The script simulates a scenario where certain activities depend on others as weak dependencies and may be restarted if the dependencies are completed.

async_loop.py

import asyncio

# weak dependencies list as (dependency, dependent)
weak_deps = [(2,3),(4,1)]
# e.g. let's say activity 2 updates input of activity 3 as a weak dependency, etc...

async def gather_with_first_completed(awaitable_results):
    # Create a list to store the completed results
    completed_results = []

    tasks = [asyncio.create_task(t) for t in awaitable_results]

    while tasks:
        # Wait for the first task to complete

        # Use asyncio.wait to wait for the first task to complete
        done, pending = await asyncio.wait(tasks, return_when=asyncio.FIRST_COMPLETED)


        # Iterate through the completed tasks
        for task in done:
            curr_result = task.result()
            print('activity ' + str(curr_result) + ' completed')
            # Here, you can restart some of the activities in completed_results 
            # if the just-finished task has updated their inputs.            
            for weak_depcy, weak_depdent in weak_deps:
                if curr_result == weak_depcy:
                    if weak_depdent in  completed_results:
                        pending = pending | set([asyncio.create_task(asyncio.sleep(2, result=weak_depdent))])
                        print('activity ' + str(weak_depdent) + ' restarted because its weak dependency ' + str(weak_depcy) + ' completed')
                        
            # Append the result of the completed task to the list
            completed_results.append(curr_result)
             

        # Remove the completed tasks from the list of tasks
        tasks = pending          

    return completed_results

async def main_loop():
    awaitable_results = [asyncio.sleep(2, result=i) for i in range(5)]
    result_list = await gather_with_first_completed(awaitable_results)
    print('all activities done')
    print(result_list)

asyncio.run(main_loop())

my_gather.py

import asyncio

async def gather_with_first_completed(*awaitable_results):
    # Create a list to store the completed results
    completed_results = []
    tasks = [asyncio.create_task(t) for t in awaitable_results]
    while tasks:
        # Wait for the first task to complete
        # Use asyncio.wait to wait for the first task to complete
        done, pending = await asyncio.wait(tasks, return_when=asyncio.FIRST_COMPLETED)
        # Iterate through the completed tasks
        for task in done:
            curr_result = task.result()
            # Append the result of the completed task to the list
            completed_results.append(curr_result)
        # Remove the completed tasks from the list of tasks
        tasks = pending          
    return completed_results

    
 # usage
 
async def t1():
   await asyncio.sleep(1)
   return 't1'

async def t5():
   await asyncio.sleep(5)
   return 't5'

async def t10():
   await asyncio.sleep(10)
   return 't10'
    
async def usage():
   my_gather = await gather_with_first_completed(t5(), t10(), t1())
   print('my gather: ', my_gather)
   # ['t1', 't5', 't10']
   
   std_gather = await asyncio.gather(t5(), t10(), t1())
   print('standard gather: ', std_gather)
   # ['t5', 't10', 't1']

asyncio.run(usage())

Example of output