dhil/phd-dissertation
1
0
Fork 0
mirror of https://github.com/dhil/phd-dissertation synced 2026-03-13 11:08:25 +00:00
Code Issues Releases Wiki Activity

Section 2.4

Browse Source
This commit is contained in:
Daniel Hillerström
2021-12-20 13:37:07 +00:00
parent 98784c59ab
commit 6c128a1181
1 changed files with 48 additions and 20 deletions
Download Patch File Download Diff File Expand all files Collapse all files

68
thesis.tex
View File

@@ -2870,13 +2870,23 @@ left hand side of $\mapsto$. We use deep pattern matching to ignore
the first element of the payload and to bind the second element of the the first element of the payload and to bind the second element of the
payload to $cs$. The resumption gets bound to the name $resume$. It is payload to $cs$. The resumption gets bound to the name $resume$. It is
worth noting that at this point, the type of $resume$ is worth noting that at this point, the type of $resume$ is
$\UnitType \to \Record{\alpha;\UFile}$, where the domain type matches (\emph{morally}) $\UnitType \to \Record{\alpha;\UFile}$, where the
the codomain type of the operation $\Write$ and the codomain type domain type matches the codomain type of the operation $\Write$ and
matches the expected type of the current context. This latter fact is the codomain type matches the expected type of the current context.
due to the deep semantics of $\Handle$-construct, which means that an (The actual type is
invocation of $resume$ implicitly installs another $\Handle$-construct $\UnitType \to \Record{\alpha;\UFile} \eff
with the same handler around the residual evaluation context embodied \{\Write:\theta;\varepsilon\}$, where $\theta$ is a presence variable
in $resume$. denoting that $\Write$ is polymorphic in whether it is present,
i.e. the ambient context which $resume$ gets invoked in is allowed to
perform another invocation of $\Write$, and $\varepsilon$ is an effect
variable, which can be instantiated with additional operation labels
to allow $resume$ to be used in a greater context. In many instances
we can ignore presence polymorphim and effect polymorphism as
described in Section~\ref{sec:effect-sugar}, hence we omit these
annotation whenever possible.) This latter fact is due to the deep
semantics of $\Handle$-construct, which means that an invocation of
$resume$ implicitly installs another $\Handle$-construct with the same
handler around the residual evaluation context embodied in $resume$.
% %
The body of the $\Write$-case extends the file by first invoking the The body of the $\Write$-case extends the file by first invoking the
resumption, which returns a pair containing the result of $m$ and the resumption, which returns a pair containing the result of $m$ and the
@@ -2980,7 +2990,9 @@ Technically, the $\Exit$-case provides access to the resumption of
$\Exit$ in $m$, however, we do not write this resumption here, because $\Exit$ in $m$, however, we do not write this resumption here, because
it is useless as its type is $\ZeroType \to \Int$. It expects as it is useless as its type is $\ZeroType \to \Int$. It expects as
argument an element of the empty type, which is of course impossible argument an element of the empty type, which is of course impossible
to provide, hence we can never invoke it. to provide, hence we can never invoke it. In general, an operation
clause may drop the provided resumption even if the resumption is
usable.
To illustrate $\status$ and $\exit$ in action consider the following To illustrate $\status$ and $\exit$ in action consider the following
example, where the computation gets terminated mid-way. example, where the computation gets terminated mid-way.
@@ -3183,13 +3195,19 @@ instance.
% %
The new instance of $\environment$ shadows the initial instance, and The new instance of $\environment$ shadows the initial instance, and
therefore it will intercept and handle any subsequent invocations of therefore it will intercept and handle any subsequent invocations of
$\Ask$ arising from running the resumption. A subsequent invocation of $\Ask$ arising from running the resumption. The next invocation of
$\Su$ will install another environment instance, which will shadow $\Su$ will install another environment instance, which will shadow
both the previously installed instance and the initial instance. both the previously installed instance and the initial instance. This
ability to dynamically overload residual operations is a key
difference between \citeauthor{PlotkinP09}'s effect handlers (as this
thesis is about) and \emph{lexical} effect handlers, as the latter
bind operations to the first suitable handler
instance~\cite{XieBHSL20,BrachthauserSO20}.
% %
To make this concrete, let us plug together the all components of our As an illustrative example of the dynamic overloading in action, let
system we have defined thus far. us plug together the all components of our system we have defined thus
far.
% %
\[ \[
\ba{@{~}l@{~}l} \ba{@{~}l@{~}l}
@@ -3310,9 +3328,12 @@ $\False$. The results are joined by list concatenation ($\concat$).
% %
Thus the handler returns a list of all the possible results of $m$. Thus the handler returns a list of all the possible results of $m$.
% %
In fact, this handler is exactly the standard handler for This handler is an instance of a \emph{multi-shot} handler, because it
nondeterministic choice, which satisfies the standard semi-lattice contains at least one operation clause which invokes the provided
equations~\cite{PlotkinP09,PlotkinP13}. resumption multiple times.
% In fact, this handler is exactly the standard handler for
% nondeterministic choice, which satisfies the standard semi-lattice
% equations~\cite{PlotkinP09,PlotkinP13}.
% \dhil{This is an instance of non-blind backtracking~\cite{FriedmanHK84}} % \dhil{This is an instance of non-blind backtracking~\cite{FriedmanHK84}}
Let us consider $\nondet$ together with the previously defined Let us consider $\nondet$ together with the previously defined
@@ -3420,8 +3441,9 @@ is it has run to completion, or 2) it is paused, meaning it has
yielded to provide room for another process to run. yielded to provide room for another process to run.
% %
We can model the state using a recursive variant type parameterised by We can model the state using a recursive variant type parameterised by
some return value $\alpha$ and a set of effects $\varepsilon$ that the some return value $\alpha$, a set of effects $\varepsilon$ that the
process may perform. process may perform, and a present variable to denote the presence of
$\Interrupt$.
% %
\[ \[
\Pstate~\alpha~\varepsilon~\theta \defas \Pstate~\alpha~\varepsilon~\theta \defas
@@ -3442,7 +3464,7 @@ $\Interrupt$ such as the following handler.
% %
\[ \[
\bl \bl
\reifyP : (\UnitType \to \alpha \eff \{\Interrupt: \UnitType \opto \UnitType;\varepsilon\}) \to \Pstate~\alpha~\varepsilon\\ \reifyP : (\UnitType \to \alpha \eff \{\Interrupt: \UnitType \opto \UnitType;\varepsilon\}) \to \Pstate~\alpha~\varepsilon~\theta\\
\reifyP~m \defas \reifyP~m \defas
\ba[t]{@{}l} \ba[t]{@{}l}
\Handle\;m\,\Unit\;\With\\ \Handle\;m\,\Unit\;\With\\
@@ -3458,8 +3480,14 @@ This handler tags and returns values with $\Done$. It also tags and
returns the resumption provided by the $\Interrupt$-case with returns the resumption provided by the $\Interrupt$-case with
$\Suspended$. $\Suspended$.
% %
This particular implementation is amounts to a handler-based variation It is worth noting that the actual type of $resume$ is
of \citeauthor{Harrison06}'s non-reactive resumption $\UnitType \to \Pstate~\alpha~\varepsilon~\theta \eff
\{\Interrupt:\theta;\varepsilon\}$, which shows us that the variables
$\varepsilon$ and $\theta$ threaded through $\Pstate$ come from the
ambient context.
%
This particular implementation amounts to a handler-based variation of
\citeauthor{Harrison06}'s non-reactive resumption
monad~\cite{Harrison06}. monad~\cite{Harrison06}.
% %
If we compose this handler with the nondeterminism If we compose this handler with the nondeterminism