ForSyDe.Shallow.MoC.Synchronous

The synchronuous library defines process constructors and processes for the synchronous computational model. A process constructor is a higher order function which together with combinational function(s) and values as arguments constructs a process.

The Core Library

Combinational process constructors

Combinational process constructors are used for processes that do not have a state.

mapSY :: (a -> b) -> Signal a -> Signal b

The process constructor mapSY takes a combinational function as argument and returns a process with one input signal and one output signal.

>>> mapSY (+1) $ signal [1,2,3,4]
{2,3,4,5}

zipWithSY :: (a -> b -> c) -> Signal a -> Signal b -> Signal c

The process constructor zipWithSY takes a combinational function as argument and returns a process with two input signals and one output signal.

>>> zipWithSY (+) (signal [1,2,3,4]) (signal [11,12,13,14,15,16,17])
{12,14,16,18}

zipWith3SY :: (a -> b -> c -> d) -> Signal a -> Signal b -> Signal c -> Signal d

The process constructor zipWith3SY takes a combinational function as argument and returns a process with three input signals and one output signal.

zipWith4SY :: (a -> b -> c -> d -> e) -> Signal a -> Signal b -> Signal c -> Signal d -> Signal e

The process constructor zipWith4SY takes a combinational function as argument and returns a process with four input signals and one output signal.

mapxSY :: (a -> b) -> Vector (Signal a) -> Vector (Signal b)

The process constructor mapxSY creates a process network that maps a function onto all signals in a vector of signals. See mapV.

>>> let s1 = signal [1,2,3,4]
>>> let s2 = signal [10,20,30,40]
>>> let s3 = signal [100,200,300]
>>> mapxSY (+1) $ vector [s1,s2,s3]
<{2,3,4,5},{11,21,31,41},{101,201,301}> 

zipWithxSY :: (Vector a -> b) -> Vector (Signal a) -> Signal b

The process constructor zipWithxSY works as zipWithSY, but takes a vector of signals as input.

>>> let s1 = signal [1,2,3,4]
>>> let s2 = signal [10,20,30,40]
>>> let s3 = signal [100,200,300]
>>> zipWithxSY (reduceV (+)) $ vector [s1,s2,s3]
{111,222,333}

combSY :: (a -> b) -> Signal a -> Signal b

The process constructor combSY is an alias to mapSY and behaves exactly in the same way.

comb2SY :: (a -> b -> c) -> Signal a -> Signal b -> Signal c

The process constructor comb2SY is an alias to zipWithSY and behaves exactly in the same way.

comb3SY :: (a -> b -> c -> d) -> Signal a -> Signal b -> Signal c -> Signal d

The process constructor comb3SY is an alias to zipWith3SY and behaves exactly in the same way.

comb4SY :: (a -> b -> c -> d -> e) -> Signal a -> Signal b -> Signal c -> Signal d -> Signal e

The process constructor comb4SY is an alias to zipWith4SY and behaves exactly in the same way.

Sequential process constructors

Sequential process constructors are used for processes that have a state. One of the input parameters is the initial state.

delaySY

Arguments

:: a

Initial state

-> Signal a

Input signal

-> Signal a

Output signal

The process constructor delaySY delays the signal one event cycle by introducing an initial value at the beginning of the output signal. Note, that this implies that there is one event (the first) at the output signal that has no corresponding event at the input signal. One could argue that input and output signals are not fully synchronized, even though all input events are synchronous with a corresponding output event. However, this is necessary to initialize feed-back loops.

>>> delaySY 1 $ signal [1,2,3,4]
{1,1,2,3,4}

delaynSY

Arguments

:: a

Initial state

-> Int

Delay cycles

-> Signal a

Input signal

-> Signal a

Output signal

The process constructor delaynSY delays the signal n events by introducing n identical default values.

>>> delaynSY 0 3 $ signal [1,2,3,4]
{0,0,0,1,2,3,4}

scanlSY

Arguments

:: (a -> b -> a)

Combinational function for next state decoder

-> a

Initial state

-> Signal b

Input signal

-> Signal a

Output signal

The process constructor scanlSY is used to construct a finite state machine process without output decoder. It takes an initial value and a function for the next state decoder. The process constructor behaves similar to the Haskell prelude function scanlSY and has the value of the new state as its output value as illustrated by the following example.

>>> scanlSY (+) 0 (signal [1,2,3,4])
{1,3,6,10}

This is in contrast to the function scanldSY, which has its current state as its output value.

scanl2SY :: (a -> b -> c -> a) -> a -> Signal b -> Signal c -> Signal a

The process constructor scanl2SY behaves like scanlSY, but has two input signals.

scanl3SY :: (a -> b -> c -> d -> a) -> a -> Signal b -> Signal c -> Signal d -> Signal a

The process constructor scanl3SY behaves like scanlSY, but has three input signals.

scanldSY

Arguments

:: (a -> b -> a)

Combinational function for next state decoder

-> a

Initial state

-> Signal b

Input signal

-> Signal a

Output signal

The process constructor scanldSY is used to construct a finite state machine process without output decoder. It takes an initial value and a function for the next state decoder. The process constructor behaves similar to the Haskell prelude function scanlSY. In contrast to the process constructor scanlSY here the output value is the current state and not the one of the next state.

>>> scanldSY (+) 0 (signal [1,2,3,4])
{0,1,3,6,10}

scanld2SY :: (a -> b -> c -> a) -> a -> Signal b -> Signal c -> Signal a

The process constructor scanld2SY behaves like scanldSY, but has two input signals.

scanld3SY :: (a -> b -> c -> d -> a) -> a -> Signal b -> Signal c -> Signal d -> Signal a

The process constructor scanld3SY behaves like scanldSY, but has three input signals.

mooreSY

Arguments

:: (a -> b -> a)

Combinational function for next state decoder

-> (a -> c)

Combinational function for output decoder

-> a

Initial state

-> Signal b

Input signal

-> Signal c

Output signal

The process constructor mooreSY is used to model state machines of "Moore" type, where the output only depends on the current state. The process constructor is based on the process constructor scanldSY, since it is natural for state machines in hardware, that the output operates on the current state and not on the next state. The process constructors takes a function to calculate the next state, another function to calculate the output and a value for the initial state.

In contrast the output of a process created by the process constructor mealySY depends not only on the state, but also on the input values.

>>> mooreSY (+) (*2) 0 $ signal [1,2,3,4,5]
{0,2,6,12,20,30}

moore2SY :: (a -> b -> c -> a) -> (a -> d) -> a -> Signal b -> Signal c -> Signal d

The process constructor moore2SY behaves like mooreSY, but has two input signals.

moore3SY :: (a -> b -> c -> d -> a) -> (a -> e) -> a -> Signal b -> Signal c -> Signal d -> Signal e

The process constructor moore3SY behaves like mooreSY, but has three input signals.

mealySY

Arguments

:: (a -> b -> a)

Combinational function for next state decoder

-> (a -> b -> c)

Combinational function for output decoder

-> a

Initial state

-> Signal b

Input signal

-> Signal c

Output signal

The process constructor melaySY is used to model state machines of "Mealy" type, where the output only depends on the current state and the input values. The process constructor is based on the process constructor scanldSY, since it is natural for state machines in hardware, that the output operates on the current state and not on the next state. The process constructors takes a function to calculate the next state, another function to calculate the output and a value for the initial state.

In contrast the output of a process created by the process constructor mooreSY depends only on the state, but not on the input values.

>>> mealySY (+) (+) 0 $ signal [1,2,3,4,5]
{1,3,6,10,15}

mealy2SY :: (a -> b -> c -> a) -> (a -> b -> c -> d) -> a -> Signal b -> Signal c -> Signal d

The process constructor mealy2SY behaves like mealySY, but has two input signals.

mealy3SY :: (a -> b -> c -> d -> a) -> (a -> b -> c -> d -> e) -> a -> Signal b -> Signal c -> Signal d -> Signal e

The process constructor mealy3SY behaves like mealySY, but has three input signals.

sourceSY :: (a -> a) -> a -> Signal a

The process sourceSY takes a function and an initial state and generates an infinite signal starting with the initial state as first output followed by the recursive application of the function on the current state. The state also serves as output value.

The process that has the infinite signal of natural numbers as output is constructed by

>>> takeS 5 $ sourceSY (+1) 0
{0,1,2,3,4}

filterSY

Arguments

:: (a -> Bool)

Predicate function

-> Signal a

Input signal

-> Signal (AbstExt a)

Output signal

The process constructor filterSY discards the values who do not fulfill a predicate given by a predicate function and replaces them with absent events.

fillSY

Arguments

:: a

Default value

-> Signal (AbstExt a)

Absent extended input signal

-> Signal a

Output signal

The process constructor fillSY creates a process that fills a signal with present values by replacing absent values with a given value. The output signal is not any more of the type AbstExt.

>>> let s = signal [Abst, Prst 1, Prst 2, Abst, Abst, Prst 4, Abst]
>>> fillSY 3 s
{3,1,2,3,3,4,3}

holdSY

Arguments

:: a

Default value

-> Signal (AbstExt a)

Absent extended input signal

-> Signal a

Output signal

The process constructor holdSY creates a process that fills a signal with values by replacing absent values by the preceding present value. Only in cases, where no preceding value exists, the absent value is replaced by a default value. The output signal is not any more of the type AbstExt.

>>> let s = signal [Abst, Prst 1, Prst 2, Abst, Abst, Prst 4, Abst]
>>> holdSY 3 s
{3,1,2,2,2,4,4}

Synchronous Processes

The library contains a few simple processes that are applicable to many cases.

whenSY :: Signal (AbstExt a) -> Signal (AbstExt b) -> Signal (AbstExt a)

The process constructor whenSY creates a process that synchronizes a signal of absent extended values with another signal of absent extended values. The output signal has the value of the first signal whenever an event has a present value and Abst when the event has an absent value.

>>> let clk = signal [Abst,    Prst (), Prst (), Abst,    Abst,    Prst (), Abst]
>>> let sig = signal [Prst 10, Prst 11, Prst 12, Prst 13, Prst 14, Prst 15]
>>> sig `whenSY` clk
{_,11,12,_,_,15}

zipSY :: Signal a -> Signal b -> Signal (a, b)

The process zipSY "zips" two incoming signals into one signal of tuples.

>>> zipSY (signal [1,2,3,4]) (signal [10,11,12,13,14])
{(1,10),(2,11),(3,12),(4,13)}

zip3SY :: Signal a -> Signal b -> Signal c -> Signal (a, b, c)

The process zip3SY works as zipSY, but takes three input signals.

zip4SY :: Signal a -> Signal b -> Signal c -> Signal d -> Signal (a, b, c, d)

The process zip4SY works as zipSY, but takes four input signals.

zip5SY :: Signal a -> Signal b -> Signal c -> Signal d -> Signal e -> Signal (a, b, c, d, e)

The process zip5SY works as zipSY, but takes four input signals.

zip6SY :: Signal a -> Signal b -> Signal c -> Signal d -> Signal e -> Signal f -> Signal (a, b, c, d, e, f)

The process zip6SY works as zipSY, but takes four input signals.

unzipSY :: Signal (a, b) -> (Signal a, Signal b)

The process unzipSY "unzips" a signal of tuples into two signals.

unzip3SY :: Signal (a, b, c) -> (Signal a, Signal b, Signal c)

The process unzip3SY works as unzipSY, but has three output signals.

unzip4SY :: Signal (a, b, c, d) -> (Signal a, Signal b, Signal c, Signal d)

The process unzip4SY works as unzipSY, but has four output signals.

unzip5SY :: Signal (a, b, c, d, e) -> (Signal a, Signal b, Signal c, Signal d, Signal e)

The process unzip5SY works as unzipSY, but has four output signals.

unzip6SY :: Signal (a, b, c, d, e, f) -> (Signal a, Signal b, Signal c, Signal d, Signal e, Signal f)

The process unzip6SY works as unzipSY, but has four output signals.

zipxSY :: Vector (Signal a) -> Signal (Vector a)

The process zipxSY transposes a signal of vectors into a vector of signals. All the events carried by the output signal are synchronized values from all input signals.

>>> let s1 = signal [1,2,3,4]
>>> let s2 = signal [10,20,30,40]
>>> let s3 = signal [100,200,300]
>>> zipxSY $ vector [s1,s2,s3]
{<1,10,100>,<2,20,200>,<3,30,300>}

unzipxSY :: Signal (Vector a) -> Vector (Signal a)

The process unzipxSY "unzips" a vector of signals into a signal of vectors.

fstSY :: Signal (a, b) -> Signal a

The process fstSY selects always the first value from a signal of pairs.

sndSY :: Signal (a, b) -> Signal b

The process sndSY selects always the second value from a signal of pairs.

Add-ons

Utility Processes

Collection of process constructors commonly used in designs.

module ForSyDe.Shallow.MoC.Synchronous.Process

Stochastic Processes

Library of stochastic process constructors

module ForSyDe.Shallow.MoC.Synchronous.Stochastic