This version differs from the parametric one in introducing autmatic
delays. In practice, if a dependency loop involves a `transfer`

primitive, it will be resolved during runtime even if transfer
functions are not delayed by default.

The interface of this module differs from the old Elerea in the following ways:

- the delta time argument is generalised to an arbitrary type, so it
is possible to do without
`external`

altogether in case someone wants to do so; - there is no
`sampler`

any more, it is substituted by`join`

, as signals are monads; -
`generator`

has been conceptually simplified, so it's a more basic primitive now; - all signals are aged regardless of whether they are sampled (i.e. their behaviour doesn't depend on the context any more);
- the user needs to cache the results of applicative operations to be
reused in multiple places explicitly using the
`memo`

combinator.

- data Signal p a
- data SignalGen p a
- start :: SignalGen p (Signal p a) -> IO (p -> IO a)
- external :: a -> IO (Signal p a, a -> IO ())
- externalMulti :: IO (SignalGen p (Signal p [a]), a -> IO ())
- delay :: a -> Signal p a -> SignalGen p (Signal p a)
- stateful :: a -> (p -> a -> a) -> SignalGen p (Signal p a)
- transfer :: a -> (p -> t -> a -> a) -> Signal p t -> SignalGen p (Signal p a)
- memo :: Signal p a -> SignalGen p (Signal p a)
- generator :: Signal p (SignalGen p a) -> SignalGen p (Signal p a)
- noise :: MTRandom a => SignalGen p (Signal p a)
- getRandom :: MTRandom a => SignalGen p a
- debug :: String -> SignalGen p ()

# Documentation

A signal can be thought of as a function of type `Nat -> a`

, and
its `Monad`

instance agrees with that intuition. Internally, is
represented by a sampling computation.

Monad (Signal p) | |

Functor (Signal p) | |

Applicative (Signal p) | |

Bounded t => Bounded (Signal p t) | |

Enum t => Enum (Signal p t) | |

Eq (Signal p a) | Equality test is impossible. |

Floating t => Floating (Signal p t) | |

Fractional t => Fractional (Signal p t) | |

Integral t => Integral (Signal p t) | |

Num t => Num (Signal p t) | |

Ord t => Ord (Signal p t) | |

Real t => Real (Signal p t) | |

Show (Signal p a) | The |

A signal generator is the only source of stateful signals. Internally, computes a signal structure and adds the new variables to an existing update pool.

:: SignalGen p (Signal p a) | the generator of the top-level signal |

-> IO (p -> IO a) | the computation to sample the signal |

Embedding a signal into an `IO`

environment. Repeated calls to
the computation returned cause the whole network to be updated, and
the current sample of the top-level signal is produced as a result.
The computation accepts a global parameter that will be distributed
to all signals. For instance, this can be the time step, if we
want to model continuous-time signals.

A signal that can be directly fed through the sink function returned. This can be used to attach the network to the outer world. Note that this is optional, as all the input of the network can be fed in through the global parameter, although that is not really convenient for many signals.

:: IO (SignalGen p (Signal p [a]), a -> IO ()) | a generator for the event signal and the associated sink |

An event-like signal that can be fed through the sink function
returned. The signal carries a list of values fed in since the
last sampling, i.e. it is constantly [] if the sink is never
invoked. The order of elements is reversed, so the last value
passed to the sink is the head of the list. Note that unlike
`external`

this function only returns a generator to be used within
the expression constructing the top-level stream, and this
generator can only be used once.

The `delay`

transfer function emits the value of a signal from
the previous superstep, starting with the filler value given in the
first argument.

stateful :: a -> (p -> a -> a) -> SignalGen p (Signal p a)Source

A pure stateful signal. The initial state is the first output, and every following output is calculated from the previous one and the value of the global parameter.

transfer :: a -> (p -> t -> a -> a) -> Signal p t -> SignalGen p (Signal p a)Source

A stateful transfer function. The current input affects the current output, i.e. the initial state given in the first argument is considered to appear before the first output, and can never be observed. Every output is derived from the current value of the input signal, the global parameter and the previous output. The only exception is when a transfer function sits in a loop without a delay. In this case, a delay will be inserted at a single place during runtime (i.e. the previous output of the node affected will be reused) to resolve the circular dependency.

Memoising combinator. It can be used to cache results of
applicative combinators in case they are used in several places.
Other than that, it is equivalent to `return`

.

A reactive signal that takes the value to output from a monad carried by its input. It is possible to create new signals in the monad.