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grammar: add typing annotations to patterns

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And remove them from lambdas
This commit is contained in:
regnat 2017-05-11 07:30:24 +02:00
parent 864957720a
commit 51468d4d15
3 changed files with 30 additions and 25 deletions
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2
common/header.tex
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@ -37,6 +37,7 @@
\def\o/{\meta{o}} \def\o/{\meta{o}}
\def\p/{\meta{p}} \def\p/{\meta{p}}
\def\q/{\meta{q}} \def\q/{\meta{q}}
\def\r/{\meta{r}}
\def\s/{\meta{s}} \def\s/{\meta{s}}
\def\t/{\meta{t}} \def\t/{\meta{t}}
\def\u/{\meta{u}} \def\u/{\meta{u}}
@ -72,6 +73,7 @@
\newcommand{\quasiconst}[1]{\overset{#1}{\twoheadrightarrow}} \newcommand{\quasiconst}[1]{\overset{#1}{\twoheadrightarrow}}
\DeclareMathOperator\dom{dom} \DeclareMathOperator\dom{dom}
\DeclareMathOperator\deff{def} \DeclareMathOperator\deff{def}
\DeclareMathOperator\var{\mathcal{V}}
\newcommand{\orthsum}{\oplus^\bot} \newcommand{\orthsum}{\oplus^\bot}
\newcommand{\orthplus}{\diamond} \newcommand{\orthplus}{\diamond}
\newcommand{\subtype}{\leq} \newcommand{\subtype}{\leq}

14
grammar/expressions.tex
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@ -3,12 +3,12 @@
<e> ::= <e> ::=
\x/ \| \c/ \x/ \| \c/
\alt \e/.\a/ \| \e/.\a/ or \e/ \alt \e/.\a/ \| \e/.\a/ or \e/
\alt $\λ$\p/:\τ.\e/ \| \e/ \e/ \alt $\λ$\p/.\e/ \| \e/ \e/
\alt \{ \e/ = \e/ \} \alt \{ \e/ = \e/ \}
\alt with \e/; \e/ \alt with \e/; \e/
\alt (\x/ := \e/ $\bm{\in}$ \t/) ? \e/ : \e/ \alt (\x/ := \e/ $\bm{\in}$ \t/) ? \e/ : \e/
\alt let \x/ = \e/; $\cdots{}$; \x/ = \e/; in \e/ \alt let \x/ = \e/; $\cdots{}$; \x/ = \e/; in \e/
\alt let rec \x/:\τ = \e/; $\cdots{}$; \x/:\τ/ = \e/; in \e/ \alt let rec \r/ = \e/; $\cdots{}$; \r/ = \e/; in \e/
\alt \o/ \alt \o/
<o> ::= attrNames(\e/) \| listToAttrs(\e/) <o> ::= attrNames(\e/) \| listToAttrs(\e/)
@ -24,12 +24,14 @@
\alt nil \alt nil
\alt $\cdots{}$ \alt $\cdots{}$
<p> ::= \q/ \| \q/@\x/ \| \x/ <p> ::= \q/ \| \q/@\x/ \| \r/
<q> ::= \{ \f/, $\cdots{}$, \f/ \} \| \{ \f/, $\cdots{}$, \f/ , \ldots{}\} <q> ::= \{ \f/, $\cdots{}$, \f/ \} \| \{ \f/, $\cdots{}$, \f/ , \ldots{}\}
\alt Cons(\x/, \x/) \| nil \alt Cons(\r/, \r/) \| nil
\alt \c/ \alt \q/:\τ
<f> ::= \x/ \| \x/ ? \c/ <r> ::= \x/ | \x/:\τ
<f> ::= \r/ \| \r/ ? \c/
\end{grammar} \end{grammar}

39
semantics/semantics.tex
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@ -36,47 +36,48 @@ figure~\pref{fig:semantics:nix-light:patterns}
\end{figure} \end{figure}
\begin{figure} \begin{figure}
% TODO Rewrite in a clear way. Exlpain the fact that we can reordonate stuff because we got a
% commutative monoid.
\begin{tabular}{rl} \begin{tabular}{rl}
\eqdefa{$\sfrac{x:t}{e}$}{$\sfrac{x}{e}$}{}
\eqdefa{$\sfrac{x}{e}$}{$\sfrac{x}{e}$}{} \eqdefa{$\sfrac{x}{e}$}{$\sfrac{x}{e}$}{}
\eqdefa{$\sfrac{q@x}{e}$}{$\sfrac{x}{e}; \sfrac{q}{x}$}{} \eqdefa{$\sfrac{q@x}{e}$}{$\sfrac{x}{e}; \sfrac{q}{e}$}{}
\eqdefa{$\sfrac{\{\}}{\{ x_1 ? c_1, \cdots, x_n ? c_n \}}$}{% \eqdefa{$\sfrac{q:t}{e}$}{$\sfrac{q}{e}$}{}
$\sfrac{x_1}{c_1}; \cdots; \sfrac{x_n}{c_n}$}{} \eqdefa{$\sfrac{\{\}}{\{ r_1 ? c_1, \cdots, r_n ? c_n \}}$}{%
$\sfrac{r_1}{c_1}; \cdots; \sfrac{r_n}{c_n}$}{}
\eqdefa{% \eqdefa{%
$\sfrac{% $\sfrac{%
\{ s_1 = e_1; \cdots; s_m = e_m; \}% \{ s_1 = e_1; \cdots; s_m = e_m; \}%
}{% }{%
\{x_1 ? c_1, \cdots, x_n ? c_n, \textbf{\ldots}\}% \{r_1 ? c_1, \cdots, r_n ? c_n, \textbf{\ldots}\}%
}$% }$%
}{% }{%
$\sfrac{x_1}{c_1}; \cdots; \sfrac{x_n}{c_n}$% $\sfrac{r_1}{c_1}; \cdots; \sfrac{r_n}{c_n}$%
}{% }{%
if % if %
$\forall (i,j) \in \discrete{1}{m} \times \discrete{1}{n}, s_i \neq s_j$% $\forall (i,j) \in \discrete{1}{m} \times \discrete{1}{n}, s_i \neq \var(r_j)$%
} }
\eqdefa{$\sfrac{\{ s = e;\}}{\{ x \}}$}{$\sfrac{x}{e}$}{if $s = x$} \eqdefa{$\sfrac{\{ s = e;\}}{\{ r \}}$}{$\sfrac{r}{e}$}{if $s = \var(r)$}
\eqdefa{$\sfrac{\{ s = e;\}}{\{ x ? c \}}$}{$\sfrac{x}{e}$}{if $s = x$} \eqdefa{$\sfrac{\{ s = e;\}}{\{ r ? c \}}$}{$\sfrac{r}{e}$}{if $s = \var(r)$}
\eqdefa{$% \eqdefa{$%
\sfrac{\{ s_1 = e_1; \cdots; s_n = e_n \}}{\{ x, f_1, \cdots, f_m \}}% \sfrac{\{ s_1 = e_1; \cdots; s_n = e_n \}}{\{ r, f_1, \cdots, f_m \}}%
$}{$% $}{$%
\sfrac{x}{e};% \sfrac{r}{e};%
\sfrac{\{ s_2 = e_2; \cdots; s_n = e_n \}}{\{ f_1, \cdots, f_m \}}% \sfrac{\{ s_2 = e_2; \cdots; s_n = e_n \}}{\{ f_1, \cdots, f_m \}}%
$}{if $s_1 = x$} $}{if $s_1 = \var(r)$}
\eqdefa{ \eqdefa{
$\sfrac{% $\sfrac{%
\{ s_1 = e_1; \cdots; s_n = e_n \}}% \{ s_1 = e_1; \cdots; s_n = e_n \}}%
{\{ x ? c, f_1 \cdots, f_m \}}$% {\{ r ? c, f_1 \cdots, f_m \}}$%
}{% }{%
$\sfrac{x}{e};% $\sfrac{r}{e};%
\sfrac{\{ s_2 = e_2; \cdots; s_n = e_n \}}% \sfrac{\{ s_2 = e_2; \cdots; s_n = e_n \}}%
{\{ f_1, \cdots, f_m \}}$% {\{ f_1, \cdots, f_m \}}$%
}{if $s_1 = x$} }{if $s_1 = \var(r)$}
\eqdefa{% \eqdefa{%
$\sfrac{\text{Cons}(e_1, e_2)}{\text{Cons}(x_1, x_2)}$% $\sfrac{\text{Cons}(e_1, e_2)}{\text{Cons}(r_1, r_2)}$%
}{$\sfrac{x_1}{e_1}; \sfrac{x_2}{e_2}$}{} }{$\sfrac{r_1}{e_1}; \sfrac{r_2}{e_2}$}{}
\end{tabular} \end{tabular}
Where we define $\var(r)$ as $\var(x) = \var(x:t) = x$
\caption{Semantic of the pattern-matching in nix-light\label{fig:semantics:nix-light:patterns}} \caption{Semantic of the pattern-matching in nix-light\label{fig:semantics:nix-light:patterns}}
\end{figure} \end{figure}