form-validation.js

// Validates a single input
function validate(input) {
  return !input.getAttribute('required')?  false  // not required, no validation
  :      !input.value?                     new Error(input.name + ' is required.')
  :      /* otherwise */                   false  // properly filled
}

// Takes in an array of inputs, and tells us if they're all valid or no
function isFormInvalid(inputs) {
  return inputs.map(validate)   // Validates all fields
               .filter(Boolean) // Keeps only the errors
               .length > 0      // Checks if we still have any errors
}

// When submitting, we check if the form is valid
form.addEventListener('submit', function(ev) {
  var fields = form.querySelectorAll('input')
  return !isFormInvalid(fields)
})