rmonad
: an introductionThis work is funded by the National Science Foundation grant NSF-IOS 1546858.
rmonad
offers
a stateful pipeline framework
pure error handling
access to the intermediate results of a pipeline
effects – e.g. plotting, caching – within a pipeline
branching and chaining of pipelines
a flexible approach to literate programming
I will introduce rmonad
with a simple sequence of squares
# %>>% corresponds to Haskell's >>=
1:5 %>>%
sqrt %>>%
sqrt %>>%
sqrt
## R> "1:5"
## R> "sqrt"
## R> "sqrt"
## R> "sqrt"
##
## -----------------
##
## [1] 1.000000 1.090508 1.147203 1.189207 1.222845
So what exactly did rmonad
do with your data? It is still there, sitting happily inside the monad.
In magrittr
you could do something similar:
1:5 %>%
sqrt %>%
sqrt %>%
sqrt
## [1] 1.000000 1.090508 1.147203 1.189207 1.222845
%>%
takes the value on the left and applies it to the function on the right. %>>%
, takes a monad on the left and a function on the right, then builds a new monad from them. This new monad holds the computed value, if the computation succeeded. It collates all errors, warnings, and messages. These are stored in step-by-step a history of the pipeline.
%>%
is an application operator, %>>%
is a monadic bind operator. magrittr
and rmonad
complement eachother. %>%
can be used inside a monadic sequence to perform operations on monads, whereas %>>%
performs operations in them. If this is all too mystical, just hold on, the examples are sensical even without an understanding of monads.
Below, we store an intermediate value in the monad:
1:5 %>>%
sqrt %v>% # store this result
sqrt %>>%
sqrt
## R> "1:5"
## R> "sqrt"
## [1] 1.000000 1.414214 1.732051 2.000000 2.236068
##
## R> "sqrt"
## R> "sqrt"
##
## -----------------
##
## [1] 1.000000 1.090508 1.147203 1.189207 1.222845
The %v>%
variant of the monadic bind operator stores the results as they are passed.
Following the example of magrittr
, arbirary anonymous functions of ‘.’ are supported
1:5 %>>% { o <- . * 2 ; { o + . } %>% { . + o } }
## R> "1:5"
## R> "function (.)
## {
## o <- . * 2
## {
## o + .
## } %>% {
## . + o
## }
## }"
##
## -----------------
##
## [1] 5 10 15 20 25
Warnings are caught and stored
-1:3 %>>%
sqrt %v>%
sqrt %>>%
sqrt
## R> "-1:3"
## R> "sqrt"
## * WARNING: NaNs produced
## [1] NaN 0.000000 1.000000 1.414214 1.732051
##
## R> "sqrt"
## R> "sqrt"
##
## -----------------
##
## [1] NaN 0.000000 1.000000 1.090508 1.147203
Similarly for errors
"wrench" %>>%
sqrt %v>%
sqrt %>>%
sqrt
## R> ""wrench""
## R> "sqrt"
## * ERROR: non-numeric argument to mathematical function
##
## -----------------
##
## [1] "wrench"
## *** FAILURE ***
The first sqrt
failed, and this step was coupled to the resultant error. Contrast this with magrittr
, where the location of the error is lost:
"wrench" %>%
sqrt %>%
sqrt %>%
sqrt
## Error in sqrt(.): non-numeric argument to mathematical function
Also note that a value was still produced. This value will never be used in the downstream monadic sequence (except when explicitly doing error handling). However it, and all other information in the monad, can be easily accessed.
rmonad
If you want to extract the terminal result from the monad, you can use the esc
function:
1:5 %>>% sqrt %>% esc
## [1] 1.000000 1.414214 1.732051 2.000000 2.236068
esc
is our first example of a class of functions that work on monads, rather than the values they wrap. We use magrittr
’s application operator %>%
here, rather than the monadic bind operator %>>%
, because we are passing a literal monad to esc
.
If the monad is in a failed state, esc
will raise an error.
"wrench" %>>% sqrt %>>% sqrt %>% esc
## Error: in "sqrt":
## non-numeric argument to mathematical function
If you prefer a tabular summary of your results, you can pipe the monad into the mtabulate
function.
1:5 %>>%
sqrt %v>%
sqrt %>>%
sqrt %>% mtabulate
## id OK cached time space is_nested nbranch nnotes nwarnings error doc
## 1 35 TRUE FALSE 0.000 72 FALSE 0 0 0 0 0
## 2 36 TRUE TRUE 0.001 88 FALSE 0 0 0 0 0
## 3 37 TRUE FALSE 0.001 88 FALSE 0 0 0 0 0
## 4 38 TRUE TRUE 0.001 88 FALSE 0 0 0 0 0
An internal states can be accessed by converting the monad to a list of past states and simple indexing out the ones you want.
All errors, warnings and notes can be extracted with the missues
command
-2:2 %>>% sqrt %>>% colSums %>% missues
## id type issue
## 2 40 warning NaNs produced
## 21 41 error 'x' must be an array of at least two dimensions
The id
column refers to row numbers in the mtabulate
output. Internal values can be extracted by converting the monad to a list and indexing:
result <- 1:5 %v>% sqrt %v>% sqrt %v>% sqrt
as.list(result)[[2]] %>% esc
## [1] 1.000000 1.414214 1.732051 2.000000 2.236068
An rmonad
can be converted to a DiagrammeR
graph (or igraph
); in this way, standard tools for network analysis can be applied to pipelines. rmonad
currently has built in support for plotting piplines and making markdown reports (experimental).
as_dgr_graph(result)
The %>_%
operator is useful when you want to include a function inside a pipeline that should be bypassed, but you want the errors, warnings, and messages to pass along with the main.
You can cache an intermediate result
cars %>_% write.csv(file="cars.tab") %>>% summary
Or plot a value along with a summary
cars %>_% plot(xlab="index", ylab="value") %>>% summary %>% forget
## R> "summary"
## speed dist
## Min. : 4.0 Min. : 2.00
## 1st Qu.:12.0 1st Qu.: 26.00
## Median :15.0 Median : 36.00
## Mean :15.4 Mean : 42.98
## 3rd Qu.:19.0 3rd Qu.: 56.00
## Max. :25.0 Max. :120.00
I pipe the final monad into forget
, which is (like esc
) a function for operating on monads. forget
removes history from a monad. I do this just to de-clutter the output.
You can call multiple effects
cars %>_%
plot(xlab="index", ylab="value") %>_%
write.csv(file="cars.tab") %>>%
summary %>% forget
Since state is passed, you can make assertions about the data inside a pipeline.
iris %>_%
{ stopifnot(is.data.frame(.)) } %>_%
{ stopifnot(sapply(.,is.numeric)) } %>>%
colSums %|>% head
## R> "iris"
## R> "function (.)
## {
## stopifnot(is.data.frame(.))
## }"
## R> "function (.)
## {
## stopifnot(sapply(., is.numeric))
## }"
## * ERROR: sapply(., is.numeric) are not all TRUE
## R> "head"
##
## -----------------
##
## Sepal.Length Sepal.Width Petal.Length Petal.Width Species
## 1 5.1 3.5 1.4 0.2 setosa
## 2 4.9 3.0 1.4 0.2 setosa
## 3 4.7 3.2 1.3 0.2 setosa
## 4 4.6 3.1 1.5 0.2 setosa
## 5 5.0 3.6 1.4 0.2 setosa
## 6 5.4 3.9 1.7 0.4 setosa
The above code will enter a failed state if the input is either not a data frame or the columns are not all numeric. The braced expressions are anonymous functions of ‘.’ (as in magrittr
). The final expression %|>%
catches an error and performs head
on the last valid input (iris
).
Errors needn’t be viewed as abnormal. For example, we might want to try several alternatives functions, and use the first that works.
1:10 %>>% colSums %|>% sum
## R> "1:10"
## R> "colSums"
## * ERROR: 'x' must be an array of at least two dimensions
## R> "sum"
##
## -----------------
##
## [1] 55
Here we will do either colSums
or sum
. The pipeline fails only if both fail.
Sometimes you want to ignore the previous failure completely, and make a new call – for example in reading files:
# try to load a cached file, on failure rerun the analysis
read.table("analyasis_cache.tab") %||% run_analysis(x)
This can also be used to replace if-else if-else strings
x <- list()
# compare
if(length(x) > 0) { x[[1]] } else { NULL }
## NULL
# to
x[[1]] %||% NULL %>% esc
## NULL
Or maybe you want to support multiple extensions for an input file
read.table("a.tab") %||% read.table("a.tsv") %>>% dostuff
Used together with %|>%
we can build full error handling pipelines
letters[1:10] %v>% colSums %|>% sum %||% message("Can't process this")
## Can't process this
## R> "letters[1:10]"
## [1] "a" "b" "c" "d" "e" "f" "g" "h" "i" "j"
##
## R> "colSums"
## * ERROR: 'x' must be an array of at least two dimensions
## R> "sum"
## * ERROR: invalid 'type' (character) of argument
## R> "message("Can't process this")"
##
## -----------------
##
## NULL
Overall, in rmonad
, errors are well-behaved. It is reasonable to write functions that return an error rather than one of the myriad default values (NULL
, NA
, logical(0)
, list()
, FALSE
). This approach is unambiguous. rmonad
can catch the error and allow allow the programmer to deal with it accordingly.
If you want to perform an operation on a value inside the chain, but don’t want to pass it, you can use the branch operator %>^%
.
rnorm(30) %>^% qplot(xlab="index", ylab="value") %>>% mean
This stores the result of qplot
in a branch off the main pipeline. This means that plot
could fail, but the rest of the pipeline could continue. You can store multiple branches.
rnorm(30) %>^% qplot(xlab="index", ylab="value") %>^% summary %>>% mean
Branches can be used as input, as well.
x <- 1:10 %>^% dgamma(10, 1) %>^% dgamma(10, 5) %^>% cor
x
## R> "dgamma(10, 5)"
## Has 1 branches
## [1] 1 2 3 4 5 6 7 8 9 10
##
## R> "do.call(func, args, envir = env)"
## [1] 1.013777e-06 1.909493e-04 2.700504e-03 1.323119e-02 3.626558e-02
## [6] 6.883849e-02 1.014047e-01 1.240769e-01 1.317556e-01 1.251100e-01
##
## R> "do.call(func, args, envir = env)"
## [1] 1.813279e-01 6.255502e-01 1.620358e-01 1.454077e-02 7.299700e-04
## [6] 2.537837e-05 6.847192e-07 1.534503e-08 2.984475e-10 5.190544e-12
##
## R> "cor"
##
## -----------------
##
## [1] -0.5838848
unbranch(x)
## [[1]]
## R> "dgamma(10, 5)"
## Has 1 branches
## [1] 1 2 3 4 5 6 7 8 9 10
##
## R> "do.call(func, args, envir = env)"
## [1] 1.013777e-06 1.909493e-04 2.700504e-03 1.323119e-02 3.626558e-02
## [6] 6.883849e-02 1.014047e-01 1.240769e-01 1.317556e-01 1.251100e-01
##
## R> "do.call(func, args, envir = env)"
## [1] 1.813279e-01 6.255502e-01 1.620358e-01 1.454077e-02 7.299700e-04
## [6] 2.537837e-05 6.847192e-07 1.534503e-08 2.984475e-10 5.190544e-12
##
## R> "cor"
##
## -----------------
##
## [1] -0.5838848
##
## [[2]]
## R> "do.call(func, args, envir = env)"
## [1] 1.013777e-06 1.909493e-04 2.700504e-03 1.323119e-02 3.626558e-02
## [6] 6.883849e-02 1.014047e-01 1.240769e-01 1.317556e-01 1.251100e-01
##
## [[3]]
## R> "do.call(func, args, envir = env)"
## [1] 1.813279e-01 6.255502e-01 1.620358e-01 1.454077e-02 7.299700e-04
## [6] 2.537837e-05 6.847192e-07 1.534503e-08 2.984475e-10 5.190544e-12
Note the branches could be long monadic chains themselves, which might have their own branches. The unbranch
function recursively extracts all branches from the tree.
If you want to connect many chains, all with independent inputs, you can do so with the %__%
operator.
runif(10) %>>% sum %__%
rnorm(10) %>>% sum %__%
rexp(10) %>>% sum
## R> "runif(10)"
## R> "sum"
## [1] 4.046273
##
## R> "rnorm(10)"
## R> "sum"
## [1] 2.153803
##
## R> "rexp(10)"
## R> "sum"
##
## -----------------
##
## [1] 4.498764
The %__%
operator records the output of the lhs and evaluates the rhs into an rmonad
. This operator is a little like a semicolon, in that it demarcates independent statements. Each statement, though, is wrapped into a graph of operations. This graph is itself data, and can be computed on. You could take any analysis and recompose it as %__%
delimited blocks. The result of running the analysis would be a data structure containing all results and errors.
program <-
{
x = 2
y = 5
x * y
} %__% {
letters %>% sqrt
} %__% {
10 * x
}
You can link chunks of code, with their results, and performance information.
So far our pipelines have been limited to either linear paths or the somewhat awkward branch merging. An easier approach is to read inputs from a list. But we want to be able to catch errors resulting from evaluation of each member of the list. We can do this with list_meval
.
funnel(
"yolo",
stop("stop, drop, and die"),
runif("simon"),
k = 2
)
## R> "2"
## [1] 2
##
## R> "runif("simon")"
## * ERROR: invalid arguments
## * WARNING: NAs introduced by coercion
## R> "stop("stop, drop, and die")"
## * ERROR: stop, drop, and die
## R> "yolo"
## [1] "yolo"
##
## R> "funnel("yolo", stop("stop, drop, and die"), runif("simon"), k = 2)"
##
## -----------------
##
## [[1]]
## [1] "yolo"
##
## [[2]]
## NULL
##
## [[3]]
## NULL
##
## $k
## [1] 2
##
## *** FAILURE ***
This returns a monad which fails if any of the components evaluate to an error. But it does not toss the rest of the inputs, instead returning a clean list with a NULL filling in missing pieces. Constrast this with normal list evaluation:
list( "yolo", stop("stop, drop, and die"), runif("simon"), 2)
## Error in eval(expr, envir, enclos): stop, drop, and die
funnel
records each failure in each element of the list independently.
This approach can also be used with the infix operator %*>%
.
funnel(read.csv("a.csv"), read.csv("b.csv")) %*>% merge
Now, of course, we can add monads to the mix
funnel(
a = read.csv("a.csv") %>>% do_analysis_a,
b = read.csv("b.csv") %>>% do_analysis_b,
k = 5
) %*>% joint_analysis
Monadic list evaluation is the natural way to build large programs from smaller pieces.
As our pipelines become more complex, it becomes essential to document them. We can do that as follows:
{
"This is docstring. The following list is metadata associated with this
node. Both the docstring and the metadata list will be processed out of
this function before it is executed. They also will not appear in the code
stored in the Rmonad object."
list(sys = sessionInfo(), foo = "This can be anything")
# This NULL is necessary, otherwise the metadata list above would be
# treated as the node output
NULL
} %__% # The %__% operator connects independent pieces of a pipeline.
"a" %>>% {
"The docstrings are stored in the Rmonad objects. They may be extracted in
the generation of reports. For example, they could go into a text block
below the code in a knitr document. The advantage of having documentation
here, is that it is coupled unambiguously to the generating function. These
annotations, together with the ability to chain chains of monads, allows
whole complex workflows to be built, with the results collated into a
single object. All errors propagate exactly as errors should, only
affecting downstream computations. The final object can be converted into a
markdown document and automatically generated function graphs."
paste(., "b")
}
##
##
## This is docstring. The following list is metadata associated with this
## node. Both the docstring and the metadata list will be processed out of
## this function before it is executed. They also will not appear in the code
## stored in the Rmonad object.
##
## R> "{
## NULL
## }"
## NULL
##
## R> ""a""
##
##
## The docstrings are stored in the Rmonad objects. They may be extracted in
## the generation of reports. For example, they could go into a text block
## below the code in a knitr document. The advantage of having documentation
## here, is that it is coupled unambiguously to the generating function. These
## annotations, together with the ability to chain chains of monads, allows
## whole complex workflows to be built, with the results collated into a
## single object. All errors propagate exactly as errors should, only
## affecting downstream computations. The final object can be converted into a
## markdown document and automatically generated function graphs.
##
## R> "function (.)
## {
## paste(., "b")
## }"
##
## -----------------
##
## [1] "a b"
rmonad
pipelines may be nested to arbitrary depth.
foo <- function(x, y) {
"This is a function containing a pipeline. It always fails"
"a" %>>% paste(x) %>>% paste(y) %>>% log
}
bar <- function(x) {
"this is another function, it doesn't fail"
funnel("b", "c") %*>% foo %>>% paste(x)
}
"d" %>>% bar
## R> "c"
## R> "b"
## R> ""a""
## R> "paste(x)"
## R> "paste(y)"
## R> "log"
## * ERROR: non-numeric argument to mathematical function
## [1] "a b c"
##
## R> "funnel("b", "c")"
##
##
## This is a function containing a pipeline. It always fails
##
## R> "foo"
## [[1]]
## [1] "b"
##
## [[2]]
## [1] "c"
##
##
## R> ""d""
##
##
## this is another function, it doesn't fail
##
## R> "bar"
##
## -----------------
##
## [1] "d"
## *** FAILURE ***
This function descends through three levels of nesting. There is a failure at the deepest level. This failing node, where a string is passed to a log
function, stores the error message and the input. Each node ascending from the point of failure stores their respective input. This allows debugging to resume from any desired level.