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welcome back everybody to

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the Anna lecture to

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about types and clash and

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this part we're going to talk about
types of

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functions and since we are dealing with
functional programming

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and functions values Antibes

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are very important and since this

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can be a little bit and difficult for
beginners

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police pay attention to this lecture in
particular biggest

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if you missed this you will have
difficulties

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in all their remaining lecture so and I
will go a little bit slow here

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and repeat many times because this is
super important

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that you understand this part monitor
function

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a function is a mapping from values

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of one type to values of another time
show here too

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very simple examples a function types
the first one

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is the function not ligation which takes
Boolean

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and breeders in Other Boleyn an

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not to nothing to end complicated

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let's look at the second function here
is digit

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is digit takes a character and checks

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writer that character is digit show
whether that character is 0-1

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up to nine the diver that is chargeable
shell

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what that means is it takes a value in
the shower all characters

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and will return a value in this ad of
booleans

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and in general a function from t1 to t2

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is a the shark dive team on a roadie to

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is the type of functions that map values

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from typed the wrong two values for

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dude of type t2 the one ish

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also sometimes called the domain of the
function

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and d2 is sometimes called their range

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the function

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now you noticed that and free rides

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the arrow of the function dive as a nice
arrow

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but when you use the key part and to
type in the actual code

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you will type that as a dash followed by
a greater than sign

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and but we will use it can I search
index here but just you

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be careful this is not you know how you
type in

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actually the arrow when you have a
function

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just like grits the doubles embed lists

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that typed for the range in the domain
are

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unrestricted for example we can ever
function here

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at that takes as the argument a top all

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of two integers and returns as a result
another integer

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so at up X camara y equals x plus why so
you see here that

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at takes it up all to of two integers

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and returns a result that is an integer
and the other French in here

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an is a function that takes and then and
returns a list of integers

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I'm perfectly fine and

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definition their $0.02 an readers the
list

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0 dot dot and we have seen in the very
first lecture

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that this square bracket with the an

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double dots denote the list from zero up
to an

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one thing

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every make the types

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did arguments and result function types

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arbitrary they can be functions
themselves and this is where

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current functions common so instead of
defining at

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to take double-a integers and return
integer

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and has college more common to define at
as follows:

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we define at as a function that takes an
integer

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and readership function that takes
another integer

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and returns an integer so

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look at this type here so at is a
function

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here we see that from this era

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that takes an integer and returns a
function

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that takes another integer and readers
an integer

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said that is curry now

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by itself carrying is not

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very complicated if you need you now
there functions are just

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values like list an integer show there's
nothing special about this

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the thing words becomes confusing is
that

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in Haskell you don't have to ride dish
arrows here

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alright because this is so common and

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the arrow associates to deride

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and which means that you can write this
diverse end

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arrow and arrow and and that's where it
becomes confusing for began

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show you have to really gonna you know
when you read these types know where to

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put the brand

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she's but for now it you now there's
nothing special here

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at is a function that takes an integer
and readers another function that takes

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an integer and then returns an integer
again

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now noticed that both at

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and at prime return the same result

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okay but at takes the

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the normal at stake should %uh polisher
takes both arguments at the same time

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where's at Brian takes the argument

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one by one and arguments that they can

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that punches take their arguments one by
one are called

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current functions an and

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the person that invented

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this an way of dealing with functions
where the functions take the arguments

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one by one

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boss has Kobe curry and Haskell

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is named after him so that's where has
gone from just like Pascal

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and was named after blaise pascal

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Haskell is named after haskell be curry

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and the person that invented carrying of
functions

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every function that takes two arguments:

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can be turned into a function that takes
these arguments one by one

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for example here's a function multi that
takes three

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parameters XY and z. and multiply stem
some old

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XYZ is X time July dime si

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one way to ride this function would be
to take a top all

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three values XY and z. and then
multiplied

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but the Haskell way of doing this is to
take these arguments one by one

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so mold axe readers a function

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that takes another argument why and then

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its readers a function that takes
another argument see

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and then why you have all these three
arguments you can multiply them

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to return that and final and

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okay so moult takes an integer

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readers a function multi axe addiction
and azure why

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that readers a new function mold actual
I that takes into Jersey

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and readers the result XY and z.

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now what we see here is that

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and it died we still ride to Brenda she
showed a brand that she's in the type

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go left to right so function the
function arrow

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binds to the right but

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when we ride here and nafta gonna go
here when we write mold

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XY we don't put branch 3.2 per

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would put a branch there you would ride
mold axe

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Iran's and then branch around that you
there the brand she's

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associate to the left a chauffeur
application

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the parentheses show she ate to the left
for the function arrow

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they are associate to the right and that
matches up perfectly show then

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in practice we don't have to write and
the brand

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now you can ask yourself

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why is this guy really useful okay

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why are we just like in other languages

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why don't we just

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have functions that take a whole list of
parameters are

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like top of parameters to be precise in
one go

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why do we do this complicated thing of
God taking one our game and and then

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returning a function that takes the
other

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parameter et cetera well the reason is

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that we can partially apply a function

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for example if we have this function at
Brian

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that was defined in a curried way we can
define a function that

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incur a man's fill you with Wong by
partially applying

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at crime to wong so if we look at that
type there

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at prime Wong is a function that takes
an integer

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everyday urge another integer when we
will talk about last

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in the future lecture we'll see that
there's many functions

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that transform lists into other lest

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and Moshe dysfunctions are also defined
in the current form

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for example the function take here take
five

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and take is defined as a current
function

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that takes an integer readers a function
from ledge to list

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which may change that we can partially
applied

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take 25 to yield a function

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that takes a list of integers to another
list of integers

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which just takes the first five
Allemands

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of the input list similarly the function
drop

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takes an integer and readers a function
from less two lists

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and what we see here is that we can now
define dropped five

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we can partially applied drop 25 and it
will return a function

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that will take a list dropped the first
five elements

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and then returned should this is super
convenient

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and and an

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its in Haskell it's very lightweight you
disinfection haskell

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is optimized to have carried functions

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and in that respect haskell is very very
different from

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most other languages that are optimized
for functions that take

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to boss a bargain I already mentioned a
couple of times

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the way we do and the breadth rent a
seizure on

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and expressions with function parameters
so the

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arrow associates to the right so if we
have the

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and the their type

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on the bottom day here so the type here
into arrow and

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arrow in Tarrant the brand she's our

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showcase do the ride and says we don't
like to write parentheses

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began ride this thing as indeed arrow in
Tarrant arrow in

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okay but if we put all the practices and
their

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we get the term here at the bottom but
this is what we gonna ride

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and I guess we we don't want a ride

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unnecessary for entities and as I said
all saw

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when we do function application the

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and Brenda sheesh Associated the left

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so when we partially apply a function
you can write Brent this is our on dad

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but we don't have to chill when you
write mold XYZ

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that really means mall tax applied

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to why apply to G okay

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but an unless

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and Angela unless you're using explicit

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the bus all functions haskell are
normally defined

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encourage for an an most languages

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all functions are defined in

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and the encourage for so I'll

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dish the part 2 and about functions
there will be

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a lot of exercises to drill this idea of
you know where to put the brand she's

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in the and function type

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and where to put the brand she's in the
expressions

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00:12:51,580 --> 00:12:56,090
and so this become second nature is this
something you really have to

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gonna keep doing until you don't think
about it then

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alright so an please do your exercises

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and see you later and in the last part

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of Chapter two