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38 lines
1.5 KiB
TeX
38 lines
1.5 KiB
TeX
\subsection{IMP Language}
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\subsubsection{The syntax}
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The allowed characters:
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\begin{code}{haskell}
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Letter = 'A' | . . . | 'Z' | 'a' | . . . | 'z'
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Digit = '0' | '1' | '2' | '3' | '4' | '5' | '6' | '7' | '8' | '9'
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\end{code}
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And the allowed tokens:
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\begin{code}{haskell}
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Ident = Letter { Letter | Digit }*
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Numeral = Digit | Numeral Digit
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Var = Ident
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\end{code}
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Arithmetic and Boolean statements could be defined in Haskell as follows
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\begin{code}{haskell}
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data Aexp = Bin Op Aexp Aexp | Var String | Num Integer
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data Op = Add | Sub | Mul
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data Bexp = Or Bexp Bexp | And Bexp Bexp | Not Bexp | Rel Rop Aexp Aexp
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data Rop = Eq | Neq | Le | Leq | Ge | Geq
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\end{code}
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Statements could be defined in Haskell as follows
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\mint{haskell}+data Stm = Skip | Assign String Aexp | Seq Stm Stm | If Bexp Stm Stm | While Bexp Stm+
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We use the following naming conventions for meta-variables:
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\begin{tables}{ll}{Variable & Type}
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$n$ & for numerals (\texttt{Numeral}) \\
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$x, y, z$ & for variables (\texttt{Var}) \\
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$e, e', e_1, e_2$ & for arithmetic expressions (\texttt{Aexp}) \\
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$b, b_1, b_2$ & for boolean expressions (\texttt{Bexp}) \\
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$s, s', s_1, s_2$ & for Statements (\texttt{Stm}) \\
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\end{tables}
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Meta-variables stand for arbitrary program variables, whereas program variables are concrete variables in a program.
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To denote \bi{syntactic equality} of two variables or statements, we use $\equiv$
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