source: Deliverables/D4.2-4.3/reports/D4-3.tex @ 1391

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1\documentclass[11pt, epsf, a4wide]{article}
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3\usepackage{../../style/cerco}
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8\usepackage[english]{babel}
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11\usepackage{listings}
12\usepackage{stmaryrd}
13\usepackage{url}
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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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28\lstset{language=matita-ocaml,basicstyle=\small\tt,columns=flexible,breaklines=false,
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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}
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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.
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155\subsection{Use of monads}
156\label{subsect.use.of.monads}
157
158Monads are a categorical notion that have recently gained an amount of traction in functional programming circles.
159In particular, it was noted by Moggi that monads could be used to sequence \emph{effectful} computations in a pure manner.
160Here, `effectful computations' cover a lot of ground, from writing to files, generating fresh names, or updating an ambient notion of state.
161
162In the semantics of both front and backend intermediate languages, we make use of monads.
163In particular, we make use of two forms of monad:
164\begin{enumerate}
165\item
166An `error monad', which signals that a computation either has completed successfully, or returns with an error message.
167The sequencing operation of the error monad ensures that the result of chained computations in return the error message of the first failed computation.
168This monad is used extensively in the semantics to signal a state which cannot be recovered from.
169For instance, in the semantics of RTLabs, we make use of the error monad to signal bad final states:
170\begin{lstlisting}
171...
172| Returnstate v dst fs m $\Rightarrow$
173  match fs with
174  [ nil ⇒ Error $\ldots$ (msg FinalState) (* Already in final state *)
175  | cons f fs' $\Rightarrow$
176    ! locals $\leftarrow$ match dst with
177    [ None $\Rightarrow$
178      match v with
179      [ None $\Rightarrow$ OK $\ldots$ (locals f)
180      | _ $\Rightarrow$ Error $\ldots$ (msg ReturnMismatch)
181      ]
182    | Some d $\Rightarrow$
183      match v with
184      [ None $\Rightarrow$ Error $\ldots$ (msg ReturnMismatch)
185      | Some v' $\Rightarrow$ reg_store d v' (locals f)
186      ]
187    ];
188    ret $\ldots$ $\langle$E0, State (mk_frame (func f) locals (next f) (sp f) (retdst f)) fs' m$\rangle$
189  ]
190...
191\end{lstlisting}
192\item
193An `IO' monad, signalling the emission or reading of data to some external location or memory address.
194Here, 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).
195Most functions in the intermediate language semantics fall into the IO monad.
196\end{enumerate}
197
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201\section{Future work}
202\label{sect.future.work}
203
204A few small axioms remain to be closed.
205These relate to fetching the next instruction to be interpreted from the control flow graph, or linearised representation, of the language.
206Closing these axioms should not be a problem.
207No further work remains, aside from `tidying up' the code.
208
209\newpage
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214\section{Code listing}
215\label{sect.code.listing}
216
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220\subsection{Listing of files}
221\label{subsect.listing.files}
222
223Semantics specific files (files relating to language translations ommitted):
224\begin{center}
225\begin{tabular*}{0.9\textwidth}{p{5cm}p{8cm}}
226Title & Description \\
227\hline
228\texttt{RTLabs/syntax.ma} & The syntax of RTLabs \\
229\texttt{RTLabs/semantics.ma} & The semantics of RTLabs \\
230\texttt{joint/Joint.ma} & Abstracted syntax for backend languages \\
231\texttt{joint/SemanticUtils.ma} & Generic utilities used in the semantics of all `joint' intermediate languages \\
232\texttt{RTL/RTL.ma} & The syntax of RTL \\
233\texttt{RTL/semantics.ma} & The semantics of RTL \\
234\texttt{ERTL/ERTL.ma} & The syntax of ERTL \\
235\texttt{ERTL/semantics.ma} & The semantics of ERTL \\
236\texttt{LTL/LTL.ma} & The syntax of LTL \\
237\texttt{LTL/semantics.ma} & The semantics of LTL \\
238\texttt{LIN/LIN.ma} & The syntax of LIN \\
239\texttt{LIN/semantics.ma} & The semantics of LIN
240\end{tabular*}
241\end{center}
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246\subsection{Listing of important functions and axioms}
247\label{subsect.listing.important.functions.axioms}
248
249We list some important functions and axioms in the backend semantics:
250
251\end{document}
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