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welcome back to the lectures on
higher-order functions

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and we just looked at the

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mother of all higher are the functions
over lists for our

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an and we will and this section

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read a few other standard a higher-order
functions that are available

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and the Haskell library and

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one of the those functions is function
composition and function composition is

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another fundamental operation

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in functional programming an functional
programming as programming with

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functions

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and if we have functions we want to
gonna

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combined two functions into another
function

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just like addition takes two numbers and
give this a new number

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we want to have a similar operator that
takes two functions

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and combines them into a new French well

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here's the and definition of that
operator

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and it's written as dot and that's cool
so unlike

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object-oriented programming where dot
means invoking the method

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and has called dot means composing to
function show

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in both cases the dot is used for the
most

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fundamental operation on there gonna be
a object

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that the language support an
object-oriented language

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bf objects and we can call methods on
them and Haskell

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we have functions that we can combo am

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and here's the type and function
composition dot

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takes a function from BTC there's the
function for b2c

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and it takes a function from a to be and
that readers a function from

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a2c now when you look at this

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type it can be a little bit confusing

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biggest there's a bee here as the output

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and the bee is here as the input cell
it's gonna be a

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seems to be that things are in the wrong
order but debt has

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everything to do with the fact that

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function application shosh age so here's
a definition

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of composition so what we do is read

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two functions and then

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we first applied G to axe

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and then reapply after to the result

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case allege now see

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if those types make sense to us an

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the title that here

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is a function from B to C the typeof

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G is a function from a to be well

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then in that case X must be a value of
type A

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so if we apply G to at

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to axe we have we are blind dysfunction
addiction a.m. 20 NB

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so the result of applying G two axes be

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hi and that fits into here and we get to
see

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show to get the

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return type here you get the value of
type A

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and we return a value of type C

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alright so at first I thought might look
a little bit confusing

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but once we figure it out and got you
know we used in fact that

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function application here shosh age to
deride

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everything's Folge falls into place I'm

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and here's an example %uh using function
composition

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suppose we want to define the function
alt that

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checks whether a an integer is art well

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alt is defined as not even

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well there we go definition it's at

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first check whether g++ even and then an

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inverter result and this definition here

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this is what people often call point
freestyle

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biggest the other way we could ride at
a.m.

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alt would be love blacks even %uh axe

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not of that but now we have a long time
brent is she said that's got kind of a

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little bit for books

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and a lot of functional programmers
preferred to you should function

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composition

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to remove all the lawn that's and the
brain disease but I have to warn you

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and and I'm I'm guilty of this too

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when you just start using function
applique a French

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in you're trying to use it everywhere
and it becomes a sport

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to write things in point freestyle ride
them very compactly

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an the price you pay said becomes very
hard to reach and now the people that

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Reacher code

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have to do all this function composition

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in order to understand what's going on
and typically

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when they understand what's going on the
light bulb goes on it

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okay but I think it's bad either to
gonna Lu's

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function composition sparingly an

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because you always have to write code
for others to read

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okay so you don't write code to look
cool yourself and see all ok I can do

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this point freestyle

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am plus there's our domestic programs
that make things point free for you show

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your not as cool as you think

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okay so use function composition
sparingly

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and don't go bananas wit function
composition

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okay

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here are a couple of a other functions

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and that are in the standard library
higher-order functions

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am these are most of them are defined

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and using and for the are using

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and comprehension these are all
interchangeably

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and I prefer using fold our

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and some people a briefer an

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this comprehension ce at the reason I
prefer for the car is dead

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for are and this concept of folding over
and

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a datatype works for any recursive data
type

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birch list comprehension am only work
for less

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an we can use general branches but it
gets all a bit tedious

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so I at some point it's just easier to

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define default function and and the fine

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and other functions on top of that all
right sir

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but let's just look at this wrong here
all is defined

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as and map

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be a VAX to the list access

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and then and Jack rather every one of
those is true

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measure a nicer definition of dish would
be

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map of P combos and any

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is the same thing remapped be a fax I P

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over the list access and then we call

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or so for example if you want to check
that

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this string here ABC space deef

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days in space you can call any Espace

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function from character to bull and this
will return true

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here's another interesting function

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take while take while takes a predicate

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and unlike filter rich goes through the
whole list and throws away all the

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elements

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for rates abroad again does not halt
take while

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is like a while loop so it goes uses
predicate

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and chop shop elements from this list
and returning them

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until this predicate this fall so let's
look at the definition

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if the list is empty well what can we do
we can only return the empty list

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in case you be have a non-empty lest

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it looks like this ex-cons excess

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and now we have two cases either

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the affects does not halt ever that case
we

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and terminates the recursion by
returning the anti lest

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and ft up if the attacks is true

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there's a trap door here and in the
stadia

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take while not fault through the

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all an FB have access through

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then we Goldman Sachs onto the recursive
call

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of P take while be affects so for
example

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began they have a string and we can take

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and characters from the string as long
as they are

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letters by the intake while is all fun
and then

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it will take ABC and since this space is
not

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and an often America character as well
terminated

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right there do I need to take while

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we have the function dropped while that
removes all the elements

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while a predicate holes show take while

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keeps all the elements until the
predicate is false

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drop while drops the element and

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until the predicate at turns falls

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so you see here that an in this case it
drops the value

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and and said every during the ante LIJ
there it just got

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yeah which the the valley on top of the
rest

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good happy hacking

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and make sure you do the exercises
because

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all the higher branches that we have
seen here like take wild ride while map

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filter

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and you will have to implement them in
terms of old R

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a ride and so please make these
exercises

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and if you're not using haskell an say
you're using Scala our job on

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you can do the same thing these
languages typically

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also have fold our and maybe it's not
called for

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are sometimes is called fourth ride or
sometimes just called fault

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but this idea of having a higher r2
function

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that captures the ass and shove rick
urging over lest

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is available and and the library

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an that that supports lists

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and for example in c-sharp it's not even
cold fold our

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it's cold San aggregate

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so that comes from Chico lawyer
aggregating over list

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so don't be fooled by the name and the
idea is what matters

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and thank you so much and see you next
week