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