1 files changed, 15 insertions, 13 deletions

diff --git a/verilog.tex b/verilog.tex
index f11b6a2..6274dcb 100644
--- a/verilog.tex
+++ b/verilog.tex
@@ -2,7 +2,7 @@
 
 Verilog is a hardware description language commonly used to design hardware.  A Verilog design can then be synthesised into more basic logic which describes how different gates connect to each other, called a netlist.  This representation can then be put onto either a field-programmable gate array (FPGA) or turned into an application-specific integrated circuit (ASIC) to implement the design that was described in Verilog.  The Verilog standard is quite large though, and not all Verilog features are needed to be able to describe hardware.  Many Verilog features are only useful for simulation and do not affect the actual hardware itself, which means that these features do not have to be modelled in the semantics.  In addition to that, as the HLS algorithm dictates which Verilog constructs are generated, meaning the Verilog subset that has to be modelled by the semantics can be reduced even further to only support the constructs that are needed.  Only supporting a smaller subset in the semantics also means that there is less chance that the standard is misunderstood, and that the semantics actually model how the Verilog is simulated.
 
-The Verilog semantics are based on the semantics proposed by \citet{loow19_verif_compil_verif_proces}, which were used to create a formal translation from HOL logic into a Verilog circuit.  These semantics are quite practical as they restrict themselves to a small subset of Verilog, which can nonetheless be used to model all hardware constructs one would want to design. An abstraction of the Verilog syntax that is generated is shown below: \JW{This verilog syntax looks weird to me. I didn't think there was a `then' keyword, for instance. Perhaps you're aiming more at some sort of abstracted syntax of Verilog? What does the semicolon on its own mean? Some sort of skip statement? The case statement looks weird too -- how do you get multiple cases in a single switch statement, and where is the default case? }\YH{I think I have fixed most cases, yes the single semicolon is a skip statement, should I make that more obvious by naming it? } \JW{It still looks a bit funny to me -- a bit of a halfway-house between `proper' Verilog syntax and `abstract' Verilog syntax. E.g. the way `begin...end' blocks contain exactly two statements, or the way that you get an erroneous double semicolon by combining the `begin...end' rule with the `e=e;' rule. People who are very familiar with C-like syntax will know that this isn't quite right... but then again, it doesn't really matter whether you handle the full syntax, because you only have to pretty-print a subset of it. So, why not stick here with a slightly abstracted Verilog syntax? It would make the operational semantics easier to read, for instance. Basically like you had it before, but explicitly labelled as a simplified syntax, so readers don't get confused!}\YH{Yeah, the syntax is a bit funny, mostly because this is actually how it is also encoded in Coq.  The main weird rule is the Seq rule, basically because it actually doesn't have a semicolon in between and no begin and end block, but it looks a bit strange to just put two $s$ next to each other.  We therefore don't really have begin and end blocks, and basically glue them to each statement instead, so in our semantics, the if statement actually looks like: if $e$ begin $s$ end else begin $s$ end, but it gets very verbose for case statements.  I got rid of the sequence for now, but now it just looks like function application, so the semi colon kind of acted like a constructor.  I can just add a \texttt{Seq} constructor though, which might be clearer.}
+The Verilog semantics are based on the semantics proposed by \citet{loow19_verif_compil_verif_proces}, which were used to create a formal translation from HOL logic into a Verilog circuit.  These semantics are quite practical as they restrict themselves to a small subset of Verilog, which can nonetheless be used to model all hardware constructs one would want to design. An abstraction of the Verilog syntax that is generated is shown below:
 
 \begin{align*}
   v\quad ::=&\; \mathit{sz} \yhkeyword{'d} n\\
@@ -66,8 +66,6 @@ The two main evaluation functions are then \textit{erun}, which takes in the cur
 %  \inferrule[Nonblocking Array]{\yhkeyword{name}\ \textit{lhs} = \yhkeyword{OK}\ n \\ \textit{erun}\  \Gamma\ \textit{rhs}\ v_{\textit{rhs}}}{\textit{srun}\  (\Gamma_{r}, \Gamma_{a}, \Delta_{r}, \Delta_{a})\ (\textit{lhs} \Leftarrow \textit{rhs})\ (\Gamma_{r}, \Gamma_{a}, \Delta_{r} // \{n \rightarrow v_{\textit{rhs}}\}, \Delta_{a})}
 \end{gather*}
 
-\YH{TODO: Add rules for blocking and nonblocking assignment to arrays.} \JW{In CondTrue and CondFalse, the relationship between $\Gamma_0$ and $\sigma_0$ needs clarifying.}\YH{Clarified now in the previous paragraph.} \JW{Hm, why not just make `erun' take the entire $\sigma$ rather than just two of its fields? That would avoid this confusion altogether.}\YH{I guess I just wanted to make it explicit that erun never looks at the nonblocking assignments, but yes, it could also just take the whole $\sigma$} \JW{In CaseNoMatch, it feels weird to me that you keep evaluating $e$ for each case of the switch, rather than just once at the start of the switch statement. I guess it's ok because a failed match doesn't change the state. Just a bit quirky, I guess.}\YH{Yes that is a bit annoying actually, however, I couldn't really figure out the best way to only evaluate it once, as there isn't really a start to the case statement, we just describe that you could start anywhere in the case statement and evaluate it.  One solution would be to define a separate inductive rule that finds a matching case based on an evaluated value, which may be cleaner actually.} \JW{In CaseDefault, I was slightly surprised to see `Some' -- is that necessary?}\YH{That's true, currently it's a \texttt{Some} because the default case is optional, however, we actually always use it, so we could change it to be mandatory.} \JW{When using subscripted variables like $\Gamma_r$, I prefer $\Gamma_{\rm r}$ because $r$ is a fixed name (short for `register'), not a variable.}\YH{That is much nicer actually!}
-
 Taking the \textsc{CondTrue} rule as an example, this rule will only apply if the Boolean result of running the expression results in a \texttt{true} value.  It then also states that the statement in the true branch of the conditional statement \textit{stt} runs from state $\sigma_{0}$ to state $\sigma_{1}$.  If both of these conditions hold, we then get that the conditional statement will also run from state $\sigma_{0}$ to state $\sigma_{1}$.  The \textsc{Blocking} and \textsc{Nonblocking} rules are a bit more interesting, as these modify the blocking and nonblocking association maps respectively.
 
 One main difference between these semantics and the Verilog semantics by \citet{loow19_verif_compil_verif_proces} is that there is no function for external nondeterministic effects, such as memories and inputs and outputs.  These are instead handled explicitly in the semantics by using two dimensional unpacked arrays to model memories and assuming that inputs to modules cannot change.  Another difference with these semantics is that partial updates to arrays are fully supported, due to the fact that there are two different queues for arrays and variables.  Originally, if there was a blocking assignment to an array, and then a nonblocking assignment to a different region in the array, then the blocking assignment would disappear at the end of the clock cycle.  This is because the complete array would be overwritten with the updated array in the nonblocking association maps.  However, in our semantics, only the values that were changed in the array are actually recorded in the nonblocking assignment queue, meaning once the blocking and nonblocking array association maps are merged, only the actual indices that changed with nonblocking assignment are updated in the blocking assignment map.
@@ -78,18 +76,22 @@ To integrate our semantics with CompCert, we need to define the same states that
 
 We then define the semantics of running the module for one clock cycle in the following way:
 
-\begin{gather*}
-  \inferrule[Module]{\Gamma_{r} ! s_{t} = \texttt{Some } v \\ (m_{i}, \Gamma_{r}^{0}, \Gamma_{a}^{0}, \epsilon, \epsilon\ l)\ \longrightarrow_{\vec{m}} (m_{i}, \Gamma_{r}^{1}, \Gamma_{a}^{1}, \Delta_{r}^{1}, \Delta_{a}^{1}) \\ (\Gamma_{r}^{1} // \Delta_{r}^{1}) ! s_{t} = \texttt{Some } v'}{\texttt{State } \textit{sf }\ m\ v\ \Gamma_{r}^{0}\ \Gamma_{a}^{0} \longrightarrow \texttt{State } \textit{sf }\ m\ v'\ (\Gamma_{r}^{1} // \Delta_{r}^{1})\ (\Gamma_{a}^{1} // \Delta_{a}^{1})}\\
-%
-  \inferrule[Finish]{\Gamma_{r}!\textit{fin} = \texttt{Some } 1 \\ \Gamma_{r}!\textit{ret} = \texttt{Some } r}{\texttt{State } \textit{sf }\ m\ s_{t}\ \Gamma_{r}\ \Gamma_{a} \longrightarrow \texttt{Returnstate } \textit{sf }\ r}\\
-%
-  \inferrule[Call]{ }{\texttt{Callstate } \textit{sf }\ m\ \vec{r} \longrightarrow \texttt{State } \textit{sf }\ m\ n\ (\textit{init\_params }\ \vec{r}\ a // \{s_{t} \rightarrow n\})}\\
-%
-  \inferrule[Return]{ }{\texttt{Returnstate } (\texttt{Stackframe } r\ m\ \textit{pc }\ \Gamma_{r}\ \Gamma_{a} :: \textit{sf}) \longrightarrow \texttt{State } \textit{sf }\ m\ \textit{pc }\ (\Gamma_{r} // \{ \textit{st} \rightarrow \textit{pc}, r \rightarrow i \})\ \epsilon}
-\end{gather*}
+\begin{figure*}
+  \centering
+  \begin{gather*}
+    \inferrule[Module]{\Gamma_{r} ! s_{t} = \texttt{Some } v \\ (m_{i}, \Gamma_{r}^{0}, \Gamma_{a}^{0}, \epsilon, \epsilon\ l)\ \longrightarrow_{\vec{m}} (m_{i}, \Gamma_{r}^{1}, \Gamma_{a}^{1}, \Delta_{r}^{1}, \Delta_{a}^{1}) \\ (\Gamma_{r}^{1} // \Delta_{r}^{1}) ! s_{t} = \texttt{Some } v'}{\texttt{State } \textit{sf }\ m\ v\ \Gamma_{r}^{0}\ \Gamma_{a}^{0} \longrightarrow \texttt{State } \textit{sf }\ m\ v'\ (\Gamma_{r}^{1} // \Delta_{r}^{1})\ (\Gamma_{a}^{1} // \Delta_{a}^{1})}\\
+    % 
+    \inferrule[Finish]{\Gamma_{r}!\textit{fin} = \texttt{Some } 1 \\ \Gamma_{r}!\textit{ret} = \texttt{Some } r}{\texttt{State } \textit{sf }\ m\ s_{t}\ \Gamma_{r}\ \Gamma_{a} \longrightarrow \texttt{Returnstate } \textit{sf }\ r}\\
+    % 
+    \inferrule[Call]{ }{\texttt{Callstate } \textit{sf }\ m\ \vec{r} \longrightarrow \texttt{State } \textit{sf }\ m\ n\ (\textit{init\_params }\ \vec{r}\ a // \{s_{t} \rightarrow n\})}\\
+    % 
+    \inferrule[Return]{ }{\texttt{Returnstate } (\texttt{Stackframe } r\ m\ \textit{pc }\ \Gamma_{r}\ \Gamma_{a} :: \textit{sf}) \longrightarrow \texttt{State } \textit{sf }\ m\ \textit{pc }\ (\Gamma_{r} // \{ \textit{st} \rightarrow \textit{pc}, r \rightarrow i \})\ \epsilon}
+  \end{gather*}
+  \caption{Inferrence rules for modules}%
+  \label{fig:inferrence_module}
+\end{figure*}
 
 \YH{TODO:\@ Need to fix the last rule, as it is actually only used for a case that shouldn't ever be hit.}
-\YH{TODO:\@ Explain // notation}
 
 The \textsc{Module} rule is the main rule for the execution of one clock cycle of the module.  Given that the value of the $s_{t}$ register is the value of the program counter at the current instruction and that the value of the $s_{t}$ register in the resulting association map is equal to the next program counter value, we can then say that if all the module items in the body go from one state to another, that the whole module will step from that state to the other.