rmonad: an introduction

Zebulun Arendsee

This work is funded by the National Science Foundation grant NSF-IOS 1546858.

rmonad offers

Monadic pipelines

I will introduce rmonad with a simple sequence of squares

# %>>% corresponds to Haskell's >>=
1:5      %>>%
    sqrt %>>%
    sqrt %>>%
    sqrt
## N1> "1:5"
## N2> "sqrt"
## N3> "sqrt"
## N4> "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
## N1> "1:5"
## N2> "sqrt"
## [1] 1.000000 1.414214 1.732051 2.000000 2.236068
## 
## N3> "sqrt"
## N4> "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 } }
## N1> "1:5"
## N2> "function (.) 
## {
##     o <- . * 2
##     {
##         o + .
##     } %>% {
##         . + o
##     }
## }"
## 
##  ----------------- 
## 
## [1]  5 10 15 20 25

Warnings are caught and stored

-1:3     %>>%
    sqrt %v>%
    sqrt %>>%
    sqrt
## N1> "-1:3"
## N2> "sqrt"
##  * WARNING: NaNs produced
## [1]      NaN 0.000000 1.000000 1.414214 1.732051
## 
## N3> "sqrt"
## N4> "sqrt"
## 
##  ----------------- 
## 
## [1]      NaN 0.000000 1.000000 1.090508 1.147203

Similarly for errors

"wrench" %>>%
    sqrt %v>%
    sqrt %>>%
    sqrt
## N1> ""wrench""
## N2> "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.

Extracting data from an 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 ndependents nnotes nwarnings error
## 1  1 TRUE  FALSE    0    72         0           1      0         0     0
## 2  2 TRUE   TRUE    0    88         0           1      0         0     0
## 3  3 TRUE  FALSE    0    88         0           1      0         0     0
## 4  4 TRUE   TRUE    0    88         0           0      0         0     0
##   doc
## 1   0
## 2   0
## 3   0
## 4   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
## 1  3   error 'x' must be an array of at least two dimensions
## 2  2 warning                                   NaNs produced

The id column refers to row numbers in the mtabulate output. Internal values can be extracted:

result <- 1:5 %v>% sqrt %v>% sqrt %v>% sqrt
get_value(result)[[2]]
## [1] 1.000000 1.414214 1.732051 2.000000 2.236068

Handling effects

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

## N1> "cars"
## N2> "plot(xlab = "index", ylab = "value")"
## N3> "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

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
## N1> "iris"
## N2> "function (.) 
## {
##     stopifnot(is.data.frame(.))
## }"
## N3> "function (.) 
## {
##     stopifnot(sapply(., is.numeric))
## }"
##  * ERROR: sapply(., is.numeric) are not all TRUE
## N4> "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).

Error handling

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
## N1> "1:10"
## N2> "colSums"
##  * ERROR: 'x' must be an array of at least two dimensions
## N3> "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
## N1> "letters[1:10]"
##  [1] "a" "b" "c" "d" "e" "f" "g" "h" "i" "j"
## 
## N2> "colSums"
##  * ERROR: 'x' must be an array of at least two dimensions
## N3> "sum"
##  * ERROR: invalid 'type' (character) of argument
## N4> "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.

Branching pipelines

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
get_value(x)
## [[1]]
##  [1]  1  2  3  4  5  6  7  8  9 10
## 
## [[2]]
##  [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]]
##  [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
## 
## [[4]]
## [1] -0.5838848

Note the branches could be long monadic chains themselves, which might have their own branches.

Tags, caches, and views

Use of the %>^% and %^>% operators is a little awkward. A more general option is to use tags and views. tag this allows the head of a pipeline to be reset.

# build memory cacher
f <- make_recacher(memory_cache)

# make core dataset
m <- as_monad(iris) %>>%
    dplyr::select(
        sepal_length = Sepal.Length,
        sepal_width = Sepal.Width,
        species = Species
    ) %>%
    # cache value with tag 'iris'
    f('iris') %>>%
    # some downstream stuff
    nrow 
# Now can pick from the tagged node
m <- view(m, 'iris') %>>% {
  qplot(
      x=sepal_length,
      y=sepal_width,
      color=species,
      data=.
  )} %>% f('plot')
# and repeat however many times we like 
m <- view(m, 'iris') %>>% summary %>% f('sum')

plot(m)
1: the original iris table, 2: stores the cached iris data, 3: nrow, 4: qplot, 5: summary.

1: the original iris table, 2: stores the cached iris data, 3: nrow, 4: qplot, 5: summary.

Chains of chains

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
## N1> "runif(10)"
## N2> "sum"
## [1] 4.583261
## 
## N3> "rexp(10)"
## N4> "sum"
## [1] -1.522069
## 
## N5> "sum"
## 
##  ----------------- 
## 
## [1] 14.88481

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.

Multiple inputs

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
)
## N1> "2"
## N2> "runif("simon")"
##  * ERROR: invalid arguments
##  * WARNING: NAs introduced by coercion
## N3> "stop("stop, drop, and die")"
##  * ERROR: stop, drop, and die
## N4> "yolo"
## N5> "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.

Annotating steps

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.
## 
## N1> "{
##     NULL
## }"
## NULL
## 
## N2> ""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.
## 
## N3> "function (.) 
## {
##     paste(., "b")
## }"
## 
##  ----------------- 
## 
## [1] "a b"

Nesting pipelines

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
## N1> ""d""
## N2> "c"
## N3> "b"
## N4> "funnel("b", "c")"
## N5> ""a""
## N6> "paste(x)"
## N7> "paste(y)"
## N8> "log"
##  * ERROR: non-numeric argument to mathematical function
## [1] "a b c"
## 
## 
## 
##     This is a function containing a pipeline. It always fails
## 
## N9> "foo"
## [[1]]
## [1] "b"
## 
## [[2]]
## [1] "c"
## 
## 
## 
## 
##     this is another function, it doesn't fail
## 
## N10> "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.

Post-processing

A feature new to rmonad v0.4 are a set of post-processors. These act on an Rmonad object after the code the object wraps has been evaluated.

Here are the currently supported post-processors:

  1. format_warnings - A function of the final value and the list of warnings, that formats the node’s warning message.

  2. format_error - Like format_warnings but for errors

  3. format_notes - Like format_warnings but for messages/notes

  4. summarize - A function of the final value that stores a summary of the data

  5. cache - A function of the final value that caches the value

  6. log - A function of the final state that prints an progress message

These are all quite experimental at this point.

The post-processors are included in the node metadata, for example

## N1> ""hello world""
## N2> "function (.) 
## {
##     sqrt(.)
## }"
##  * ERROR: Failure on input 'hello world': non-numeric argument to mathematical function
## 
##  ----------------- 
## 
## [1] "hello world"
##  *** FAILURE ***

summarize is useful since it is often useful to store information about an intermediate step but storing the full data is too memory intensive. Rather than stopping the flow of an analysis with a bunch of intermediate analytic code, a summary function can be nested in a node that holds an arbitrary description of the data, coupled immediately to the function that produced it.

## [[1]]
##       mpg             cyl             disp              hp       
##  Min.   :21.00   Min.   :4.000   Min.   : 71.10   Min.   : 52.0  
##  1st Qu.:21.43   1st Qu.:4.000   1st Qu.: 83.03   1st Qu.: 66.0  
##  Median :23.60   Median :4.000   Median :120.20   Median : 94.0  
##  Mean   :25.48   Mean   :4.429   Mean   :123.89   Mean   : 88.5  
##  3rd Qu.:29.62   3rd Qu.:4.000   3rd Qu.:145.22   3rd Qu.:109.8  
##  Max.   :33.90   Max.   :6.000   Max.   :258.00   Max.   :113.0  
##       drat             wt             qsec             vs        
##  Min.   :3.080   Min.   :1.513   Min.   :16.46   Min.   :0.0000  
##  1st Qu.:3.790   1st Qu.:1.986   1st Qu.:17.39   1st Qu.:1.0000  
##  Median :3.910   Median :2.393   Median :18.75   Median :1.0000  
##  Mean   :3.976   Mean   :2.418   Mean   :18.82   Mean   :0.7857  
##  3rd Qu.:4.103   3rd Qu.:2.851   3rd Qu.:19.79   3rd Qu.:1.0000  
##  Max.   :4.930   Max.   :3.215   Max.   :22.90   Max.   :1.0000  
##        am              gear        carb      
##  Min.   :0.0000   Min.   :3   Min.   :1.000  
##  1st Qu.:0.2500   1st Qu.:4   1st Qu.:1.000  
##  Median :1.0000   Median :4   Median :2.000  
##  Mean   :0.7143   Mean   :4   Mean   :1.857  
##  3rd Qu.:1.0000   3rd Qu.:4   3rd Qu.:2.000  
##  Max.   :1.0000   Max.   :5   Max.   :4.000

The summary information will tucked away invisibly in the Rmonad object until a debugger or report generator extracts it. Of course, this could also be used to just store a full copy of the output in memory, by setting the summarize function to identity.

Summaries like this will be more useful in the rmonad world when a Shiny app (or something comparable) makes the workflow graph interactive. Then the summary for a node can automatically be displayed when the node is accessed.

The cache and log post-processors are not yet well developed. But they are intended to do what their names suggest. cache is not yet useful since I don’t have the infrastructure to test whether the cache is valid. log will eventually allow progress messages to be passed to STDOUT as rmonad is running (by default messages are captured and stored).