source: Deliverables/D4.2-4.3/reports/D4-3.tex @ 1394

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1\documentclass[11pt, epsf, a4wide]{article}
2
3\usepackage{../../style/cerco}
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5\usepackage{amsfonts}
6\usepackage{amsmath}
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8\usepackage[english]{babel}
9\usepackage{graphicx}
10\usepackage[utf8x]{inputenc}
11\usepackage{listings}
12\usepackage{stmaryrd}
13\usepackage{url}
14
15\title{
16INFORMATION AND COMMUNICATION TECHNOLOGIES\\
17(ICT)\\
18PROGRAMME\\
19\vspace*{1cm}Project FP7-ICT-2009-C-243881 \cerco{}}
20
21\lstdefinelanguage{matita-ocaml}
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26  }
27
28\lstset{language=matita-ocaml,basicstyle=\small\tt,columns=flexible,breaklines=false,
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31        keywordstyle=[3]\color{blue}\bfseries,
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40\DeclareUnicodeCharacter{9001}{\ensuremath{\langle}}
41\DeclareUnicodeCharacter{9002}{\ensuremath{\rangle}}
42
43\date{}
44\author{}
45
46\begin{document}
47
48\thispagestyle{empty}
49
50\vspace*{-1cm}
51\begin{center}
52\includegraphics[width=0.6\textwidth]{../../style/cerco_logo.png}
53\end{center}
54
55\begin{minipage}{\textwidth}
56\maketitle
57\end{minipage}
58
59\vspace*{0.5cm}
60\begin{center}
61\begin{LARGE}
62\textbf{
63Report n. D4.3\\
64Formal semantics of intermediate languages
65}
66\end{LARGE} 
67\end{center}
68
69\vspace*{2cm}
70\begin{center}
71\begin{large}
72Version 1.0
73\end{large}
74\end{center}
75
76\vspace*{0.5cm}
77\begin{center}
78\begin{large}
79Main Authors:\\
80Dominic P. Mulligan and Claudio Sacerdoti Coen
81\end{large}
82\end{center}
83
84\vspace*{\fill}
85
86\noindent
87Project Acronym: \cerco{}\\
88Project full title: Certified Complexity\\
89Proposal/Contract no.: FP7-ICT-2009-C-243881 \cerco{}\\
90
91\clearpage
92\pagestyle{myheadings}
93\markright{\cerco{}, FP7-ICT-2009-C-243881}
94
95\newpage
96
97\vspace*{7cm}
98\paragraph{Abstract}
99
100\newpage
101
102\tableofcontents
103
104\newpage
105
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109\section{Task}
110\label{sect.task}
111
112The Grant Agreement states that Task T4.3, entitled `Formal semantics of intermediate languages' has associated Deliverable D4.3, consisting of the following:
113\begin{quotation}
114Executable 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.
115\end{quotation}
116This report details our implementation of this deliverable.
117
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121\subsection{Connections with other deliverables}
122\label{subsect.connections.with.other.deliverables}
123
124Deliverable D4.3 enjoys a close relationship with three other deliverables, namely deliverables D2.2, D4.3 and D4.4.
125
126Deliverable 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.
127In 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.
128Any 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.
129
130Deliverable D4.2 can be seen as a `sister' deliverable to the deliverable reported on herein.
131In 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.
132As a result, a substantial amount of Matita code is shared between the two deliverables.
133
134Deliverable D4.4, the backend correctness proofs, is the immediate successor of this deliverable.
135
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139\section{The backend intermediate languages' semantics in Matita}
140\label{sect.backend.intermediate.languages.semantics.matita}
141
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145\subsection{Abstracting related languages}
146\label{subsect.abstracting.related.languages}
147
148As 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.
149In 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.
150Equivalent intermediate languages to those present in the O'Caml code can be recovered by specialising this joint structure.
151
152As 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.
153However, 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.
154In particular, the semantics of both LTL and LIN are implemented in exactly the same way.
155The only difference between the two languages is how the next instruction to be interpreted is fetched.
156In LTL, this involves looking up in a graph, whereas in LTL, this involves fetching from a list of instructions.
157
158As 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.
159Furthermore, any prospective proof that the semantics of LTL and LIN are identical is not almost trivial, saving a deal of work in Deliverable D4.4.
160
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164\subsection{Use of monads}
165\label{subsect.use.of.monads}
166
167Monads are a categorical notion that have recently gained an amount of traction in functional programming circles.
168In particular, it was noted by Moggi that monads could be used to sequence \emph{effectful} computations in a pure manner.
169Here, `effectful computations' cover a lot of ground, from writing to files, generating fresh names, or updating an ambient notion of state.
170
171In the semantics of both front and backend intermediate languages, we make use of monads.
172In particular, we make use of two forms of monad:
173\begin{enumerate}
174\item
175An `error monad', which signals that a computation either has completed successfully, or returns with an error message.
176The sequencing operation of the error monad ensures that the result of chained computations in return the error message of the first failed computation.
177This monad is used extensively in the semantics to signal a state which cannot be recovered from.
178For instance, in the semantics of RTLabs, we make use of the error monad to signal bad final states:
179\begin{lstlisting}
180...
181| Returnstate v dst fs m $\Rightarrow$
182  match fs with
183  [ nil ⇒ Error $\ldots$ (msg FinalState) (* Already in final state *)
184  | cons f fs' $\Rightarrow$
185    ! locals $\leftarrow$ match dst with
186    [ None $\Rightarrow$
187      match v with
188      [ None $\Rightarrow$ OK $\ldots$ (locals f)
189      | _ $\Rightarrow$ Error $\ldots$ (msg ReturnMismatch)
190      ]
191    | Some d $\Rightarrow$
192      match v with
193      [ None $\Rightarrow$ Error $\ldots$ (msg ReturnMismatch)
194      | Some v' $\Rightarrow$ reg_store d v' (locals f)
195      ]
196    ];
197    ret $\ldots$ $\langle$E0, State (mk_frame (func f) locals (next f) (sp f) (retdst f)) fs' m$\rangle$
198  ]
199...
200\end{lstlisting}
201\item
202An `IO' monad, signalling the emission or reading of data to some external location or memory address.
203Here, the monads sequencing operation ensures that emissions and reads are maintained in the correct order (i.e. it maintains a `trace', or ordered sequence of IO events).
204Most functions in the intermediate language semantics fall into the IO monad.
205\end{enumerate}
206This monadic infrastructure is shared between the frontend and backend languages.
207
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211\section{Future work}
212\label{sect.future.work}
213
214A few small axioms remain to be closed.
215These relate to fetching the next instruction to be interpreted from the control flow graph, or linearised representation, of the language.
216Closing these axioms should not be a problem.
217No further work remains, aside from `tidying up' the code.
218
219\newpage
220
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224\section{Code listing}
225\label{sect.code.listing}
226
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230\subsection{Listing of files}
231\label{subsect.listing.files}
232
233Semantics specific files (files relating to language translations ommitted):
234\begin{center}
235\begin{tabular*}{0.9\textwidth}{p{5cm}p{8cm}}
236Title & Description \\
237\hline
238\texttt{RTLabs/syntax.ma} & The syntax of RTLabs \\
239\texttt{RTLabs/semantics.ma} & The semantics of RTLabs \\
240\texttt{joint/Joint.ma} & Abstracted syntax for backend languages \\
241\texttt{joint/SemanticUtils.ma} & Generic utilities used in the semantics of all `joint' intermediate languages \\
242\texttt{RTL/RTL.ma} & The syntax of RTL \\
243\texttt{RTL/semantics.ma} & The semantics of RTL \\
244\texttt{ERTL/ERTL.ma} & The syntax of ERTL \\
245\texttt{ERTL/semantics.ma} & The semantics of ERTL \\
246\texttt{LTL/LTL.ma} & The syntax of LTL \\
247\texttt{LTL/semantics.ma} & The semantics of LTL \\
248\texttt{LIN/LIN.ma} & The syntax of LIN \\
249\texttt{LIN/semantics.ma} & The semantics of LIN
250\end{tabular*}
251\end{center}
252
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256\subsection{Listing of important functions and axioms}
257\label{subsect.listing.important.functions.axioms}
258
259We list some important functions and axioms in the backend semantics:
260
261\end{document}
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