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Unstable-Funcons-beta : Postponing.cbs | PLAIN | PDF

Postponing

\[\begin{align*} [ \ \KEY{Entity} \quad & \NAMEREF{postponing} \\ \KEY{Funcon} \quad & \NAMEREF{postpone} \\ \KEY{Funcon} \quad & \NAMEREF{postpone-after-effect} \\ \KEY{Funcon} \quad & \NAMEREF{after-effect} \ ] \end{align*}\]

A funcon term can extend itself (e.g., with code to release the resources allocated to it) using general funcons for postponed execution. When a step from \(\SHADE{\VAR{X}}\) to \(\SHADE{\VAR{X}'}\) executes \(\SHADE{\NAMEREF{postpone} ( \VAR{Y} )}\) (which computes \(\SHADE{\NAMEHYPER{../../../../Funcons-beta/Values/Primitive}{Null}{null}}\)), the corresponding step of \(\SHADE{\NAMEREF{postpone-after-effect} ( \VAR{X} )}\) gives \(\SHADE{\NAMEREF{postpone-after-effect} ( \NAMEREF{after-effect} ( \VAR{X}', \VAR{Y} ) )}\), so that normal termination of \(\SHADE{\VAR{X}'}\) is followed by the effect of \(\SHADE{\VAR{Y}}\).

The control entity \(\SHADE{\NAMEREF{postponing} ( \VAR{A} )}\) signals that the execution of the body of the abstraction \(\SHADE{\VAR{A}}\) is postponed:

\[\begin{align*} \KEY{Entity} \quad & \_ \xrightarrow{\NAMEDECL{postponing}(\_ : ( \NAMEHYPER{../../../../Funcons-beta/Values/Abstraction}{Generic}{abstractions} ( \TO \NAMEHYPER{../../../../Funcons-beta/Values/Primitive}{Null}{null-type} ) )\QUERY)} \_ \end{align*}\]

The funcon \(\SHADE{\NAMEREF{postpone} ( \VAR{X} )}\) forms a closure from \(\SHADE{\VAR{X}}\) and signals that its execution is postponed:

\[\begin{align*} \KEY{Funcon} \quad & \NAMEDECL{postpone}( \_ : \TO \NAMEHYPER{../../../../Funcons-beta/Values}{Value-Types}{values}) : \TO \NAMEHYPER{../../../../Funcons-beta/Values/Primitive}{Null}{null-type} \\ \KEY{Rule} \quad & \RULE{ & \NAMEHYPER{../../../../Funcons-beta/Computations/Normal}{Giving}{given-value} ( \VAR{V} ) \vdash \NAMEHYPER{../../../../Funcons-beta/Values/Abstraction}{Generic}{closure} \ \NAMEHYPER{../../../../Funcons-beta/Computations/Normal}{Giving}{give} ( \VAR{V}, \VAR{X} ) \xrightarrow{\NAMEREF{postponing}( \ )}_{} \VAR{A} }{ & \NAMEHYPER{../../../../Funcons-beta/Computations/Normal}{Giving}{given-value} ( \VAR{V} ) \vdash \NAMEREF{postpone} ( \VAR{X} ) \xrightarrow{\NAMEREF{postponing}( \VAR{A} )}_{} \NAMEHYPER{../../../../Funcons-beta/Values/Primitive}{Null}{null-value} } \\ \KEY{Rule} \quad & \RULE{ & \NAMEHYPER{../../../../Funcons-beta/Computations/Normal}{Giving}{given-value} ( \ ) \vdash \NAMEHYPER{../../../../Funcons-beta/Values/Abstraction}{Generic}{closure} \ \NAMEHYPER{../../../../Funcons-beta/Computations/Normal}{Giving}{no-given} \ \VAR{X} \xrightarrow{\NAMEREF{postponing}( \ )}_{} \VAR{A} }{ & \NAMEHYPER{../../../../Funcons-beta/Computations/Normal}{Giving}{given-value} ( \ ) \vdash \NAMEREF{postpone} ( \VAR{X} ) \xrightarrow{\NAMEREF{postponing}( \VAR{A} )}_{} \NAMEHYPER{../../../../Funcons-beta/Values/Primitive}{Null}{null-value} } \end{align*}\]

The funcon \(\SHADE{\NAMEREF{postpone-after-effect} ( \VAR{X} )}\) handles each signal \(\SHADE{\NAMEREF{postponing} ( \VAR{A} )}\) by adding it as an after-effect of \(\SHADE{\VAR{X}}\):

\[\begin{align*} \KEY{Funcon} \quad & \NAMEDECL{postpone-after-effect}( \_ : \TO \VAR{T}) : \TO \VAR{T} \\ \KEY{Rule} \quad & \RULE{ & \VAR{X} \xrightarrow{\NAMEREF{postponing}( \ )}_{} \VAR{X}' }{ & \NAMEREF{postpone-after-effect} ( \VAR{X} ) \xrightarrow{\NAMEREF{postponing}( \ )}_{} \\&\quad \NAMEREF{postpone-after-effect} ( \VAR{X}' ) } \\ \KEY{Rule} \quad & \RULE{ & \VAR{X} \xrightarrow{\NAMEREF{postponing}( \VAR{A} )}_{} \VAR{X}'\\& \VAR{A} \leadsto \NAMEHYPER{../../../../Funcons-beta/Values/Abstraction}{Generic}{abstraction} \ \VAR{Y} }{ & \NAMEREF{postpone-after-effect} ( \VAR{X} ) \xrightarrow{\NAMEREF{postponing}( \ )}_{} \\&\quad \NAMEREF{postpone-after-effect} ( \NAMEREF{after-effect} ( \VAR{X}', \VAR{Y} ) ) } \\ \KEY{Rule} \quad & \NAMEREF{postpone-after-effect} ( \VAR{V} : \NAMEHYPER{../../../../Funcons-beta/Values}{Value-Types}{values} ) \leadsto \VAR{V} \end{align*}\]

The funcon \(\SHADE{\NAMEREF{after-effect} ( \VAR{X}, \VAR{Y} )}\) first executes \(\SHADE{\VAR{X}}\). If \(\SHADE{\VAR{X}}\) computes a value \(\SHADE{\VAR{V}}\), it then executes \(\SHADE{\VAR{Y}}\), and computes \(\SHADE{\VAR{V}}\):

\[\begin{align*} \KEY{Funcon} \quad & \NAMEDECL{after-effect}( \VAR{X} : \TO \VAR{T}, \VAR{Y} : \TO \NAMEHYPER{../../../../Funcons-beta/Values/Primitive}{Null}{null-type}) : \TO \VAR{T} \\&\quad \leadsto \NAMEHYPER{../../../../Funcons-beta/Computations/Normal}{Giving}{give} ( \VAR{X}, \NAMEHYPER{../../../../Funcons-beta/Computations/Normal}{Flowing}{sequential} ( \VAR{Y}, \NAMEHYPER{../../../../Funcons-beta/Computations/Normal}{Giving}{given} ) ) \end{align*}\]

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