Reasoning ab out Continuations
with Control E ects
1;2
Pierre Jouvelot
2
David K. Gi ord
Categories and Sub ject Descriptions: D.1.3 [Program- Abstract
ming Techniques] { Concurrent Programming: E ect
We present a new static analysis metho d for rst-class
systems; D.1.m [Programming Techniques] { Mis-
continuations that uses an e ect system to classify the
cellaneous: First-class continuations; D.3.1 [Program-
control domain b ehavior of expressions in a typ ed p oly-
ming Languages] { Formal De nitions and Theory;
morphic language. We intro duce two new control ef-
D.3.3 [Programming Languages] { Language Con-
fects, goto and comefrom, that describ e the control ow
structs: Control structures, e ect systems; D.3.4 [Pro-
prop erties of expressions. An expression that do es not
gramming Languages] { Pro cessors: Compilers, op-
havea goto e ect is said to be continuation fol lowing
timization.
b ecause it will always call its passed return continua-
tion. An expression that do es not havea comefrom ef-
General Terms: Languages, Theory,Veri cation.
fect is said to b e continuation discarding b ecause it will
never preserve its return continuation for later use. Un-
Additional Key Words and Phrases: e ect systems, typ e
observable control e ects can be masked by the e ect
systems, control e ects, e ect masking, control ow
system. Control e ect soundness theorems guarantee
analysis, FX-87.
that the e ects computed statically by the e ect sys-
tem are a conservative approximation of the dynamic
b ehavior of an expression.
1 Intro duction
The e ect system that we describ e p erforms certain
kinds of control ow analysis that were not previously
First-class continuations add a great deal of expressive
feasible. We discuss how this analysis can enable a va-
power to a programming language as they p ermit the
riety of compiler optimizations, including parallel ex-
implementation of a wide varietyofcontrol structures,
pression scheduling in the presence of complex control
including jumps, error-handlers, and coroutines [F87].
structures, and stack allo cation of continuations. The
With this p ower comes substantial semantic [MR88] and
e ect system we describ e has b een implemented as an
implementation [CHO88] complexities. Thus it would
extension to the FX-87 programming language.
be very useful to be able to precisely identify which
expressions in a program use rst-class continuations
and in what manner.
We present a new static metho d for control ow anal-
This researchwas supp orted by the Defense Advanced Research
ysis that p erforms certain kinds of analysis that were
Pro jects Agency of the Department of Defense and was monitored
by the Oce of Naval Research under contract numb er N00014-
not previously feasible. Sp eci cally,wehave develop ed
83-K-0125.
the rst static metho d of determining which expressions
may not exhibit sequential control ow in a program-
1
CAI, Ecole des Mines, 60 bvd Saint-Michel, 75272, PARIS,
ming language with rst-class continuations.
France E-mail: [email protected]
Our static analysis technique is based on the use of an
2
LCS, Massachusetts Institute of Technology , 545 Techno-
e ect system [LG88] to classify the p ossible control do-
logy Square, Cambridge, MA 02139, USA E-mail:
main b ehavior of expressions. An e ect system is based
[email protected]. EDU
on a kinded typ e system for the second-order lambda
calculus [M79]. Kinds are the \typ es" of descriptions
which include typ es and e ects. Our typ e and e ect
system has three base kinds: types, which describ e the
value that an expression may return; e ects, which de-
scrib e the side-e ects that an expression mayhave; and 1
regions, which are used to describ e where side-e ects or goto e ects, the problem of a variable \redef-
may o ccur. An expression that do es not have an ob- inition" by a \return" inside its define form is
servable e ect is said to b e pure. Expressions that are avoided. In the same manner, mutations that are
pure are referentially transparent. p erformed by taking advantage of the implementa-
Typ es, e ects and regions are closely interrelated; in tion of recursive de nitions by letrec [B89] can b e
prohibited.
particular, a function typ e incorp orates a latent e ect
that describ es the side-e ects that the function may
p erform when it is applied, and a reference typ e in-
Control e ects let the compiler writer p erform safe
corp orates a region that describ es where the reference
optimizations in the presence of rst-class continu-
is allo cated. The kind system is used to verify the well-
ations. For instance, if a given cwcc expression has
formedness of descriptions; the typ e and e ect system
a masked control e ect, then the internal contin-
is used to verify the well-formedness of expressions.
uation will be used only as a \downward funarg"
We can use an e ect system for control ow analysis
[S78] and thus the expression's continuation struc-
by intro ducing two typ es of control e ects, goto and
ture control frames can b e stack allo cated.
comefrom, that describ e the control ow prop erties of
expressions. An expression that do es not havea goto
e ect is said to b e continuation fol lowing b ecause it will
Control e ects also allow sequential semantics to b e pre-
always call its return continuation in the usual way. An
served in the presence of b oth rst-class continuations
expression that do es not havea comefrom e ect is said
and automatic compile-time detection of parallelism.
to b e continuation discarding b ecause it will never pre-
When compiling for a parallel target machine, the com-
serve its return continuation for later use. This \dou-
piler can guarantee sequential semantics which is in-
ble negation" style of de nitions is necessary when one
timately related to the notion of continuations, which
wants to express conservative approximations of run-
represent the state of a sequential evaluation by con-
time program b ehaviors.
sidering that control e ects interfere with all e ects.
Unobservable control e ects can b e masked by the ef-
In the remainder of this pap er we describ e the kernel
fect system. Our masking rule applies to expressions
language KFX of FX-87 Section 2 , integrate control
that are externally well-b ehaved, even if they use con-
e ects into KFX Section 3 , state two control e ect
tinuations internally. Control e ect soundness theorems
soundness theorems Section 4 , give precise conditions
guarantee that the e ects computed statically by the
when it is p ossible to mask unobservable control e ects
e ect system are a conservative approximation of the
Section 5 , survey related work Section 6 , and sum-
dynamic b ehavior of an expression.
marize our results Section 7 .
We showhow our e ect system can b e used with the
pro cedure call-with-current-continuation inspired
from [R86], hereafter noted cwcc. This pro cedure allows
rst-class access to the current continuation. Simpler
2 KFX - A Kernel Language for
control structures based on lab els and jumps can be
FX-87
treated in a similar way.
Control e ects are useful to the programmer, the lan-
guage designer and the compiler writer:
For p edagogical purp oses we will study control e ects
in the context of KFX, the kernel language of FX-87.
Control e ects let the programmer sp ecify, in
FX-87 [GJLS87][LG88] is a p olymorphic typ ed language
machine-veri able form, the exp ected run-time
that allows side-e ects and rst-class functions. Its syn-
control b ehavior of a given program, thus increas-
tax and most of its standard op erations are strongly in-
ing do cumentation, mo dularity and maintainabil-
spired byScheme [R86] which will b e used in most of our
ity of programs. Control e ects also provide a pro-
examples. The language KFX has the following Kind,
grammer with a new framework in which to rea-
Description Region, E ect and Typ e and Expression
son ab out languages with rst-class continuations.
domains where I is the domain of identi ers :
Moreover, when unobservable control e ects are
masked, a programmer knows that an expression
K ::= region
will b e well-b ehaved.
effect
Control e ects let the language designer limit the
type
use of continuations to simplify the semantics of
the language. For instance, by saying that top-
R ::= I
level de nitions are not allowed to have comefrom
@I region constant 2
F ::= I
Note that twice is abstracted over the typ e t of the
pure no e ect
argumentof f and its latent e ect e. The typ e of twice
write R write on R
is:
read R read on R
twice : poly t type
alloc R allo cation on R
poly e effect
maxeff F0 F1 combination
subr pure
subr e t t
T ::= I
subr e t t
subr F T T function
poly I K T p olymorphic typ e
The typ e and e ect rules for application, abstraction,
ref T R reference to T in
1
p olymorphic abstraction and pro jection follow. Just as
region R
\:" is used to denote the \typ e of " relation, \!" is used
D ::= R
to denote the \e ect of " relation. T is the typ e and
F
kind assignment function that maps variables to their
T
typ e or kind.
E ::= I
hE0;Ti : subr e t t ! e
1 2 0
lambda I T E lambda
hE1;Ti : t ! e
1 1
abstraction
h E0 E1 ;Ti : t ! maxeff e
2
E0 E1 application
maxeff e e
0 1
plambda I K E p olymorphic
abstraction
hE;T[t =I]i : t ! e
1 2
proj E D pro jection
h lambda I t E ;Ti : subr e t t ! pure
1 1 2
new R T E allo cation
get E dereference
hE;T[k=I]i : t ! pure
set E0 E1 mutation
h plambda I k E ;Ti : poly I k t ! pure
hE;Ti : poly I k t ! e
In the e ect domain, a pure expression is referentially
0 0
h proj E k ;Ti : t[k =I] ! e
transparent. Impure expressions can write, read or
allo cate alloc memory in regions which denote sets
where f [y=x] z is y if z is x and fz otherwise the same
of memory lo cations. Combined e ects are intro duced
notation on typ es is used to denote syntactic substitu-
by maxeff.
tion . The remaining e ect and typ e rules of KFX are
In the typ e domain, the subr typ e of a function en-
presented in [LG88].
co des its latent e ect F, the typ e of its argument and its
The standard semantics [S86] of KFX is de ned on
return typ e. Poly represents the typ e of p olymorphic
typ e-erased KFX expressions. A program is typ e-erased
values abstracted over kind K. Ref T R is the typ e of
by reducing plambda and proj expressions to their em-
a reference in the region R to a value of typ e T.
b edded expressions and eliminating all typ e information
In the expression domain, just as lambda abstracts
see [L87] for a formal de nition of typ e erasure .
E over the ordinary variable I of typ e T, plambda ab-
The domain equations for lo cations, basic values, clo-
stracts E over the description variable I of kind K to
sures, values, environment, stores, results and continu-
yield a p olymorphic value. A p olymorphic value is in-
ations in our standard semantics are as follows:
stantiated with the proj construct. New allo cates i.e.,
has an alloc latent e ect a reference in region R to
l : Loc
the value of E of typ e T, get reads and returns the value
b : B asic
stored into the reference E and set writes E1 in the ref-
p : Clo = Val ! C ont ! S tor e ! Answ er
erence E0. As an example, we give b elow the co de of the
v : Val = B asic + Clo + Loc
p olymorphic twice function that applies the function f
u : Env = I ! Val
twice on its argument x:
s : S tor e = Loc ! Val
a : Answ er = Val
plambda t type
k : C ont = Val ! S tor e ! Answ er
plambda e effect
lambda f subr e t t
where + means disjoint sum and ! is right-associative.
lambda x t
1
f f x We supp ose alpha-renaming to avoid name capture. 3
The de nition of Eval, of typ e E ! Env ! C ont ! The cwcc function cannot be treated as pure. The
S tor e ! Answ er , is fairly simple [S86]: comefrom e ect corresp onds to the capture of a con-
tinuation and it is intro duced by providing cwcc with
a comefrom r latent e ect, where r is a region.
E [[ I ]]uk = k u[[ I ]]
The region restricts the domain of in uence of a given
E [[ lambda I E ]]uk = k e:E [[ E ]]u[e=I]
continuation-capturing expression see b elow . The fol-
E [[ E0 E1 ]]uk = E [[ E0 ]]u e :
0
lowing Scheme program shows that a compiler cannot
E [[ E1 ]]u e :
1
common sub expression eliminate calls to cwcc since
e e k
0 1
calling f1 would p erform horrible-effects on the
E [[ new E ]]uk = E [[ E ]]u es:k l s[e=l ]
store; these e ects would not o ccur if f2 were called.
where l = new Loc
Thus the cwcc calls cannot b e pure.
E [[ get E ]]uk = E [[ E ]]u es:k se s
let* f1 cwcc lambda x x
E [[ set E0 E1 ]]uk = E [[ E0 ]]u e :
x horrible-effects
0
E [[ E1 ]]u e s :
f2 cwcc lambda x x
1 1
ke s [e =e ]
...
1 1 1 0
The goto e ect corresp onds to the \escaping" call of a
where new Loc is a function that allo cates fresh mem-
continuation and is intro duced by providing a continua-
ory lo cations. Note that, contrarily to the Scheme set!
tion with a goto r latent e ect, where r is the region
sp ecial form, the function set evaluates its rst argu-
used in the cwcc expression that created the continua-
ment, which is a reference. For clarity,we omitted in-
tion. The following Scheme program shows that any
jection and pro jection op erations in sum domains.
e ect can b e exercised by the evaluation of a continua-
tion:
let x cwcc lambda f
3 Control E ects Describ e Po-
cwcc lambda g f g
tential Behavior
h
f
The material of the previous section is a simpli ed pre-
horrible-effects
sentation of the e ect system that is the basis of the
...
FX-87 programming language [GJLS87]. This static
x 0
system was mainly designed to cleanly deal with mem-
...
ory side-e ects within a typ ed p olymorphic language
In this example, between the evaluations of f g
which allows rst-class functions. We show b elowhow
and h , horrible-effects will be executed; thus
this framework can b e easily extended to deal with the
these expressions cannot be reordered. The e ects of
a-priori unrelated control side-e ects that are caused by
horrible-effects will also b e p erformed after any
rst-class continuations. This shows the p ower and ex-
call to x, since it is b ound to the continuation that binds
ibility of an e ect system.
the result of the call of cwcc to x.
Weintro duce rst-class continuations into KFX with
the Scheme function cwcc. The function cwcc passes a
In summary, the KFX typ e and e ect rules can be
pro cedural representation of its return continuation to
used to compute control e ects by assigning cwcc the
its argument, whichmust b e a one-argument function.
2
following typ e :
In order to add cwcc to KFX we need merely to bind
cwcc to its value in the initial environment u. So, we
cwcc: poly r region
have:
poly t type
poly e effect
0 0 0
u[[ cwcc ]]=ek :e e k :k e k
subr maxeff comefrom r e
subr e
subr goto r
The cwcc function gives the programmer access to
t
continuations. As rst-class values, these continuations
void
can subsequently b e stored into global variables or re-
t
turned, allowing a given expression to b e evaluated more
t
than once to return a result more than once or to es-
2
cap e from its current continuation to discard its current
Without loss of generality,we assume that the anti-aliasing
continuation by applying another one . rule of FX-87 [GJLS87] is eliminated. 4
The function cwcc is abstracted over the region r in lowing a lo ok at the semantic de nition shows that
which the continuation is lo cated, the typ e t of the every equation of E ends by calling the continuation it
eventual result and the latent e ect e of the function is passed , except the application E0 E1 . There are
passed as argument. The latent e ect of cwcc denotes twoways we can generate a function in KFX:
the combined e ects of calling its argument and cap-
if e is obtained byevaluating a lamb da expression,
0
turing a continuation in r. The argumentto cwcc is a
then it is continuation following if its b o dy is,
function that exp ects as argument the captured contin-
uation seen as a function with a goto r latent e ect.
otherwise e comes from a continuation created by
0
The typ e void indicates that a call to the continuation
a cwcc expression, and then the expression isn't
will never return to its caller.
continuation following. But, this continuation has
latent e ect goto r where r is the region that
The control e ects of an expression can b e masked if
cwcc has b een pro jected onto. Therefore, the ap-
the e ects cannot b e observed outside of the expression.
plication will have e ect goto r . 2
For instance, if we follow the typing rules of KFX, then
With this theorem, we know that the goto e ect in-
we deduce that the following expression
formation collected by the KFX typ e system is a con-
+ cwcc lambda f f 0 1
servative i.e. safe approximation of the run-time b e-
havior of a program.
has b oth goto r and comefrom r e ects for some
region r. However, it is easy to prove that this expres-
We now prove the soundness of comefrom e ects.
sion is well-b ehaved; it will call its return continuation
This asp ect is a bit more complex, so we need some
it is continuation fol lowing and will not preserve its
preliminary de nitions.
continuation it is continuation discarding . Its control
e ects can thus b e masked as we discuss further in sec-
De nition. A continuation col lecting semantics of a
tion 5; in consequence, the continuation f will not need
programming language L is a non-standard semantics of
to be heap allo cated, thus improving run-time p erfor-
L in whichevery evaluation of an expression E returns an
mance and saving on memory consumption.
ordered pair made of the standard value of E and the set
of intermediate continuations captured while evaluating
E i.e. continuations made available by calls to cwcc .
4 Soundness of comefrom and
goto e ects
De nition. E is the continuation collecting seman-
c
tics of E .
Wenow need to show that the comefrom and goto ef-
fects we compute for an expression are a conservative
The precise de nition of E is an extension of E , where
c
estimate of the expression's dynamic b ehavior. With-
the set of continuations is passed along the computation
out loss of generality,we restrict our soundness pro ofs
and up dated by cwcc. For every function F used in the
to terminating expressions.
semantics of KFX, there is an equivalent one in the con-
tinuation collecting semantics of KFX; we will note it
De nition. An expression E is continuation fol low-
F . Note that the continuations k successively take
c c
ing i , for every environment u and store s, there exist
the value to b e passed, the set of p otentially available
two continuations k and k such that
1 2
continuations and the current store. For instance, here
are the equations de ning E for identi er, lamb da ex-
E [[ E ]]uk s 6= E [[ E ]]uk s
c
1 2
pression and application j denotes the current set of
The de nition of equalitywe use is extensional. The
intermediate continuations :
evaluation of a continuation-following expression ends
E [[ I ]]u jk = k u [[ I ]] j
by calling the continuation it is passed and never escap es
c c c c c
via some continuation available in the environment or
E [[ lambda I E ]]u jk = k ej:
c c c c
store.
E [[ E ]]u [e=I]j j
c c
E [[ E0 E1 ]]u jk = E [[ E0 ]]u j e j :
c c c c c 0 0
Theorem Goto Soundness . If there does not
E [[ E1 ]]u j e j :
c c 0 1 1
exist a region r such that E has e ect goto r , then E
e e j k
0 1 1 c
is continuation fol lowing.
and the de nition for cwcc:
Pro of sketch. By induction on the domain of ex-
0 0 0 0 0
pressions. Every construct of KFX is continuation fol- :k e j fk g[ j k u cwcc = ej k :e e j k
c c c c c c 5
if no free variable uses the region r in its typ e, then De nition. An expression context Ec is an expres-
read and write e ects on r can b e masked, sion with a \hole" in it, identi ed by []. It can b e lled
with E by writing Ec[E].
if r do es not app ear in the typ e of the result of the
De nition. An expression context Ec is wel l-behaved
expression, then allo c e ects on r can b e masked.
i for every environment u , store s and continuation
c c
k , there exist an expression E and a value v such that
c
E ect masking can b e easily extended to deal with con-
trol e ects. Control e ect masking soundness a direct
E [[ Ec[E]]]u fgk s = v; fg
c c c c
extension of FX-87 typ e soundness and e ect masking
where x; y is the ordered pair made of x and y and fg the
soundness [GJLS87]. We use the following lemma:
empty set. A well-b ehaved expression context do esn't
capture any continuation on its own.
Lemma. When evaluating E in the environment u,
continuation k and store s, the value passedtok is de-
De nition. An expression E is continuation discard-
termined by the values of the free variables and the stor-
ing i for every well-b ehaved expression context Ec, en-
age locations accessible via these free variables.
vironment u , store s , continuation k ,value v and list
c c c
of continuations j :
Pro of sketch. By induction on E equations with the
use of the \lo cation invariance" prop erty of [L87] which
E [[ Ec[E]]]u fgk s = v; j = v 62 j
c c c c
expresses that the choice of b ound lo cations do es not
in uence the nal result of the evaluation. 2
The idea b ehind this de nition is that it isn't p ossible,
from the evaluation of E, to recover some continuation
caught in some global variable or returned by E. For
Theorem. A goto r e ect of an expression E can
instance, the following expression :
be maskedifE does not import variables or return values
in the type of which r appears.
begin cwcc lambda f
set x lambda f
Pro of sketch: Wehave to show that if the preceding
h
condition is veri ed, then E is continuation following, i.e.
isn't continuation discarding, since the well-b ehaved
that for every u and s there exist k and k such that
1 2
context begin [] get x returns a caught con-
E [[ E ]]uk s 6= E [[ E ]]uk s. By the previous lemma, the
1 2
tinuation if we replace the hole by the previous expres-
value of E passed to k and k is de ned only by the
1 2
sion.
values of the free variables of E, which app ear in u, and
accessible i.e. in the returned value lo cations, in s. If r
Theorem Comefrom Soundness . If there does
do es not app ear in the typ e of any of these values, then,
not exist a region r such that E has e ect comefrom r ,
by application of FX-87 typ e soundness, no goto r
thenEiscontinuation discarding.
e ect can b e p erformed by an external i.e. not de ned
in E continuation. By goto e ect soundness, E is then
Pro of sketch. The pro of is by induction on the equa-
continuation-following, and cho osing k = es:0 and
1
tions of E . The only way the set of caught continuations
c
k = es:1 will suce. 2
2
can b e extended is by a call to cwcc, which implies, fol-
lowing KFX typing rules, that there is a region r such
Theorem. A comefrom r e ect of an expression
that this call has a comefrom r e ect. 2
E can be maskedifE does not import variables or return
values which have r in their type.
With this theorem, we know that the comefrom ef-
fect information collected by the KFX typ e system is a
Pro of sketch. In the same way, we have to show
conservative i.e. safe approximation of the run-time
that if the preceding condition is veri ed, then E is con-
b ehavior of a program.
tinuation discarding. We wanttoprove that for every
Ec, u , s and k , v is not a member of j where v and j
c c c
are as in the de nition of \continuation discarding". As
5 Control E ect Masking
b efore, Ec[E] can only refer to free variables of E or its
FX-87 e ect masking detects and eliminates e ects of returned value. If r do es not app ear in the typ e of any
an expression that are not observable e.g., mutation of of these, then, by application of FX-87 typ e soundness,
lo cally allo cated references under the following condi- no continuation e ectively caughtby cwcc forms inside
tions: of E pro jected on r can b e returned by Ec[E]. 2 6
Not surprisingly these control e ect masking rules are is captured are the ones that are agged with the same
very similar to the ones already in FX-87 for memory comefrom r e ect. These are precisely the control
e ects. One can view a call to cwcc as allo cating some frames that corresp ond to the dynamic extent of the
data in the heap region to store the current stack and a captured continuation up to the p oint where the control
call to a continuation as reading a stored stack and writ- e ect is masked. We know that the control frames that
ing to the current stack. This analogy is not quite right app ear after this p ointwon't b e needed. Note that this
since the goto e ect requires a more stringent rule as optimization is not of utmost imp ortance in a system
seen ab ove. This can b e demonstrated by the following that uses a stack/heap strategy for the implementation
admittedly contrived Scheme program which shows an of continuations [CHO88]. It can however b e useful in
expression with a goto e ect that cannot be masked, an implementation that supp orts parallel evaluation of
even though this expression has no free variables: expressions since it avoids stack sharing b etween di er-
ent pro cesses.
let x cwcc lambda f
let y cons f f
cwcc lambda g
6 Related Work
set-cdr! y g
f y
A related approach to our compile-time analysis of
car y y
programs uses the notion of \abstract interpretation"
cwcc lambda h
[CC77]. Results in the area of functional languages
set-car! x h
[AH87] with higher-order functions and p olymorphism
cdr x x
cannot yet equal the outcome of our typ e and e ect sys-
tem. For instance, the only analysis of continuations we
In this example, by calling f,we rst bind x to the pair
found [H87] do es not address rst-class continuations.
y that contains f and the continuation g that precedes
[F88a] prop osed the -v-CS formal system to deal
the evaluation of car y y . The rst elementofx
with higher-order functions in the presence of imp era-
is mutated with h that corresp onds to the rest of the
tive constructs. Continuations can b e describ ed in such
program and x's binding expression is reentered at the
a framework and prop erties ab out them can b e proved.
p oint where car y y is evaluated; this evaluation
However, these pro ofs are not currently automated and
is not continuation-following. Although there are no
therefore cannot b e used in compiling systems.
free variables in the expression x is b ound to, the goto
Thus, the compile time analysis of programming lan-
e ect of the call car y y cannot b e masked; rst-
guages with rst-class continuations app ears to b e new.
class continuations allow the programmer to temp orar-
Most of the literature dealing with continuations gen-
ily exp ort and mutate lo cal lo cations, thus requiring the
erally fo cuses on their run-time characteristics and ap-
supplementary check on the regions app earing in return
plications to various problems like coroutines [HFW86],
typ e which is also, by construction, the typ e of values
multipro cessing [W80] or backtracking [SM72].
passed to the captured continuation .
The p ossibility of stack-allo cation of continuation
structure, which is a ma jor asset of the control e ect
The ma jor practical b ene t of control e ect mask-
masking we presented ab ove, is often presented, e.g. in
ing is the p ossibility of compile-time detection of exter-
[HF87], but with an \interpreter view" of the problem.
nally well-b ehaved expressions that internally use com-
The detection is done at run time e.g., by checking
plex control structures. This allows a programmer to
that a continuation is not used in away incompatible
formally reason ab out his program as if he were not
with its implementation . Our system p erforms a safe
using rst-class continuations, thus easing program cor-
approximation of this optimization at compile time.
rectness pro ofs. In addition, this allows compile-time
Control e ect masking allows the run-time system to
optimizations such as parallel evaluation of expressions
limit the amountofcontrol information that has to b e
that haveinternal control e ects or recognition of stack-
dump ed in the heap when a continuation is captured;
allo catable continuations, in which case cwcc can b e im-
the \prompts" prop osed in [F88b] or the \shift/reset"
plemented with a more ecient catch-throw mechanism
of [DF89] o er the same kind of facility, but they have
[M74].
to b e intro duced by the programmer.
When an expression has a masked control e ect, it
may use full- edged continuations internally. If con- We showed elsewhere [JG89a, JG89b] how e ect sys-
trol e ects are kept at run time, control e ects can b e tems can b e also used to describ e communication side-
used to dynamically optimize these internal continua- e ects arising when communicating parallel pro cesses
tions as well. The only control frames that havetobe are added to a language that uses and e ect systems.
dump ed into the heap when a continuation in region r Communication e ects describ e transmission op erations 7
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