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Funcons-beta : Controlling.cbs | PLAIN | PDF

Controlling

\[\begin{align*} [ \ \KEY{Datatype} \quad & \NAMEREF{continuations} \\ \KEY{Funcon} \quad & \NAMEREF{continuation} \\ \KEY{Entity} \quad & \NAMEREF{plug-signal} \\ \KEY{Funcon} \quad & \NAMEREF{hole} \\ \KEY{Funcon} \quad & \NAMEREF{resume-continuation} \\ \KEY{Entity} \quad & \NAMEREF{control-signal} \\ \KEY{Funcon} \quad & \NAMEREF{control} \\ \KEY{Funcon} \quad & \NAMEREF{delimit-current-continuation} \\ \KEY{Alias} \quad & \NAMEREF{delimit-cc} \ ] \end{align*}\] \[\begin{align*} \KEY{Meta-variables} \quad & \VAR{T}, \VAR{T}\SUB{1}, \VAR{T}\SUB{2} <: \NAMEHYPER{../../../Values}{Value-Types}{values} \end{align*}\] \[\begin{align*} \KEY{Datatype} \quad \NAMEDECL{continuations}( \VAR{T}\SUB{1} , \VAR{T}\SUB{2} ) \ ::= \ & \NAMEDECL{continuation}( \_ : \NAMEHYPER{../../../Values/Abstraction}{Generic}{abstractions} ( ( \ ) \TO \VAR{T}\SUB{2} )) \end{align*}\]

\(\SHADE{\NAMEREF{continuations} ( \VAR{T}\SUB{1}, \VAR{T}\SUB{2} )}\) consists of abstractions whose bodies contain a \(\SHADE{\NAMEREF{hole}}\), and which will normally compute a value of type \(\SHADE{\VAR{T}\SUB{2}}\) when the \(\SHADE{\NAMEREF{hole}}\) is plugged with a value of type \(\SHADE{\VAR{T}\SUB{1}}\).

\[\begin{align*} \KEY{Entity} \quad & \_ \xrightarrow{\NAMEDECL{plug-signal}(\VAR{V}\QUERY : \NAMEHYPER{../../../Values}{Value-Types}{values}\QUERY)} \_ \end{align*}\]

A plug-signal contains the value to be filled into a \(\SHADE{\NAMEREF{hole}}\) in a continuation, thereby allowing a continuation to resume.

\[\begin{align*} \KEY{Funcon} \quad & \NAMEDECL{hole} : \TO \NAMEHYPER{../../../Values}{Value-Types}{values} \end{align*}\]

A \(\SHADE{\NAMEREF{hole}}\) in a term cannot proceed until it receives a plug-signal containing a value to plug the hole.

\[\begin{align*} \KEY{Rule} \quad & \NAMEREF{hole} \xrightarrow{\NAMEREF{plug-signal}( \VAR{V} )}_{} \VAR{V} \end{align*}\] \[\begin{align*} \KEY{Funcon} \quad & \NAMEDECL{resume-continuation}( \VAR{K} : \NAMEREF{continuations} ( \VAR{T}\SUB{1}, \VAR{T}\SUB{2} ), \VAR{V} : \VAR{T}\SUB{1}) : \TO \VAR{T}\SUB{2} \end{align*}\]

\(\SHADE{\NAMEREF{resume-continuation} ( \VAR{K}, \VAR{V} )}\) resumes a continuation \(\SHADE{\VAR{K}}\) by plugging the value \(\SHADE{\VAR{V}}\) into the \(\SHADE{\NAMEREF{hole}}\) in the continuation.

\[\begin{align*} \KEY{Rule} \quad & \RULE{ & \VAR{X} \xrightarrow{\NAMEREF{plug-signal}( \VAR{V} )}_{} \VAR{X}' }{ & \NAMEREF{resume-continuation} ( \NAMEREF{continuation} ( \NAMEHYPER{../../../Values/Abstraction}{Generic}{abstraction} ( \VAR{X} ) ), \VAR{V} : \VAR{T} ) \xrightarrow{\NAMEREF{plug-signal}( \ )}_{} \VAR{X}' } \end{align*}\] \[\begin{align*} \KEY{Entity} \quad & \_ \xrightarrow{\NAMEDECL{control-signal}(\VAR{F}\QUERY : ( \NAMEHYPER{../../../Values/Abstraction}{Functions}{functions} ( \NAMEREF{continuations} ( \VAR{T}\SUB{1}, \VAR{T}\SUB{2} ), \VAR{T}\SUB{2} ) )\QUERY)} \_ \end{align*}\]

A control-signal contains the function to which control is about to be passed by the enclosing \(\SHADE{\NAMEREF{delimit-current-continuation} ( \VAR{X} )}\).

\[\begin{align*} \KEY{Funcon} \quad & \NAMEDECL{control}( \VAR{F} : \NAMEHYPER{../../../Values/Abstraction}{Functions}{functions} ( \NAMEREF{continuations} ( \VAR{T}\SUB{1}, \VAR{T}\SUB{2} ), \VAR{T}\SUB{2} )) : \TO \VAR{T}\SUB{1} \end{align*}\]

\(\SHADE{\NAMEREF{control} ( \VAR{F} )}\) emits a control-signal that, when handled by an enclosing \(\SHADE{\NAMEREF{delimit-current-continuation} ( \VAR{X} )}\), will apply \(\SHADE{\VAR{F}}\) to the current continuation of \(\SHADE{\NAMEREF{control} ( \VAR{F} )}\), (rather than proceeding with that current continuation).

\[\begin{align*} \KEY{Rule} \quad & \NAMEREF{control} ( \VAR{F} : \NAMEHYPER{../../../Values/Abstraction}{Functions}{functions} ( \_, \_ ) ) \xrightarrow{\NAMEREF{control-signal}( \VAR{F} )}_{} \NAMEREF{hole} \end{align*}\] \[\begin{align*} \KEY{Funcon} \quad & \NAMEDECL{delimit-current-continuation}( \VAR{X} : \TO \VAR{T}) : \TO \VAR{T} \\ \KEY{Alias} \quad & \NAMEDECL{delimit-cc} = \NAMEREF{delimit-current-continuation} \end{align*}\]

\(\SHADE{\NAMEREF{delimit-current-continuation} ( \VAR{X} )}\) delimits the scope of captured continuations.

\[\begin{align*} \KEY{Rule} \quad & \NAMEREF{delimit-current-continuation} ( \VAR{V} : \VAR{T} ) \leadsto \VAR{V} \\ \KEY{Rule} \quad & \RULE{ & \VAR{X} \xrightarrow{\NAMEREF{control-signal}( \ )}_{} \VAR{X}' }{ & \NAMEREF{delimit-current-continuation} ( \VAR{X} ) \xrightarrow{\NAMEREF{control-signal}( \ )}_{} \\&\quad \NAMEREF{delimit-current-continuation} ( \VAR{X}' ) } \\ \KEY{Rule} \quad & \RULE{ & \VAR{X} \xrightarrow{\NAMEREF{control-signal}( \VAR{F} )}_{} \VAR{X}' }{ & \NAMEREF{delimit-current-continuation} ( \VAR{X} ) \xrightarrow{\NAMEREF{control-signal}( \ )}_{} \\&\quad \NAMEREF{delimit-current-continuation} ( \NAMEHYPER{../../../Values/Abstraction}{Functions}{apply} ( \VAR{F}, \NAMEREF{continuation} \ \NAMEHYPER{../../../Values/Abstraction}{Generic}{closure} ( \VAR{X}' ) ) ) } \end{align*}\]

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