Uiua

This turned out to be reasonably easy in Uiua, though this solution relies on macros which maybe slow it down.

(edit: removing one macro sped it up quite a bit)

(edit2: Letting Uiua build up an n-dimensional array turned out to be the solution, though sadly my mind only works in 3 dimensions. Now runs against the live data in around 0.3 seconds.)

Try it here

Data   ← ⊜(□⊜⋕⊸(¬∈": "))⊸≠@\n "190: 10 19\n3267: 81 40 27\n83: 17 5\n156: 15 6\n7290: 6 8 6 15\n161011: 16 10 13\n192: 17 8 14\n21037: 9 7 18 13\n292: 11 6 16 20"
Calib! ← ≡◇⊢▽⊸≡◇(∈♭/[^0]:°⊂) # Calibration targets which can be constructed from their values.
&p/+Calib!⊃(+|×)Data
&p/+Calib!⊃(+|×|+×ⁿ:10+1⌊ₙ₁₀,)Data

Python

It is a tree search

def parse_input(path):

  with path.open("r") as fp:
    lines = fp.read().splitlines()

  roots = [int(line.split(':')[0]) for line in lines]
  node_lists = [[int(x)  for x in line.split(':')[1][1:].split(' ')] for line in lines]

  return roots, node_lists

def construct_tree(root, nodes, include_concat):

  levels = [[] for _ in range(len(nodes)+1)]
  levels[0] = [(str(root), "")]
  # level nodes are tuples of the form (val, operation) where both are str
  # val can be numerical or empty string
  # operation can be *, +, || or empty string

  for indl, level in enumerate(levels[1:], start=1):

    node = nodes[indl-1]

    for elem in levels[indl-1]:

      if elem[0]=='':
        continue

      if elem[0][-len(str(node)):] == str(node) and include_concat:
        levels[indl].append((elem[0][:-len(str(node))], "||"))
      if (a:=int(elem[0]))%(b:=int(node))==0:
        levels[indl].append((str(int(a/b)), '*'))
      if (a:=int(elem[0])) - (b:=int(node))>0:
        levels[indl].append((str(a - b), "+"))

  return levels[-1]

def solve_problem(file_name, include_concat):

  roots, node_lists = parse_input(Path(cwd, file_name))
  valid_roots = []

  for root, nodes in zip(roots, node_lists):

    top = construct_tree(root, nodes[::-1], include_concat)

    if any((x[0]=='1' and x[1]=='*') or (x[0]=='0' and x[1]=='+') or
           (x[0]=='' and x[1]=='||') for x in top):

      valid_roots.append(root)

  return sum(valid_roots)

Haskell

A surprisingly gentle one for the weekend! Avoiding string operations for concatenate got the runtime down below one second on my machine.

import Control.Arrow
import Control.Monad
import Data.List
import Data.Maybe

readInput :: String -> [(Int, [Int])]
readInput = lines >>> map (break (== ':') >>> (read *** map read . words . tail))

equatable :: [Int -> Int -> Int] -> (Int, [Int]) -> Bool
equatable ops (x, y : ys) = elem x $ foldM apply y ys
  where
    apply a y = (\op -> a `op` y) <$> ops

concatenate :: Int -> Int -> Int
concatenate x y = x * mag y + y
  where
    mag z = fromJust $ find (> z) $ iterate (* 10) 10

main = do
  input <- readInput <$> readFile "input07"
  mapM_
    (print . sum . map fst . (`filter` input) . equatable)
    [ [(+), (*)],
      [(+), (*), concatenate]
    ]

Haskell

import Control.Arrow
import Data.Char
import Text.ParserCombinators.ReadP

numP = read <$> munch1 isDigit
parse = endBy ((,) <$> (numP <* string ": ") <*> sepBy numP (char ' ')) (char '\n')

valid n [m] = m == n
valid n (x : xs) = n > 0 && valid (n - x) xs || (n `mod` x) == 0 && valid (n `div` x) xs

part1 = sum . fmap fst . filter (uncurry valid . second reverse)

concatNum r = (+r) . (* 10 ^ digits r)
    where
        digits = succ . floor . logBase 10 . fromIntegral

allPossible [n] = [n]
allPossible (x:xs) = ((x+) <$> rest) ++ ((x*) <$> rest) ++ (concatNum x <$> rest)
    where
        rest = allPossible xs

part2 = sum . fmap fst . filter (uncurry elem . second (allPossible . reverse))

main = getContents >>= print . (part1 &&& part2) . fst . last . readP_to_S parse

Uiua

Credits to @mykl@lemmy.world for the approach of using reduce and also how to split the input by multiple characters.
I can happily say that I learned quite a bit today, even though the first part made me frustrated enough that I went searching for other approaches ^^

Part two just needed a simple modification. Changing how the input is parsed and passed to the adapted function took longer than changing the function itself actually.

Run with example input here

PartOne ← (
  &rs ∞ &fo "input-7.txt"
  ⊜□≠@\n.
  ≡◇(⊜□≠@:.)
  ≡⍜⊡⋕0
  ≡⍜(°□⊡1)(⊜⋕≠@ .)
  ⟜(⊡0⍉)

  # own attempt, produces a too low number
  # ≡(:∩°□°⊟
  #   ⍣(⍤.◡⍣(1⍤.(≤/×)⍤.(≥/+),,)0
  #     ⊙¤⋯⇡ⁿ:2-1⊸⧻
  #     ⊞(⍥(⟜⍜(⊙(↙2))(⨬+×⊙°⊟⊡0)
  #         ↘1
  #       )⧻.
  #       ⍤.=0⧻.
  #     )
  #     ∈♭◌
  #   )0)

  # reduce approach found on the programming.dev AoC community by mykl@lemmy.world
  ≡(◇(∈/(◴♭[⊃(+|×)]))⊡0:°⊂)
  °□/+▽
)

PartTwo ← (
  &rs ∞ &fo "input-7.txt"
  ⊜(□⊜⋕¬∈": ".)≠@\n.
  ⟜≡◇⊢
  ≡◇(∈/(◴♭[≡⊃⊃(+|×|⋕$"__")]):°⊂)
  °□/+▽
)

&p "Day 7:"
&pf "Part 1: "
&p PartOne
&pf "Part 2: "
&p PartTwo