This work is funded by the National Science Foundation grant NSF-IOS 1546858.
You probably don't need to read this. Certainly you should read the
introduction
vignette first.
This vignette is under construction
This vignette consists of four parts. First I will describe the monad
hidden in the R runtime. Second, I will describe how rmonad
can serve as a
replacement. Third, I will contrast the monadic pipelines of rmonad
with the
compositional pipelines of magrittr
. Finally, I will discuss rmonad
from the
Haskell perspective.
I will introduce the concept of a monad incrementally through the first three
sections. However, monads in the programming context are notoriously difficult
to understand. If you are not familiar with them, you may try studying a few
online tutorials first. That said, rmonad
can be used without understanding
monads.
What does sqrt
do? You may answer, "return the square root of an input". But
this is not quite right. The function sqrt
maps an input to a set of possible
values:
NaN
with a warningEvery R function maps a pure value to a computational context with possible undefined behavior and side effects. We can describe the action of a function abstractly as
a -> m b
Where a
is the pure input value, b
is the pure output value, and m
represents the output context. The sqrt
function can be described as number*
-> m number
. Where number*
represents an input value that should be a
number, but, since R is dynamic, may be anything. m numeric
represents a
context that holds either a number or some effect.
When we build a pipeline, we chain many functions together. Say, for example, we have the expression:
sqrt(sum(x))
Borrowing a bit of Haskell syntax
sqrt :: numeric* -> m numeric sum :: numeric* -> m numeric
numeric*
represents something that should be numeric. Again, since R is
dynamically typed, we have no guaranttees that the input actually is numeric.
Each function takes a pure value and maps to a value wrapped in a context.
sum(x)
outputs m numeric*
, but sqrt
wants a numeric*
. We need a
function to mediate this. A function with the form:
bind :: (m numeric*) -> (numeric* -> m numeric*) -> (m numeric) ^ ^ ^ / / / sum(x) sqrt sqrt(sum(x))
We can express this more generally as
bind :: m1 a -> (a -> m2 b) -> m3 b
Where a
and b
are data types. m1
, m2
and m3
are contexts. Every bind
operation takes 1) a value in a context (m1 a
) and 2) a function that maps
that value to m2 b
. The prior state m1
, as well as the intermediate state
m2
, are in the scope of the bind
function. This allows contextual
information to propagate from the m1
to m3
.
A monad is a pattern consisting of a context m
, two functions, and three
laws. The functions are bind
and return
(not to be confused with the
return
used to terminate a function). bind
we have already seen. return
takes a pure value and lifts it into a context. return
has the form a -> m
a
.
Before we cover the monad laws, and before we learn exactly what the monad is
in the rmonad
context, we will walk step by step through one example. rmonad
uses the infix operator %>>%
as bind
(rmonad
's %>>%
corresponds to
Haskell's >>=
).
rmonad
The goal of rmonad
is to ditch the existing impure R monad and replace it
with a clean explicit monad.
x %>>% sum %>>% sqrt
The initial %>>% operators acts as both a return
and bind
function. It first evaluates the
m b
is dependent on m a
, not just on a
. The bind
function can pass
information from one step in the pipeline m a
to the next m b
.
m2 b
is equal to m3 b
only for the trivial case where the context is
identity
.
R users normally rely on the R session to automatically perform these binds.
But what exactly is m
? In an R session, the R runtime handles errors. If one
function raises an error, the error is propagated to functions that use its
input.
In rmonad
, the m
is an object, that catches all undefined behavior.
rmonad
versus magrittrTo understand the monadic nature of rmonad
it is useful to compare it to
magrittr
. In magrittr
, the expression x %>% foo %>% bar
is the same as
bar(foo(x))
. From a monadic point of view, x
is first implicitly raised
into an 'Identity' monad (which is quite formless here) m1 x
. Then
bind :: m1 x -> (x -> m2 y) -> m3 y
The bind
function above executes foo
on x
, yielding m2 y
. It then
reduces this to m3 y
in the presence of m1
. But magrittr
passes no
information from m1
to m3
. The pipeline is context indepent.
In rmonad
, the pipeline x %>>% foo %>>% bar
will pass a record of past
events at each bind operation, thus incrementally building a graph of the
pipeline.
rmonad
for HaskellersThe name rmonad
is a nod to Xmonad
(no relation to the Restricted Monad
package). Where Xmonad
wraps the X window system, rmonad
wraps evaluation
of R expressions.
Only a few R expressions are pure. If a function is given an invalid input at
runtime (e.g. sqrt("wtf")
), it will die with a message printed to stderr.
rmonad
wraps all R calls in a monad, intercepting all messages, so that the
result of a computation is returned as a pure object.
The 'R monad' is one monad to rule the all. There is no monad stack and no support for monad transformers. In addition to error handling, The monad stores the history of every previous operation. It also performs basic benchmarking, recording the time required for each operation and the size of the returned object. All this weight might seem like a performance killer, but R programmers are used to function calls being slow, so if they care about performance, they wouldn't use a function in a tight loop anyways.
The return
function is a little complex in rmonad
. It is a special case of
the as_monad
function:
as_monad = a -> m b
Where a
can be one of three types
an unevaluated R expression - as_monad
evaluates the expression,
capturing any exceptions, warnings or messages. as_monad
is used inside
the bind
function in this capacity.
a pure R value - acts as return
The %>>%
operator is like the Haskell >>=
operator, but with some of the
sloppiness expected of a dynamic language:
%>>% :: m a -> (a -> m b) -> m b | a -> (a -> m b) -> m b | (a -> r b) -> (a -> m b) -> m b
%>>%
differs from >>=
in that %>>%
automatically loads the left-hand-side
value into a monad.
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