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

Memos

\[\begin{align*} [ \ \KEY{Entity} \quad & \NAMEREF{memo-map} \\ \KEY{Funcon} \quad & \NAMEREF{initialise-memos} \\ \KEY{Funcon} \quad & \NAMEREF{memo-value} \\ \KEY{Funcon} \quad & \NAMEREF{initialise-memo-value} \\ \KEY{Funcon} \quad & \NAMEREF{memo-value-recall} \ ] \end{align*}\]

A memo is like a mutable variable, except that the memo is updated and accessed by a specified key, rather than by an allocated location. The collection of memos is represented by a mutable entity that maps keys to values.

\[\begin{align*} \KEY{Entity} \quad & \langle \_, \NAMEDECL{memo-map}(\_ : \NAMEHYPER{../../../../Funcons-beta/Values/Composite}{Maps}{maps} ( \NAMEHYPER{../../../../Funcons-beta/Values}{Value-Types}{ground-values}, \NAMEHYPER{../../../../Funcons-beta/Values}{Value-Types}{values} )) \rangle \TRANS \\& \langle \_, \NAME{memo-map}(\_ : \NAME{maps} ( \NAME{ground-values}, \NAME{values} )) \rangle \end{align*}\] \[\begin{align*} \KEY{Funcon} \quad & \NAMEDECL{initialise-memos}( \_ : \TO \NAMEHYPER{../../../../Funcons-beta/Values}{Value-Types}{values}) : \TO \NAMEHYPER{../../../../Funcons-beta/Values}{Value-Types}{values} \\ \KEY{Rule} \quad & \langle \NAMEREF{initialise-memos} ( \VAR{X} ), \NAMEREF{memo-map} ( \_ ) \rangle \TRANS \langle \VAR{X}, \NAMEREF{memo-map} ( \NAMEHYPER{../../../../Funcons-beta/Values/Composite}{Maps}{map} ( \ ) ) \rangle \end{align*}\]

When key \(\SHADE{\VAR{K}}\) is associated with value \(\SHADE{\VAR{V}}\), the funcon \(\SHADE{\NAMEREF{memo-value} ( \VAR{K}, \VAR{X} )}\) simply gives \(\SHADE{\VAR{V}}\), without evaluating \(\SHADE{\VAR{X}}\). When \(\SHADE{\VAR{K}}\) is not currently associated with any value, it associates \(\SHADE{\VAR{K}}\) with the value computed by \(\SHADE{\VAR{X}}\).

\[\begin{align*} \KEY{Funcon} \quad & \NAMEDECL{memo-value}( \VAR{K} : \NAMEHYPER{../../../../Funcons-beta/Values}{Value-Types}{ground-values}, \VAR{X} : \TO \NAMEHYPER{../../../../Funcons-beta/Values}{Value-Types}{values}) : \TO \NAMEHYPER{../../../../Funcons-beta/Values}{Value-Types}{values} \\&\quad \leadsto \NAMEHYPER{../../../../Funcons-beta/Computations/Abnormal}{Failing}{else} ( \\&\quad\quad\quad\quad \NAMEREF{memo-value-recall} ( \VAR{K} ), \\&\quad\quad\quad\quad \NAMEHYPER{../../../../Funcons-beta/Computations/Normal}{Giving}{give} ( \\&\quad\quad\quad\quad\quad \VAR{X}, \\&\quad\quad\quad\quad\quad \NAMEHYPER{../../../../Funcons-beta/Computations/Normal}{Flowing}{sequential} ( \\&\quad\quad\quad\quad\quad\quad \NAMEHYPER{../../../../Funcons-beta/Computations/Abnormal}{Failing}{else} ( \NAMEREF{initialise-memo-value} ( \VAR{K}, \NAMEHYPER{../../../../Funcons-beta/Computations/Normal}{Giving}{given} ), \NAMEHYPER{../../../../Funcons-beta/Values/Primitive}{Null}{null-value} ), \\&\quad\quad\quad\quad\quad\quad \NAMEREF{memo-value-recall} ( \VAR{K} ) ) ) ) \end{align*}\]

The initialisation could fail due to memoisation of a (potentially different) value for \(\SHADE{\VAR{K}}\) during the computation \(\SHADE{\VAR{X}}\). In that case, the value computed by \(\SHADE{\VAR{X}}\) is simply discarded; a resource-safe funcon would take an extra argument to roll back the effects of \(\SHADE{\VAR{X}}\).

\[\begin{align*} \KEY{Funcon} \quad & \NAMEDECL{initialise-memo-value}( \_ : \NAMEHYPER{../../../../Funcons-beta/Values}{Value-Types}{ground-values}, \_ : \NAMEHYPER{../../../../Funcons-beta/Values}{Value-Types}{values}) : \TO \NAMEHYPER{../../../../Funcons-beta/Values/Primitive}{Null}{null-type} \\ \KEY{Rule} \quad & \RULE{ & \NAMEHYPER{../../../../Funcons-beta/Values/Composite}{Maps}{map-unite} ( \VAR{M}, \{ \VAR{K} \mapsto \VAR{V} \} ) \leadsto \VAR{M}' }{ & \langle \NAMEREF{initialise-memo-value} ( \VAR{K} : \NAMEHYPER{../../../../Funcons-beta/Values}{Value-Types}{ground-values}, \VAR{V} : \NAMEHYPER{../../../../Funcons-beta/Values}{Value-Types}{values} ), \NAMEREF{memo-map} ( \VAR{M} ) \rangle \TRANS \\&\quad \langle \NAMEHYPER{../../../../Funcons-beta/Values/Primitive}{Null}{null-value}, \NAMEREF{memo-map} ( \VAR{M}' ) \rangle } \\ \KEY{Rule} \quad & \RULE{ & \NAMEHYPER{../../../../Funcons-beta/Values/Composite}{Maps}{map-unite} ( \VAR{M}, \{ \VAR{K} \mapsto \VAR{V} \} ) \leadsto ( \ ) }{ & \langle \NAMEREF{initialise-memo-value} ( \VAR{K} : \NAMEHYPER{../../../../Funcons-beta/Values}{Value-Types}{ground-values}, \VAR{V} : \NAMEHYPER{../../../../Funcons-beta/Values}{Value-Types}{values} ), \NAMEREF{memo-map} ( \VAR{M} ) \rangle \TRANS \\&\quad \langle \NAMEHYPER{../../../../Funcons-beta/Computations/Abnormal}{Failing}{fail}, \NAMEREF{memo-map} ( \VAR{M} ) \rangle } \end{align*}\] \[\begin{align*} \KEY{Funcon} \quad & \NAMEDECL{memo-value-recall}( \_ : \NAMEHYPER{../../../../Funcons-beta/Values}{Value-Types}{ground-values}) : \TO \NAMEHYPER{../../../../Funcons-beta/Values}{Value-Types}{values} \\ \KEY{Rule} \quad & \RULE{ & \NAMEHYPER{../../../../Funcons-beta/Values/Composite}{Maps}{lookup} ( \VAR{M}, \VAR{K} ) \leadsto \VAR{V} }{ & \langle \NAMEREF{memo-value-recall} ( \VAR{K} : \NAMEHYPER{../../../../Funcons-beta/Values}{Value-Types}{ground-values} ), \NAMEREF{memo-map} ( \VAR{M} ) \rangle \TRANS \langle \VAR{V}, \NAMEREF{memo-map} ( \VAR{M} ) \rangle } \\ \KEY{Rule} \quad & \RULE{ & \NAMEHYPER{../../../../Funcons-beta/Values/Composite}{Maps}{lookup} ( \VAR{M}, \VAR{K} ) \leadsto ( \ ) }{ & \langle \NAMEREF{memo-value-recall} ( \VAR{K} : \NAMEHYPER{../../../../Funcons-beta/Values}{Value-Types}{ground-values} ), \NAMEREF{memo-map} ( \VAR{M} ) \rangle \TRANS \langle \NAMEHYPER{../../../../Funcons-beta/Computations/Abnormal}{Failing}{fail}, \NAMEREF{memo-map} ( \VAR{M} ) \rangle } \end{align*}\]

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