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

Here is the Code from Vitus as a running example that uses the Agda Prelude

module Parse where

open import Prelude

-- Install Prelude
---- clone this git repo:
---- https://github.com/fkettelhoit/agda-prelude

-- Configure Prelude
--- press Meta/Alt and the letter X together
--- type "customize-group" (i.e. in the mini buffer)
--- type "agda2"
--- expand the Entry "Agda2 Include Dirs:"
--- add the directory 



open import Data.Product using (uncurry′)
open import Data.Maybe using ()
open import Data.List using (sequence)

splitBy : ∀ {a} {A : Set a} → (A → Bool) → List A → List (List A)
splitBy {A = A} p = uncurry′ _∷_ ∘ foldr step ([] , [])
  where
    step : A → List A × List (List A) → List A × List (List A)
    step x (cur , acc) with p x
    ... | true  = x ∷ cur , acc
    ... | false = []      , cur ∷ acc


charsToℕ : List Char → Maybe ℕ
charsToℕ []   = nothing
charsToℕ list = stringToℕ (fromList list)

notComma : Char → Bool
notComma c = not (c == ',')

-- Finally:

charListToℕ : List Char → Maybe (List ℕ)
charListToℕ = Data.List.sequence Data.Maybe.monad ∘ map charsToℕ ∘ splitBy     notComma

stringListToℕ : String → Maybe (List ℕ)
stringListToℕ = charListToℕ ∘ toList


-- Test

test1 : charListToℕ ('1' ∷ '2' ∷ ',' ∷ '3' ∷ []) ≡ just (12 ∷ 3 ∷ [])
test1 = refl

test2 : stringListToℕ "12,33" ≡ just (12 ∷ 33 ∷ [])
test2 = refl

test3 : stringListToℕ ",,," ≡ nothing
test3 = refl

test4 : stringListToℕ "abc,def" ≡ nothing
test4 = refl