[Currying and partial application](http://www.2ality.com/2011/09/currying-vs-part-eval.html) are two ways of transforming a function into another function with a generally smaller arity. While they are often confused with each other, they work differently. The goal is to learn to differentiate them.

## Currying

> Is the technique of transforming a function that takes multiple arguments in such a way that it can be called as a chain of functions each with a single argument.

Currying takes a function:

```
f: X × Y → R
```

and turns it into a function:

```
f': X → (Y → R)
```

Instead of calling `f` with two arguments, we invoke `f'` with the first argument. The result is a function that we then call with the second argument to produce the result. Thus, if the uncurried `f` is invoked as:

```
f(3, 5)
```

then the curried `f'` is invoked as:

`f'(3)(5)`

### Example

Given this function:

```python
def add(x, y, z):
  return x + y + z
```

We can call in a normal way:

```python
add(1, 2, 3) # => 6
```

But we can create a curried version of `add(a, b, c)`function:

```python
curriedAdd = lambda a: (lambda b: (lambda c: add(a,b,c)))
curriedAdd(1)(2)(3) # => 6
```

## Partial application

> Is the process of fixing a number of arguments to a function, producing another function of smaller arity.

Partial application takes a function:

```
f: X × Y → R
```

and a fixed value `x` for the first argument to produce a new function

```
f': Y → R
```

`f'` does the same as `f`, but only has to fill in the second parameter which is why its arity is one less than the arity of `f`. One says that the first argument is bound to `x`.

### Example

```python
partialAdd = lambda a: (lambda *args: add(a,*args))
partialAdd(1)(2, 3) # => 6
```

-------------

Your work is to implement a generic `curryPartial()` function allows either currying or partial application.

For example:

```python
curriedAdd = curryPartial(add)
curriedAdd(1)(2)(3) # => 6

partialAdd = curryPartial(add, 1)
partialAdd(2, 3) # => 6
```

We want the function be very flexible.

All these examples should produce the same result:

```python
curryPartial(add)(1)(2)(3) # =>6 
curryPartial(add, 1)(2)(3) # =>6 
curryPartial(add, 1)(2, 3) # =>6 
curryPartial(add, 1, 2)(3) # =>6 
curryPartial(add, 1, 2, 3) # =>6 
curryPartial(add)(1, 2, 3) # =>6 
curryPartial(add)(1, 2)(3) # =>6 
curryPartial(add)()(1, 2, 3) # =>6 
curryPartial(add)()(1)()()(2)(3) # =>6 

curryPartial(add)()(1)()()(2)(3, 4, 5, 6) # =>6 
curryPartial(add, 1)(2, 3, 4, 5) # =>6 
```

And also all of these:

```python
curryPartial(curryPartial(curryPartial(add, 1), 2), 3) # =>6
curryPartial(curryPartial(add, 1, 2), 3) # =>6
curryPartial(curryPartial(add, 1), 2, 3) # =>6
curryPartial(curryPartial(add, 1), 2)(3) # =>6
curryPartial(curryPartial(add, 1)(2), 3) # =>6
curryPartial(curryPartial(curryPartial(add, 1)), 2, 3) # =>6
```

Difficulty: MEDIUM_HARD

Starter code:
def curry_partial(f,*args):
	

Solutions:
class CurryPartial:

	def __init__(self, func, *args):
		self.func = func
		self.args = args

	def __call__(self, *args):
		return CurryPartial(self.func, *self.args + args)

	def __eq__(self, other):
		try:
			return self.func(*self.args) == other
		except TypeError:
			return CurryPartial(self.func, *self.args[:-1]) == other

def curry_partial(f, *initial_args):
	return CurryPartial(f, *initial_args)


def curry_partial(f, *args):
	if not callable(f):
		return f
	try:
		return f(*args)
	except:
		pass
	try:
		return f()
	except:
		pass
	if args:
		return curry_partial(lambda *a: f(args[0], *a), *args[1:])
	else:
		return lambda *a: curry_partial(f, *a)


import inspect

def curry_partial(f, *args):
	if not callable(f):
		return f
	req = list(inspect.signature(f).parameters)
	return f(*args) if req and req[0] == '_e' else f(*args[:len(req)]) if len(req) <= len(args) else lambda *_e: curry_partial(f, *args + _e)


def curry_partial(f, *initial_args):
	if not callable(f):
		return f
	exp_n_args = f.__code__.co_argcount
	given_n_args = len(initial_args)
	if exp_n_args - given_n_args > 0:
		return lambda *args: curry_partial(f, *initial_args + args)
	if exp_n_args == 0:
		return f(*initial_args)
	else:
		return f(*initial_args[:exp_n_args])


def curry_partial(f, *args):
	if not callable(f):
		return f
	if len(args) < f.__code__.co_argcount:
		return lambda *a: curry_partial(f, *args + a)
	return f(*args[:f.__code__.co_argcount or None])


def curry_partial(fn, *x):
	if not callable(fn):
		return fn
	size = fn.__code__.co_argcount or None
	return fn(*x[:size]) if size <= len(x) else lambda *y: curry_partial(fn, *x + y)


def curry_partial(f, *initial_args):

	def f1(*args):

		def f2(*args2):
			if not callable(f):
				return f
			elif f.__code__.co_argcount == 0:
				return f(*args + args2)
			elif f.__code__.co_argcount > len(args + args2):
				return f1(*args + args2)
			else:
				return f(*(args + args2)[0:f.__code__.co_argcount])
		return f2
	return f1(*initial_args)()


from inspect import getfullargspec

def curry_partial(f, *initial_args, arg_spec=None):
	if not arg_spec:
		if not callable(f):
			return f
		arg_spec = getfullargspec(f)
	param_l = len(arg_spec.args)
	if param_l < len(initial_args) + 1:
		if arg_spec.varargs:
			return f(*initial_args)
		else:
			return f(*initial_args[:param_l])
	else:

		def fun(*args):
			return curry_partial(f, *initial_args + args, arg_spec=arg_spec)
		return fun