foc 0.6.4

A collection of python functions for somebody's sanity

foc

Func-Oriented Code or Francis' Odd Collection.

foc is a non-frilled and seamlessly integrated functional Python tool.

• provides a collection of higher-order functions and placeholder lambda syntax (_)
• provides an easy way to compose functions with symbols. (. and |)

>>> from foc import *

# in standard Python, we normally use, 
>>> sum(map(lambda x: x+1, range(10))) 
55

# 'foc' allows three more things:
>>> cf_(sum, map(_ + 1))(range(10))    # using the 'cf_' compose function
55

>>> (sum . map(_ + 1))(range(10))      # using '.' mathematical symbol (:P)
55

>>> range(10) | map(_ + 1) | sum       # using '|' Unix pipeline style
55

# Scala-style placeholder syntax lambda expression 
>>> (_ + 7)(3)                  # same as (lambda x: x + 7)(3)
10

# (3 + 4) * 6
>>> cf_(_ * 6, _ + 4)(3)        # function.
42                             
                               
>>> 3 | _ + 4 | _ * 6           # pipeline.
42                             
                               
>>> ((_ * 6) . fx(_ + 4))(3)    # dot. Wrap 'lambda expression' in 'fx' when using '.'.
42

Remember that it is only necessary to use fx when using lambda expressions and ..
That's all.

For more examples, see the documentation provided with each function.

>>> (rev . filter(even) . range)(10)  # list(reversed(filter(even, range(10))))
[8, 6, 4, 2, 0]

>>> ((_ * 5) . nth(3) . range)(5)  # range(5)[3] * 5
10

>>> (collect . filter(_ == "f"))("fun-on-functions")  # list(filter(lambda x: x == "f", "fun-on-functions"))
['f', 'f']

# To use built-ins 'list' on the fly, 
>>> (fx(list) . map(abs) . range)(-2, 3)  # list(map(abs, range(-2, 3)))
[2, 1, 0, 1, 2]

>>> range(73, 82) | map(chr) | unchars  # unchars(map(chr, range(73, 82)))
'IJKLMNOPQ'

To see all the functions provided by foc,

>>> from ouch import pp
>>> catalog() | pp

Install

$ pip install -U foc

What is fx?

fx (Function eXtension) is the backbone of foc and provides a new syntax when composing functions.
fx basically maps every function in Python to a monadic function in fx monad.
More precisely, fx is a lift function, but here, I also refer to the functions generated by fx as fx.

1. fx is a composable function using symbols.

There are two ways to compose functions with symbols as shown in the previous section.

Symbol	Description	Evaluation Order	Same as in Haskell
. (dot)	Same as dot(.) mathematical symbol	Right-to-Left	(<=<)
| (pipeline)	In Unix pipeline manner	Left-to-Right	(>=>)
fx	Lift function. Convert functions into monadic forms	-	(pure .)

If you don't like function composition using symbols, use cf_.
In fact, it's the most reliable and safe way to use it for all functions.

2. fx is really easy to make.

fx is just a function decorated by @fx.
Wrap any function in fx when you need function composition on the fly.

>>> [1, 2, 3] | sum | (lambda x: x * 7)    # error, lambda is not a 'fx'
TypeError: unsupported operand ...

>>> [1, 2, 3] | sum | fx(lambda x: x * 7)  # just wrap it in 'fx'.
42

>>> @fx
... def func(arg):    # place @fx above the definition or bind 'g = fx(func)'
...     ...           # 'func' is now 'composable' with symbols

Most of the functions provided by foc are fx functions.
If you don't have one, you can just create one and use it.

3. fx is a curried function.

# currying 'map' -> map(predicate)(iterable)
>>> map(_ * 8)(seq(1,...)) | takel(5)   # seq(1,...) == [1,2,3,..], 'infinite' sequence
[8, 16, 24, 32, 40]                    

# bimap := bimap(f, g, tuple), map over both 'first' and 'second' argument
>>> bimap(_ + 3)(_ * 7)((5, 7))
(8, 49)
>>> foldl(op.sub)(10)(range(1, 5))
0
>>> @fx
... def args(a, b, c, d):
...     return f"{a}-{b}-{c}-{d}"
>>> args(1)(2)(3)(4) == args(1,2)(3,4) == args(1,2,3)(4) == args(1)(2,3,4) == args(1,2,3,4)
True

You can get the curried function of g with fx(g).
But if you want to get a curried function other than fx, use curry(g).

4. Lambdas with _ are fx.

>>> [1, 2, 3] | sum | (_ * 7)    # Use '_' lambda instead.
42
>>> ((_ * 6) . fx(_ + 4))(3)     # (3 + 4) * 6
42
>>> 2 | (_ * 7) | (60 % _) | (_ // 3)   # (60 % (2 * 7)) // 3
1

Partial application driven by _ is also possible when accessing dict, object or iterable, or even calling functions.

Operator	Equivalent Function
_[_]	op.getitem
_[item]	op.itemgetter(item)
_._	getattr
_.attr	op.attrgetter(attr)
_(_)	apply
_(*a, **k)	lambda f: f(*a, **k)

# dict
>>> d = dict(one=1, two=2, three="three")
>>> _[_](d)("two")  # curry(lambda a, b: a[b])(d)("two")
2
>>> _["one"](d)  # (lambda x: x["one"])(d)
1
>>> cf_(_[2:4], _["three"])(d)  # d["three"][2:4]
're'

# iterable
>>> r = range(5)
>>> _[_](r)(3)  # curry(lambda a, b: a[b])(r)(3)
3
>>> _[3](r)     # (lambda x: x[3])(r)
3

# object
>>> o = type('', (), {"one": 1, "two": 2, "three": "three"})()
>>> _._(o)("two")  # curry(lambda a, b: getattr(a, b))(o)("two")
2
>>> _.one(o)  # (lambda x: x.one)(o)
1
>>> o | _.three | _[2:4]  # o.three[2:4]
're'

# function caller 
>>> _(_)(foldl)(op.add)(0)(range(5))
10
>>> _(7 * _)(mapl)(range(1, 10))
[7, 14, 21, 28, 35, 42, 49, 56, 63]

# Not seriously, this creates multiplication table.
>>> [ mapl(f)(range(1, 10)) for f in _(_ * _)(map)(range(1, 10)) ]

Don't forget that foc is a collection, albeit very odd.

Everything in one place.

• fx pure basic functions id, const, take, drop, repeat, replicate..
• higher-order functions like cf_, f_, ob, curry, uncurry, map, filter, zip,..
• useful yet very fundamental like seq, force, trap, error, guard,..

Real-World Example

A causal self-attention of the transformer model based on pytorch can be described as follows.
Some claim that this helps follow the workflow of tensor operation without distraction. (plus, 3-5% speed-up)

    def forward(self, x):
        B, S, E = x.size()  # size_batch, size_block (sequence length), size_embed
        N, H = self.config.num_heads, E // self.config.num_heads  # E == (N * H)

        q, k, v = self.c_attn(x).split(self.config.size_embed, dim=2)
        q = q.view(B, S, N, H).transpose(1, 2)  # (B, N, S, H)
        k = k.view(B, S, N, H).transpose(1, 2)  # (B, N, S, H)
        v = v.view(B, S, N, H).transpose(1, 2)  # (B, N, S, H)

        # Attention(Q, K, V)
        #   = softmax( Q*K^T / sqrt(d_k) ) * V
        #         // q*k^T: (B, N, S, H) x (B, N, H, S) -> (B, N, S, S)
        #   = attention-prob-matrix * V
        #         // prob @ v: (B, N, S, S) x (B, N, S, H) -> (B, N, S, H)
        #   = attention-weighted value (attention score)

        return cf_(
            self.dropout,  # dropout of layer's output
            self.c_proj,  # linear projection
            ob(_.view)(B, S, E),  # (B, S, N, H) -> (B, S, E)
            torch.Tensor.contiguous,  # contiguos in-memory tensor
            ob(_.transpose)(1, 2),  # (B, S, N, H)
            _ @ v,  # (B, N, S, S) x (B, N, S, H) -> (B, N, S, H)
            self.dropout_attn,  # attention dropout
            f_(F.softmax, dim=-1),  # softmax
            ob(_.masked_fill)(mask == 0, float("-inf")),  # no-look-ahead
            _ / math.sqrt(k.size(-1)),  # / sqrt(d_k)
            _ @ k.transpose(-2, -1),  # Q @ K^T -> (B, N, S, S)
        )(q)