\(
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% \SHADE{MATH} can be defined to produce a shaded background to highlight
% inline MATH in running text:
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% \KEY{TEXT}, \STRING{TEXT}, \ATOM{TEXT}, \LEX{TEXT} can be used in math mode:
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\newcommand{\LEFTBRACE}{\char`\{}
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% \NAME{name} highlights the name;
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% \NAMEREF{name} links name to the target Name.name in the current file;
% \NAMEHYPER{url}{file}{name} links name to Name.name at url/file/file.pdf.
% Similarly for \VAR{partvariable}, \SYN{syntaxname}, \SEM{semanticsName},
% and \SECT{sectionnumber}
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\newcommand{\NAMEDECL}[1]{\DECL{Name}{#1}{\NAME{#1}}}
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% ...
% -----------
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%
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%
\)
Languages-beta : SIMPLE-2-Expressions.cbs | PLAIN | PDF
\[\KEY{Language} \quad \STRING{SIMPLE}\]
\(\SECT{2}\) Expressions
\[\begin{align*}
\KEY{Syntax} \quad
\VARDECL{Exp} : \SYNDECL{exp}
\ ::= \ & \
\LEX{{(}} \ \SYNREF{exp} \ \LEX{{)}} \\
\ \mid \ & \ \SYNHYPER{../.}{SIMPLE-1-Lexical}{value} \\
\ \mid \ & \ \SYNREF{lexp} \\
\ \mid \ & \ \SYNREF{lexp} \ \LEX{{=}} \ \SYNREF{exp} \\
\ \mid \ & \ \LEX{{+}{+}} \ \SYNREF{lexp} \\
\ \mid \ & \ \LEX{{-}} \ \SYNREF{exp} \\
\ \mid \ & \ \SYNREF{exp} \ \LEX{{(}} \ \SYNREF{exps}\QUERY \ \LEX{{)}} \\
\ \mid \ & \ \LEX{sizeOf} \ \LEX{{(}} \ \SYNREF{exp} \ \LEX{{)}} \\
\ \mid \ & \ \LEX{read} \ \LEX{{(}} \ \LEX{{)}} \\
\ \mid \ & \ \SYNREF{exp} \ \LEX{{+}} \ \SYNREF{exp} \\
\ \mid \ & \ \SYNREF{exp} \ \LEX{{-}} \ \SYNREF{exp} \\
\ \mid \ & \ \SYNREF{exp} \ \LEX{{*}} \ \SYNREF{exp} \\
\ \mid \ & \ \SYNREF{exp} \ \LEX{{/}} \ \SYNREF{exp} \\
\ \mid \ & \ \SYNREF{exp} \ \LEX{{\PERCENT}} \ \SYNREF{exp} \\
\ \mid \ & \ \SYNREF{exp} \ \LEX{{<}} \ \SYNREF{exp} \\
\ \mid \ & \ \SYNREF{exp} \ \LEX{{<}{=}} \ \SYNREF{exp} \\
\ \mid \ & \ \SYNREF{exp} \ \LEX{{>}} \ \SYNREF{exp} \\
\ \mid \ & \ \SYNREF{exp} \ \LEX{{>}{=}} \ \SYNREF{exp} \\
\ \mid \ & \ \SYNREF{exp} \ \LEX{{=}{=}} \ \SYNREF{exp} \\
\ \mid \ & \ \SYNREF{exp} \ \LEX{{!}{=}} \ \SYNREF{exp} \\
\ \mid \ & \ \LEX{{!}} \ \SYNREF{exp} \\
\ \mid \ & \ \SYNREF{exp} \ \LEX{{\AMPERSAND}{\AMPERSAND}} \ \SYNREF{exp} \\
\ \mid \ & \ \SYNREF{exp} \ \LEX{{|}{|}} \ \SYNREF{exp}
\end{align*}\]
\[\begin{align*}
\KEY{Rule} \quad
& \LEFTPHRASE \
\LEX{{(}} \ \VARREF{Exp} \ \LEX{{)}} \
\RIGHTPHRASE : \SYNREF{exp} =
\LEFTPHRASE \
\VAR{Exp} \
\RIGHTPHRASE
\end{align*}\]
\[\begin{align*}
\KEY{Semantics} \quad
& \SEMDECL{rval} \LEFTPHRASE \ \_ : \SYNREF{exp} \ \RIGHTPHRASE
: \TO \NAMEHYPER{../../../../../Funcons-beta/Values}{Value-Types}{values}
\\
\KEY{Rule} \quad
& \SEMREF{rval} \LEFTPHRASE \
\VARHYPER{../.}{SIMPLE-1-Lexical}{V} \
\RIGHTPHRASE =
\SEMHYPER{../.}{SIMPLE-1-Lexical}{val} \LEFTPHRASE \
\VAR{V} \
\RIGHTPHRASE
\\
\KEY{Rule} \quad
& \SEMREF{rval} \LEFTPHRASE \
\VARREF{LExp} \
\RIGHTPHRASE =
\NAMEHYPER{../../../../../Funcons-beta/Computations/Normal}{Storing}{assigned}
( \SEMREF{lval} \LEFTPHRASE \
\VAR{LExp} \
\RIGHTPHRASE )
\\
\KEY{Rule} \quad
& \SEMREF{rval} \LEFTPHRASE \
\VARREF{LExp} \ \LEX{{=}} \ \VARREF{Exp} \
\RIGHTPHRASE = \\&\quad
\NAMEHYPER{../../../../../Funcons-beta/Computations/Normal}{Giving}{give}
( \\&\quad\quad \SEMREF{rval} \LEFTPHRASE \
\VAR{Exp} \
\RIGHTPHRASE , \\&\quad\quad
\NAMEHYPER{../../../../../Funcons-beta/Computations/Normal}{Flowing}{sequential}
( \\&\quad\quad\quad \NAMEHYPER{../../../../../Funcons-beta/Computations/Normal}{Storing}{assign}
( \SEMREF{lval} \LEFTPHRASE \
\VAR{LExp} \
\RIGHTPHRASE ,
\NAMEHYPER{../../../../../Funcons-beta/Computations/Normal}{Giving}{given} ), \\&\quad\quad\quad
\NAMEHYPER{../../../../../Funcons-beta/Computations/Normal}{Giving}{given} ) )
\\
\KEY{Rule} \quad
& \SEMREF{rval} \LEFTPHRASE \
\LEX{{+}{+}} \ \VARREF{LExp} \
\RIGHTPHRASE = \\&\quad
\NAMEHYPER{../../../../../Funcons-beta/Computations/Normal}{Giving}{give}
( \\&\quad\quad \SEMREF{lval} \LEFTPHRASE \
\VAR{LExp} \
\RIGHTPHRASE , \\&\quad\quad
\NAMEHYPER{../../../../../Funcons-beta/Computations/Normal}{Flowing}{sequential}
( \\&\quad\quad\quad \NAMEHYPER{../../../../../Funcons-beta/Computations/Normal}{Storing}{assign}
( \NAMEHYPER{../../../../../Funcons-beta/Computations/Normal}{Giving}{given},
\NAMEHYPER{../../../../../Funcons-beta/Values/Primitive}{Integers}{integer-add}
( \NAMEHYPER{../../../../../Funcons-beta/Computations/Normal}{Storing}{assigned}
( \NAMEHYPER{../../../../../Funcons-beta/Computations/Normal}{Giving}{given} ),
1 ) ), \\&\quad\quad\quad
\NAMEHYPER{../../../../../Funcons-beta/Computations/Normal}{Storing}{assigned}
( \NAMEHYPER{../../../../../Funcons-beta/Computations/Normal}{Giving}{given} ) ) )
\\
\KEY{Rule} \quad
& \SEMREF{rval} \LEFTPHRASE \
\LEX{{-}} \ \VARREF{Exp} \
\RIGHTPHRASE =
\NAMEHYPER{../../../../../Funcons-beta/Values/Primitive}{Integers}{integer-negate}
( \SEMREF{rval} \LEFTPHRASE \
\VAR{Exp} \
\RIGHTPHRASE )
\\
\KEY{Rule} \quad
& \SEMREF{rval} \LEFTPHRASE \
\VARREF{Exp} \ \LEX{{(}} \ \VARREF{Exps}\QUERY \ \LEX{{)}} \
\RIGHTPHRASE =
\NAMEHYPER{../../../../../Funcons-beta/Values/Abstraction}{Functions}{apply}
( \SEMREF{rval} \LEFTPHRASE \
\VAR{Exp} \
\RIGHTPHRASE ,
\NAMEHYPER{../../../../../Funcons-beta/Values/Composite}{Tuples}{tuple}
( \SEMREF{rvals} \LEFTPHRASE \
\VAR{Exps}\QUERY \
\RIGHTPHRASE ) )
\\
\KEY{Rule} \quad
& \SEMREF{rval} \LEFTPHRASE \
\LEX{sizeOf} \ \LEX{{(}} \ \VARREF{Exp} \ \LEX{{)}} \
\RIGHTPHRASE =
\NAMEHYPER{../../../../../Funcons-beta/Values/Composite}{Sequences}{length}
( \NAMEHYPER{../../../../../Funcons-beta/Values/Composite}{Vectors}{vector-elements}
( \SEMREF{rval} \LEFTPHRASE \
\VAR{Exp} \
\RIGHTPHRASE ) )
\\
\KEY{Rule} \quad
& \SEMREF{rval} \LEFTPHRASE \
\LEX{read} \ \LEX{{(}} \ \LEX{{)}} \
\RIGHTPHRASE =
\NAMEHYPER{../../../../../Funcons-beta/Computations/Normal}{Interacting}{read}
\\
\KEY{Rule} \quad
& \SEMREF{rval} \LEFTPHRASE \
\VARREF{Exp}\SUB{1} \ \LEX{{+}} \ \VARREF{Exp}\SUB{2} \
\RIGHTPHRASE =
\NAMEHYPER{../../../../../Funcons-beta/Values/Primitive}{Integers}{integer-add}
( \SEMREF{rval} \LEFTPHRASE \
\VAR{Exp}\SUB{1} \
\RIGHTPHRASE ,
\SEMREF{rval} \LEFTPHRASE \
\VAR{Exp}\SUB{2} \
\RIGHTPHRASE )
\\
\KEY{Rule} \quad
& \SEMREF{rval} \LEFTPHRASE \
\VARREF{Exp}\SUB{1} \ \LEX{{-}} \ \VARREF{Exp}\SUB{2} \
\RIGHTPHRASE =
\NAMEHYPER{../../../../../Funcons-beta/Values/Primitive}{Integers}{integer-subtract}
( \SEMREF{rval} \LEFTPHRASE \
\VAR{Exp}\SUB{1} \
\RIGHTPHRASE ,
\SEMREF{rval} \LEFTPHRASE \
\VAR{Exp}\SUB{2} \
\RIGHTPHRASE )
\\
\KEY{Rule} \quad
& \SEMREF{rval} \LEFTPHRASE \
\VARREF{Exp}\SUB{1} \ \LEX{{*}} \ \VARREF{Exp}\SUB{2} \
\RIGHTPHRASE =
\NAMEHYPER{../../../../../Funcons-beta/Values/Primitive}{Integers}{integer-multiply}
( \SEMREF{rval} \LEFTPHRASE \
\VAR{Exp}\SUB{1} \
\RIGHTPHRASE ,
\SEMREF{rval} \LEFTPHRASE \
\VAR{Exp}\SUB{2} \
\RIGHTPHRASE )
\\
\KEY{Rule} \quad
& \SEMREF{rval} \LEFTPHRASE \
\VARREF{Exp}\SUB{1} \ \LEX{{/}} \ \VARREF{Exp}\SUB{2} \
\RIGHTPHRASE =
\NAMEHYPER{../../../../../Funcons-beta/Computations/Abnormal}{Failing}{checked} \
\NAMEHYPER{../../../../../Funcons-beta/Values/Primitive}{Integers}{integer-divide}
( \SEMREF{rval} \LEFTPHRASE \
\VAR{Exp}\SUB{1} \
\RIGHTPHRASE ,
\SEMREF{rval} \LEFTPHRASE \
\VAR{Exp}\SUB{2} \
\RIGHTPHRASE )
\\
\KEY{Rule} \quad
& \SEMREF{rval} \LEFTPHRASE \
\VARREF{Exp}\SUB{1} \ \LEX{{\PERCENT}} \ \VARREF{Exp}\SUB{2} \
\RIGHTPHRASE =
\NAMEHYPER{../../../../../Funcons-beta/Computations/Abnormal}{Failing}{checked} \
\NAMEHYPER{../../../../../Funcons-beta/Values/Primitive}{Integers}{integer-modulo}
( \SEMREF{rval} \LEFTPHRASE \
\VAR{Exp}\SUB{1} \
\RIGHTPHRASE ,
\SEMREF{rval} \LEFTPHRASE \
\VAR{Exp}\SUB{2} \
\RIGHTPHRASE )
\\
\KEY{Rule} \quad
& \SEMREF{rval} \LEFTPHRASE \
\VARREF{Exp}\SUB{1} \ \LEX{{<}} \ \VARREF{Exp}\SUB{2} \
\RIGHTPHRASE =
\NAMEHYPER{../../../../../Funcons-beta/Values/Primitive}{Integers}{is-less}
( \SEMREF{rval} \LEFTPHRASE \
\VAR{Exp}\SUB{1} \
\RIGHTPHRASE ,
\SEMREF{rval} \LEFTPHRASE \
\VAR{Exp}\SUB{2} \
\RIGHTPHRASE )
\\
\KEY{Rule} \quad
& \SEMREF{rval} \LEFTPHRASE \
\VARREF{Exp}\SUB{1} \ \LEX{{<}{=}} \ \VARREF{Exp}\SUB{2} \
\RIGHTPHRASE =
\NAMEHYPER{../../../../../Funcons-beta/Values/Primitive}{Integers}{is-less-or-equal}
( \SEMREF{rval} \LEFTPHRASE \
\VAR{Exp}\SUB{1} \
\RIGHTPHRASE ,
\SEMREF{rval} \LEFTPHRASE \
\VAR{Exp}\SUB{2} \
\RIGHTPHRASE )
\\
\KEY{Rule} \quad
& \SEMREF{rval} \LEFTPHRASE \
\VARREF{Exp}\SUB{1} \ \LEX{{>}} \ \VARREF{Exp}\SUB{2} \
\RIGHTPHRASE =
\NAMEHYPER{../../../../../Funcons-beta/Values/Primitive}{Integers}{is-greater}
( \SEMREF{rval} \LEFTPHRASE \
\VAR{Exp}\SUB{1} \
\RIGHTPHRASE ,
\SEMREF{rval} \LEFTPHRASE \
\VAR{Exp}\SUB{2} \
\RIGHTPHRASE )
\\
\KEY{Rule} \quad
& \SEMREF{rval} \LEFTPHRASE \
\VARREF{Exp}\SUB{1} \ \LEX{{>}{=}} \ \VARREF{Exp}\SUB{2} \
\RIGHTPHRASE =
\NAMEHYPER{../../../../../Funcons-beta/Values/Primitive}{Integers}{is-greater-or-equal}
( \SEMREF{rval} \LEFTPHRASE \
\VAR{Exp}\SUB{1} \
\RIGHTPHRASE ,
\SEMREF{rval} \LEFTPHRASE \
\VAR{Exp}\SUB{2} \
\RIGHTPHRASE )
\\
\KEY{Rule} \quad
& \SEMREF{rval} \LEFTPHRASE \
\VARREF{Exp}\SUB{1} \ \LEX{{=}{=}} \ \VARREF{Exp}\SUB{2} \
\RIGHTPHRASE =
\NAMEHYPER{../../../../../Funcons-beta/Values}{Value-Types}{is-equal}
( \SEMREF{rval} \LEFTPHRASE \
\VAR{Exp}\SUB{1} \
\RIGHTPHRASE ,
\SEMREF{rval} \LEFTPHRASE \
\VAR{Exp}\SUB{2} \
\RIGHTPHRASE )
\\
\KEY{Rule} \quad
& \SEMREF{rval} \LEFTPHRASE \
\VARREF{Exp}\SUB{1} \ \LEX{{!}{=}} \ \VARREF{Exp}\SUB{2} \
\RIGHTPHRASE =
\NAMEHYPER{../../../../../Funcons-beta/Values/Primitive}{Booleans}{not}
( \NAMEHYPER{../../../../../Funcons-beta/Values}{Value-Types}{is-equal}
( \SEMREF{rval} \LEFTPHRASE \
\VAR{Exp}\SUB{1} \
\RIGHTPHRASE ,
\SEMREF{rval} \LEFTPHRASE \
\VAR{Exp}\SUB{2} \
\RIGHTPHRASE ) )
\\
\KEY{Rule} \quad
& \SEMREF{rval} \LEFTPHRASE \
\LEX{{!}} \ \VARREF{Exp} \
\RIGHTPHRASE =
\NAMEHYPER{../../../../../Funcons-beta/Values/Primitive}{Booleans}{not}
( \SEMREF{rval} \LEFTPHRASE \
\VAR{Exp} \
\RIGHTPHRASE )
\\
\KEY{Rule} \quad
& \SEMREF{rval} \LEFTPHRASE \
\VARREF{Exp}\SUB{1} \ \LEX{{\AMPERSAND}{\AMPERSAND}} \ \VARREF{Exp}\SUB{2} \
\RIGHTPHRASE =
\NAMEHYPER{../../../../../Funcons-beta/Computations/Normal}{Flowing}{if-else}
( \SEMREF{rval} \LEFTPHRASE \
\VAR{Exp}\SUB{1} \
\RIGHTPHRASE ,
\SEMREF{rval} \LEFTPHRASE \
\VAR{Exp}\SUB{2} \
\RIGHTPHRASE ,
\NAMEHYPER{../../../../../Funcons-beta/Values/Primitive}{Booleans}{false} )
\\
\KEY{Rule} \quad
& \SEMREF{rval} \LEFTPHRASE \
\VARREF{Exp}\SUB{1} \ \LEX{{|}{|}} \ \VARREF{Exp}\SUB{2} \
\RIGHTPHRASE =
\NAMEHYPER{../../../../../Funcons-beta/Computations/Normal}{Flowing}{if-else}
( \SEMREF{rval} \LEFTPHRASE \
\VAR{Exp}\SUB{1} \
\RIGHTPHRASE ,
\NAMEHYPER{../../../../../Funcons-beta/Values/Primitive}{Booleans}{true},
\SEMREF{rval} \LEFTPHRASE \
\VAR{Exp}\SUB{2} \
\RIGHTPHRASE )
\end{align*}\]
\[\begin{align*}
\KEY{Syntax} \quad
\VARDECL{Exps} : \SYNDECL{exps}
\ ::= \ & \
\SYNREF{exp} \ \LEFTGROUP \LEX{{,}} \ \SYNREF{exps} \RIGHTGROUP\QUERY
\end{align*}\]
\[\begin{align*}
\KEY{Semantics} \quad
& \SEMDECL{rvals} \LEFTPHRASE \ \_ : \SYNREF{exps}\QUERY \ \RIGHTPHRASE
: ( \TO \NAMEHYPER{../../../../../Funcons-beta/Values}{Value-Types}{values} )\STAR
\\
\KEY{Rule} \quad
& \SEMREF{rvals} \LEFTPHRASE \
\
\RIGHTPHRASE =
( \ )
\\
\KEY{Rule} \quad
& \SEMREF{rvals} \LEFTPHRASE \
\VARREF{Exp} \
\RIGHTPHRASE =
\SEMREF{rval} \LEFTPHRASE \
\VAR{Exp} \
\RIGHTPHRASE
\\
\KEY{Rule} \quad
& \SEMREF{rvals} \LEFTPHRASE \
\VARREF{Exp} \ \LEX{{,}} \ \VARREF{Exps} \
\RIGHTPHRASE =
\SEMREF{rval} \LEFTPHRASE \
\VAR{Exp} \
\RIGHTPHRASE ,
\SEMREF{rvals} \LEFTPHRASE \
\VAR{Exps} \
\RIGHTPHRASE
\end{align*}\]
\[\begin{align*}
\KEY{Syntax} \quad
\VARDECL{LExp} : \SYNDECL{lexp}
\ ::= \ & \
\SYNHYPER{../.}{SIMPLE-1-Lexical}{id} \mid \SYNREF{lexp} \ \LEX{{[}} \ \SYNREF{exps} \ \LEX{{]}}
\end{align*}\]
\[\begin{align*}
\KEY{Rule} \quad
& \LEFTPHRASE \
\VARREF{LExp} \ \LEX{{[}} \ \VARREF{Exp} \ \LEX{{,}} \ \VARREF{Exps} \ \LEX{{]}} \
\RIGHTPHRASE : \SYNREF{lexp} = \\&
\LEFTPHRASE \
\VAR{LExp} \ \LEX{{[}} \ \VAR{Exp} \ \LEX{{]}} \ \LEX{{[}} \ \VAR{Exps} \ \LEX{{]}} \
\RIGHTPHRASE
\end{align*}\]
\[\begin{align*}
\KEY{Semantics} \quad
& \SEMDECL{lval} \LEFTPHRASE \ \_ : \SYNREF{lexp} \ \RIGHTPHRASE
: \TO \NAMEHYPER{../../../../../Funcons-beta/Computations/Normal}{Storing}{variables}
\\
\KEY{Rule} \quad
& \SEMREF{lval} \LEFTPHRASE \
\VARHYPER{../.}{SIMPLE-1-Lexical}{Id} \
\RIGHTPHRASE =
\NAMEHYPER{../../../../../Funcons-beta/Computations/Normal}{Binding}{bound}
( \SEMHYPER{../.}{SIMPLE-1-Lexical}{id} \LEFTPHRASE \
\VAR{Id} \
\RIGHTPHRASE )
\\
\KEY{Rule} \quad
& \SEMREF{lval} \LEFTPHRASE \
\VARREF{LExp} \ \LEX{{[}} \ \VARREF{Exp} \ \LEX{{]}} \
\RIGHTPHRASE = \\&\quad
\NAMEHYPER{../../../../../Funcons-beta/Computations/Abnormal}{Failing}{checked} \
\NAMEHYPER{../../../../../Funcons-beta/Values/Composite}{Sequences}{index}
( \NAMEHYPER{../../../../../Funcons-beta/Values/Primitive}{Integers}{integer-add}
( 1,
\SEMREF{rval} \LEFTPHRASE \
\VAR{Exp} \
\RIGHTPHRASE ),
\NAMEHYPER{../../../../../Funcons-beta/Values/Composite}{Vectors}{vector-elements}
( \SEMREF{rval} \LEFTPHRASE \
\VAR{LExp} \
\RIGHTPHRASE ) )
\end{align*}\]
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