# [Rd] List comprehensions for R

David C. Norris david at unusualsolutionsthatwork.com
Sat Dec 15 23:15:03 CET 2007

```Gabor,

Thank you for drawing this previous work to my attention.  I've attached
below code that extends the list comprehension to include logical
'guard' expressions, as in

> leap.years <- .[ x ~ x <- 1900:2100 | (x %% 400 == 0 || x %% 100 != 0
&& x %% 4 == 0) ]
> leap.years
[1] 1904 1908 1912 1916 1920 1924 1928 1932 1936 1940 1944 1948 1952
1956 1960
[16] 1964 1968 1972 1976 1980 1984 1988 1992 1996 2000 2004 2008 2012
2016 2020
[31] 2024 2028 2032 2036 2040 2044 2048 2052 2056 2060 2064 2068 2072
2076 2080
[46] 2084 2088 2092 2096
>

I wonder, would many (most?) R users be "mathematically-trained
statisticians first, and programmers second", and therefore find a
mathematical notation like the list comprehension more natural than less
declarative programming constructs?  I would be genuinely interested in
your (and others') thoughts on that question, based on your knowledge of
the R user community.

Regards,
David

Gabor Grothendieck wrote:
> That seems quite nice.
>
> Note that there has been some related code posted.  See:
> http://tolstoy.newcastle.edu.au/R/help/03b/6406.html
> which discusses some R idioms for list comprehensions.
>
> Also the gsubfn package has some functionality in this direction.  We
> preface any function with fn\$ to allow functions in its arguments
> to be specified as formulas.  Its more R-ish than your code and
> applies to more than just list comprehensions while your code is
> more faithful to list comprehensions.
>
>
>>
## Updated to include logical guards in list comprehensions

##
## Define syntax for list/vector/array comprehensions
##

. <<- structure(NA, class="comprehension")

comprehend <- function(expr, vars, seqs, guard, comprehension=list()){
if(length(vars)==0){  # base case of recursion
if(eval(guard)) comprehension[[length(comprehension)+1]] <- eval(expr)
} else {
for(elt in eval(seqs[[1]])){
assign(vars[1], elt, inherits=TRUE)
comprehension <- comprehend(expr, vars[-1], seqs[-1], guard,
comprehension)
}
}
comprehension
}

## List comprehensions specified by close approximation to set-builder
notation:
##
##   { x+y | 0<x<9, 0<y<x, x*y<30 } ---> .[ x+y ~ {x<-0:9; y<-0:x} |
x*y<30 ]
##
"[.comprehension" <- function(x, f){
f <- substitute(f)
## First, we pluck out the optional guard, if it is present:
if(is.call(f) && is.call(f[[3]]) && f[[3]][[1]]=='|'){
guard <- f[[3]][[3]]
f[[3]] <- f[[3]][[2]]
} else {
guard <- TRUE
}
## To allow omission of braces around a lone comprehension generator,
## as in 'expr ~ var <- seq' we make allowances for two shapes of f:
##
## (1)    (`<-` (`~` expr
##                   var)
##              seq)
## and
##
## (2)    (`~` expr
##             (`{` (`<-` var1 seq1)
##                  (`<-` var2 seq2)
##                      ...
##                  (`<-` varN <- seqN)))
##
## In the former case, we set gens <- list(var <- seq), unifying the
## treatment of both shapes under the latter, more general one.
syntax.error <- "Comprehension expects 'expr ~ {x1 <- seq1; ... ; xN
<- seqN}'."
if(!is.call(f) || (f[[1]]!='<-' && f[[1]]!='~'))
stop(syntax.error)
if(is(f,'<-')){ # (1)
lhs <- f[[2]]
if(!is.call(lhs) || lhs[[1]] != '~')
stop(syntax.error)
expr <- lhs[[2]]
var <- as.character(lhs[[3]])
seq <- f[[3]]
gens <- list(call('<-', var, seq))
} else { # (2)
expr <- f[[2]]
gens <- as.list(f[[3]])[-1]
if(any(lapply(gens, class) != '<-'))
stop(syntax.error)
}
## Fill list comprehension .LC
vars <- as.character(lapply(gens, function(g) g[[2]]))
seqs <- lapply(gens, function(g) g[[3]])
.LC <- comprehend(expr, vars, seqs, guard)
## Provided the result is rectangular, convert it to a vector or array
## TODO: Extend to handle .LC structures more than 2-deep.
## TODO: Avoid rectangularizing nested comprehensions along guarded
dimensions?
if(!length(.LC))
return(.LC)
dim1 <- dim(.LC[[1]])
if(is.null(dim1)){
lengths <- sapply(.LC, length)
if(all(lengths == lengths[1])){ # rectangular
.LC <- unlist(.LC)
if(lengths[1] > 1) # matrix
dim(.LC) <- c(lengths[1], length(lengths))
} else { # ragged
# leave .LC as a list
}
} else { # elements of .LC have dimension
dim <- c(dim1, length(.LC))
.LC <- unlist(.LC)
dim(.LC) <- dim
}
.LC
}

```