From david at unusualsolutionsthatwork.com  Sun Dec  9 22:41:46 2007
From: david at unusualsolutionsthatwork.com (David C. Norris)
Date: Sun, 09 Dec 2007 13:41:46 -0800
Subject: [Rd] List comprehensions for R
Message-ID: <475C611A.8000302@unusualsolutionsthatwork.com>

Below is code that introduces a list comprehension syntax into R, 
allowing expressions like:

 > .[ sin(x) ~ x <- (0:11)/11 ]
 [1] 0.00000000 0.09078392 0.18081808 0.26935891 0.35567516 0.43905397
 [7] 0.51880673 0.59427479 0.66483486 0.72990422 0.78894546 0.84147098
 > .[ .[x*y ~ x <- 0:3] ~ y <- 0:4]
     [,1] [,2] [,3] [,4] [,5]
[1,]    0    0    0    0    0
[2,]    0    1    2    3    4
[3,]    0    2    4    6    8
[4,]    0    3    6    9   12
 > .[ .[x+y ~ x <- 0:y] ~ y <- 0:4]
[[1]]
[1] 0

[[2]]
[1] 1 2

[[3]]
[1] 2 3 4

[[4]]
[1] 3 4 5 6

[[5]]
[1] 4 5 6 7 8

 > .[ x*y ~ {x <- 1:4; y<-1:x} ]
 [1]  1  2  4  3  6  9  4  8 12 16

These constructions are supported by the following code.

Regards,
David

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

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

comprehend <- function(expr, vars, seqs, comprehension=list()){
  if(length(vars)==0) # base case
    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], comprehension)
    }
  comprehension
}

## Support general syntax like .[{exprs} ~ {generators}]
"[.comprehension" <- function(x, f){
  f <- substitute(f)
  ## 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)
  ## Provided the result is rectangular, convert it to a vector or array
  ## TODO: Extend to handle .LC structures more than 2-deep.
  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
}



[Rd] List comprehensions for R
David C. Norris