Document expressions

3 files changed, 297 insertions, 63 deletions

diff --git a/doc/appendix.tex b/doc/appendix.tex
index 9d92d53..0777d55 100644
--- a/doc/appendix.tex
+++ b/doc/appendix.tex
@@ -1,6 +1,7 @@
 \part{Appendix}
+\appendix
 
-\addchap{Syntax}
+\chapter{Syntax}
 
 \begin{grammar}
 <letter> = `A' | `B' | … | `Z' | `a' | `b' | … | `z' | `\_'.
diff --git a/doc/language.tex b/doc/language.tex
index a18dac8..9112127 100644
--- a/doc/language.tex
+++ b/doc/language.tex
@@ -15,60 +15,325 @@ where a statement has control over the evaluation of its components.
 Statements can also modify the state of the procedure or the program by
 mutating variables.
 
-Most simple expressions are identifiers referencing program's symbols and
-literals. These atomic expressions can be combined to more complex expressions
-by applying various operations to one or more expressions.
-
 \chapter{Expressions}
 
-The expression \verb|@r.field| includes 3 expressions:
+Expressions are constructs denoting rules of computation whereby constants and current values of
+variables are combined to derive other values by the application of operators and function
+procedures. Expressions consist of operands and operators. Parentheses may be used to express
+specific associations of operators and operands.
+
+\section{Literal constants}
+
+\begin{grammar}
+<literal> = <integer-literal> | <word-literal> | <real-literal>
+	\alt{} <string-literal> | <character-literal>
+	\alt{} `true' | `false' | `nil'.
+\end{grammar}
+
+Literal constants are
+
+\begin{itemize}
+	\item signed and unsigned integers,
+	\item real numbers,
+	\item booleans,
+	\item characters,
+	\item strings,
+	\item and enumerations.
+\end{itemize}
+
+\section{Call expressions}
+
+\subsection*{Procedure call}
+
+\begin{grammar}
+<procedure-call> = <designator> `(' [<expressions>] `)'.
+\end{grammar}
+
+If the designator object is a procedure followed by a (possibly empty) parameter list,
+the designator implies an activation of the procedure and stands for the value resulting
+from its execution. The (types of the) actual parameters must correspond to the formal
+parameters as specified in the procedure's declaration.
+
+\subsection*{Type cast}
+
+\begin{grammar}
+<cast> = `cast' `(' <expression> `:\@' <type> `)'.
+\end{grammar}
+
+The type of an object can be reinterpreted with a cast expression: \\
+\verb|cast(object: Type)|.
+
+\subsection*{Traits}
+
+\begin{grammar}
+<trait-identifier> = `#' <identifier>.
+
+<trait> = <trait-identifier> `(' [<types>] `)'.
+\end{grammar}
+
+Traits allow to query some information about the types, like their size or
+field offset or alignment. Calling a trait looks like a procedure call but
+trait names start with a \verb|#| and their arguments are type expressions and
+not value expressions.
+
+Supported compiler traits:
+
+\begin{itemize}
+	\item \verb|#size(T)| queries type size.
+	\item \verb|#align(T)| queries type alignment.
+	\item \verb|#offset(T, F)| queries the offset of the field \verb|F| in the record \verb|T|.
+\end{itemize}
+
+\section{Object designators}
+
+\begin{grammar}
+<selector> = `[' <expression> `]' | `.\@' <identifier> | `^'.
+
+<designator> = <reference> <selector> | <identifier>.
+
+<reference> = <literal>
+	\alt{} <designator>
+	\alt{} <trait>
+	\alt{} <cast>
+	\alt{} <procedure-call>
+	\alt{} `(' <expression> `)'.
+\end{grammar}
+
+With the exception of literal constants and call expressions, operands are denoted by
+\textit{designators}. A designator consists of an identifier referring to the constant,
+variable, or procedure to be designated. This identifier or any other expression may be
+followed by selectors, if the designated object is an element of a structure.
+
+Designators are addressable, meaning that it is possible to get the address of the
+designated object or assign a value to it (if the designated object is mutable).
+
+\subsection*{Subscript selector}
+
+If \verb|A| designates an array or a string, then \verb|A[E]| denotes that element of
+\verb|A| whose index is the current value of the expression \verb|E|. The type of
+\verb|E| must be of type \verb|Word| or \verb|Int|. The first element has index 1,
+the second 2 and so on.
+
+\subsection*{Dereference selector}
+
+If \verb|P| designates a pointer, \verb|P^| denotes the object which is
+referenced by \verb|P|.
+
+\subsection*{Field selector}
+
+If \verb|R| designates a record, then \verb|R.f| denotes the field \verb|f| of
+\verb|R|.
+
+\subsection*{Variable designator}
+
+If the designated object is a variable, then the designator refers to the
+variable's current value.
+
+If the designated object is a procedure, a designator without parameter list
+refers to the address of the procedure. Procedure designators designate
+immutable objects.
+
+\subsection*{Selector evaluation order}
+
+Selectors are evaluated from left to right.
+
+For example the expression \verb|r^.field| includes 3 designators:
 
 \begin{enumerate}
-	\item Variable expression \verb|r|.
-	\item Field access \verb|(r).field|.
-	\item Address taking \verb|@(r.field)|.
+	\item Variable designator \verb|r|.
+	\item \verb|r^| dereferences the pointer \verb|r| and refers
+		to the object at the address in \verb|r|.
+	\item \verb|r^.field| accesses the field \verb|field| in that object.
 \end{enumerate}
 
-The expression is evaluated in the above order. The postfix expressions
-like field access have higher precedence than prefix operators.
+\section{Unary expressions}
+
+\begin{grammar}
+<unary-operator> = `@' | `~' | `-'.
 
-\section{Binary expressions}
+<factor> = <unary-operator> <factor> | <reference>.
+\end{grammar}
 
-\begin{table}
+Unary expressions are expressions with a prefix operator followed by one
+operand. Unary operators in table~\ref{table:unary} associate from right
+to left.
+
+$@$ takes the address of its operand. The operand expression should be
+addressable.
+
+$\sim$ applied on a boolean acts as logical not. Applied on an integer --- as
+bitwise not.
+
+\begin{table}[ht]
 \centering
-\begin{tabularx}{0.8\textwidth}{%
+\begin{tabularx}{0.7\textwidth}{%
+	r
 	l
 	>{\centering\arraybackslash}X
+}
+	\textbf{Symbol} & \textbf{Symbol name} & \textbf{Description} \\
+	\toprule
+	$@$ & \textit{at sign} & Address \\
+	\midrule
+	$-$ & \textit{minus} & Sign inversion \\
+	\midrule
+	$+$ & \textit{plus} & Identity operation \\
+	\midrule
+	$\sim$ & \textit{tilde} & Negation \\
+	\bottomrule
+\end{tabularx}
+\caption{Unary operators}\label{table:unary}
+\end{table}
+
+\section{Binary expressions}
+
+\begin{grammar}
+<term> = <factor> \{<multiplication-operator> <factor>\}.
+
+<simple-expression> = <term> \{<addition-operator> <term>\}.
+
+<comparand> = <simple-expression> \{<shift-operator> <simple-expression>\}.
+
+<relation> = <comparand> \{<relation-operator> <comparand>\}.
+
+<operand> = <relation> \{`&' <relation>\}.
+
+<expression> = <operand> \{(`or' | `xor') <operand>\}.
+\end{grammar}
+
+The syntax of expressions distinguishes between several classes of
+operators with different precedences (binding strengths). Operators of
+the same precedence associate from left to right. For example, $x - y - z$
+stands for $(x - y) - z$.
+
+The available operators are listed in the table~\ref{table:binary}.
+In some instances, several different operations are designated by
+the same operator symbol. In these cases, the actual operation is
+identified by the type of the operands.
+
+\begin{table}[ht]
+\centering
+\begin{tabularx}{\textwidth}{%
+	c
+	>{\centering\arraybackslash}X
 	>{\raggedright\arraybackslash}X
 }
-	\textbf{Precedence} & \textbf{Operator} & \textbf{Description}\\
+	\textbf{Precedence} & \textbf{Operator} & \textbf{Description} \\
 	\toprule
-	1 & $* \quad / \quad \%$ & Multiplication, division and remainder.\\
+	1 & $* \quad / \quad \%$ & Multiplication, division and remainder. \\
 	\midrule
-	2 & $+ \quad -$ & Addition and subtraction.\\
+	2 & $+ \quad -$ & Addition and subtraction. \\
 	\midrule
-	3 & $<< \quad >>$ & Left and right shifts.\\
+	3 & $<< \quad >>$ & Left and right shifts. \\
 	\midrule
-	4 & $= \quad <> \quad > \quad < \quad <= \quad >=$ & Relational operators.\\
+	4 & $= \quad <> \quad > \quad < \quad <= \quad >=$ & Relational operators. \\
 	\midrule
-	5 & $or \quad xor \quad \&$ & Logical operators.\\
+	5 & $\&$ & Logical conjuction. \\
+	\midrule
+	6 & $or \quad xor \quad$ & Logical disjunction operators. \\
 	\bottomrule
 \end{tabularx}
-\caption{Operator precedence}
+\caption{Operator precedence}\label{table:binary}
 \end{table}
 
-\section{Unary expressions}
+\subsection*{Logical and bitwise operators}
 
-Unary expressions are expressions with a prefix operator followed by one
-operand.
+Meaning of the operators in table~\ref{table:logical} depends on the
+operand type:
 
-\verb|@| (\textit{at sign}) takes the address of its operand. The operand expression should be
-addressable.
+Applied on booleans they act as logical operators.
 
-\verb|-| (\textit{minus}) negates a numeric value.
+Applied on integers they perform the corresponding logical operation
+bitwise, on each pair of bits of their operands.
 
-\verb|~| (\textit{tilde}) applied on a boolean acts as logical not. Applied on a numeric – as
-bitwise not.
+$or$ and $\&$ are short-circuiting, if the evaluation of the left
+side of the operation is enough to determine the final result,
+the right side should not be evaluated.
+
+\begin{table}[ht]
+\centering
+\begin{tabularx}{\textwidth}{%
+	r
+	l
+	>{\centering\arraybackslash}X
+	>{\centering\arraybackslash}X
+}
+	\textbf{Symbol} & \textbf{Description} &
+		\textbf{$p \cdot q$ with $\cdot$ as logical operator stands for} &
+		\textbf{As bitwise operator} \\
+	\toprule
+	$or$ & Inclusive disjunction & If $p$ then $true$, else $q$ & Bitwise or \\
+	\midrule
+	$xor$ & Exclusive disjunction & If $p$ then not $q$, else $q$ & Bitwise xor \\
+	\midrule
+	$\&$ & Conjuction & If $p$ then $q$, else $false$ & Bitwise and \\
+	\bottomrule
+\end{tabularx}
+\caption{Logical operators}\label{table:logical}
+\end{table}
+
+\subsection*{Arithmetic operators}
+
+Operators in table~\ref{table:arithmetic} apply to operands of numeric
+types. Both operands must be of the same type, which is also the type of
+the result.
+
+Let $q = x / y$, and $r = x \% y$. Then quotient $q$ and remainder $r$ are
+defined by the equation
+
+\[
+x = q * y + r \mid 0 \leq r < y
+\]
+
+Division on integer operands performs integer division.
+
+\begin{table}[ht]
+\centering
+\begin{tabular}{r l}
+	\textbf{Symbol} & \textbf{Result} \\
+	\toprule
+	$+$ & Sum \\
+	\midrule
+	$-$ & Difference \\
+	\midrule
+	$*$ & Product \\
+	\midrule
+	$/$ & Quotient \\
+	\midrule
+	$\%$ & Modulus \\
+	\bottomrule
+\end{tabular}
+\caption{Arithmetic operators}\label{table:arithmetic}
+\end{table}
+
+\subsection*{Relations}
+
+Relations in table~\ref{table:relation} are boolean. The ordering
+relations $<$, $<=$, $>$, $>=$ apply to the numeric types. The
+relations $=$ and $<>$ apply to all types.
+
+\begin{table}[ht]
+\centering
+\begin{tabular}{r l}
+	\textbf{Symbol} & \textbf{Result} \\
+	\toprule
+	$=$ & Equal \\
+	\midrule
+	$<>$ & Unequal \\
+	\midrule
+	$<$ & Less \\
+	\midrule
+	$<=$ & Less or equal \\
+	\midrule
+	$>$ & Greater \\
+	\midrule
+	$>=$ & Greater or equal \\
+	\bottomrule
+\end{tabular}
+\caption{Relational operators}\label{table:relation}
+\end{table}
+
+\chapter{Statements}
 
-\chapter{Conditional statements}
-\chapter{Loop statements}
+\section{Conditional statements}
+\section{Loop statements}
diff --git a/doc/type-system.tex b/doc/type-system.tex
index 4ac36e4..3ae8a30 100644
--- a/doc/type-system.tex
+++ b/doc/type-system.tex
@@ -124,35 +124,3 @@ begin
   e := E.one
 end.
 \end{lstlisting}
-
-\chapter{Type operations}
-
-\chapter{Cast}
-
-\begin{grammar}
-<cast> = `cast' `(' <expression> `:\@' <type> `)'.
-\end{grammar}
-
-The type of an object can be reinterpreted with a cast expression: \\
-\verb|cast(object: Type)|.
-
-\chapter{Traits}
-
-\begin{grammar}
-<trait-identifier> = `#' <identifier>.
-
-<trait> = <trait-identifier> `(' [<types>] `)'.
-\end{grammar}
-
-Traits allow to query some information about the types, like their size or
-field offset or alignment. Calling a trait looks like a procedure call but
-traits names start with a \verb|#| and their arguments are type expressions and
-not value expressions.
-
-Supported compiler traits:
-
-\begin{itemize}
-	\item \verb|#size(T)| queries type size.
-	\item \verb|#align(T)| queries type alignment.
-	\item \verb|#offset(T, F)| queries the offset of the field \verb|F| in the record \verb|T|.
-\end{itemize}