I have two GRange Lists and I am trying to apply countOverlaps function to each combination of the lists and return a list of results like this:

    gr1 <-  GRanges(seqnames = "chr2", ranges = IRanges(3, 6),strand = "+", score = 5L, GC = 0.45)
    gr2 <- GRanges(seqnames = c("chr1", "chr1"), ranges = IRanges(c(7,13), width = 3), strand = c("+", "-"), score = 3:4, GC = c(0.3, 0.5))
    grlA <- GRangesList("a" = gr1, "b" = gr2)

    gr1 <-  GRanges(seqnames = "chr2", ranges = IRanges(1, 10),strand = "+", score = 5L, GC = 0.45)
    gr2 <- GRanges(seqnames = c("chr1", "chr1"), ranges = IRanges(c(3,13), width = 3), strand = c("+", "-"), score = 3:4, GC = c(0.2, 0.3))
    grlB <- GRangesList("c" = gr1, "d" = gr2)

I would like to get a list of object "a" and object "b" in grlA containing the results of the function for each value of grlB:

(list $a, $b and dataframes for c,d)

$a

c d

$b

c d

I have tried this to get all the combinations of the list but I get an error...

    comb_apply <- function(f,..., MoreArgs=list()){
      exp <- unname(expand.grid(...,stringsAsFactors = FALSE))
      do.call(mapply, c(list(FUN=f, SIMPLIFY=FALSE, MoreArgs=MoreArgs), exp))
    }

    comb_apply(countOverlaps,grlA,grlB)

    Error in as.vector(x, mode = "character") : 
    no method for coercing this S4 class to a vector

What am I doing wrong?
Thank you for help/suggestions!

We would need to add a method for expand.grid() on Vector (now added in S4Vectors 0.9.4). Until then, you can use the old index trick instead, e.g.,

comb_apply(function(i, j) countOverlaps(grlA[[i]], grlB[[j]]), seq_along(grlA), seq_along(grlB))

Note that the new expand.grid,Vector returns a DataFrame, which rightfully won't let you unname it. Coerce to list first:

comb_apply <- function(f,..., MoreArgs=list()){
      exp <- unname(as.list(expand.grid(...,stringsAsFactors = FALSE)))
      do.call(mapply, c(list(FUN=f, SIMPLIFY=FALSE, MoreArgs=MoreArgs), exp))
}

Thanks very much for your help! 
SORRY I realise I gave a bad example because the columns would not be all the same in the data frames! Here is a new example:

    gr1 <- GRanges(seqnames = c("chr1", "chr2"), ranges = IRanges(c(7,13), width = 3), strand = c("+", "-"))
    gr2 <- GRanges(seqnames = c("chr1", "chr3"), ranges = IRanges(c(5,13), width = 3), strand = c("+", "-"))
    grlA <- GRangesList("a" = gr1, "b" = gr2)

    gr1 <- GRanges(seqnames = c("chr1", "chr2"), ranges = IRanges(c(1,13), width = 3), strand = c("+", "-"))
    gr2 <- GRanges(seqnames = c("chr1", "chr3"), ranges = IRanges(c(3,13), width = 3), strand = c("+", "-"))
    grlB <- GRangesList("c" = gr1, "d" = gr2)

The problem that I was finding is to get the data frames within the grlB:

  comb_apply <- function(f,..., MoreArgs=list()){
      exp <- unname(as.list(expand.grid(...,stringsAsFactors = FALSE)))
      do.call(mapply, c(list(FUN=f, SIMPLIFY=FALSE, MoreArgs=MoreArgs), exp))
   }

   t= comb_apply(function(i, j) countOverlaps(grlA[[i]], grlB[[j]]), seq_along(grlA), seq_along(grlB))
    names(t)=apply(expand.grid(names(grlA), names(grlB)), 1, paste, collapse="_")

> t

$a_c

[1] 1

$b_c

[1] 0 0

$a_d

[1] 0

$b_d

[1] 0 1

While I was looking for a list of data frames... I can do this with a grep command to select out the data frames that are part of grlB and save them in a separate list, but it is again veeery slow...

    new=list()

    for (i in names(grlB)) {

    df = as.data.frame(t[grep(i,names(t))])

    new[[length(new)+1]] <- df

    }

I did it like this at the end:

         d <- do.call(rbind, t)

         rownames(d)=as.character(lapply(strsplit(as.character(rownames(d)), "_", fixed=TRUE), "[", 2))

         d=as.data.frame(d)

         new2=split(d, rownames(d))

         lapply(new2, t)