A short one for today: in this post we will learn how to easily create *truth tables* with R and will contribute our code to the growing repository of *Rosetta code*. I hope that you will learn a few tricks along the way, so read on!

We have covered bits of code that I contributed to Rosetta Code on this blog before (see Category: Rosetta Code). This time we want to solve the following task:

Truth table

A truth table is a display of the inputs to, and the output of a Boolean function organized as a table where each row gives one combination of input values and the corresponding value of the function.

Task

- Input a Boolean function from the user as a string then calculate and print a formatted truth table for the given function.

(One can assume that the user input is correct).- Print and show output for Boolean functions of two and three input variables, but any program should not be limited to that many variables in the function.
- Either reverse-polish or infix notation expressions are allowed.

The core of a truth table is a permutation of all `TRUE`

and `FALSE`

statements for all variables (= letters), which we extract from a Boolean function `x`

. Fortunately, we created such a permutation function a few posts ago (see Learning R: Permutations and Combinations with Base R), so that we can adapt it accordingly: `expand.grid(rep(list(c(FALSE, TRUE)), length(vars)))`

. We then add another column with the resulting evaluation of the Boolean function and return the resulting table:

truth_table <- function(x) { vars <- unique(unlist(strsplit(x, "[^a-zA-Z]+"))) vars <- vars[vars != ""] perm <- expand.grid(rep(list(c(FALSE, TRUE)), length(vars))) names(perm) <- vars perm[ , x] <- with(perm, eval(parse(text = x))) perm }

Now, let us try some examples:

"%^%" <- xor # define unary xor operator truth_table("!A") # not ## A !A ## 1 FALSE TRUE ## 2 TRUE FALSE truth_table("A | B") # or ## A B A | B ## 1 FALSE FALSE FALSE ## 2 TRUE FALSE TRUE ## 3 FALSE TRUE TRUE ## 4 TRUE TRUE TRUE truth_table("A & B") # and ## A B A & B ## 1 FALSE FALSE FALSE ## 2 TRUE FALSE FALSE ## 3 FALSE TRUE FALSE ## 4 TRUE TRUE TRUE truth_table("A %^% B") # xor ## A B A %^% B ## 1 FALSE FALSE FALSE ## 2 TRUE FALSE TRUE ## 3 FALSE TRUE TRUE ## 4 TRUE TRUE FALSE truth_table("S | (T %^% U)") # 3 variables with brackets ## S T U S | (T %^% U) ## 1 FALSE FALSE FALSE FALSE ## 2 TRUE FALSE FALSE TRUE ## 3 FALSE TRUE FALSE TRUE ## 4 TRUE TRUE FALSE TRUE ## 5 FALSE FALSE TRUE TRUE ## 6 TRUE FALSE TRUE TRUE ## 7 FALSE TRUE TRUE FALSE ## 8 TRUE TRUE TRUE TRUE truth_table("A %^% (B %^% (C %^% D))") # 4 variables with nested brackets ## A B C D A %^% (B %^% (C %^% D)) ## 1 FALSE FALSE FALSE FALSE FALSE ## 2 TRUE FALSE FALSE FALSE TRUE ## 3 FALSE TRUE FALSE FALSE TRUE ## 4 TRUE TRUE FALSE FALSE FALSE ## 5 FALSE FALSE TRUE FALSE TRUE ## 6 TRUE FALSE TRUE FALSE FALSE ## 7 FALSE TRUE TRUE FALSE FALSE ## 8 TRUE TRUE TRUE FALSE TRUE ## 9 FALSE FALSE FALSE TRUE TRUE ## 10 TRUE FALSE FALSE TRUE FALSE ## 11 FALSE TRUE FALSE TRUE FALSE ## 12 TRUE TRUE FALSE TRUE TRUE ## 13 FALSE FALSE TRUE TRUE FALSE ## 14 TRUE FALSE TRUE TRUE TRUE ## 15 FALSE TRUE TRUE TRUE TRUE ## 16 TRUE TRUE TRUE TRUE FALSE

Looks good! The full code can also be found here: Rosetta Code: Truth Table: R.

I suspect that this function will come in handy for solving further tasks in the future, so stay tuned!

Very nice, even if… (submitted entirely humorously)

fortune(106)

If the answer is parse() you should usually rethink the question.

— Thomas Lumley

R-help (February 2005

fortune(181)

Personally I have never regretted trying not to underestimate my own future

stupidity.

— Greg Snow (explaining why eval(parse(…)) is often suboptimal, answering

a question triggered by the infamous fortune(106))

R-help (January 2007)