Update 2 @G. Grothendieck posted two approaches. The second one is changing the function environment inside a function. This solves my problem of too many coding replicates. I am not sure if this is a good method to pass through the CRAN check when making my scripts into a package. I will update again when I have some conclusions.
Update
I am trying to pass a lot of input argument variables to f2 and do not want to index every variable inside the function as env$c, env$d, env$calls, that is why I tried to use with in f5 and f6(a modified f2). However, assign does not work with with inside the {}, moving assign outside with will do the job but in my real case I have a few assigns inside the with expressions which I do not know how to move them out of the with function easily.
Here is an example:
## In the <environment: R_GlobalEnv>
a <- 1
b <- 2
f1 <- function(){
    c <- 3
d <- 4
f2 <- function(P){
    assign("calls", calls+1, inherits=TRUE)
    print(calls)
    return(P+c+d)
 }
calls <- 0
v <- vector()
for(i in 1:10){
    v[i] <- f2(P=0)
    c <- c+1
    d <- d+1
  }
 return(v)
}
f1()
Function f2 is inside f1, when f2 is called, it looks for variables calls,c,d in the environment environment(f1). This is what I wanted.
However, when I want to use f2 also in the other functions, I will define this function in the Global environment instead, call it f4.
f4 <- function(P){
  assign("calls", calls+1, inherits=TRUE)
  print(calls)
  return(P+c+d)
}
This won't work, because it will look for calls,c,d in the Global environment instead of inside a function where the function is called. For example:
f3 <- function(){
  c <- 3
  d <- 4
  calls <- 0
  v <- vector()
  for(i in 1:10){
    v[i] <- f4(P=0) ## or replace here with f5(P=0)
    c <- c+1
    d <- d+1
  }
  return(v)
}
f3()
The safe way should be define calls,c,d in the input arguments of f4 and then pass these parameters into f4. However, in my case, there are too many variables to be passed into this function f4 and it would be better that I can pass it as an environment and tell f4 do not look in the Global environment(environment(f4)), only look inside the environment when f3 is called. 
The way I solve it now is to use the environment as a list and use the with function. 
f5 <- function(P,liste){
  with(liste,{
     assign("calls", calls+1, inherits=TRUE)
     print(calls)
     return(P+c+d)
     }
  )
}
f3 <- function(){
  c <- 3
  d <- 4
  calls <- 0
  v <- vector()
  for(i in 1:10){
    v[i] <- f5(P=0,as.list(environment())) ## or replace here with f5(P=0)
    c <- c+1
    d <- d+1
  }
  return(v)
}
f3()
However, now assign("calls", calls+1, inherits=TRUE) does not work as it should be since assign does not modify the original object. The variable calls is connected to an optimization function where the objective function is f5. That is the reason I use assign instead of passing calls as an input arguments. Using attach is also not clear to me. Here is my way to correct the assign issue:
f7 <- function(P,calls,liste){
  ##calls <<- calls+1
  ##browser()
  assign("calls", calls+1, inherits=TRUE,envir = sys.frame(-1))
  print(calls)
  with(liste,{
    print(paste('with the listed envrionment, calls=',calls))
    return(P+c+d)
  }
  )
}
########
##################
f8 <- function(){
  c <- 3
  d <- 4
  calls <- 0
  v <- vector()
  for(i in 1:10){
    ##browser()
    ##v[i] <- f4(P=0) ## or replace here with f5(P=0)
    v[i] <- f7(P=0,calls,liste=as.list(environment()))
    c <- c+1
    d <- d+1
  }
  f7(P=0,calls,liste=as.list(environment()))
  print(paste('final call number',calls))
  return(v)
}
f8()
I am not sure how this should be done in R. Am I on the right direction, especially when passing through the CRAN check? Anyone has some hints on this?
 
     
     
     
    