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\section{Informal Language Definition}
Below the abstract syntax of the language is given in VDM-SL.
In order to keep the language simple, only Integer and Boolean types are
defined.
A program consists of a declaration part followed by a statement.
\begin{vdm_al}
module AST
exports all
definitions
types
Program :: decls : seq of Declaration
stmt : Stmt;
\end{vdm_al}
A (variable) declaration consists of an identifier, an associated
type and an optional initial value.
\begin{vdm_al}
Declaration :: id : Identifier
tp : Type
val : [Value];
\end{vdm_al}
An identifier is a sequence of characters. In our language two types
are known, Boolean and Integer. The two types of values in the language are
modeled as the corresponding VDM-SL types {\tt bool} and {\tt int}.
\begin{vdm_al}
Identifier = seq1 of char;
Type = <BoolType> | <IntType> ;
Value = BoolVal | IntVal;
BoolVal :: val : bool;
IntVal :: val : int;
\end{vdm_al}
Our simple language only knows four kinds of statements: block
statements, assignments, a conditional statement, a for-loop and a
repeat-loop\footnote{A while loop was not part of the assignment,
because it has served as a demonstrating example for loop semantics
during the course. It is left as an exercise to the reader.}.
\begin{vdm_al}
Stmt = BlockStmt | AssignStmt | CondStmt | ForStmt | RepeatStmt;
\end{vdm_al}
A block statement consists of local variable declarations and a
non-empty sequence of statements.
\begin{vdm_al}
BlockStmt :: decls : seq of Declaration
stmts : seq1 of Stmt;
\end{vdm_al}
The left-hand side of an assignment is a variable, which is simply
an identifier. The right-hand side is defined as an expression.
\begin{vdm_al}
AssignStmt :: lhs : Variable
rhs : Expr;
Variable :: id : Identifier;
\end{vdm_al}
An expression could be a binary expression, a value or a variable.
A binary expression consists of a left-hand expression, an operator
and a right-hand expression.
\begin{vdm_al}
Expr = BinaryExpr | Value | Variable;
BinaryExpr :: lhs : Expr
op : Operator
rhs : Expr;
\end{vdm_al}
The numeric operators of the language are addition, subtraction,
Integer-division, and multiplication. The Boolean operators are
less-than, greater-then, equality, conjunction, and finally disjunction.
\begin{vdm_al}
Operator = <Add> | <Sub> | <Div> | <Mul> | <Lt> | <Gt> | <Eq> | <And> | <Or>;
\end{vdm_al}
A conditional if-statement consists of a guard predicate, the
then- and else-branch.
\begin{vdm_al}
CondStmt :: guard : Expr
thenst : Stmt
elsest : Stmt;
\end{vdm_al}
The for-loop consists of an initial assignment to the
loop-variable, followed by an expression, which defines the stop
value of the loop-variable, and the statement to be repeated. It is allowed to modify the loop-variable inside the body of the loop.
\begin{vdm_al}
ForStmt :: start : AssignStmt
stop : Expr
stmt : Stmt;
\end{vdm_al}
Finally, the repeat-loop consists of the statement to be repeated
and its stop condition.
\begin{vdm_al}
RepeatStmt :: repeat : Stmt
until : Expr;
end AST
\end{vdm_al}
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