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[phd-thesis.git] / top / imp.tex

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\chapter{Implementation}%
\label{chp:implementation}
\begin{chapterabstract}
        \noindent This chapter shows the implementation of the \gls{MTASK} system by:
        \begin{itemize}
                \item gives details of the implementation of \gls{MTASK}'s \gls{TOP} engine that executes the \gls{MTASK} tasks on the microcontroller;
                \item shows the implementation of the byte code compiler for \gls{MTASK}'s \gls{TOP} language;
                \item explains the machinery used to automatically serialise and deserialise data to-and-fro the device.
        \end{itemize}
\end{chapterabstract}

Microcontrollers usually have flash-based program memory which wears out fairly quick.
For example, the atmega328p in the \gls{ARDUINO} UNO is rated for 10000 write cycles.
While this sounds like a lot, if new tasks are sent to the device every minute or so, a lifetime of only seven days is guaranteed.
Hence, for dynamic applications, interpretation on the device is necessary, saving precious write cycles of the program memory.

In order to provide the device with the tools to interpret the byte code, it is programmed with a \gls{RTS}, a customisable domain-specific \gls{OS} that takes care of the execution of tasks but also low-level mechanisms such as the communication, multi tasking, and memory management.
Once the device is programmed with the \gls{MTASK} \gls{RTS}, it can continuously receive new tasks without the need for reprogramming.
The \gls{OS} is written in portable \ccpp{} and only contains a small device-specific portion.

\section{\texorpdfstring{\Glsxtrlong{RTS}}{Run time system}}
The event loop of the \gls{RTS} is executed repeatedly and consists of three distinct phases.
After doing the three phases, the devices goes to sleep for as long as possible (see \cref{chp:green_computing_mtask}).

\subsection{Communication}
In the first phase, the communication channels are processed.
The exact communication method is a customisable device-specific option baked into the \gls{RTS}.
The interface is deliberately kept simple and consists of a two layer interface: a link interface and a communication interface.
Besides opening, closing and cleaning up, the link interface has only three functions that are shown in \cref{lst:link_interface}.
Consequently, implementing this link interface is very simple but allows for many more advanced link settings such as buffering.
There are implementations for this interface for serial or Wi-Fi connections using \gls{ARDUINO} and \gls{TCP} connections for Linux.

\begin{lstArduino}[caption={Link interface of the \gls{MTASK} \gls{RTS}.},label={lst:link_interface}]
bool link_input_available(void);
uint8_t link_read_byte(void);
void link_write_byte(uint8_t b);
\end{lstArduino}

The communication interface abstracts away from this link interface and is typed instead.
It contains only two functions as seen in \cref{lst:comm_interface}.
There are implementations for direct communication, or communication using an \gls{MQTT} broker.
Both use the automatic serialisation and deserialisation shown in \cref{sec:ccodegen}.

\begin{lstArduino}[caption={Communication interface of the \gls{MTASK} \gls{RTS}.},label={lst:comm_interface}]
struct MTMessageTo receive_message(void);
void send_message(struct MTMessageFro msg);
\end{lstArduino}

Processing the received messages from the communication channels happens synchronously and the channels are exhausted completely before moving on to the next phase.
There are several possible messages that can be received from the server:

\begin{description}
        \item[SpecRequest]
                is a message instructing the device to send its specification and is sent usually immediately after connecting.
                The \gls{RTS} responds with a \texttt{Spec} answer containing the specification.
        \item[TaskPrep]
                tells the device a (big) task is on its way.
                Especially on faster connections, it may be the case that the communication buffers overflow because a big message is sent while the \gls{RTS} is busy executing tasks.
                This allows the \gls{RTS} to postpone execution for a while, until the big task has been received.
                The server sends the big task when the device acknowledges (by sending a \texttt{TaskPrepAck} message) the preparation.
        \item[Task]
                contains a new task, its peripheral configuration, the \glspl{SDS}, and the bytecode.
                The new task is immediately copied to the task storage but is only initialised during the next phase after which a \texttt{TaskAck} is sent.
                Tasks are stored below the stack, but since the stack is only used in the middle phase, execution, it is no problem that it moves.
        \item[SdsUpdate]
                notifies the device of the new value for a lowered \gls{SDS}.
                The old value of the lowered \gls{SDS} is immediately replaced with the new one.
                There is no acknowledgement required.
        \item[TaskDel]
                instructs the device to delete a running task.
                Tasks are automatically deleted when they become stable.
                However, a task may also be deleted when the surrounding task on the server is deleted, for example when the task is on the left-hand side of a step combinator and the condition to step holds.
                The device acknowledges by sending a \texttt{TaskDelAck}.
        \item[Shutdown]
                tells the device to reset.
\end{description}

\subsection{Execution}
The second phase consists of performing one execution step for all tasks that wish for it.
Tasks are ordered in a priority queue ordered by the time a task needs to be executed, the \gls{RTS} selects all tasks that can be scheduled, see \cref{sec:scheduling} for more details.
Execution of a task is always an interplay between the interpreter and the \emph{rewriter}.

If a task is not initialized yet, i.e.\ the pointer to the current task tree is still null, the byte code of the main function is interpreted.
The main expression always produces a task tree.
Execution of a task consists of continuously rewriting the task until its value is stable.
Rewriting is a destructive process, i.e.\ the rewriting is done in place.
The rewriting engine uses the interpreter when needed, e.g.\ to calculate the step continuations.
The rewriter and the interpreter use the same stack to store intermediate values.
Rewriting steps are small so that interleaving results in seemingly parallel execution.
In this phase new task tree nodes may be allocated.
Both rewriting and initialization are atomic operations in the sense that no processing on SDSs is done other than SDS operations from the task itself.
The host is notified if a task value is changed after a rewrite step.

\subsection{Memory management}
The third and final phase is memory management.
The \gls{MTASK} \gls{RTS} is designed to run on systems with as little as \qty{2}{\kibi\byte} of \gls{RAM}.
Aggressive memory management is therefore vital.
Not all firmwares for microprocessors support heaps and---when they do---allocation often leaves holes when not used in a \emph{last in first out} strategy.
The \gls{RTS} uses a chunk of memory in the global data segment with its own memory manager tailored to the needs of \gls{MTASK}.
The size of this block can be changed in the configuration of the \gls{RTS} if necessary.
On an \gls{ARDUINO} UNO---equipped with \qty{2}{\kibi\byte} of \gls{RAM}---the maximum viable size is about \qty{1500}{\byte}.
The self-managed memory uses a similar layout as the memory layout for \gls{C} programs only the heap and the stack are switched (see \cref{fig:memory_layout}).

\begin{figure}
        \centering
        \includestandalone{memorylayout}
        \caption{Memory layout}\label{fig:memory_layout}
\end{figure}

A task is stored below the stack and its complete state is a \gls{CLEAN} record contain most importantly the task id, a pointer to the task tree in the heap (null if not initialised yet), the current task value, the configuration of \glspl{SDS}, the configuration of peripherals, the byte code and some scheduling information.

In memory, task data grows from the bottom up and the interpreter stack is located directly on top of it growing in the same direction.
As a consequence, the stack moves when a new task is received.
This never happens within execution because communication is always processed before execution.
Values in the interpreter are always stored on the stack.
Compound data types are stored unboxed and flattened.
Task trees grow from the top down as in a heap.
This approach allows for flexible ratios, i.e.\ many tasks and small trees or few tasks and big trees.

Stable tasks, and unreachable task tree nodes are removed.
If a task is to be removed, tasks with higher memory addresses are moved down.
For task trees---stored in the heap---the \gls{RTS} already marks tasks and task trees as trash during rewriting so the heap can be compacted in a single pass.
This is possible because there is no sharing or cycles in task trees and nodes contain pointers pointers to their parent.

\todo{plaa\-tje van me\-mo\-ry hier uitbreiden}

\section{Compiler}
\subsection{Instruction set}
The instruction set is a fairly standard stack machine instruction set extended with special \gls{TOP} instructions for creating task tree nodes.
All instructions are housed in a \gls{CLEAN} \gls{ADT} and serialised to the byte representation using a generic function.
Type synonyms (\cref{lst:type_synonyms}) are used to provide insight on the arguments of the instructions.
Labels are always two bytes long, all other arguments are one byte long.

\begin{lstClean}[caption={Type synonyms for instructions arguments.},label={lst:type_synonyms}]
:: ArgWidth    :== UInt8         :: ReturnWidth :== UInt8
:: Depth       :== UInt8         :: Num         :== UInt8
:: SdsId       :== UInt8         :: JumpLabel   =: JL UInt16
\end{lstClean}

\Cref{lst:instruction_type} shows an excerpt of the \gls{CLEAN} type that represents the instruction set.
For example, shorthand instructions are omitted for brevity.
Detailed semantics for the instructions are given in \cref{chp:bytecode_instruction_set}.
One notable instruction is the \cleaninline{MkTask} instruction, it allocates and initialises a task tree node and pushes a pointer to it on the stack.

\begin{lstClean}[caption={The type housing the instruction set.},label={lst:instruction_type}]
:: BCInstr
        //Jumps
        = BCJumpF JumpLabel | BCJump JumpLabel | BCLabel JumpLabel | BCJumpSR ArgWidth JumpLabel
        | BCReturn ReturnWidth ArgWidth | BCTailcall ArgWidth ArgWidth JumpLabel
        //Arguments
        | BCArgs ArgWidth ArgWidth
        //Task node creation and refinement
        | BCMkTask BCTaskType | BCTuneRateMs | BCTuneRateSec
        //Stack ops
        | BCPush String255 | BCPop Num | BCRot Depth Num | BCDup | BCPushPtrs
        //Casting
        | BCItoR | BCItoL | BCRtoI | ...
        // arith
        | BCAddI | BCSubI | ...
        ...

:: BCTaskType
        = BCStableNode ArgWidth | BCUnstableNode ArgWidth
        // Pin io
        | BCReadD | BCWriteD | BCReadA | BCWriteA | BCPinMode
        // Interrupts
        | BCInterrupt
        // Repeat
        | BCRepeat
        // Delay
        | BCDelay | BCDelayUntil
        // Parallel
        | BCTAnd | BCTOr
        //Step
        | BCStep ArgWidth JumpLabel
        //Sds ops
        | BCSdsGet SdsId | BCSdsSet SdsId | BCSdsUpd SdsId JumpLabel
        // Rate limiter
        | BCRateLimit
        ////Peripherals
        //DHT
        | BCDHTTemp UInt8 | BCDHTHumid UInt8
        ...
\end{lstClean}

\subsection{Compiler}
The bytecode compiler interpretation for the \gls{MTASK} language is implemented as a monad stack containing a writer monad and a state monad.
The writer monad is used to generate code snippets locally without having to store them in the monadic values.
The state monad accumulates the code, and stores the stateful data the compiler requires.
\Cref{lst:compiler_state} shows the data type for the state, storing:
function the compiler currently is in;
code of the main expression;
context (see \cref{ssec:step});
code for the functions;
next fresh label;
a list of all the used \glspl{SDS}, either local \glspl{SDS} containing the initial value (\cleaninline{Left}) or lifted \glspl{SDS} (see \cref{sec:liftsds}) containing a reference to the associated \gls{ITASK} \gls{SDS};
and finally there is a list of peripherals used.

\begin{lstClean}[label={lst:compiler_state},caption={\Gls{MTASK}'s byte code compiler type}]
:: BCInterpret a :== StateT BCState (WriterT [BCInstr] Identity) a
:: BCState =
        { bcs_infun        :: JumpLabel
        , bcs_mainexpr     :: [BCInstr]
        , bcs_context      :: [BCInstr]
        , bcs_functions    :: Map JumpLabel BCFunction
        , bcs_freshlabel   :: JumpLabel
        , bcs_sdses        :: [Either String255 MTLens]
        , bcs_hardware     :: [BCPeripheral]
        }
:: BCFunction =
        { bcf_instructions :: [BCInstr]
        , bcf_argwidth     :: UInt8
        , bcf_returnwidth  :: UInt8
        }
\end{lstClean}

Executing the compiler is done by providing an initial state.
After compilation, several post-processing steps are applied to make the code suitable for the microprocessor.
First, in all tail call \cleaninline{BCReturn}'s are replaced by \cleaninline{BCTailCall} to implement tail call elimination.
Furthermore, all byte code is concatenated, resulting in one big program.
Many instructions have commonly used arguments so shorthands are introduced to reduce the program size.
For example, the \cleaninline{BCArg} instruction is often called with argument \qtyrange{0}{2} and can be replaced by the \cleaninline{BCArg0}--\cleaninline{BCArg2} shorthands.
Furthermore, redundant instructions (e.g.\ pop directly after push) are removed as well in order not to burden the code generation with these intricacies.
Finally the labels are resolved to represent actual program addresses instead of freshly generated identifiers.
After the byte code is ready, the lifted \glspl{SDS} are resolved to provide an initial value for them.
The result---byte code, \gls{SDS} specification and perpipheral specifications---are the result of the process, ready to be sent to the device.

\section{Compilation rules}
This section describes the compilation rules, the translation from abstract syntax to byte code.
The compilation scheme consists of three schemes\slash{}functions.
When something is surrounded by double vertical bars, e.g.\ $\stacksize{a_i}$, it denotes the number of stack cells required to store it.

Some schemes have a \emph{context} $r$ as an argument which contains information about the location of the arguments in scope.
More information is given in the schemes requiring such arguments.

\newcommand{\cschemeE}[2]{\mathcal{E}\llbracket#1\rrbracket~#2}
\newcommand{\cschemeF}[1]{\mathcal{F}\llbracket#1\rrbracket}
\newcommand{\cschemeS}[3]{\mathcal{S}\llbracket#1\rrbracket~#2~#3}
\begin{table}
        \centering
        \begin{tabularx}{\linewidth}{l X}
                \toprule
                Scheme & Description\\
                \midrule
                $\cschemeE{e}{r}$ & Produces the value of expression $e$ given the context $r$ and pushes it on the stack.
                        The result can be a basic value or a pointer to a task.\\
                $\cschemeF{e}$ & Generates the bytecode for functions.\\
                $\cschemeS{e}{r}{w} $ & Generates the function for the step continuation given the context $r$ and the width $w$ of the left-hand side task value.\\
                \bottomrule
        \end{tabularx}
\end{table}

\subsection{Expressions}
Almost all expression constructions are compiled using $\mathcal{E}$.
The argument of $\mathcal{E}$ is the context (see \cref{ssec:functions}).
Values are always placed on the stack; tuples and other compound data types are unpacked.
Function calls, function arguments and tasks are also compiled using $\mathcal{E}$ but their compilations is explained later.

\begin{align*}
        \cschemeE{\text{\cleaninline{lit}}~e}{r} & = \text{\cleaninline{BCPush (bytecode e)}};\\
        \cschemeE{e_1\mathbin{\text{\cleaninline{+.}}}e_2}{r} & = \cschemeE{e_1}{r};
                        \cschemeE{e_2}{r};
                        \text{\cleaninline{BCAdd}};\\
                {} & \text{\emph{Similar for other binary operators}}\\
        \cschemeE{\text{\cleaninline{Not}}~e}{r} & =
                        \cschemeE{e}{r};
                        \text{\cleaninline{BCNot}};\\
                {} & \text{\emph{Similar for other unary operators}}\\
        \cschemeE{\text{\cleaninline{If}}~e_1~e_2~e_3}{r} & =
                        \cschemeE{e_1}{r};
                        \text{\cleaninline{BCJmpF}}\enskip l_{else}; \mathbin{\phantom{=}} \cschemeE{e_2}{r}; \text{\cleaninline{BCJmp}}\enskip l_{endif};\\
                {} & \mathbin{\phantom{=}} \text{\cleaninline{BCLabel}}\enskip l_{else}; \cschemeE{e_3}{r}; \mathbin{\phantom{=}} \text{\cleaninline{BCLabel}}\enskip l_{endif};\\
                {} & \text{\emph{Where $l_{else}$ and $l_{endif}$ are fresh labels}}\\
        \cschemeE{\text{\cleaninline{tupl}}~e_1~e_2}{r} & =
                        \cschemeE{e_1}{r};
                        \cschemeE{e_2}{r};\\
                {} & \text{\emph{Similar for other unboxed compound data types}}\\
        \cschemeE{\text{\cleaninline{first}}~e}{r} & =
                        \cschemeE{e}{r};
                        \text{\cleaninline{BCPop}}\enskip w;\\
                {} & \text{\emph{Where $w$ is the width of the left value and}}\\
                {} & \text{\emph{similar for other unboxed compound data types}}\\
        \cschemeE{\text{\cleaninline{second}}\enskip e}{r} & =
                        \cschemeE{e}{r};
                        \text{\cleaninline{BCRot}}\enskip w_1\enskip (w_1+w_2);
                        \text{\cleaninline{BCPop}}\enskip w_2;\\
                {} & \text{\emph{Where $w_1$ is the width of the left and, $w_2$ of the right value}}\\
                {} & \text{\emph{similar for other unboxed compound data types}}\\
\end{align*}

Translating $\mathcal{E}$ to \gls{CLEAN} code is very straightforward, it basically means executing the monad.
Almost always, the type of the interpretation is not used, i.e.\ it is a phantom type.
To still have the functions return the correct type, the \cleaninline{tell`}\footnote{\cleaninline{tell` :: [BCInstr] -> BCInterpret a}} helper is used.
This function is similar to the writer monad's \cleaninline{tell} function but is casted to the correct type.
\Cref{lst:imp_arith} shows the implementation for the arithmetic and conditional expressions.
Note that $r$, the context, is not an explicit argument but stored in the state.

\begin{lstClean}[caption={Interpretation implementation for the arithmetic and conditional classes.},label={lst:imp_arith}]
instance expr BCInterpret where
        lit   t   = tell` [BCPush (toByteCode{|*|} t)]
        (+.)  a b = a >>| b >>| tell` [BCAdd]
        ...
        If c t e = freshlabel >>= \elselabel->freshlabel >>= \endiflabel->
                c >>| tell` [BCJumpF elselabel] >>|
                t >>| tell` [BCJump endiflabel,BCLabel elselabel] >>|
                e >>| tell` [BCLabel endiflabel]
\end{lstClean}

\subsection{Functions}\label{ssec:functions}
Compiling functions occurs in $\mathcal{F}$, which generates bytecode for the complete program by iterating over the functions and ending with the main expression.
When compiling the body of the function, the arguments of the function are added to the context so that the addresses can be determined when referencing arguments.
The main expression is a special case of $\mathcal{F}$ since it neither has arguments nor something to continue.
Therefore, it is just compiled using $\mathcal{E}$.

\begin{align*}
        \cschemeF{main=m} & =
                \cschemeE{m}{[]};\\
        \cschemeF{f~a_0 \ldots a_n = b~\text{\cleaninline{In}}~m} & =
                \text{\cleaninline{BCLabel}}~f; \cschemeE{b}{[\langle f, i\rangle, i\in \{(\Sigma^n_{i=0}\stacksize{a_i})..0\}]};\\
                {} & \mathbin{\phantom{=}} \text{\cleaninline{BCReturn}}~\stacksize{b}~n; \cschemeF{m};\\
\end{align*}

A function call starts by pushing the stack and frame pointer, and making space for the program counter (\cref{lst:funcall_pushptrs}) followed by evaluating the arguments in reverse order (\cref{lst:funcall_args}).
On executing \cleaninline{BCJumpSR}, the program counter is set and the interpreter jumps to the function (\cref{lst:funcall_jumpsr}).
When the function returns, the return value overwrites the old pointers and the arguments.
This occurs right after a \cleaninline{BCReturn} (\cref{lst:funcall_ret}).
Putting the arguments on top of pointers and not reserving space for the return value uses little space and facilitates tail call optimization.

\begin{figure}
        \begin{subfigure}{.24\linewidth}
                \centering
                \includestandalone{memory1}
                \caption{\cleaninline{BCPushPtrs}}\label{lst:funcall_pushptrs}
        \end{subfigure}
        \begin{subfigure}{.24\linewidth}
                \centering
                \includestandalone{memory2}
                \caption{Arguments}\label{lst:funcall_args}
        \end{subfigure}
        \begin{subfigure}{.24\linewidth}
                \centering
                \includestandalone{memory3}
                \caption{\cleaninline{BCJumpSR}}\label{lst:funcall_jumpsr}
        \end{subfigure}
        \begin{subfigure}{.24\linewidth}
                \centering
                \includestandalone{memory4}
                \caption{\cleaninline{BCReturn}}\label{lst:funcall_ret}
        \end{subfigure}
        \caption{The stack layout during function calls.}%
\end{figure}

Calling a function and referencing function arguments are an extension to $\mathcal{E}$ as shown below.
Arguments may be at different places on the stack at different times (see \cref{ssec:step}) and therefore the exact location always has to be determined from the context using \cleaninline{findarg}\footnote{\cleaninline{findarg [l`:r] l = if (l == l`) 0 (1 + findarg r l)}}.
Compiling argument $a_{f^i}$, the $i$th argument in function $f$, consists of traversing all positions in the current context.
Arguments wider than one stack cell are fetched in reverse to preserve the order.

\begin{align*}
        \cschemeE{f(a_0, \ldots, a_n)}{r} & =
                \text{\cleaninline{BCPushPtrs}}; \cschemeE{a_n}{r}; \cschemeE{a_{\ldots}}{r}; \cschemeE{a_0}{r}; \text{\cleaninline{BCJumpSR}}~n~f;\\
        \cschemeE{a_{f^i}}{r} & =
                \text{\cleaninline{BCArg}~findarg}(r, f, i)~\text{for all}~i\in\{w\ldots v\};\\
                {} & v = \Sigma^{i-1}_{j=0}\stacksize{a_{f^j}}~\text{ and }~ w = v + \stacksize{a_{f^i}}\\
\end{align*}

Translating the compilation schemes for functions to Clean is not as straightforward as other schemes due to the nature of shallow embedding.\todo{deze \P{} moet ge\-\"up\-da\-ted worden}
The \cleaninline{fun} class has a single function with a single argument.
This argument is a Clean function that---when given a callable Clean function representing the mTask function---will produce \cleaninline{main} and a callable function.
To compile this, the argument must be called with a function representing a function call in mTask.
\Cref{lst:fun_imp} shows the implementation for this as Clean code.
To uniquely identify the function, a fresh label is generated.
The function is then called with the \cleaninline{callFunction} helper function that generates the instructions that correspond to calling the function.
That is, it pushes the pointers, compiles the arguments, and writes the \cleaninline{JumpSR} instruction.
The resulting structure (\cleaninline{g In m}) contains a function representing the mTask function (\cleaninline{g}) and the \cleaninline{main} structure to continue with.
To get the actual function, \cleaninline{g} must be called with representations for the argument, i.e.\ using \cleaninline{findarg} for all arguments.
The arguments are added to the context and \cleaninline{liftFunction} is called with the label, the argument width and the compiler.
This function executes the compiler, decorates the instructions with a label and places them in the function dictionary together with the metadata such as the argument width.
After lifting the function, the context is cleared again and compilation continues with the rest of the program.

\begin{lstClean}[label={lst:fun_imp},caption={The backend implementation for functions.}]
instance fun (BCInterpret a) BCInterpret | type a where
        fun def = {main=freshlabel >>= \funlabel->
                let (g In m) = def \a->callFunction funlabel (toByteWidth a) [a]
                    argwidth = toByteWidth (argOf g)
                in  addToCtx funlabel zero argwidth
                >>| infun funlabel
                        (liftFunction funlabel argwidth
                                (g (retrieveArgs funlabel zero argwidth)
                                ) ?None)
                >>| clearCtx >>| m.main
                }

argOf :: ((m a) -> b) a -> UInt8 | toByteWidth a
callFunction :: JumpLabel UInt8 [BCInterpret b] -> BCInterpret c | ...
liftFunction :: JumpLabel UInt8 (BCInterpret a) (?UInt8) -> BCInterpret ()
\end{lstClean}

\subsection{Tasks}\label{ssec:scheme_tasks}
Task trees are created with the \cleaninline{BCMkTask} instruction that allocates a node and pushes it to the stack.
It pops arguments from the stack according to the given task type.
The following extension of $\mathcal{E}$ shows this compilation scheme (except for the step combinator, explained in \cref{ssec:step}).

\begin{align*}
        \cschemeE{\text{\cleaninline{rtrn}}~e}{r} & =
                        \cschemeE{e}{r};
                        \text{\cleaninline{BCMkTask BCStable}}_{\stacksize{e}};\\
        \cschemeE{\text{\cleaninline{unstable}}~e}{r} & =
                        \cschemeE{e}{r};
                        \text{\cleaninline{BCMkTask BCUnstable}}_{\stacksize{e}};\\
        \cschemeE{\text{\cleaninline{readA}}~e}{r} & =
                        \cschemeE{e}{r};
                        \text{\cleaninline{BCMkTask BCReadA}};\\
        \cschemeE{\text{\cleaninline{writeA}}~e_1~e_2}{r} & =
                        \cschemeE{e_1}{r};
                        \cschemeE{e_2}{r};
                        \text{\cleaninline{BCMkTask BCWriteA}};\\
        \cschemeE{\text{\cleaninline{readD}}~e}{r} & =
                        \cschemeE{e}{r};
                        \text{\cleaninline{BCMkTask BCReadD}};\\
        \cschemeE{\text{\cleaninline{writeD}}~e_1~e_2}{r} & =
                        \cschemeE{e_1}{r};
                        \cschemeE{e_2}{r};
                        \text{\cleaninline{BCMkTask BCWriteD}};\\
        \cschemeE{\text{\cleaninline{delay}}~e}{r} & =
                        \cschemeE{e}{r};
                        \text{\cleaninline{BCMkTask BCDelay}};\\
        \cschemeE{\text{\cleaninline{rpeat}}~e}{r} & =
                        \cschemeE{e}{r};
                        \text{\cleaninline{BCMkTask BCRepeat}};\\
        \cschemeE{e_1\text{\cleaninline{.\|\|.}}e_2}{r} & =
                        \cschemeE{e_1}{r};
                        \cschemeE{e_2}{r};
                        \text{\cleaninline{BCMkTask BCOr}};\\
        \cschemeE{e_1\text{\cleaninline{.&&.}}e_2}{r} & =
                        \cschemeE{e_1}{r};
                        \cschemeE{e_2}{r};
                        \text{\cleaninline{BCMkTask BCAnd}};\\
\end{align*}

This simply translates to Clean code by writing the correct \cleaninline{BCMkTask} instruction as exemplified in \cref{lst:imp_ret}.

\begin{lstClean}[caption={The backend implementation for \cleaninline{rtrn}.},label={lst:imp_ret}]
instance rtrn BCInterpret
where
        rtrn m = m >>| tell` [BCMkTask (bcstable m)]
\end{lstClean}

\subsection{Sequential combinator}\label{ssec:step}
The \cleaninline{step} construct is a special type of task because the task value of the left-hand side may change over time.
Therefore, the continuation tasks on the right-hand side are \emph{observing} this task value and acting upon it.
In the compilation scheme, all continuations are first converted to a single function that has two arguments: the stability of the task and its value.
This function either returns a pointer to a task tree or fails (denoted by $\bot$).
It is special because in the generated function, the task value of a task can actually be inspected.
Furthermore, it is a lazy node in the task tree: the right-hand side may yield a new task tree after several rewrite steps (i.e.\ it is allowed to create infinite task trees using step combinators).
The function is generated using the $\mathcal{S}$ scheme that requires two arguments: the context $r$ and the width of the left-hand side so that it can determine the position of the stability which is added as an argument to the function.
The resulting function is basically a list of if-then-else constructions to check all predicates one by one.
Some optimization is possible here but has currently not been implemented.

\begin{align*}
        \cschemeE{t_1\text{\cleaninline{>>*.}}t_2}{r} & =
                \cschemeE{a_{f^i}}{r}, \langle f, i\rangle\in r;
                \text{\cleaninline{BCMkTask}}~\text{\cleaninline{BCStable}}_{\stacksize{r}}; \cschemeE{t_1}{r};\\
        {} & \mathbin{\phantom{=}} \text{\cleaninline{BCMkTask}}~\text{\cleaninline{BCAnd}}; \text{\cleaninline{BCMkTask}}~(\text{\cleaninline{BCStep}}~(\cschemeS{t_2}{(r + [\langle l_s, i\rangle])}{\stacksize{t_1}}));\\
\end{align*}

\begin{align*}
        \cschemeS{[]}{r}{w} & =
                \text{\cleaninline{BCPush}}~\bot;\\
        \cschemeS{\text{\cleaninline{IfValue}}~f~t:cs}{r}{w} & =
                \text{\cleaninline{BCArg}} (\stacksize{r} + w);
                \text{\cleaninline{BCIsNoValue}};\\
        {} & \mathbin{\phantom{=}} \cschemeE{f}{r};
                \text{\cleaninline{BCAnd}};\\
        {} & \mathbin{\phantom{=}} \text{\cleaninline{BCJmpF}}~l_1;\\
        {} & \mathbin{\phantom{=}} \cschemeE{t}{r};
                \text{\cleaninline{BCJmp}}~l_2;\\
        {} & \mathbin{\phantom{=}} \text{\cleaninline{BCLabel}}~l_1;
                \cschemeS{cs}{r}{w};\\
        {} & \mathbin{\phantom{=}} \text{\cleaninline{BCLabel}}~l_2;\\
        {} & \text{\emph{Where $l_1$ and $l_2$ are fresh labels}}\\
        {} & \text{\emph{Similar for \cleaninline{IfStable} and \cleaninline{IfUnstable}}}\\
\end{align*}

First the context is evaluated.
The context contains arguments from functions and steps that need to be preserved after rewriting.
The evaluated context is combined with the left-hand side task value by means of a \cleaninline{.&&.} combinator to store it in the task tree so that it is available after a rewrite.
This means that the task tree is be transformed as follows:

\begin{lstClean}
t1 >>= \v1->t2 >>= \v2->t3 >>= ...
//is transformed to
t1 >>= \v1->rtrn v1 .&&. t2 >>= \v2->rtrn (v1, v2) .&&. t3 >>= ...
\end{lstClean}

The translation to \gls{CLEAN} is given in \cref{lst:imp_seq}.

\begin{lstClean}[caption={Backend implementation for the step class.},label={lst:imp_seq}]
instance step BCInterpret where
        (>>*.) lhs cont
                //Fetch a fresh label and fetch the context
                =   freshlabel >>= \funlab->gets (\s->s.bcs_context)
                //Generate code for lhs
                >>= \ctx->lhs
                //Possibly add the context
                >>| tell` (if (ctx =: []) []
                                //The context is just the arguments up till now in reverse
                                (  [BCArg (UInt8 i)\\i<-reverse (indexList ctx)]
                                ++ map BCMkTask (bcstable (UInt8 (length ctx)))
                                ++ [BCMkTask BCTAnd]
                                ))
                //Increase the context
                >>| addToCtx funlab zero lhswidth
                //Lift the step function
                >>| liftFunction funlab
                                //Width of the arguments is the width of the lhs plus the
                                //stability plus the context
                                (one + lhswidth + (UInt8 (length ctx)))
                                //Body     label  ctx width            continuations
                                (contfun funlab (UInt8 (length ctx)))
                                //Return width (always 1, a task pointer)
                                (Just one)
                >>| modify (\s->{s & bcs_context=ctx})
                >>| tell` [BCMkTask (instr rhswidth funlab)]

toContFun :: JumpLabel UInt8 -> BCInterpret a
toContFun steplabel contextwidth
        = foldr tcf (tell` [BCPush fail]) cont
where
        tcf (IfStable f t)
                = If ((stability >>| tell` [BCIsStable]) &. f val)
                        (t val >>| tell` [])
        ...
        stability = tell` [BCArg (lhswidth + contextwidth)]
        val = retrieveArgs steplabel zero lhswidth
\end{lstClean}

\subsection{\texorpdfstring{\Glspl{SDS}}{Shared data sources}}
The compilation scheme for \gls{SDS} definitions is a trivial extension to $\mathcal{F}$ since there is no code generated as seen below.

\begin{align*}
        \cschemeF{\text{\cleaninline{sds}}~x=i~\text{\cleaninline{In}}~m} & =
                \cschemeF{m};\\
\end{align*}

The \gls{SDS} access tasks have a compilation scheme similar to other tasks (see \cref{ssec:scheme_tasks}).
The \cleaninline{getSds} task just pushes a task tree node with the \gls{SDS} identifier embedded.
The \cleaninline{setSds} task evaluates the value, lifts that value to a task tree node and creates an \gls{SDS} set node.

\begin{align*}
        \cschemeE{\text{\cleaninline{getSds}}~s}{r} & =
                \text{\cleaninline{BCMkTask}} (\text{\cleaninline{BCSdsGet}} s);\\
        \cschemeE{\text{\cleaninline{setSds}}~s~e}{r} & =
                \cschemeE{e}{r};
                \text{\cleaninline{BCMkTask BCStable}}_{\stacksize{e}};\\
        {} & \mathbin{\phantom{=}} \text{\cleaninline{BCMkTask}} (\text{\cleaninline{BCSdsSet}} s);\\
\end{align*}

While there is no code generated in the definition, the byte code compiler is storing the \gls{SDS} data in the \cleaninline{bcs_sdses} field in the compilation state.
The \glspl{SDS} are typed as functions in the host language so an argument for this function must be created that represents the \gls{SDS} on evaluation.
For this, an \cleaninline{BCInterpret} is created that emits this identifier.
When passing it to the function, the initial value of the \gls{SDS} is returned.
This initial value is stored as a byte code encoded value in the state and the compiler continues with the rest of the program.

Compiling \cleaninline{getSds} is a matter of executing the \cleaninline{BCInterpret} representing the \gls{SDS}, which yields the identifier that can be embedded in the instruction.
Setting the \gls{SDS} is similar: the identifier is retrieved and the value is written to put in a task tree so that the resulting task can remember the value it has written.
Lifted SDSs are compiled in a very similar way \cref{sec:liftsds}.

% VimTeX: SynIgnore on
\begin{lstClean}[caption={Backend implementation for the SDS classes.},label={lst:comp_sds}]
:: Sds a = Sds Int
instance sds BCInterpret where
        sds def = {main = freshsds >>= \sdsi->
                        let sds = modify (\s->{s & bcs_sdses=put sdsi
                                                (Left (toByteCode t)) s.bcs_sdses})
                                        >>| pure (Sds sdsi)
                            (t In e) = def sds
                        in e.main}
        getSds f   = f >>= \(Sds i)-> tell` [BCMkTask (BCSdsGet (fromInt i))]
        setSds f v = f >>= \(Sds i)->v >>| tell`
                (  map BCMkTask (bcstable (byteWidth v))
                ++ [BCMkTask (BCSdsSet (fromInt i))])
\end{lstClean}
% VimTeX: SynIgnore off

\section{\texorpdfstring{\Gls{C}}{C} code generation}\label{sec:ccodegen}
All communication between the \gls{ITASK} server and the \gls{MTASK} server is type-parametrised.
From the structural representation of the type, a \gls{CLEAN} parser and printer is constructed using generic programming.
Furthermore, a \ccpp{} parser and printer is generated for use on the \gls{MTASK} device.
The technique for generating the \ccpp{} parser and printer is very similar to template metaprogramming and requires a generic programming library or compiler support that includes a lot of metadata in the record and constructor nodes.

\section{Conclusion}
%\todo[inline]{conclusion}

\input{subfilepostamble}
\end{document}