How do I pre-determine mutually exclusive comparisons? - r

Question

The human eye can see that no value x satisfies the condition
x<1 & x>2
but how can I make R see that. I want to use this in a function which gets passed comparisons (say as strings) and not necessarily data. Let's say I want to write a function that checks whether a combination of comparisons can ever be fulfilled anyway, like this
areTherePossibleValues <- function(someString){
someCode
}
areTherePossibleValues("x<1 & x>2")
[1] FALSE
I mean one could do that by interpreting the substrings that are comparison signs and so on, but I feel like there's got to be a better way. The R comparison functions ('<','>','=' and so on) themselves actually might be the answer to this, right?

Answer 1

Another option is to use the library validatetools (disclaimer, I'm its author).
library(validatetools)
rules <- validator( r1 = x < 1, r2 = x > 2)
is_infeasible(rules)
# [1] TRUE
make_feasible(rules)
# Dropping rule(s): "r1"
# Object of class 'validator' with 1 elements:
# r2: x > 2
# Rules are evaluated using locally defined options
# create a set of rules that all must hold:
rules <- validator( x > 1, x < 2, x < 2.5)
is_infeasible(rules)
# [1] FALSE
remove_redundancy(rules)
# Object of class 'validator' with 2 elements:
# V1: x > 1
# V2: x < 2
rules <- validator( x >= 1, x < 1)
is_infeasible(rules)
# [1] TRUE

Answer 2

To compare among ranges, min of the range max(s) should always be greater than the max of the range min(s), showed as below:
library(dplyr)
library(stringr)
areTherePossibleValues <- function(s) {
str_split(s, pattern = " *& *", simplify = TRUE)[1, ] %>%
{lapply(c("max" = "<", "min" = ">"), function(x) str_subset(., pattern = x) %>% str_extract(., pattern = "[0-9]+"))} %>%
{as.numeric(min(.$max)) > as.numeric(max(.$min))}
}
Update: add inclusion comparison
The only difference is that min of the range max(s) can be equal to the max of the range min(s).
library(dplyr)
library(stringr)
areTherePossibleValues <- function(s) {
str_split(s, pattern = " *& *", simplify = TRUE)[1, ] %>%
{lapply(c("max" = "<", "min" = ">"), function(x) str_subset(., pattern = x) %>% str_remove(., pattern = paste0("^.*", x)))} %>%
{ifelse(sum(grepl(pattern = "=", unlist(.))),
as.numeric(min(str_remove(.$max, "="))) >= as.numeric(max(str_remove(.$min, "="))),
as.numeric(min(.$max)) > as.numeric(max(.$min)))}
}
areTherePossibleValues("x<1 & x>2")
areTherePossibleValues("x>1 & x<2")
areTherePossibleValues("x>=1 & x<1")

Answer 3

Here is my way of solving it, it may not be the best, but it should work even you have many comparisons.
Let's call the numbers appeared in your comparisons 'cutoffs', then all we need to do is to test 1 number between each pair of cutoffs, 1 number that is larger than the max cutoff, and 1 number that is smaller than the min cutoff.
The intuition is illustrated with the plot:
Here is the code:
areTherePossibleValues <- function(s){
# first get the numbers that appeared in your string, sort them, and call them the cutoffs
cutoffs = sort(as.numeric(gsub("\\D", "", strsplit(s, "&")[[1]])))
# get the numbers that in between each cutoffs, and a bit larger/smaller than the max/min in the cutoffs
testers = (c(min(cutoffs)-1, cutoffs) + c( cutoffs ,max(cutoffs) + 1))/2
# take out each comparisons
comparisons = strsplit(s, "&")[[1]]
# check if ANY testers statisfy all comparisons
any(sapply(testers, function(te){
# check if a test statisfy ALL comparisons
all(sapply(comparisons, function(co){eval(parse(text =gsub(pattern = 'x',replacement =te, co)))}))
}))
}
areTherePossibleValues("x<1 & x>2")
#[1] FALSE
areTherePossibleValues("x>1 & x<2 & x < 2.5")
#[1] TRUE
areTherePossibleValues("x=> 1 & x < 1")
#[1] FALSE

Answer 4

We see x<1 & x>2 is impossible because we are taught a simple rule: if a number x is smaller than another number a then it can not be bigger than another number that is bigger than a, or more fundamentally we are using the transitivity property of any partially ordered set. There is no reason we can not teach a computer (or R) to see that. If your logic string in your question only consists of statements in the forms x # a where # can be <, >, <=, and >=, and the operator is always &, then Yue Y's solution above perfectly answers your question. It can be even generalized to include the | operator. Beyond this you'll have to be more specific what the logic expression can be.