source: Deliverables/D4.2-4.3/reports/D4-3.tex @ 1427

Last change on this file since 1427 was 1427, checked in by mulligan, 9 years ago

more added to d4.3 report

File size: 34.2 KB
Line 
1\documentclass[11pt, epsf, a4wide]{article}
2
3\usepackage{../../style/cerco}
4
5\usepackage{amsfonts}
6\usepackage{amsmath}
7\usepackage{amssymb} 
8\usepackage[english]{babel}
9\usepackage{graphicx}
10\usepackage[utf8x]{inputenc}
11\usepackage{listings}
12\usepackage{lscape}
13\usepackage{stmaryrd}
14\usepackage{threeparttable}
15\usepackage{url}
16
17\title{
18INFORMATION AND COMMUNICATION TECHNOLOGIES\\
19(ICT)\\
20PROGRAMME\\
21\vspace*{1cm}Project FP7-ICT-2009-C-243881 \cerco{}}
22
23\lstdefinelanguage{matita-ocaml}
24  {keywords={definition,coercion,lemma,theorem,remark,inductive,record,qed,let,let,in,rec,match,return,with,Type,try},
25   morekeywords={[2]whd,normalize,elim,cases,destruct},
26   morekeywords={[3]type,of},
27   mathescape=true,
28  }
29
30\lstset{language=matita-ocaml,basicstyle=\small\tt,columns=flexible,breaklines=false,
31        keywordstyle=\color{red}\bfseries,
32        keywordstyle=[2]\color{blue},
33        keywordstyle=[3]\color{blue}\bfseries,
34        commentstyle=\color{green},
35        stringstyle=\color{blue},
36        showspaces=false,showstringspaces=false}
37
38\lstset{extendedchars=false}
39\lstset{inputencoding=utf8x}
40\DeclareUnicodeCharacter{8797}{:=}
41\DeclareUnicodeCharacter{10746}{++}
42\DeclareUnicodeCharacter{9001}{\ensuremath{\langle}}
43\DeclareUnicodeCharacter{9002}{\ensuremath{\rangle}}
44
45\date{}
46\author{}
47
48\begin{document}
49
50\thispagestyle{empty}
51
52\vspace*{-1cm}
53\begin{center}
54\includegraphics[width=0.6\textwidth]{../../style/cerco_logo.png}
55\end{center}
56
57\begin{minipage}{\textwidth}
58\maketitle
59\end{minipage}
60
61\vspace*{0.5cm}
62\begin{center}
63\begin{LARGE}
64\textbf{
65Report n. D4.3\\
66Formal semantics of intermediate languages
67}
68\end{LARGE} 
69\end{center}
70
71\vspace*{2cm}
72\begin{center}
73\begin{large}
74Version 1.0
75\end{large}
76\end{center}
77
78\vspace*{0.5cm}
79\begin{center}
80\begin{large}
81Main Authors:\\
82Dominic P. Mulligan and Claudio Sacerdoti Coen
83\end{large}
84\end{center}
85
86\vspace*{\fill}
87
88\noindent
89Project Acronym: \cerco{}\\
90Project full title: Certified Complexity\\
91Proposal/Contract no.: FP7-ICT-2009-C-243881 \cerco{}\\
92
93\clearpage
94\pagestyle{myheadings}
95\markright{\cerco{}, FP7-ICT-2009-C-243881}
96
97\newpage
98
99\vspace*{7cm}
100\paragraph{Abstract}
101We describe the encoding in the Calculus of Constructions of the semantics of the CerCo compiler's backend intermediate languages.
102The CerCo backend consists of five distinct languages: RTL, RTLntl, ERTL, LTL and LIN.
103We describe a process of heavy abstraction of the intermediate languages and their semantics.
104We hope that this process will ease the burden of Deliverable D4.4, the proof of correctness for the compiler.
105
106\newpage
107
108\tableofcontents
109
110\newpage
111
112%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%
113% SECTION.                                                                    %
114%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%
115\section{Task}
116\label{sect.task}
117
118The Grant Agreement states that Task T4.3, entitled `Formal semantics of intermediate languages' has associated Deliverable D4.3, consisting of the following:
119\begin{quotation}
120Executable Formal Semantics of back-end intermediate languages: This prototype is the formal counterpart of deliverable D2.1 for the back end side of the compiler and validates it.
121\end{quotation}
122This report details our implementation of this deliverable.
123
124%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%
125% SECTION.                                                                    %
126%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%
127\subsection{Connections with other deliverables}
128\label{subsect.connections.with.other.deliverables}
129
130Deliverable D4.3 enjoys a close relationship with three other deliverables, namely deliverables D2.2, D4.3 and D4.4.
131
132Deliverable D2.2, the O'Caml implementation of a cost preserving compiler for a large subset of the C programming language, is the basis upon which we have implemented the current deliverable.
133In particular, the architecture of the compiler, its intermediate languages and their semantics, and the overall implementation of the Matita encodings has been taken from the O'Caml compiler.
134Any variations from the O'Caml design are due to bugs identified in the prototype compiler during the Matita implementation, our identification of code that can be abstracted and made generic, or our use of Matita's much stronger type system to enforce invariants through the use of dependent types.
135
136Deliverable D4.2 can be seen as a `sister' deliverable to the deliverable reported on herein.
137In particular, where this deliverable reports on the encoding in the Calculus of Constructions of the backend semantics, D4.2 is the encoding in the Calculus of Constructions of the mutual translations of those languages.
138As a result, a substantial amount of Matita code is shared between the two deliverables.
139
140Deliverable D4.4, the backend correctness proofs, is the immediate successor of this deliverable.
141
142%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%
143% SECTION.                                                                    %
144%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%
145\section{The backend intermediate languages' semantics in Matita}
146\label{sect.backend.intermediate.languages.semantics.matita}
147
148%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%
149% SECTION.                                                                    %
150%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%
151\subsection{Abstracting related languages}
152\label{subsect.abstracting.related.languages}
153
154As mentioned in the report for Deliverable D4.2, a systematic process of abstraction, over the O'Caml code, has taken place in the Matita encoding.
155In particular, we have merged many of the syntaxes of the intermediate languages (i.e. RTL, ERTL, LTL and LIN) into a single `joint' syntax, which is parameterised by various types.
156Equivalent intermediate languages to those present in the O'Caml code can be recovered by specialising this joint structure.
157
158As mentioned in the report for Deliverable D4.2, there are a number of advantages that this process of abstraction brings, from code reuse to allowing us to get a clearer view of the intermediate languages and their structure.
159However, the semantics of the intermediate languages allow us to concretely demonstrate this improvement in clarity, by noting that the semantics of the LTL and the semantics of the LIN languages are identical.
160In particular, the semantics of both LTL and LIN are implemented in exactly the same way.
161The only difference between the two languages is how the next instruction to be interpreted is fetched.
162In LTL, this involves looking up in a graph, whereas in LTL, this involves fetching from a list of instructions.
163
164As a result, we see that the semantics of LIN and LTL are both instances of a single, more general language that is parametric in how the next instruction is fetched.
165Furthermore, any prospective proof that the semantics of LTL and LIN are identical is now almost trivial, saving a deal of work in Deliverable D4.4.
166
167%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%
168% SECTION.                                                                    %
169%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%
170\subsection{Type parameters, and their purpose}
171\label{subsect.type.parameters.their.purpose}
172
173We mentioned in the Deliverable D4.2 report that all joint languages are parameterised by a number of types, which are later specialised to each distinct intermediate language.
174As this parameterisation process is also dependent on designs decisions in the language semantics, we have so far held off summarising the role of each parameter.
175
176We begin the abstraction process with the \texttt{params\_\_} record.
177This holds the types of the representations of the different register varieties in the intermediate languages:
178\begin{lstlisting}
179record params__: Type[1] ≝
180{
181  acc_a_reg: Type[0];
182  acc_b_reg: Type[0];
183  dpl_reg: Type[0];
184  dph_reg: Type[0];
185  pair_reg: Type[0];
186  generic_reg: Type[0];
187  call_args: Type[0];
188  call_dest: Type[0];
189  extend_statements: Type[0]
190}.
191\end{lstlisting}
192We summarise what these types mean, and how they are used in both the semantics and the translation process:
193\begin{center}
194\begin{tabular*}{\textwidth}{p{4cm}p{11cm}}
195Type & Explanation \\
196\hline
197\texttt{acc\_a\_reg} & The type of the accumulator A register.  In some languages this is implemented as the hardware accumulator, whereas in others this is a pseudoregister.\\
198\texttt{acc\_b\_reg} & Similar to the accumulator A field, but for the processor's auxilliary accumulator, B. \\
199\texttt{dpl\_reg} & The type of the representation of the low eight bit register of the MCS-51's single 16 bit register, DPL.  Can be either a pseudoregister or the hardware DPL register. \\
200\texttt{dph\_reg} & Similar to the DPL register but for the eight high bits of the 16-bit register. \\
201\texttt{pair\_reg} & Various different `move' instructions have been merged into a single move instruction in the joint language.  A value can either be moved to or from the accumulator in some languages, or moved to and from an arbitrary pseudoregister in others.  This type encodes how we should move data around the registers and accumulators. \\
202\texttt{generic\_reg} & The representation of generic registers (i.e. those that are not devoted to a specific task). \\
203\texttt{call\_args} & The actual arguments passed to a function.  For some languages this is simply the number of arguments passed to the function. \\
204\texttt{call\_dest} & The destination of the function call. \\
205\texttt{extend\_statements} & Instructions that are specific to a particular intermediate language, and which cannot be abstracted into the joint language.
206\end{tabular*}
207\end{center}
208
209As mentioned in the report for Deliverable D4.2, the record \texttt{params\_\_} is enough to be able to specify the instructions of the joint languages:
210\begin{lstlisting}
211inductive joint_instruction (p: params__) (globals: list ident): Type[0] :=
212  | COMMENT: String → joint_instruction p globals
213  | COST_LABEL: costlabel → joint_instruction p globals
214  ...
215  | OP1: Op1 → acc_a_reg p → acc_a_reg p → joint_instruction p globals
216  ...
217\end{lstlisting}
218Here, we see that the instruction \texttt{OP1} (a unary operation on the accumulator A) can be given quite a specific type, through the use of the \texttt{params\_\_} data structure.
219
220Joint statements can be split into two subclasses: those who simply pass the flow of control onto their successor statement, and those that jump to a potentially remote location in the program.
221Naturally, as some intermediate languages are graph based, and others linearised, the passing act of passing control on to the `successor' instruction can either be the act of following a graph edge in a control flow graph, or incrementing an index into a list.
222We make a distinction between instructions that pass control onto their immediate successors, and those that jump elsewhere in the program, through the use of \texttt{succ}, denoting the immediate successor of the current instruction, in the \texttt{params\_} record described below.
223\begin{lstlisting}
224record params_: Type[1] ≝
225{
226  pars__ :> params__;
227  succ: Type[0]
228}.
229\end{lstlisting}
230The type \texttt{succ} corresponds to labels, in the case of control flow graph based languages, or is instantiated to the unit type for the linearised language, LIN.
231Using \texttt{param\_} we can define statements of the joint language:
232\begin{lstlisting}
233inductive joint_statement (p:params_) (globals: list ident): Type[0] :=
234  | sequential: joint_instruction p globals → succ p → joint_statement p globals
235  | GOTO: label → joint_statement p globals
236  | RETURN: joint_statement p globals.
237\end{lstlisting}
238Note that in the joint language, instructions are `linear', in that they have an immediate successor.
239Statements, on the other hand, consist of either a linear instruction, or a \texttt{GOTO} or \texttt{RETURN} statement, both of which can jump to an arbitrary place in the program.
240
241For the semantics, we need further parametererised types.
242In particular, we parameterise the result and parameter type of an internal function call in \texttt{params0}:
243\begin{lstlisting}
244record params0: Type[1] ≝
245 { pars__' :> params__
246 ; resultT: Type[0]
247 ; paramsT: Type[0]
248 }.
249\end{lstlisting}
250Here, \texttt{resultT} and \texttt{resultT} typically are the (pseudo)registers that store the parameters and result of a function.
251
252We further extend \texttt{params0} with a type for local variables in internal function calls:
253\begin{lstlisting}
254record params1 : Type[1] ≝
255 { pars0 :> params0
256 ; localsT: Type[0]
257 }.
258\end{lstlisting}
259Again, we expand our parameters with types corresponding to the code representation (either a control flow graph or a list of statements).
260Further, we hypothesise a generic method for looking up the next instruction in the graph, called \texttt{lookup}.
261Note that \texttt{lookup} may fail, and returns an \texttt{option} type:
262\begin{lstlisting}
263record params (globals: list ident): Type[1] ≝
264 { succ_ : Type[0]
265 ; pars1 :> params1
266 ; codeT: Type[0]
267 ; lookup: codeT → label → option (joint_statement (mk_params_ pars1 succ_) globals)
268 }.
269\end{lstlisting}
270We now have what we need to define internal functions for the joint language.
271The first two `universe' fields are only used in the compilation process, for generating fresh names, and do not affect the semantics.
272The rest of the fields affect both compilation and semantics.
273In particular, we have a description of the result, parameters and the local variables of a function.
274Note also that we have lifted the hypothesised \texttt{lookup} function from \texttt{params} into a dependent sigma type, which combines a label (the entry and exit points of the control flow graph or list) combined with a proof that the label is in the graph structure:
275\begin{lstlisting}
276record joint_internal_function (globals: list ident) (p:params globals) : Type[0] :=
277{
278  joint_if_luniverse: universe LabelTag;
279  joint_if_runiverse: universe RegisterTag;
280  joint_if_result   : resultT p;
281  joint_if_params   : paramsT p;
282  joint_if_locals   : localsT p;
283  joint_if_stacksize: nat;
284  joint_if_code     : codeT … p;
285  joint_if_entry    : $\Sigma$l: label. lookup … joint_if_code l ≠ None ?;
286  joint_if_exit     : $\Sigma$l: label. lookup … joint_if_code l ≠ None ?
287}.
288\end{lstlisting}
289Naturally, a question arises as to why we have chosen to split up the parameterisation into so many intermediate records, each slightly extending earlier ones.
290The reason is because some intermediate languages share a host of parameters, and only differ on some others.
291For instance, in instantiating the ERTL language, certain parameters are shared with RTL, whilst others are ERTL specific:
292\begin{lstlisting}
293...
294definition ertl_params__: params__ :=
295 mk_params__ register register register register (move_registers × move_registers)
296  register nat unit ertl_statement_extension.
297...
298definition ertl_params1: params1 := rtl_ertl_params1 ertl_params0.
299definition ertl_params: ∀globals. params globals ≝ rtl_ertl_params ertl_params0.
300...
301definition ertl_statement := joint_statement ertl_params_.
302
303definition ertl_internal_function :=
304  $\lambda$globals.joint_internal_function … (ertl_params globals).
305\end{lstlisting}
306Here, \texttt{rtl\_ertl\_params1} are the common parameters of the ERTL and RTL languages:
307\begin{lstlisting}
308definition rtl_ertl_params1 := $\lambda$pars0. mk_params1 pars0 (list register).
309\end{lstlisting}
310
311The record \texttt{more\_sem\_params} bundles together functions that store and retrieve values in various forms of register:
312\begin{lstlisting}
313record more_sem_params (p:params_): Type[1] :=
314{
315  framesT: Type[0];
316  empty_framesT: framesT;
317
318  regsT: Type[0];
319  empty_regsT: regsT;
320
321  call_args_for_main: call_args p;
322  call_dest_for_main: call_dest p;
323
324  succ_pc: succ p → address → res address;
325
326  greg_store_: generic_reg p → beval → regsT → res regsT;
327  greg_retrieve_: regsT → generic_reg p → res beval;
328  acca_store_: acc_a_reg p → beval → regsT → res regsT;
329  acca_retrieve_: regsT → acc_a_reg p → res beval;
330  ...
331  dpl_store_: dpl_reg p → beval → regsT → res regsT;
332  dpl_retrieve_: regsT → dpl_reg p → res beval;
333  ...
334  pair_reg_move_: regsT → pair_reg p → res regsT;
335  pointer_of_label: label → $\Sigma$p:pointer. ptype p = Code
336}.
337\end{lstlisting}
338Here, the fields \texttt{empty\_framesT}, \texttt{empty\_regsT}, \texttt{call\_args\_for\_main} and \texttt{call\_dest\_for\_main} are used for state initialisation.
339
340The field \texttt{succ\_pc} takes an address, and a `successor' label, and returns the address of the instruction immediately succeeding the one at hand.
341
342The fields \texttt{greg\_store\_} and \texttt{greg\_retrieve\_} store and retrieve values from a generic register, respectively.
343Similarly, \texttt{pair\_reg\_move} implements the generic move instruction of the joint language.
344Here \texttt{framesT} is the type of stack frames, with \texttt{empty\_framesT} an empty stack frame.
345
346The two hypothesised values \texttt{call\_args\_for\_main} and \texttt{call\_dest\_for\_main} deal with problems with the \texttt{main} function of the program, and how it is handled.
347In particular, we need to know when the \texttt{main} function has finished executing.
348But this is complicated, in C, by the fact that the \texttt{main} function is explicitly allowed to be recursive (disallowed in C++).
349Therefore, to understand whether the exiting \texttt{main} function is really exiting, or just recursively calling itself, we need to remember the address to which \texttt{main} will return control once the initial call to \texttt{main} has finished executing.
350This is done with \texttt{call\_dest\_for\_main}, whereas \texttt{call\_args\_for\_main} holds the \texttt{main} function's arguments.
351
352We extend \texttt{more\_sem\_params} with yet more parameters via \texttt{more\_sem\_params2}:
353\begin{lstlisting}
354record more_sem_params2 (globals: list ident) (p: params globals) : Type[1] :=
355{
356  more_sparams1 :> more_sem_params p;
357  fetch_statement:
358    genv … p → state (mk_sem_params … more_sparams1) →
359    res (joint_statement (mk_sem_params … more_sparams1) globals);
360  ...
361  save_frame:
362    address → nat → paramsT … p → call_args p → call_dest p →
363    state (mk_sem_params … more_sparams1) →
364    res (state (mk_sem_params … more_sparams1));
365  pop_frame:
366    genv globals p → state (mk_sem_params … more_sparams1) →
367    res ((state (mk_sem_params … more_sparams1)));
368  ...
369  set_result:
370    list val → state (mk_sem_params … more_sparams1) →
371    res (state (mk_sem_params … more_sparams1));
372  exec_extended:
373    genv globals p → extend_statements (mk_sem_params … more_sparams1) →
374    succ p → state (mk_sem_params … more_sparams1) →
375    IO io_out io_in (trace × (state (mk_sem_params … more_sparams1)))
376 }.
377\end{lstlisting}
378Here, \texttt{fetch\_statement} fetches the next statement to be executed.
379The fields \texttt{save\_frame} and \texttt{pop\_frame} manipulate stack frames.
380In particular, \texttt{save\_frame} creates a new stack frame on the top of the stack, saving the destination and parameters of a function, and returning an updated state.
381The field \texttt{pop\_frame} destructively pops a stack frame from the stack, returning an updated state.
382Further, \texttt{set\_result} saves the result of the function computation, and \texttt{exec\_extended} is a function that executes the extended statements, peculiar to each individual intermediate language.
383
384We bundle \texttt{params} and \texttt{sem\_params} together into a single record.
385This will be used in the function \texttt{eval\_statement} which executes a single statement of the joint language:
386\begin{lstlisting}
387record sem_params2 (globals: list ident): Type[1] :=
388{
389  p2 :> params globals;
390  more_sparams2 :> more_sem_params2 globals p2
391}.
392\end{lstlisting}
393\noindent
394The \texttt{state} record holds the current state of the interpreter:
395\begin{lstlisting}
396record state (p: sem_params): Type[0] :=
397{
398  st_frms: framesT ? p;
399  pc: address;
400  sp: pointer;
401  isp: pointer;
402  carry: beval;
403  regs: regsT ? p;
404  m: bemem
405}.
406\end{lstlisting}
407Here \texttt{st\_frms} represent stack frames, \texttt{pc} the program counter, \texttt{sp} the stack pointer, \texttt{isp} the internal stack pointer, \texttt{carry} the carry flag, \texttt{regs} the registers (hardware and pseudoregisters) and \texttt{m} external RAM.
408Note that we have two stack pointers, as we have two stacks: the physical stack of the MCS-51 microprocessor, and an emulated stack in external RAM.
409The MCS-51's own stack is minuscule, therefore it is usual to emulate a much larger, more useful stack in external RAM.
410We require two stack pointers as the MCS-51's \texttt{PUSH} and \texttt{POP} instructions manipulate the physical stack, and not the emulated one.
411
412We use the function \texttt{eval\_statement} to evaluate a single joint statement:
413\begin{lstlisting}
414definition eval_statement:
415  ∀globals: list ident.∀p:sem_params2 globals.
416    genv globals p → state p → IO io_out io_in (trace × (state p)) :=
417...
418\end{lstlisting}
419We examine the type of this function.
420Note that it returns a monadic action, \texttt{IO}, denoting that it may have an IO \emph{side effect}, where the program reads or writes to some external device or memory address.
421Monads and their use are further discussed in Subsection~\ref{subsect.use.of.monads}.
422Further, the function returns a new state, updated by the single step of execution of the program.
423Finally, a \emph{trace} is also returned, which records externally observable `events', such as the calling of external functions and the emission of cost labels.
424
425%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%
426% SECTION.                                                                    %
427%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%
428\subsection{Use of monads}
429\label{subsect.use.of.monads}
430
431Monads are a categorical notion that have recently gained an amount of traction in functional programming circles.
432In particular, it was noted by Moggi that monads could be used to sequence \emph{effectful} computations in a pure manner.
433Here, `effectful computations' cover a lot of ground, from writing to files, generating fresh names, or updating an ambient notion of state.
434
435A monad can be characterised by the following:
436\begin{itemize}
437\item
438A data type, $M$.
439For instance, the \texttt{option} type in O'Caml or Matita.
440\item
441A way to `inject' or `lift' pure values into this data type (usually called \texttt{return}).
442We call this function \texttt{return} and say that it must have type $\alpha \rightarrow M \alpha$, where $M$ is the name of the monad.
443In our example, the `lifting' function for the \texttt{option} monad can be implemented as:
444\begin{lstlisting}
445let return x = Some x
446\end{lstlisting}
447\item
448A way to `sequence' monadic functions together, to form another monadic function, usually called \texttt{bind}.
449Bind has type $M \alpha \rightarrow (\alpha \rightarrow M \beta) \rightarrow M \beta$.
450We can see that bind `unpacks' a monadic value, applies a function after unpacking, and `repacks' the new value in the monad.
451In our example, the sequencing function for the \texttt{option} monad can be implemented as:
452\begin{lstlisting}
453let bind o f =
454  match o with
455    None -> None
456    Some s -> f s
457\end{lstlisting}
458\item
459A series of algebraic laws that relate \texttt{return} and \texttt{bind}, ensuring that the sequencing operation `does the right thing' by retaining the order of effects.
460These \emph{monad laws} should also be useful in reasoning about monadic computations in the proof of correctness of the compiler.
461\end{itemize}
462In the semantics of both front and backend intermediate languages, we make use of monads.
463This monadic infrastructure is shared between the frontend and backend languages.
464
465In particular, an `IO' monad, signalling the emission of a cost label, or the calling of an external function, is heavily used in the semantics of the intermediate languages.
466Here, the monad's sequencing operation ensures that cost label emissions and function calls are maintained in the correct order.
467We have already seen how the \texttt{eval\_statement} function of the joint language is monadic, with type:
468\begin{lstlisting}
469definition eval_statement:
470  ∀globals: list ident.∀p:sem_params2 globals.
471    genv globals p → state p → IO io_out io_in (trace × (state p)) :=
472...
473\end{lstlisting}
474If we examine the body of \texttt{eval\_statement}, we may also see how the monad sequences effects.
475For instance, in the case for the \texttt{LOAD} statement, we have the following:
476\begin{lstlisting}
477definition eval_statement:
478  ∀globals: list ident. ∀p:sem_params2 globals.
479    genv globals p → state p → IO io_out io_in (trace × (state p)) :=
480  $\lambda$globals, p, ge, st.
481  ...
482  match s with
483  | LOAD dst addrl addrh ⇒
484    ! vaddrh $\leftarrow$ dph_retrieve … st addrh;
485    ! vaddrl $\leftarrow$ dpl_retrieve … st addrl;
486    ! vaddr $\leftarrow$ pointer_of_address 〈vaddrl,vaddrh〉;
487    ! v $\leftarrow$ opt_to_res … (msg FailedLoad) (beloadv (m … st) vaddr);
488    ! st $\leftarrow$ acca_store p … dst v st;
489    ! st $\leftarrow$ next … l st ;
490      ret ? $\langle$E0, st$\rangle$
491\end{lstlisting}
492Here, we employ a certain degree of syntactic sugaring.
493The syntax
494\begin{lstlisting}
495  ...
496! vaddrh $\leftarrow$ dph_retrieve … st addrh;
497! vaddrl $\leftarrow$ dpl_retrieve … st addrl;
498  ...
499\end{lstlisting}
500is sugaring for the \texttt{IO} monad's binding operation.
501We can expand this sugaring to the following much more verbose code:
502\begin{lstlisting}
503  ...
504  bind (dph_retrieve … st addrh) ($\lambda$vaddrh. bind (dpl_retrieve … st addrl)
505    ($\lambda$vaddrl. ...))
506\end{lstlisting}
507Note also that the function \texttt{ret} is implementing the `lifting', or return function of the \texttt{IO} monad.
508
509We believe the sugaring for the monadic bind operation makes the program much more readable, and therefore easier to reason about.
510In particular, note that the functions \texttt{dph\_retrieve}, \texttt{pointer\_of\_address}, \texttt{acca\_store} and \texttt{next} are all monadic.
511
512Note, however, that inside this monadic code, there is also another monad hiding.
513The \texttt{res} monad signals failure, along with an error message.
514The monad's sequencing operation ensures the order of error messages does not get rearranged.
515The function \texttt{opt\_to\_res} lifts an option type into this monad, with an error message to be used in case of failure.
516The \texttt{res} monad is then coerced into the \texttt{IO} monad, ensuring the whole code snippet typechecks.
517
518\subsection{Memory models}
519\label{subsect.memory.models}
520
521Currently, the semantics of the front and backend intermediate languages are built around two distinct memory models.
522The frontend languages reuse the CompCert memory model, whereas the backend languages employ a bespoke model tailored to their needs.
523This split between the memory models is reflective of the fact that the front and backend language have different requirements from their memory models, to a certain extent.
524
525In particular, the CompCert memory model places quite heavy restrictions on where in memory one can read from.
526To read a value in this memory model, you must supply an address, complete with a number of `chunks' to read following that address.
527The read is only successful if you attempt to read at a genuine `value boundary', and read the appropriate number of memory chunks for that value.
528As a result, with the CompCert memory model you are unable to read the third byte of a 32-bit integer value directly from memory, for instance.
529This has some consequences for the CompCert compiler, namely an inability to write a \texttt{memcpy} routine.
530
531However, the CerCo memory model operates differently, as we need to move data `piecemeal' between stacks in the backend of the compiler.
532As a result, the bespoke memory model allows one to read data at any memory location, not just on value boundaries.
533This has the advantage that we can successfully write a \texttt{memcpy} routine with the CerCo compiler (remembering that \texttt{memcpy} is nothing more than `read a byte, copy a byte' repeated in a loop), an advantage over CompCert.
534
535Right now, the two memory models are interfaced during the translation from RTLabs to RTL.
536It is an open question whether we will unify the two memory models, using only the backend, bespoke memory model throughout the compiler, as the CompCert memory model seems to work fine for the frontend, where such byte-by-byte copying is not needed.
537However, should we decide to port the frontend to the new memory model, it has been written in such an abstract way that doing so would be relatively straightforward.
538
539%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%
540% SECTION.                                                                    %
541%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%
542\section{Future work}
543\label{sect.future.work}
544
545A few small axioms remain to be closed.
546These relate to fetching the next instruction to be interpreted from the control flow graph, or linearised representation, of the language.
547Closing these axioms should not be a problem.
548
549Most things related to external function calls are currently axiomatised.
550This is due to there being a difficulty with how stackframes are handled with external function calls.
551We leave this for further work, due to there being no pressing need to implement this feature at the present time.
552
553There is also, as mentioned, an open problem as to whether the frontend languages should use the same memory model as the backend languages, as opposed to reusing the CompCert memory model.
554Should this decision be taken, this will likely be straightforward but potentially time consuming.
555
556\newpage
557
558%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%
559% SECTION.                                                                    %
560%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%
561\section{Code listing}
562\label{sect.code.listing}
563
564%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%
565% SECTION.                                                                    %
566%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%
567\subsection{Listing of files}
568\label{subsect.listing.files}
569
570Semantics specific files (files relating to language translations ommitted).
571Syntax specific files are presented in Table~\ref{table.syntax}.
572\begin{landscape}
573\begin{table}
574\begin{threeparttable}
575\begin{tabular}{llll}
576Title & Description & O'Caml & Ratio \\
577\hline
578\texttt{joint/Joint.ma} & Abstracted syntax for backend languages & N/A & N/A \\
579\texttt{RTLabs/syntax.ma} & The syntax of RTLabs & \texttt{RTLabs/RTLabs.mli} & 0.65 \\
580\texttt{RTL/RTL.ma} & The syntax of RTL & \texttt{RTL/RTL.mli} & 1.85\tnote{b} \\
581\texttt{ERTL/ERTL.ma} & The syntax of ERTL & \texttt{ERTL/ERTL.mli} & 1.04\tnote{b} \\
582\texttt{LIN/joint\_LTL\_LIN.ma} & The syntax of the abstracted combined LTL and LIN language & N/A & N/A \\
583\texttt{LTL/LTL.ma} & The specialisation of the above file to the syntax of LTL & \texttt{LTL/LTL.mli} & 1.86\tnote{a} \\
584\texttt{LIN/LIN.ma} & The specialisation of the above file to the syntax of LIN & \texttt{LIN/LIN.mli} & 2.27\tnote{a}
585\end{tabular}
586\begin{tablenotes}
587  \item[a] Includes \texttt{joint/Joint\_LTL\_LIN.ma} and \texttt{joint/Joint.ma}.
588  \item[b] Includes \texttt{joint/Joint.ma}. \\
589  Total lines of Matita code for the above files: 347. \\
590  Total lines of O'Caml code for the above files: 616. \\
591  Ration of total lines: 0.56.
592\end{tablenotes}
593\end{threeparttable}
594\caption{Syntax specific files in the intermediate language semantics}
595\label{table.syntax}
596\end{table}
597\end{landscape}
598Here, the O'Caml column denotes the O'Caml source file in the prototype compiler's implementation that corresponds to the Matita script in question.
599The ratios are the linecounts of the Matita file divided by the line counts of the corresponding O'Caml file.
600These are computed with \texttt{wc -l}, a standard Unix tool.
601
602Individual file's ratios are an over approximation, due to the fact that it's hard to relate an individual O'Caml file to the abstracted Matita code that has been spread across multiple files.
603The ratio between total Matita code lines and total O'Caml code lines is more reflective of the compressed and abstracted state of the Matita translation.
604
605Semantics specific files are presented in Table~\ref{table.semantics}.
606\begin{landscape}
607\begin{table}
608\begin{threeparttable}
609\begin{tabular}{llll}
610Title & Description & O'Caml & Ratio \\
611\hline
612\texttt{joint/semantics.ma} & Semantics of the abstracted languages & N/A & N/A  \\
613\texttt{joint/SemanticUtils.ma} & Generic utilities used in semantics `joint' languages & N/A & N/A \\
614\texttt{RTLabs/semantics.ma} & Semantics of RTLabs & \texttt{RTLabs/RTLabsInterpret.ml} & 0.63 \\
615\texttt{RTL/semantics.ma} & Semantics of RTL & \texttt{RTL/RTLInterpret.ml} & 1.88\tnote{a} \\
616\texttt{ERTL/semantics.ma} & Semantics of ERTL & \texttt{ERTL/ERTLInterpret.ml} & 1.22\tnote{a} \\
617\texttt{LTL/semantics.ma} & Semantics of LTL & \texttt{LTL/LTLInterpret.ml} & 1.25\tnote{c} \\
618\texttt{LIN/joint\_LTL\_LIN\_semantics.ma} & Semantics of the joint LTL-LIN language & N/A & N/A \\
619\texttt{LIN/semantics.ma} & Semantics of LIN & \texttt{LIN/LINInterpret.ml} & 1.52\tnote{c}
620\end{tabular}
621\begin{tablenotes}
622  \item{a} Includes \texttt{joint/semantics.ma} and \texttt{joint/SemanticUtils.ma}.
623  \item{b} Includes \texttt{joint/joint\_LTL\_LIN\_semantics.ma}.
624  \item{c} Includes \texttt{joint/semantics.ma}, \texttt{joint/SemanticUtils.ma} and \texttt{joint/joint\_LTL\_LIN\_semantics.ma}. \\
625  Total lines of Matita code for the above files: 1125. \\
626  Total lines of O'Caml code for the above files: 1978. \\
627  Ration of total lines: 0.57.
628\end{tablenotes}
629\end{threeparttable}
630\caption{Semantics specific files in the intermediate language semantics}
631\label{table.semantics}
632\end{table}
633\end{landscape}
634
635%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%
636% SECTION.                                                                    %
637%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%
638\subsection{Listing of important functions and axioms}
639\label{subsect.listing.important.functions.axioms}
640
641We list some important functions and axioms in the backend semantics:
642
643\end{document}
Note: See TracBrowser for help on using the repository browser.