Valid characters in a String

I am given a string and have to return False if there is one or more invalid characters, otherwise True. The caveat is that I can only built-in functions and str operations (for example: in, +, indexing, len) and recursion. What I have so far is not working:

def is_valid_sequence(dna):
""" (str) -> bool

Return True if and only if the DNA sequence is valid
(A, T, C, and G)
:param dna: string sequence
:return: true or false
>>> is_valid_sequence('ATTAC')
True
>>> is_valid_sequence('FBSSS')
False
"""
valid_seq = 0

if len(dna) == 1 and dna in ['A', 'T', 'C', 'G']:
        valid_seq += 1
else:
    return is_valid_sequence(dna[1:])

Obviously, this code doesn't work because of recursion and adding 1 to the valid_seq variable just gets wiped after the next recursive iteration.

For DNA sequences of a small size (around a thousand characters), this is a practical implementation

def is_valid_sequence (dna):
  # base case
  if len (dna) == 0:
    return True
  # check if first character is valid
  elif dna [0] not in ['A', 'T', 'C', 'G']:
    return False
  # otherwise, recurse on the rest of the characters
  else:
    return is_valid_sequence (dna [1:])

print (is_valid_sequence ('AATGCGA'))  # True
print (is_valid_sequence ('AATXGCGA')) # False

---

A word of caution

Be careful with recursion in python tho – a long dna string will cause a stack overflow. Attempting to validate even a sequence this "large" would fail

GATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACA

You can easily avoid this by implementing is_valid_sequence using a Clojure-style loop/recur mechanism for constant-space recursion

def recur (*values):
  return (recur, values)

def loop (f):
  acc = f ()
  while type (acc) is tuple and acc [0] is recur:
    acc = f (*acc [1])
  return acc

def is_valid_sequence (dna):
  # stack-safe loop/recur implementation
  # initialize loop state variable `s` to value of `dna`
  return loop (lambda s = dna:
    # base case
    True if len (s) == 0 else
    # check if first character valid
    False if s [0] not in ['A', 'T', 'C', 'G'] else
    # else recurse on the rest of the characters
    recur (s [1:]))

# does not overflow stack
print (is_valid_sequence ('GATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACAGATTACA'))
# True

---

Continued improvements

The loop/recur implementation exposes an additional opportunity to tune the performance of our function. Slicing the string as we have done with dna[0] and dna[1:] creates new strings in memory; this was only necessary because of the recursion API used in the first function we wrote

The loop/recur interface allows us to use whatever data type is suitable for computing our output – in this case, a simple integer index will do. Lexical scoping takes care of the rest – dna is accessible within our lambda and does not need to do dna[1:] slicing which will save a lot of time/space for large inputs

def is_valid_sequence (dna):
  # only create this array once
  valid_chars = ['A', 'T', 'C', 'G']
  # initialize loop state variable `i` with 0
  return loop (lambda i = 0:
    True if len (dna) == i else
    False if dna [i] not in valid_chars else
    recur (i + 1))

---

Python and the Unruly Lambda

Notice how we were forced to use a pure expression inside the lambda instead of the traditional if/elif/else statement syntax – this is not a problem for simple programs, but more complex programs might be difficult to express this way in python.

This works identically to the program above but uses a plain old function instead of a lambda

def is_valid_sequence (dna):
  valid_chars = ['A', 'T', 'C', 'G']
  # plain old function; replaces lambda
  def myloop (i = 0):
    if len (dna) == 0:
      return True
    elif dna [i] not in valid_chars:
      return False
    else:
      return recur (i + 1)
  # use plain old function instead of lambda
  return loop (myloop)