ocaml 3.09 transition

[helm.git] / helm / DEVEL / mathml_editor / doc / spec.tex

diff --git a/helm/DEVEL/mathml_editor/doc/spec.tex b/helm/DEVEL/mathml_editor/doc/spec.tex
index 87e2cd603a2817b34689fdb559c9a4dc2519db8e..a9ccdc2637a59eefd9bc8c2f311e9073670eb86a 100644 (file)
--- a/helm/DEVEL/mathml_editor/doc/spec.tex
+++ b/helm/DEVEL/mathml_editor/doc/spec.tex
@@ -858,6 +858,7 @@ cursor with \ONODE{}, append $\tadvance$ after the \ONODE{} node
 \newcommand{\FSEM}[2]{\mathcal{F}\llbracket#1\rrbracket(#2)}
 \newcommand{\PARENT}[1]{\mathit{parent}(#1)}
 \newcommand{\CHILDREN}[1]{\mathit{children}(#1)}
+\newcommand{\CHILD}[1]{\mathit{child}(#1)}
 \newcommand{\ANCESTORS}[1]{\mathit{ancestors}(#1)}
 \newcommand{\DESCENDANTS}[1]{\mathit{descendants}(#1)}
 \newcommand{\HASATTRIBUTE}[2]{\mathit{hasAttribute}(#1,#2)}
@@ -870,9 +871,18 @@ cursor with \ONODE{}, append $\tadvance$ after the \ONODE{} node
 \newcommand{\PREDICATE}[1]{\mathit{predicate}(#1)}
 \newcommand{\IFV}[3]{\begin{array}[t]{@{}l}\mathbf{if}~#1~\mathbf{then}\\\quad#2\\\mathbf{else}\\\quad#3\end{array}}
 \newcommand{\IFH}[3]{\mathbf{if}~#1~\mathbf{then}~#2~\mathbf{else}~#3}
-\newcommand{\TRUE}{\mathit{true}}
-\newcommand{\FALSE}{\mathit{false}}
+\newcommand{\TRUE}{\mathbf{true}}
+\newcommand{\FALSE}{\mathbf{false}}
 \newcommand{\FUN}[2]{\lambda#1.#2}
+\newcommand{\LET}[3]{\mathbf{let}~#1=#2~\mathbf{in}~#3}
+\newcommand{\REC}[2]{\mathbf{rec}~#1=#2}
+\newcommand{\APPLY}[2]{(#1\;#2)}
+\newcommand{\APPLYX}[3]{(#1\;#2\;#3)}
+\newcommand{\AND}{\wedge}
+\newcommand{\OR}{\vee}
+\newcommand{\AAND}{\,\vec{\AND}\,}
+\newcommand{\AOR}{\,\vec{\OR}\,}
+\newcommand{\MATCH}[4]{\begin{array}[t]{@{}c@{~\to~}l@{}l@{}}\multicolumn{2}{@{}l@{}}{\mathbf{match}~#1~\mathbf{with}}\\\phantom{|}\quad\{#2\}&#3\\|\quad\emptyset&#4\end{array}}
 
 \[
 \begin{array}{rcl}
@@ -885,29 +895,23 @@ cursor with \ONODE{}, append $\tadvance$ after the \ONODE{} node
   \CSEM{c_1\&c_2}{x} &=& \CSEM{c_1}{x} \cap \CSEM{c_2}{x}\\
   \CSEM{c_1\mid c_2}{x} &=& \CSEM{c_1}{x} \cup \CSEM{c_2}{x}\\
   \CSEM{c+}{x} &=& \CSEM{c}{x} \cup \CSEM{c+}{\CSEM{c}{x}}\\
-  \CSEM{c?}{x} &=& \CSEM{.\mid c}{x}\\
+  \CSEM{c?}{x} &=& \{x\}\cup\CSEM{c}{x}\\
   \CSEM{c*}{x} &=& \CSEM{{c+}?}{x}\\[3ex]
   \QSEM{c}{x} &=& \CSEM{c}{x}\ne\emptyset\\
   \QSEM{!c}{x} &=& \CSEM{c}{x}=\emptyset\\
-  \QSEM{.}{x} &=& \TRUE\\
-  \QSEM{\langle*\rangle}{x} &=& \ISELEMENT{x}\\
-  \QSEM{\langle n\rangle}{x} &=& \ISELEMENT{x}\wedge\NAME{x}=n\\
-  \QSEM{@n}{x} &=& \ISELEMENT{x}\wedge\HASATTRIBUTE{x}{n}\\
-  \QSEM{@n=v}{x} &=& \ISELEMENT{x}\wedge\ATTRIBUTE{x}{n}=v\\
-  \QSEM{[p_1\#p_2]}{x} &=& \ISELEMENT{x}\wedge\LSEM{p_1}{\PREV{x}}\wedge\RSEM{p_2}{\NEXT{x}}\\[3ex]
+  \QSEM{\langle*\rangle}{x} &=& \TRUE\\
+  \QSEM{\langle n\rangle}{x} &=& \NAME{x}=n\\
+  \QSEM{@n}{x} &=& \HASATTRIBUTE{x}{n}\\
+  \QSEM{@n=v}{x} &=& \ATTRIBUTE{x}{n}=v\\
+  \QSEM{[p_1\#p_2]}{x} &=& \LSEM{p_1}{\PREV{x}}\wedge\RSEM{p_2}{\NEXT{x}}\\[3ex]
   \LSEM{}{\alpha} &=& \TRUE\\
   \LSEM{\cent}{\alpha} &=& \alpha=\emptyset\\
-  \LSEM{p\;q}{\emptyset} &=& \mathit{false}\\
+  \LSEM{p\;q}{\emptyset} &=& \FALSE\\
   \LSEM{p\;q}{\{x\}} &=& \QSEM{q}{x}\wedge\LSEM{p}{\PREV{x}}\\[3ex]
   \RSEM{}{\alpha} &=& \TRUE\\
   \RSEM{\$}{\alpha} &=& \alpha=\emptyset\\
-  \RSEM{q\;p}{\emptyset} &=& \mathit{false}\\
-  \RSEM{q\;p}{\{x\}} &=& \QSEM{q}{x}\wedge\RSEM{p}{\NEXT{x}}\\
-\end{array}
-\]
-
-\[
-\begin{array}{rcl}
+  \RSEM{q\;p}{\emptyset} &=& \FALSE\\
+  \RSEM{q\;p}{\{x\}} &=& \QSEM{q}{x}\wedge\RSEM{p}{\NEXT{x}}\\[3ex]
   \PREDICATE{q} &=& \TRUE\\
   \PREDICATE{..} &=& \FALSE\\
   \PREDICATE{/} &=& \FALSE\\
@@ -923,27 +927,47 @@ cursor with \ONODE{}, append $\tadvance$ after the \ONODE{} node
 
 \[
 \begin{array}{rcl}
-  \PSEM{q} &=& \FUN{x}{\QSEM{q}{x}} \\
-  \PSEM{..} &=& \FUN{x}{\PARENT{x}\ne\emptyset}\\
-  \PSEM{/} &=& \FUN{x}{\CHILDREN{x}\ne\emptyset}\\
-  \PSEM{c_1\;c_2} &=& \IFV{\PREDICATE{c_1}}{\FUN{x}{(\PSEM{c_1}\;x)\wedge(\PSEM{c_2}\;x)}}{\FSEM{c_1}{\PSEM{c_2}}}\\
+  \PSEM{q} &=& \FUN{x}{\APPLY{\QSEM{q}{}}{x}} \\
+  \PSEM{..} &=& \FUN{x}{\neg\APPLY{\mathit{null}}{\PARENT{x}}}\\
+  \PSEM{/} &=& \FUN{x}{\neg\APPLY{\mathit{null}}{\CHILD{x}}}\\
   \PSEM{(c)} &=& \PSEM{c}\\
-  \PSEM{c_1\&c_2} &=& \IFV{\PREDICATE{c_1}\wedge\PREDICATE{c_2}}{\FUN{x}{(\PSEM{c_1}\;x)\wedge(\PSEM{c_2}\;x)}}{\FSEM{c_1\&c_2}{\FUN{\_}{\TRUE}}}\\
+  \PSEM{\{c:\alpha\}} &=& \FUN{x}{\APPLY{\PSEM{c}}{x}\AAND\APPLY{\alpha}{x}}\\
+  \PSEM{c_1\;c_2} &=& \IFV{\PREDICATE{c_1}}{\FUN{x}{(\PSEM{c_1}\;x)\wedge(\PSEM{c_2}\;x)}}{\FSEM{c_1}{\PSEM{c_2},\FUN{\_}{\FALSE}}}\\
+  \PSEM{c_1\&c_2} &=& \IFV{\PREDICATE{c_1}\wedge\PREDICATE{c_2}}{\FUN{x}{(\PSEM{c_1}\;x)\wedge(\PSEM{c_2}\;x)}}{\FSEM{c_1\&c_2}{\FUN{\_}{\TRUE},\FUN{\_}{\FALSE}}}\\
   \PSEM{c_1\mid c_2} &=& \FUN{x}{(\PSEM{c_1}\;x)\vee(\PSEM{c_2}\;x)}\\
   \PSEM{c+} &=& \PSEM{c}\\
   \PSEM{c?} &=& \FUN{\_}{\TRUE}\\
-  \PSEM{c*} &=& \FUN{\_}{\TRUE}\\
-  \PSEM{!c} &=& \FUN{x}{\neg(\PSEM{c}\;x)}\\[3ex]
-  \FSEM{q}{l} &=& \FUN{x}{\IFH{(\PSEM{q}\;x)}{(l\;x)}{\FALSE}}\\
-  \FSEM{..}{l} &=& \FUN{x}{\IFH{\PARENT{x}=\{y\}}{(l\;y)}{\FALSE}}\\
-  \FSEM{/}{l} &=& \FUN{x}{\vee_{p\in\CHILDREN{x}} (l\;p)}\\
-  \FSEM{c_1\;c_2}{l} &=& \FUN{x}{(\FSEM{c_1}{\FSEM{c_2}{l}}\;x)}\\
-  \FSEM{c_1\&c_2}{l} &=& \FUN{x}{(\FSEM{c_1}{\FUN{y}{\IFH{(l\;y)}{(\FSEM{c_2}{\FUN{z}{z=y}}\;x)}{\FALSE}}}\;x)}\\
-  \FSEM{c_1\mid c_2}{l} &=& \FUN{x}{(\FSEM{c_1}{l}\;x)\vee(\FSEM{c_2}{l}\;x)}\\
-  \FSEM{c+}{l} &=& \FUN{x}{(\FSEM{c}{\FUN{y}{(l\;y)\vee(\FSEM{c+}{l}\;y)}}\;x)}\\
-  \FSEM{c?}{l} &=& \FUN{x}{(l\;x)\vee(\FSEM{c}{l}\;x)}\\
-  \FSEM{c*}{l} &=& \FSEM{{c+}?}{l}\\
+  \PSEM{c*} &=& \FUN{\_}{\TRUE}\\[3ex]
+  \FSEM{q}{t,f} &=& \FUN{x}{(\APPLY{\PSEM{q}}{x}\AAND\APPLY{t}{x})\AOR\APPLY{f}{x}}\\
+  \FSEM{..}{t,f} &=& \FUN{x}{\MATCH{\PARENT{x}}{y}{\APPLY{t}{y}}{\APPLY{f}{x}}}\\
+%  \FSEM{/}{t,f} &=& \FUN{x}{(\vee_{y\in\CHILDREN{x}} \APPLY{t}{y})\AOR\APPLY{f}{x}}\\
+  \FSEM{/}{t,f} &=& \FUN{x}{\APPLYX{\mathit{exists}}{t}{\CHILD{x}}\AOR\APPLY{f}{x}}\\
+  \FSEM{(c)}{t,f} &=& \FSEM{c}{t,f}\\
+  \FSEM{\{c:\alpha\}}{t,f} &=& \FSEM{c}{\FUN{x}{\PSEM{c}\AAND\APPLY{\alpha}{x}\AAND\APPLY{t}{x},f}}\\
+  \FSEM{c_1\;c_2}{t,f} &=& \FUN{x}{\APPLY{\FSEM{c_1}{\FSEM{c_2}{t,\FUN{\_}{\APPLY{f}{x}}},f}}{x}}\\
+  \FSEM{c_1\&c_2}{t,f} &=& \FUN{x}{\APPLY{\FSEM{c_1}{\FUN{y}{\APPLY{\FSEM{c_2}{\FUN{z}{(y=z)\AAND\APPLY{t}{z}},\FUN{\_}{\APPLY{f}{x}}}}{x}},f}}{x}}\\
+  \FSEM{c_1\mid c_2}{t,f} &=& \FSEM{c_1}{t,\FSEM{c_2}{t,f}}\\
+  \FSEM{c+}{t,f} &=& \FSEM{c}{\FSEM{c+}{t,t},f}\\
+  \FSEM{c?}{t,f} &=& \FSEM{c}{t,t}\\
+  \FSEM{c*}{t,f} &=& \FSEM{{c+}?}{t,f}\\[3ex]
+  \QSEM{c}{} &=& \PSEM{c}\\
+  \QSEM{!c}{} &=& \FUN{x}{\neg\APPLY{\PSEM{c}}{x}}\\
+  \QSEM{\langle*\rangle}{} &=& \FUN{\_}{\TRUE}\\
+  \QSEM{\langle n\rangle}{} &=& \FUN{x}{\NAME{x}=n}\\
+  \QSEM{@n}{} &=& \FUN{x}{\HASATTRIBUTE{x}{n}}\\
+  \QSEM{@n=v}{} &=& \FUN{x}{\ATTRIBUTE{x}{n}=v}\\
+  \QSEM{[p_1\#p_2]}{} &=& \FUN{x}{\APPLY{\LSEM{p_1}{}}{\PREV{x}}\wedge\APPLY{\RSEM{p_2}{}}{\NEXT{x}}}\\[3ex]
+  \LSEM{}{} &=& \FUN{\_}{\TRUE}\\
+  \LSEM{\cent}{} &=& \mathit{null}\\
+  \LSEM{p\;q}{} &=& \FUN{x}{\MATCH{x}{y}{\QSEM{q}{y}\AAND\APPLY{\LSEM{p}}{\PREV{y}}}{\FALSE}}\\
+  \RSEM{}{} &=& \FUN{\_}{\TRUE}\\
+  \RSEM{\$}{} &=& \mathit{null}\\
+  \RSEM{p\;q}{} &=& \FUN{x}{\MATCH{x}{y}{\QSEM{q}{y}\AAND\APPLY{\RSEM{p}}{\NEXT{y}}}{\FALSE}}\\
+  \mathit{null} &=& \FUN{x}{\MATCH{x}{\_}{\FALSE}{\TRUE}}\\
+  \mathit{exists} &=& \FUN{t}{\REC{a}{\FUN{x}{\MATCH{x}{y}{\APPLY{t}{y}\AOR\APPLY{a}{\NEXT{x}}}{\FALSE}}}}
 \end{array}
 \]
 
+
+
 \end{document}