dhil/phd-dissertation
1
0
Fork 0
mirror of https://github.com/dhil/phd-dissertation synced 2026-03-13 02:58:26 +00:00
Code Issues Releases Wiki Activity

fix typos

Browse Source
This commit is contained in:
Daniel Hillerström
2021-05-21 18:51:24 +01:00
parent eefa6e4ad4
commit c254d293a9
1 changed files with 17 additions and 16 deletions
Download Patch File Download Diff File Expand all files Collapse all files

33
thesis.tex
View File

@@ -600,7 +600,7 @@ to manipulate the contents of some global state cell $st$.
\[
\bl
\incrEven : \UnitType \to \Bool\\
\incrEven\,\Unit \defas \Let\;v \revto !st\;\In\;st \defnas 1 + v;\,\even~st
\incrEven\,\Unit \defas \Let\;v \revto !st\;\In\;st \defnas 1 + v;\,\even~v
\el
\]
%
@@ -993,7 +993,7 @@ follows.
\bl
T~A \defas \Int \to (A \times \Int)\smallskip\\
\incrEven : \UnitType \to T~\Bool\\
\incrEven~\Unit \defas \getF
\incrEven~\Unit \defas \getF\,\Unit
\bind (\lambda st.
\putF\,(1+st)
\bind \lambda\Unit. \Return\;(\even~st)))
@@ -1364,10 +1364,10 @@ Monadic reflection is a technique due to
delimited control to perform a local switch from monadic style into
direct-style and vice versa. The key insight is that a control reifier
provides an escape hatch that makes it possible for computation to
locally unseal the monad, as it were. The scope of this escape hatch
is restricted by the control delimiter, which seals computation back
into the monad. Monadic reflection introduces two operators, which are
defined over some monad $T$ and some fixed result type $R$.
locally jump out of the monad, as it were. The scope of this escape
hatch is restricted by the control delimiter, which forces computation
back into the monad. Monadic reflection introduces two operators,
which are defined over some monad $T$ and some fixed result type $R$.
%
\[
\ba{@{~}l@{\qquad\quad}@{~}r}
@@ -1386,17 +1386,18 @@ defined over some monad $T$ and some fixed result type $R$.
\]
%
The first operator $\reify$ (pronounced `reify') performs
\emph{monadic unsealing}, which means it makes the effect
corresponding to $T$ in the thunk $m$ transparent. The implementation
installs a reset instance to delimit control effects of $m$. The
result of forcing $m$ gets lifted into the monad $T$.
\emph{monadic reification}. Semantically it makes the effect
corresponding to $T$ transparent. The implementation installs a reset
instance to delimit control effects of $m$. The result of forcing $m$
gets lifted into the monad $T$.
%
The second operator $\reflect$ (pronounced `reflect') performs
\emph{monadic sealing}. It makes the effect corresponding to $T$ in
its parameter $m$ opaque. The implementation applies $\shift$ to
capture the current continuation (up to the nearest instance of
reset). Subsequently, it evaluates the monadic computation $m$ and
passes the result of this evaluation to the continuation $k$.
\emph{monadic reflection}. It makes the effect corresponding to $T$
opaque. The implementation applies $\shift$ to capture the current
continuation (up to the nearest instance of reset). Subsequently, it
evaluates the monadic computation $m$ and passes the result of this
evaluation to the continuation $k$, which effectively performs the
jump out of the monad.
Suppose we instantiate $T = \State~S$ for some type $S$, then we can
@@ -1434,7 +1435,7 @@ defined in terms of the state monad runner.
\[
\bl
\runState : (\UnitType \to R) \to S \to R \times S\\
\runState~m~st_0 \defas T.\runState~(\reify m)~st_0
\runState~m~st_0 \defas T.\runState~(\lambda\Unit.\reify m)~st_0
\el
\]
%