Reactive.Banana.Model

Synopsis

Model implementation for learning and testing.

Overview

This module reimplements the key FRP types and functions from the module Reactive.Banana.Combinators in a way that is hopefully easier to understand. Thereby, this model also specifies the semantics of the library. Of course, the real implementation is much more efficient than this model here.

To understand the model in detail, look at the source code! (If there is no link to the source code at every type signature, then you have to run cabal with --hyperlink-source flag.)

This model is authoritative: Event functions that have been constructed using the same combinators must give the same results when run with the interpret function from either the module Reactive.Banana.Combinators or the module Reactive.Banana.Model. This must also hold for recursive and partial definitions (at least in spirit, I'm not going to split hairs over _|_ vs \_ -> _|_).

Core Combinators

Event and Behavior

type Nat = Int

Natural numbers (poorly represented).

type Time = Nat

The FRP model used in this library is actually a model with continuous time.

However, it can be shown that this model is observationally equivalent to a particular model with (seemingly) discrete time steps, which is implemented here. The main reason for doing this is to be able to handle recursion correctly. Details will be explained elsewhere.

newtype Event a

Event is modeled by an infinite list of Maybe values. It is isomorphic to Time -> Maybe a.

Nothing indicates that no occurrence happens, while Just indicates that an occurrence happens.

Constructors

E

Fields

unE :: [Maybe a]

Instances

Functor Event

Show a => Show (Event a)

newtype Behavior a

Behavior is modeled by an infinite list of values. It is isomorphic to Time -> a.

Constructors

B

Fields

unB :: [a]

Instances

Functor Behavior

Applicative Behavior

Show a => Show (Behavior a)

interpret :: (Event a -> Moment (Event b)) -> [Maybe a] -> [Maybe b]

First-order

module Control.Applicative

never :: Event a

unionWith :: (a -> a -> a) -> Event a -> Event a -> Event a

filterJust :: Event (Maybe a) -> Event a

apply :: Behavior (a -> b) -> Event a -> Event b

Moment and accumulation

newtype Moment a

Constructors

M

Fields

unM :: Time -> a

Instances

Monad Moment

Functor Moment

MonadFix Moment

Applicative Moment

accumE :: a -> Event (a -> a) -> Moment (Event a)

stepper :: a -> Event a -> Moment (Behavior a)

Higher-order

valueB :: Behavior a -> Moment a

observeE :: Event (Moment a) -> Event a

switchE :: Event (Event a) -> Moment (Event a)

switchB :: Behavior a -> Event (Behavior a) -> Moment (Behavior a)