expressions are evaluated right to left instead of left to right.

[HeardACat]

See example.r

[HeardACat]

To solve this we need to implement an alternative version to alt which does sequencing of recognizers (see wiki: https://en.wikipedia.org/wiki/Parser_combinator)

The sequencing of recognizers is done with the ⊛ parser combinator. Like ⊕, it is used as an infix operator between p and q. But it applies the first recognizer p to the input position j, and if there is any successful result of this application, then the second recognizer q is applied to every element of the result set returned by the first recognizer. ⊛ ultimately returns the union of these applications of q.

Instead what we're after is this one:

The ‘alternative’ parser combinator, ⊕, applies both of the recognizers on the same input position j and sums up the results returned by both of the recognizers, which is eventually returned as the final result. It is used as an infix operator between p and q as follows:

[pkri0]

This can be done using chainl1. To implement that, a monadic bind would be nice. Like this:

library(Ramble)

bind <- function(p,f) {
  function(string) {
    result <- p(string)
    if (length(result) == 0) {
      list()
    }
    else {
      (f(result$result))(result$leftover)
    }
  }
}

`%bind%` <- bind

chainl1 <- function(p, op) {
  rest <- \(x) (op %bind% \(f) p %bind% \(y) rest(f(x,y))) %alt% succeed(x)
  p %bind% rest
}

skip <- function(p) {
  p %using% \(x) list()
}

between <- function(open, p, close) {
  skip(open) %then% p %then% skip(close)
}

sumop <- (literal('+') %using% \(s) \(x,y) x+y) %alt%
  (literal('-') %using% \(s) \(x,y) x-y)
mulop <- (literal('*') %using% \(s) \(x,y) x*y) %alt%
  (literal('/') %using% \(s) \(x,y) x/y)
expr <- chainl1(term, sumop)
term <- chainl1(factor, mulop)
factor <- between(literal('('), expr, literal(')')) %alt%
  natural() %using% as.numeric

expr("4-2+3") # order is done correctly.