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\( % cbs-katex.sty % \newcommand{\STYLE}[2]{\htmlClass{cbs-#1}{#2}} \newcommand{\DECL}[3]{\htmlId{#1:#2}{#3}} \newcommand{\REF}[3]{\href{###1:#2}{#3}} \newcommand{\HYPER}[5]{\href{#1/#2/index.html###3:#4}{#5}} % \SHADE{MATH} can be defined to produce a shaded background to highlight % inline MATH in running text: \newcommand{\SHADE}[1]{#1} % \KEY{TEXT}, \STRING{TEXT}, \ATOM{TEXT}, \LEX{TEXT} can be used in math mode: \newcommand{\KEY}[1]{\textsf{\textit{\STYLE{Key}{#1}}}} \newcommand{\STRING}[1]{\textsf{``\texttt{#1}''}} \newcommand{\ATOM}[1]{\textsf{`\texttt{#1}'}} \newcommand{\LEX}[1]{\textsf{\STYLE{Key}{`}\texttt{#1}\STYLE{Key}{'}}} % The following commands produce ASCII characters that are treated specially by LaTeX: \newcommand{\HASH}{\char`\#} \newcommand{\DOLLAR}{\char`\$} \newcommand{\PERCENT}{\char`\%} \newcommand{\AMPERSAND}{\char`\&} \newcommand{\APOSTROPHE}{\char`\'} \newcommand{\BACKSLASH}{\char`\\} \newcommand{\CARET}{\char`\^} \newcommand{\UNDERSCORE}{\char`\_} \newcommand{\GRAVE}{\char`\`} \newcommand{\LEFTBRACE}{\char`\{} \newcommand{\RIGHTBRACE}{\char`\}} \newcommand{\TILDE}{\textasciitilde} % {\char`\~} % \NAME{name} highlights the name; % \NAMEDECL{name} declares Name.name as the target of links to name; % \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} % The kerns in \SUB and \VAR avoid overlaps with primes: \newcommand{\SUB}[1]{_{\kern-2mu\STYLE{PartVariable}{\textsf{#1}}}} % PLAIN \newcommand{\VAR}[1]{\STYLE{PartVariable}{\textsf{\textit{#1}\kern2mu}}} \newcommand{\NAME}[1]{\STYLE{Name}{\textsf{#1}}} \newcommand{\SYN}[1]{\STYLE{SyntaxName}{\textsf{#1}}} \newcommand{\SEM}[1]{\STYLE{SemanticsName}{\textsf{#1}}} \newcommand{\SECT}[1]{\STYLE{SectionNumber}{\textsf{#1}}} % DECL \newcommand{\VARDECL}[1]{\DECL{PartVariable}{#1}{\VAR{#1}}} \newcommand{\NAMEDECL}[1]{\DECL{Name}{#1}{\NAME{#1}}} \newcommand{\SYNDECL}[1]{\DECL{SyntaxName}{#1}{\SYN{#1}}} \newcommand{\SEMDECL}[1]{\DECL{SemanticsName}{#1}{\SEM{#1}}} \newcommand{\SECTDECL}[1]{\DECL{SectionNumber}{#1}{\textsf{#1}}} % REF \newcommand{\VARREF}[1]{\REF{PartVariable}{#1}{\VAR{#1}}} \newcommand{\NAMEREF}[1]{\REF{Name}{#1}{\NAME{#1}}} \newcommand{\SYNREF}[1]{\REF{SyntaxName}{#1}{\SYN{#1}}} \newcommand{\SEMREF}[1]{\REF{SemanticsName}{#1}{\SEM{#1}}} \newcommand{\SECTREF}[1]{\REF{SectionNumber}{#1}{\SECT{#1}}} % HYPER \newcommand{\VARHYPER}[3]{\HYPER{#1}{#2}{PartVariable}{#3}{\VAR{#3}}} \newcommand{\NAMEHYPER}[3]{\HYPER{#1}{#2}{Name}{#3}{\NAME{#3}}} \newcommand{\SYNHYPER}[3]{\HYPER{#1}{#2}{SyntaxName}{#3}{\SYN{#3}}} \newcommand{\SEMHYPER}[3]{\HYPER{#1}{#2}{SemanticsName}{#3}{\SEM{#3}}} \newcommand{\SECTHYPER}[3]{\HYPER{#1}{#2}{SectionNumber}{#3}{\SECT{#3}}} % \LEFTPHRASE MATH \RIGHTPHRASE produces [[ MATH ]] with proper brackets: \newcommand{\LEFTPHRASE}{\llbracket} \newcommand{\RIGHTPHRASE}{\rrbracket} % \LEFTGROUP MATH \RIGHTGROUP produces ( MATH ) where the parentheses are % highlighted the same as keywords: \newcommand{\LEFTGROUP}{\STYLE{Key}{(}} \newcommand{\RIGHTGROUP}{\STYLE{Key}{)}} % MATH\PLUS produces a superscript + % MATH\STAR produces a superscript * % MATH\QUERY produces a superscript ? \newcommand{\PLUS}{{}^{\texttt{+}}} \newcommand{\STAR}{{}^{\texttt{*}}} \newcommand{\QUERY}{{}^{\texttt{?}}} % \RULE{& PREMISE \\ & ...}{& FORMULA ... \\ & ...} produces an inference rule % with separately aligned premises and conclusion % PREMISE % ... % ----------- % FORMULA ... % ... \newcommand{\RULE}[2] {\frac{\begin{aligned}#1\end{aligned}}{\begin{aligned}#2\end{aligned}}} % \AXIOM{& FORMULA ... \\ & ...} produces an aligned formula % % FORMULA ... % ... \newcommand{\AXIOM}[1]{\begin{aligned}#1\end{aligned}} % \TO TYPE produces => TYPE \newcommand{\TO}{\mathop{\Rightarrow}} % TERM \TRANS TERM produces TERM ---> TERM \newcommand{\TRANS}{\longrightarrow} % TERM \xrightarrow{LABEL} TERM puts the label above the long arrow % \)

Languages-beta : SL-Funcons.cbs | PLAIN | PDF

OUTLINE

\[\KEY{Language} \quad \STRING{SL}\] \[\begin{align*} [ \ \KEY{Funcon} \quad & \NAMEREF{sl-to-string} \\ \KEY{Funcon} \quad & \NAMEREF{integer-add-else-string-append} \\ \KEY{Funcon} \quad & \NAMEREF{int} \\ \KEY{Funcon} \quad & \NAMEREF{bool} \\ \KEY{Funcon} \quad & \NAMEREF{str} \\ \KEY{Funcon} \quad & \NAMEREF{obj} \\ \KEY{Funcon} \quad & \NAMEREF{fun} \\ \KEY{Funcon} \quad & \NAMEREF{scope-closed} \\ \KEY{Funcon} \quad & \NAMEREF{initialise-local-variables} \\ \KEY{Funcon} \quad & \NAMEREF{local-variable} \\ \KEY{Funcon} \quad & \NAMEREF{local-variable-initialise} \\ \KEY{Funcon} \quad & \NAMEREF{local-variable-assign} \\ \KEY{Funcon} \quad & \NAMEREF{initialise-global-bindings} \\ \KEY{Funcon} \quad & \NAMEREF{override-global-bindings} \\ \KEY{Funcon} \quad & \NAMEREF{global-bound} \\ \KEY{Funcon} \quad & \NAMEREF{read-line} \\ \KEY{Funcon} \quad & \NAMEREF{print-line} \ ] \end{align*}\]

SL-specific funcons

\[\begin{align*} \KEY{Funcon} \quad & \NAMEDECL{sl-to-string}( \VAR{V} : \NAMEHYPER{../.}{SL-2-Expressions}{sl-values}) : \TO \NAMEHYPER{../../../../../Funcons-beta/Values/Composite}{Strings}{strings} \\ \KEY{Rule} \quad & \NAMEREF{sl-to-string} ( \NAMEHYPER{../../../../../Funcons-beta/Values/Primitive}{Null}{null-value} ) \leadsto \STRING{null} \\ \KEY{Rule} \quad & \NAMEREF{sl-to-string} ( \VAR{V} : \mathop{\sim} \NAMEHYPER{../../../../../Funcons-beta/Values/Primitive}{Null}{null-type} ) \leadsto \NAMEHYPER{../../../../../Funcons-beta/Values/Composite}{Strings}{to-string} ( \VAR{V} ) \end{align*}\] \[\begin{align*} \KEY{Funcon} \quad & \NAMEDECL{integer-add-else-string-append}( \VAR{V}\SUB{1} : \NAMEHYPER{../.}{SL-2-Expressions}{sl-values}, \VAR{V}\SUB{2} : \NAMEHYPER{../.}{SL-2-Expressions}{sl-values}) : \TO \NAMEHYPER{../.}{SL-2-Expressions}{sl-values} \\&\quad \leadsto \NAMEHYPER{../../../../../Funcons-beta/Computations/Abnormal}{Failing}{else} ( \\&\quad\quad\quad\quad \NAMEHYPER{../../../../../Funcons-beta/Values/Primitive}{Integers}{integer-add} ( \NAMEREF{int} \ \VAR{V}\SUB{1}, \NAMEREF{int} \ \VAR{V}\SUB{2} ), \\&\quad\quad\quad\quad \NAMEHYPER{../../../../../Funcons-beta/Values/Composite}{Strings}{string-append} ( \NAMEREF{sl-to-string} \ \VAR{V}\SUB{1}, \NAMEREF{sl-to-string} \ \VAR{V}\SUB{2} ) ) \end{align*}\]

Abbreviations

\[\begin{align*} \KEY{Funcon} \quad & \NAMEDECL{int}( \VAR{V} : \NAMEHYPER{../.}{SL-2-Expressions}{sl-values}) : \TO \NAMEHYPER{../../../../../Funcons-beta/Values/Primitive}{Integers}{integers} \\&\quad \leadsto \NAMEHYPER{../../../../../Funcons-beta/Computations/Abnormal}{Failing}{checked} \ \NAMEHYPER{../../../../../Funcons-beta/Values}{Value-Types}{cast-to-type} ( \VAR{V}, \NAMEHYPER{../../../../../Funcons-beta/Values/Primitive}{Integers}{integers} ) \end{align*}\] \[\begin{align*} \KEY{Funcon} \quad & \NAMEDECL{bool}( \VAR{V} : \NAMEHYPER{../.}{SL-2-Expressions}{sl-values}) : \TO \NAMEHYPER{../../../../../Funcons-beta/Values/Primitive}{Booleans}{booleans} \\&\quad \leadsto \NAMEHYPER{../../../../../Funcons-beta/Computations/Abnormal}{Failing}{checked} \ \NAMEHYPER{../../../../../Funcons-beta/Values}{Value-Types}{cast-to-type} ( \VAR{V}, \NAMEHYPER{../../../../../Funcons-beta/Values/Primitive}{Booleans}{booleans} ) \end{align*}\] \[\begin{align*} \KEY{Funcon} \quad & \NAMEDECL{str}( \VAR{V} : \NAMEHYPER{../.}{SL-2-Expressions}{sl-values}) : \TO \NAMEHYPER{../../../../../Funcons-beta/Values/Composite}{Strings}{strings} \\&\quad \leadsto \NAMEHYPER{../../../../../Funcons-beta/Computations/Abnormal}{Failing}{checked} \ \NAMEHYPER{../../../../../Funcons-beta/Values}{Value-Types}{cast-to-type} ( \VAR{V}, \NAMEHYPER{../../../../../Funcons-beta/Values/Composite}{Strings}{strings} ) \end{align*}\] \[\begin{align*} \KEY{Funcon} \quad & \NAMEDECL{obj}( \VAR{V} : \NAMEHYPER{../.}{SL-2-Expressions}{sl-values}) : \TO \NAMEHYPER{../../../../../Funcons-beta/Values/Composite}{Objects}{objects} \\&\quad \leadsto \NAMEHYPER{../../../../../Funcons-beta/Computations/Abnormal}{Failing}{checked} \ \NAMEHYPER{../../../../../Funcons-beta/Values}{Value-Types}{cast-to-type} ( \VAR{V}, \NAMEHYPER{../../../../../Funcons-beta/Values/Composite}{Objects}{objects} ) \end{align*}\] \[\begin{align*} \KEY{Funcon} \quad & \NAMEDECL{fun}( \VAR{V} : \NAMEHYPER{../../../../../Funcons-beta/Values}{Value-Types}{values}) : \TO \NAMEHYPER{../../../../../Funcons-beta/Values/Abstraction}{Functions}{functions} ( \_, \_ ) \\&\quad \leadsto \NAMEHYPER{../../../../../Funcons-beta/Computations/Abnormal}{Failing}{checked} \ \NAMEHYPER{../../../../../Funcons-beta/Values}{Value-Types}{cast-to-type} ( \VAR{V}, \NAMEHYPER{../../../../../Funcons-beta/Values/Abstraction}{Functions}{functions} ( \_, \_ ) ) \end{align*}\]

Further funcons

Some of the funcons defined below might be sufficiently reuseful for inclusion in Funcons-beta.

Binding

\[\begin{align*} \KEY{Funcon} \quad & \NAMEDECL{scope-closed}( \VAR{Env} : \NAMEHYPER{../../../../../Funcons-beta/Computations/Normal}{Binding}{envs}, \VAR{X} : \TO \VAR{T}) : \TO \VAR{T} \\&\quad \leadsto \NAMEHYPER{../../../../../Funcons-beta/Computations/Normal}{Binding}{closed} \ \NAMEHYPER{../../../../../Funcons-beta/Computations/Normal}{Binding}{scope} ( \VAR{Env}, \VAR{X} ) \end{align*}\]

\(\SHADE{\NAMEREF{scope-closed} ( \VAR{D}, \VAR{X} )}\) evaluates \(\SHADE{\VAR{D}}\) in the current environment, then evaluates \(\SHADE{\VAR{X}}\) in the resulting environment. Note the difference between \(\SHADE{\NAMEREF{scope-closed} ( \VAR{D}, \VAR{X} )}\) and \(\SHADE{\NAMEHYPER{../../../../../Funcons-beta/Computations/Normal}{Binding}{closed} ( \NAMEHYPER{../../../../../Funcons-beta/Computations/Normal}{Binding}{scope} ( \VAR{D}, \VAR{X} ) )}\): the latter is equivalent to \(\SHADE{\NAMEHYPER{../../../../../Funcons-beta/Computations/Normal}{Binding}{closed} ( \NAMEHYPER{../../../../../Funcons-beta/Computations/Normal}{Binding}{scope} ( \NAMEHYPER{../../../../../Funcons-beta/Computations/Normal}{Binding}{closed} \ \VAR{D}, \VAR{X} ) )}\), where \(\SHADE{\VAR{D}}\) cannot reference any bindings.

Local variables

The local variable map is stored in a variable bound to “local-variables”. Initialising a local variable updates the stored local variable map. Subsequent assignments to a local variable do not change the stored map.

\[\begin{align*} \KEY{Funcon} \quad & \NAMEDECL{initialise-local-variables} : \TO \NAMEHYPER{../../../../../Funcons-beta/Computations/Normal}{Binding}{environments} \\&\quad \leadsto \NAMEHYPER{../../../../../Funcons-beta/Computations/Normal}{Binding}{bind} ( \\&\quad\quad\quad\quad \STRING{local{-}variables}, \\&\quad\quad\quad\quad \NAMEHYPER{../../../../../Funcons-beta/Computations/Normal}{Storing}{allocate-initialised-variable} ( \NAMEHYPER{../../../../../Funcons-beta/Computations/Normal}{Binding}{environments}, \NAMEHYPER{../../../../../Funcons-beta/Values/Composite}{Maps}{map} ( \ ) ) ) \end{align*}\] \[\begin{align*} \KEY{Funcon} \quad & \NAMEDECL{local-variable}( \VAR{I} : \NAMEHYPER{../../../../../Funcons-beta/Computations/Normal}{Binding}{ids}) : \TO \NAMEHYPER{../../../../../Funcons-beta/Computations/Normal}{Storing}{variables} \\&\quad \leadsto \NAMEHYPER{../../../../../Funcons-beta/Computations/Abnormal}{Failing}{checked} \ \NAMEHYPER{../../../../../Funcons-beta/Values/Composite}{Maps}{lookup} ( \NAMEHYPER{../../../../../Funcons-beta/Computations/Normal}{Storing}{assigned} \ \NAMEHYPER{../../../../../Funcons-beta/Computations/Normal}{Binding}{bound} \ \STRING{local{-}variables}, \VAR{I} ) \end{align*}\] \[\begin{align*} \KEY{Funcon} \quad & \NAMEDECL{local-variable-initialise}( \VAR{I} : \NAMEHYPER{../../../../../Funcons-beta/Computations/Normal}{Binding}{ids}, \VAR{V} : \NAMEHYPER{../../../../../Funcons-beta/Values}{Value-Types}{values}) : \TO \NAMEHYPER{../../../../../Funcons-beta/Values/Primitive}{Null}{null-type} \\&\quad \leadsto \NAMEHYPER{../../../../../Funcons-beta/Computations/Normal}{Storing}{assign} ( \\&\quad\quad\quad\quad \NAMEHYPER{../../../../../Funcons-beta/Computations/Normal}{Binding}{bound} \ \STRING{local{-}variables}, \\&\quad\quad\quad\quad \NAMEHYPER{../../../../../Funcons-beta/Values/Composite}{Maps}{map-override} ( \\&\quad\quad\quad\quad\quad \{ \VAR{I} \mapsto \NAMEHYPER{../../../../../Funcons-beta/Computations/Normal}{Storing}{allocate-initialised-variable} ( \NAMEHYPER{../../../../../Funcons-beta/Values}{Value-Types}{values}, \VAR{V} ) \}, \\&\quad\quad\quad\quad\quad \NAMEHYPER{../../../../../Funcons-beta/Computations/Normal}{Storing}{assigned} \ \NAMEHYPER{../../../../../Funcons-beta/Computations/Normal}{Binding}{bound} \ \STRING{local{-}variables} ) ) \end{align*}\] \[\begin{align*} \KEY{Funcon} \quad & \NAMEDECL{local-variable-assign}( \VAR{I} : \NAMEHYPER{../../../../../Funcons-beta/Computations/Normal}{Binding}{ids}, \VAR{V} : \NAMEHYPER{../../../../../Funcons-beta/Values}{Value-Types}{values}) : \TO \NAMEHYPER{../../../../../Funcons-beta/Values/Primitive}{Null}{null-type} \\&\quad \leadsto \NAMEHYPER{../../../../../Funcons-beta/Computations/Abnormal}{Failing}{else} ( \\&\quad\quad\quad\quad \NAMEHYPER{../../../../../Funcons-beta/Computations/Normal}{Storing}{assign} ( \NAMEREF{local-variable} \ \VAR{I}, \VAR{V} ), \\&\quad\quad\quad\quad \NAMEREF{local-variable-initialise} ( \VAR{I}, \VAR{V} ) ) \end{align*}\]

Global bindings

The global bindings map is stored in a variable bound to “global-bindings”. Global declaration or redeclaration of an identifier involves updating the stored global environment.

\[\begin{align*} \KEY{Funcon} \quad & \NAMEDECL{initialise-global-bindings} : \TO \NAMEHYPER{../../../../../Funcons-beta/Computations/Normal}{Binding}{environments} \\&\quad \leadsto \NAMEHYPER{../../../../../Funcons-beta/Computations/Normal}{Binding}{bind} ( \\&\quad\quad\quad\quad \STRING{global{-}bindings}, \\&\quad\quad\quad\quad \NAMEHYPER{../../../../../Funcons-beta/Computations/Normal}{Storing}{allocate-initialised-variable} ( \NAMEHYPER{../../../../../Funcons-beta/Computations/Normal}{Binding}{environments}, \NAMEHYPER{../../../../../Funcons-beta/Values/Composite}{Maps}{map} ( \ ) ) ) \end{align*}\] \[\begin{align*} \KEY{Funcon} \quad & \NAMEDECL{override-global-bindings}( \VAR{E} : \NAMEHYPER{../../../../../Funcons-beta/Computations/Normal}{Binding}{environments}) : \TO \NAMEHYPER{../../../../../Funcons-beta/Values/Primitive}{Null}{null-type} \\&\quad \leadsto \NAMEHYPER{../../../../../Funcons-beta/Computations/Normal}{Storing}{assign} ( \\&\quad\quad\quad\quad \NAMEHYPER{../../../../../Funcons-beta/Computations/Normal}{Binding}{bound} \ \STRING{global{-}bindings}, \\&\quad\quad\quad\quad \NAMEHYPER{../../../../../Funcons-beta/Values/Composite}{Maps}{map-override} ( \VAR{E}, \NAMEHYPER{../../../../../Funcons-beta/Computations/Normal}{Storing}{assigned} \ \NAMEHYPER{../../../../../Funcons-beta/Computations/Normal}{Binding}{bound} \ \STRING{global{-}bindings} ) ) \end{align*}\] \[\begin{align*} \KEY{Funcon} \quad & \NAMEDECL{global-bound}( \VAR{I} : \NAMEHYPER{../../../../../Funcons-beta/Computations/Normal}{Binding}{ids}) : \TO \NAMEHYPER{../../../../../Funcons-beta/Values}{Value-Types}{values} \\&\quad \leadsto \NAMEHYPER{../../../../../Funcons-beta/Computations/Abnormal}{Failing}{checked} \ \NAMEHYPER{../../../../../Funcons-beta/Values/Composite}{Maps}{lookup} ( \NAMEHYPER{../../../../../Funcons-beta/Computations/Normal}{Storing}{assigned} \ \NAMEHYPER{../../../../../Funcons-beta/Computations/Normal}{Binding}{bound} \ \STRING{global{-}bindings}, \VAR{I} ) \end{align*}\]

Composite input and output

\[\begin{align*} \KEY{Funcon} \quad & \NAMEDECL{read-line} : \TO \NAMEHYPER{../../../../../Funcons-beta/Values/Composite}{Strings}{strings} \\&\quad \leadsto \NAMEHYPER{../../../../../Funcons-beta/Computations/Normal}{Giving}{give} ( \\&\quad\quad\quad\quad \NAMEHYPER{../../../../../Funcons-beta/Computations/Normal}{Interacting}{read}, \\&\quad\quad\quad\quad \NAMEHYPER{../../../../../Funcons-beta/Computations/Normal}{Flowing}{if-true-else} ( \\&\quad\quad\quad\quad\quad \NAMEHYPER{../../../../../Funcons-beta/Values}{Value-Types}{is-eq} ( \NAMEHYPER{../../../../../Funcons-beta/Computations/Normal}{Giving}{given}, \ATOM{{\BACKSLASH}n} ), \\&\quad\quad\quad\quad\quad \NAMEHYPER{../../../../../Funcons-beta/Values/Composite}{Lists}{nil}, \\&\quad\quad\quad\quad\quad \NAMEHYPER{../../../../../Funcons-beta/Values/Composite}{Lists}{cons} ( \NAMEHYPER{../../../../../Funcons-beta/Computations/Normal}{Giving}{given}, \NAMEREF{read-line} ) ) ) \end{align*}\]

\(\SHADE{\NAMEREF{read-line}}\) reads characters from the standard input until a linefeed character, giving the string formed from the sequence of characters excluding the newline. If the input ends before the end of the line, it fails.

\[\begin{align*} \KEY{Funcon} \quad & \NAMEDECL{print-line}( \VAR{S} : \NAMEHYPER{../../../../../Funcons-beta/Values/Composite}{Strings}{strings}) : \TO \NAMEHYPER{../../../../../Funcons-beta/Values/Primitive}{Null}{null-type} \\&\quad \leadsto \NAMEHYPER{../../../../../Funcons-beta/Computations/Normal}{Interacting}{print} ( \VAR{S}, \STRING{{\BACKSLASH}n} ) \end{align*}\]