Agda: parse a string with numbers

Question

I am trying to parse a string with natural numbers in Agda. e.g., the result of stringListToℕ \"1,2,3\" should be Just (1 ∷ 2 ∷ 3 ∷ [])

My

Answer 1

I had a go at it trying not to be clever and using simple recursive functions rather than stdlib magic. parse xs m ns parses xs by recording the (possibly empty) prefix already read in m while keeping the list of numbers already parsed in the accumulator ns.

If a parsing failure happens (non recognized character, two consecutive ,, etc.) everything is thrown away and we return nothing.

module parseList where

open import Data.Nat
open import Data.List
open import Data.Maybe
open import Data.Char
open import Data.String

isDigit : Char → Maybe ℕ
isDigit '0' = just 0
isDigit '1' = just 1
isDigit '2' = just 2
isDigit '3' = just 3
isDigit _   = nothing

attach : Maybe ℕ → ℕ → ℕ
attach nothing  n = n
attach (just m) n = 10 * m + n

Quote : List Char → Maybe (List ℕ)
Quote xs = parse xs nothing []
  where
    parse : List Char → Maybe ℕ → List ℕ → Maybe (List ℕ)
    parse []         nothing  ns = just ns
    parse []         (just n) ns = just (n ∷ ns)
    parse (',' ∷ tl) (just n) ns = parse tl nothing (n ∷ ns)
    parse (hd ∷ tl)  m        ns with isDigit hd
    ... | nothing = nothing
    ... | just n  = parse tl (just (attach m n)) ns

stringListToℕ : String → Maybe (List ℕ)
stringListToℕ xs with Quote (toList xs)
... | nothing = nothing
... | just ns = just (reverse ns)

open import Relation.Binary.PropositionalEquality

test : stringListToℕ ("12,3") ≡ just (12 ∷ 3 ∷ [])
test = refl