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Fixed typos in doc

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Dmitry Boulytchev 2018-02-15 23:40:23 +03:00
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doc/01.tex
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@ -132,7 +132,7 @@ eval : \mathscr L \to \mbox{\lstinline|Input|} \to \mbox{\lstinline|Output|}
$$
where \lstinline|Input| and \lstinline|Output| are sets of (all possible) inputs and outputs for the programs in the language $\mathscr L$. We claim $eval$ to
posess the following property
possess the following property
$$
\forall p \in \mathscr L,\, \forall x\in \mbox{\lstinline|Input|} : \sembr{p}_{\mathscr L}\;x = eval\; p\; x
@ -163,7 +163,7 @@ $$
comp :\mathscr L \to \mathscr M
$$
for two languages $\mathscr L$ and $\mathscr M$; we expect a compilerto be total and to posess the following property:
for two languages $\mathscr L$ and $\mathscr M$; we expect a compiler to be total and to possess the following property:
$$
\forall p\in\mathscr L\;\;\sembr{p}_{\mathscr L}=\sembr{comp\; p}_{\mathscr M}
@ -173,7 +173,7 @@ Again, the equality in this definition is understood functionally. The property
compilers are \emph{partially} correct, which means, that the domain of compiled programs can be wider.
And, again, we expect compilers to be defined in terms of some implementation language. Thus, a compiler is a program (in, say, ocaml), such, that
its semantics in ocaml posesses the following property (fill the rest yourself).
its semantics in ocaml possesses the following property (fill the rest yourself).
\section{The first example: language of expressions}
@ -225,7 +225,7 @@ $$
\lstinline|>| & \lstinline|>| \\
\lstinline|<=| & \lstinline|<=| \\
\lstinline|>=| & \lstinline|>=| \\
\lstinline|==| & \lstinline|==| \\
\lstinline|==| & \lstinline|=| \\
\lstinline|!=| & \lstinline|<>| \\
\lstinline|&&| & \lstinline|&&| & \rdelim\}{2}{5mm}[ see note 2 below]\\
\lstinline|!!| & \lstinline/||/
@ -234,7 +234,8 @@ $$
Note 1: the result is converted into integers (true $\to$ 1, false $\to$ 0).
Note 2: the arguments are converted to booleans (0 $\to$ false, not 0 $\to$ true), the result is converted to integers as in the previous note.
Note 2: the arguments are converted to booleans (0 $\to$ false, not 0 $\to$ true), the result is converted to
integers as in the previous note.
Important observations: