal function can be constructed as follows:
newtype SF a b = SF { step :: a -> Double -> (b, SF a b) }Ah, but can we not also define another possible SF from the same encoding?
newtype GeneralizedSF t a b = GSF { step :: a -> t -> (b, GeneralizedSF t a b) }This is the importance of differentiating between the definition and encoding for arrow primitives in AFRP. There can be many valid definitions that can be derived from the same encoding, however the encoding is important as a standalone concept in optimizing arrow performance and memory semantics.
By convention, the standard encoding X above will be referred to as automaton encoding. Why, you ask? From Control.Arrow.Transformer.Automaton:
newtype Automaton a b c = Automaton (a b (c, Automaton a b c))If you specialize this to Automaton (->), you get:
newtype Automaton' b c = Automaton' (b -> (c, Automaton' b c))Which is of course, the same as the defnition of X.
A common derivative of standard automaton encoding is monadic automaton encoding:
newtype Y m a b = Y { step :: a -> m (b, Y m a b) }This is the encoding behind dunai's MSF, varying's VarT, etc.
These two encodings, X and Y, generalize the vast majority of AFRP arrow primitives encountered in the wild. However, it does not mean these encodings are ideal. By experimenting with different encodings, not only can we lift restrictions on the expressivity of AFRP networks, but also optimize performance in a way that does not require rewriting networks in strange or unconventional manners, often with excessive boilerplate as a fundamental byproduct.