tesi coppo
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Francesco Mecca
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.7.5"
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"version": "3.7.7"
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}
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},
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"nbformat": 4,
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digraph Tree {
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node [shape=box] ;
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0 [label="X[2] <= 2.45\nentropy = 1.585\nsamples = 150\nvalue = [50, 50, 50]"] ;
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1 [label="entropy = 0.0\nsamples = 50\nvalue = [50, 0, 0]"] ;
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0 -> 1 [labeldistance=2.5, labelangle=45, headlabel="True"] ;
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2 [label="X[3] <= 1.75\nentropy = 1.0\nsamples = 100\nvalue = [0, 50, 50]"] ;
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0 -> 2 [labeldistance=2.5, labelangle=-45, headlabel="False"] ;
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3 [label="X[2] <= 4.95\nentropy = 0.445\nsamples = 54\nvalue = [0, 49, 5]"] ;
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4 [label="X[0] <= 5.15\nentropy = 0.146\nsamples = 48\nvalue = [0, 47, 1]"] ;
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5 [label="entropy = 0.722\nsamples = 5\nvalue = [0, 4, 1]"] ;
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6 [label="entropy = 0.0\nsamples = 43\nvalue = [0, 43, 0]"] ;
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7 [label="entropy = 0.918\nsamples = 6\nvalue = [0, 2, 4]"] ;
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8 [label="X[2] <= 4.95\nentropy = 0.151\nsamples = 46\nvalue = [0, 1, 45]"] ;
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9 [label="entropy = 0.65\nsamples = 6\nvalue = [0, 1, 5]"] ;
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10 [label="entropy = 0.0\nsamples = 40\nvalue = [0, 0, 40]"] ;
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}
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digraph Tree {
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node [shape=box] ;
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0 [label="X[2] <= 2.45\nentropy = 1.585\nsamples = 150\nvalue = [50, 50, 50]"] ;
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1 [label="entropy = 0.0\nsamples = 50\nvalue = [50, 0, 0]"] ;
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0 -> 1 [labeldistance=2.5, labelangle=45, headlabel="True"] ;
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2 [label="X[3] <= 1.75\nentropy = 1.0\nsamples = 100\nvalue = [0, 50, 50]"] ;
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0 -> 2 [labeldistance=2.5, labelangle=-45, headlabel="False"] ;
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3 [label="X[2] <= 4.95\nentropy = 0.445\nsamples = 54\nvalue = [0, 49, 5]"] ;
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2 -> 3 ;
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4 [label="X[0] <= 5.15\nentropy = 0.146\nsamples = 48\nvalue = [0, 47, 1]"] ;
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3 -> 4 ;
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5 [label="entropy = 0.722\nsamples = 5\nvalue = [0, 4, 1]"] ;
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4 -> 5 ;
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6 [label="entropy = 0.0\nsamples = 43\nvalue = [0, 43, 0]"] ;
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7 [label="entropy = 0.918\nsamples = 6\nvalue = [0, 2, 4]"] ;
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8 [label="X[2] <= 4.95\nentropy = 0.151\nsamples = 46\nvalue = [0, 1, 45]"] ;
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9 [label="entropy = 0.65\nsamples = 6\nvalue = [0, 1, 5]"] ;
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8 -> 9 ;
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10 [label="entropy = 0.0\nsamples = 40\nvalue = [0, 0, 40]"] ;
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}
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@ -130,7 +130,9 @@ compiler avoid the introduction of new bugs and that such
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modifications don't result in a different behavior than the current one.
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\\
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One possible approach is to formally verify the pattern matching compiler
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implementation using a machine checked proof.
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implementation using a machine checked proof. Much effort has been
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spent on this topic and whole compilers have been proven either
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manually\cite{compuno,compdue,comptre} or using a proof assistant\cite{compquattro,compfive,compsei}.
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Another possibility, albeit with a weaker result, is to verify that
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each source program and target program pair are semantically correct.
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We chose the latter technique, translation validation because is easier to adopt in
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@ -238,15 +240,6 @@ expressions that are lowered by the compiler into lambda expressions.
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possible immediate-integer or block-tag values.
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\end{comment}
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\begin{mathpar}
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\begin{array}{l@{~}r@{~}r@{~}l}
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\text{\emph{decision trees}} & D(\pi, e)
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& \bnfeq & \Leaf {\cle(a)} \\
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& & \bnfor & \Failure \\
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& & \bnfor & \Switch a {\Fam {i \in I} {\pi_i, D_i}} \Dfb \\
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& & \bnfor & \Guard {\cle(a)} {D_0} {D_1} \\
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& & \bnfor & Unreachable
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\end{array}
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\quad
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\begin{array}{l@{~}r@{~}r@{~}l}
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\text{\emph{environment}} & \sigma(v)
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& \bnfeq & [x_1 \mapsto v_1, \dots, v_n \mapsto v_n] \\
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@ -265,76 +258,28 @@ expressions that are lowered by the compiler into lambda expressions.
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a(v_S), a(v_T), D_S(v_S), D_T(v_T) \quad (\text{\emph{omitted})}
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\end{array}
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\end{mathpar}
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\begin{mathpar}
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\begin{array}{l@{~}r@{~}r@{~}l}
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\text{\emph{decision trees}} & D(\pi, e)
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& \bnfeq & \Leaf {\cle(a)} \\
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& & \bnfor & \Failure \\
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& & \bnfor & \Switch a {\Fam {i \in I} {\pi_i, D_i}} \Dfb \\
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& & \bnfor & \Guard {\cle(a)} {D_0} {D_1} \\
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& & \bnfor & Unreachable
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\end{array}
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\end{mathpar}
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The tree $\Leaf \cle$ returns a leaf expression $e$ in a captured
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environment $\sigma$ mapping variables to accessors.\\
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$\Failure$ expresses a match failure that occurs when no clause matches the input
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value.
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\\
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$\Switch a {\Fam {i \in I} {\pi_i, D_i}} D_{fallback}$ has one subtree $D_i$
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$\Switch a {\Fam {i \in I} {\pi_i, D_i}} {D_{fallback}}$ has one subtree $D_i$
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for every head constructor that appears in the pattern matching
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clauses, and a fallback case that is used when at least one variant of
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the constructor doesn't appear in the clauses. The presence of the
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fallback case does not imply non-exhaustive match clauses.
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\begin{minipage}{0.3\linewidth}
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\scriptsize
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\begin{lstlisting}
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let f1 = function
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| true -> 1
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| false -> 0
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\end{lstlisting}
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\end{minipage}
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\hfill\vline\hfill
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\begin{minipage}{0.3\linewidth}
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\scriptsize
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\begin{lstlisting}
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let f1 = function
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| true -> 1
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| _ -> 0
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\end{lstlisting}
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\end{minipage}
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\hfill\vline\hfill
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\begin{minipage}{0.3\linewidth}
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\scriptsize
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\begin{lstlisting}
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let f1 = function
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| true -> 1
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\end{lstlisting}
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\end{minipage}
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\begin{minipage}{0.3\linewidth}
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\scriptsize
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\begin{verbatim}
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Switch(Root)
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/ \
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(Bool true) (Bool false)
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/ \
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Leaf(Int 1) Leaf(Int 0)
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\end{verbatim}
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\end{minipage}
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\hfill\vline\hfill
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\begin{minipage}{0.3\linewidth}
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\scriptsize
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\begin{verbatim}
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Switch(Root)
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/ \
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(Bool true) (`Fallback`)
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/ \
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Leaf(Int 1) Leaf(Int 0)
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\end{verbatim}
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\end{minipage}
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\hfill\vline\hfill
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\begin{minipage}{0.3\linewidth}
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\scriptsize
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\begin{verbatim}
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Switch(Root)
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/ \
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(Bool true) (`Fallback`)
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/ \
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Leaf(Int 1) Failure
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\end{verbatim}
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\end{minipage}
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\hfill \\
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[[./files/table.png]]
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As we can see from these simple examples in which we pattern match on a
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boolean constructor the fallback node in the second case implicitly
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covers the path in which the value is equal to false while in the
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@ -2169,12 +2114,78 @@ In this example the tool correctly handles /Failure/ nodes on both decision tree
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;; include_file example9bis.lambda
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;; include_file example9bis.trace
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* Conclusions
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In recent years bugs in the OCaml pattern matching compiler have
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been infrequent: only one in the last four years\cite{bug}.
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The main motivation for this work is the ongoing efforts of the OCaml
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core developers towards towards refactoring the
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OCaml pattern matching
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compiler\cite{ref1,ref2,ref3,ref4,ref5,ref6,ref7,ref8,ref9,ref10,ref11,ref12,ref13}.
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The prototype presented in this dissertation shows a
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sound approach for the verification of a correct compilation.
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Compared to similar works in the field, this work differs from Necula
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et al.\cite{trans_due} for the absence of false positives cases.
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The work of Kirchner et al.\cite{trans_55} is the most similar to this
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dissertation but has the drawbacks of introducing a new /IL/, requires
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a full fledged SAT solver (Zenon) and does not handle guards.
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The internship was focused on providing a working MVP. In order for
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the work to be integrated into the OCaml compiler toolchain the
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prototype needs to handle all primitive datatypes.
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While string and floats are trivial to add to the current
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implementation, OCaml supports extensible sum types\cite{exn} that may
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require a lot of effort to be successfully integrated into the tool.
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Extensible sum types are a product type whose set
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of values can be extended by declaring new constructors at runtime.
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Pattern matching on extensible sum types requires a wildcard pattern
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to handle unknown variant constructors. Exceptions were the first type
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of extensible sum type implemented in the language.
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The prototype uses /observe/ and /guard/ directives as a shortcut to
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avoid depending on the compiler. In order to support real-world code
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we need to instrument the compiler-libs to provide a two pass
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compilation where guards and leaf expressions can be compiled to
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Lambda code indipendently from the rest of the pattern match code.
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\begin{thebibliography}{9}
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\bibitem{cpp_pat}
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Sergei Murzin, Michael Park, David Sankel, Dan Sarginson.
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\textit{P1371R1: Pattern Matching Proposal for C++}.
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http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2019/p1371r1.pdf
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\bibitem{compuno}
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John McCarthy and James Painter.
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\textit{Correctness of a compiler for arithmetic expressions}.
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Proceedings Symposium in Applied Mathematics, Vol. 19, pages 33–41. AMS, 1967.
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\bibitem{compdue}
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F. Lockwood Morris.
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\textit{Advice on structuring compilers and proving them correct}.
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1st annual ACM SIGACT-SIGPLAN Symposium on
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Principles of Programming Languages, pages 144–152.
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ACM Press, 1973
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\bibitem{comptre}
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David Lacey, Neil D. Jones, Eric Van Wyk, and
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Carl Christian Frederiksen.
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\textit{Proving correctness of compiler optimizations by temporal logic}.
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29th ACM Symposium on Principles of Programming
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Languages, pages 283–294. ACM Press, 2002.
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\bibitem{compquattro}
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Leroy Xavier.
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\textit{Formal verification of a realistic compiler}.
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Communications of the ACM 52.7 (2009): 107-115.
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\bibitem{compfive}
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Berghofer, Stefan, and Martin Strecker.
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\textit{Extracting a formally verified, fully executable compiler from a proof assistant}.
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Electronic Notes in Theoretical Computer Science 82.2 (2004): 377-394.
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\bibitem{compsei}
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Lochbihler, Andreas.
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\textit{Verifying a compiler for Java threads}.
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European Symposium on Programming. Springer, Berlin, Heidelberg, 2010.
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\bibitem{swift}
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Nayebi, Fatih.
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\textit{Swift Functional Programming}.
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@ -2258,4 +2269,44 @@ Régis-Gianas, François Pottier Yann.
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\bibitem{internship}
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https://github.com/FraMecca/inria-internship
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\bibitem{bug}
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https://github.com/ocaml/ocaml/issues/7390
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\bibitem{ref1}
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https://github.com/ocaml/ocaml/issues/7390
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\bibitem{ref2}
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https://github.com/ocaml/ocaml/pull/8768
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\bibitem{ref3}
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https://github.com/ocaml/ocaml/pull/8850
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\bibitem{ref4}
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https://github.com/ocaml/ocaml/pull/9447
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\bibitem{ref5}
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https://github.com/ocaml/ocaml/pull/9464
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\bibitem{ref6}
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https://github.com/ocaml/ocaml/pull/9493
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\bibitem{ref7}
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https://github.com/ocaml/ocaml/pull/9646
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\bibitem{ref8}
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https://github.com/ocaml/ocaml/pull/9608
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\bibitem{ref9}
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https://github.com/ocaml/ocaml/pull/9599
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\bibitem{ref10}
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https://github.com/ocaml/ocaml/pull/9563
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\bibitem{ref11}
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https://github.com/ocaml/ocaml/pull/9520
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\bibitem{ref12}
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https://github.com/ocaml/ocaml/pull/9511
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\bibitem{ref13}
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https://github.com/ocaml/ocaml/pull/9647
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\bibitem{trans_55}
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Kirchner, Claude, Pierre-Etienne Moreau, and Antoine Reilles.
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\textit{Formal validation of pattern matching code}.
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Proceedings of the 7th ACM SIGPLAN international conference on Principles and practice of declarative programming. 2005.
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\bibitem{exn}
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OCaml core developers.
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\textit{OCaml Manual}
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https://caml.inria.fr/pub/docs/manual-ocaml/extensiblevariants.html
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\end{thebibliography}
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9
todo.org
9
todo.org
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@ -54,11 +54,11 @@
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- [X] segreteria: tesi inglese
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- [X] Gatti: inglese
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- [X] Gatti: Coppo mio relatore
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- [-] correzioni Coppo [0/5]
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- [ ] esempi di esecuzione + test
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- [-] correzioni Coppo [2/5]
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- [X] esempi di esecuzione + test
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- [ ] esplicitare mio contributo a fine introduzione o abstract
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- [ ] spiegare meglio ruolo symbolic exec
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- [ ] Cosa manca per implementare al compilatore: passare da prototipo a cosa finita
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- [X] Cosa manca per implementare al compilatore: passare da prototipo a cosa finita
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- [-] Introduzione [2/4]
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- [ ] dovrebbe essere un po' ampliata e migliorata verso la fine
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- [X] snellendo un po' la presentazione formale.
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@ -80,6 +80,3 @@
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- [X] Gabriel: quello che penso sulle equivalenze omesse e` giusto?
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- [X] Cambia le C di constraint tree in D
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- [ ] TODO on the org file
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HALP
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HALP!
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