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welcome back an I'll be at some fun with
curry and two balls and function types

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about we're going to talk about now is
at

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type clash and polymorphic functions

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an Baltimore for functions

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are functions dead are not defiant

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on concrete types but that are defiant
using type variable

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and here is a.m. a very polymorphic
example of a polymorphic funtion

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the function Lancs so if I want to
calculate

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the length of a list every lead doesn't
matter at all

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what the type of the elements of the
list is

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if I have the list 123 order lists

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it three characters ABC help

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both in both cases the length love this
list three

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so the type of the elements doesn't
matter

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when I want to calculate the length of
the list when we look at the type a

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blank here

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we see it length has type list of a

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arrow and and that a is a type very ball

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has called thats you can see that
biggest

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types start with an uppercase per case

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letter here so n you can see that and is
a concrete die because it started in

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obrigado I and the a here

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the lower case a that's a type variable

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to really but this type says is that

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length has type for all types a

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list a to end an

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and if you're used to Java generics are
c-sharp generics

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and typically the

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type fair ball is declared explicitly

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am and in the type of the function so

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for example in c-sharp you will be fine
length of tea

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and and and would have argument list of
tea

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and return an int but in Haskell this
dick this

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a here is since it's a dive hairball

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its implicitly quantified am so you
don't have to kind

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appointed an angle brackets or anything
again

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and has college optimized for this case
ride

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but the price that you pay is that type
variables start

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lower case and type start with an
uppercase

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K but if we look at this type here lank

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has type for any type A Lancs takes a
list of values of Taipei

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and returns an integer again this is
what you expect

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and it doesn't matter what did I i of
the

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element is of the list your only
interested

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in counting how many there are but
you're not

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interesting interested what these values
actually

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again so that should hear the length of
false true

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then in this case a hedged eyeball

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s2 and here we have a list of

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integers so a would-be in that case ent

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but the land here is for a showboat

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in both cases an we can use a length

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of died for all AAA to end

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and in the first case a is pool and in
the second case

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agent as a set

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the price we pay for not having to
declare

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you know on what type length is
polymorphic

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is that we differentiate the namespaces

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of types and dive verboten ist and has
called

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type variables must begin with a lower
case letter

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and by convention reuse

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ABC and Zach are four types variables

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barriers in languages like Java our C
sharp

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typically we use S&T are

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for type variables capital St nr

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in Haskell its lower case AB and C so

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where in sharp you would write list ft

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in as call you dried list Ave

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okay here are an

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a number of polymorphic functions from
the Haskell standard prelude to the

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stand the prelude is dick and Haskell
SDK or the Haskell BC I L

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and a standard library like every
language comes with the standard library

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and and the types of these functions

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reveal why the law about their
implementation show for example let's

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look at the first one

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first takes ate up all of

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a NB and returns a value of type A

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but can destruction do I'll

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it think should %uh Paul a and it
returns a value of type A

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so really it's quite obvious from that
type

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that what this function does is it gonna
readers the first

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and element of the double now let's look
at the type of hat

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had to take a less to pay for any type A

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and readers and a in this case

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you have more choice right because you
know I given a list of Taipei

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if I have to return a value of type A I
can pick

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Andy value in that last and had to get
you the first one

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now one of the interesting things here's
what happens

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when a.m. you give head to the empty
list

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in that case this function will return

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undefined are well-drawn exception an

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so that is not given in this types are
the types said

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for all lists you now of Taipei

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and will return a value of type A an

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but that's not really true because when
I gave it the empty list

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it will fail and not really give me

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value third example here take

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takes an integer and readership function

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that takes a list and returns a list
remember

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when we have a dive with arrows the

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parentheses show she to the right to
take

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is if we put in the brand she's would be
end arrow

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brent is %eh lester a to a

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take takes number and

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last takes the first and elements have
the less and returns that

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not an extra engineers ship

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is each Nystrom and it takes two lists

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and and readers a list of bears

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and the way it works is dead it takes to
do less and

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takes each element these delicious and
combines them

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into a double now I think

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dive ship looks a little bit nicer

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when you don't write that encourage form
so when you would ride it i blessed

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an isn't %uh Paul's it would have died

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couple a blessed a endless to be

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to list of double and a comedy show
there you can really see in the type

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that and sip an

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in our tourists to Leicester Oct and
then the loss function here

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an that's perhaps the simplest function
you can imagine has college the identity

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function

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it takes at value of Taipei and breeders
valuable time

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died a for any a a man if you think a
little bit about that

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the only thing this function can do is
you know just return its value because

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otherwise

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it will be hard to work on Anne

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Taipei okay so an

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the identity goes from

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ole a2a jodie

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only thing really that it can do is it
can take the argument

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and immediately returned if you're
interested

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in in this thing where you know you look
at the type and then you get the

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property

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about the implementation you she should
read

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bill Watters paper teams for free and

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and yard that paper will explain that
all

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everybody more for dive gives you a tear
and that holds

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and for that function and

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but again that's a little bit advance so

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you can read that if you want there will
be a link to the paper

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00:08:36,490 --> 00:08:40,560
on the core structure the Las topic

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ever going to do and in the context
functions

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are overloaded functions

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we all know overloaded function most
languages support them

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for example in Java you can overlords

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function with different parameter type
so

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a.m. I can define a function food
addiction and

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and then I can have an overloaded takes
a ball and then I can I have a number

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another overloaded take Celeste and the
name

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00:09:11,800 --> 00:09:15,930
up that function is to shame but the
types of the parameters

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is different and Haskell overloaded is

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00:09:20,990 --> 00:09:24,400
you done in a slightly different form
and

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it corresponds more to the notion of
interfaces

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in object-oriented languages joined
Haskell

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when you overloaded function is really
mean

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me means not overloading in the
object-oriented sans

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it really mean stager restricting

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the die did the

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types of the parameters so in this case
when I want to see some

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00:09:51,060 --> 00:09:55,420
the elements on the list and I cannot
say

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that type some hedge type lester a2a

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because wat by and

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have alleged characters I cannot

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00:10:06,320 --> 00:10:12,460
at characters together and maybe you can
say all I can define threat characters

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but thats a tan

165
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that we have a list of tuples well

166
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in that case some on the list of top
also of Taipei gonna be

167
00:10:21,620 --> 00:10:26,240
doesn't really return a double up a
committee that doesn't make sense

168
00:10:26,240 --> 00:10:29,870
so what we want to do is you want to
restricted type

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the elements in the list such that they
can be some

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and that is what has school overloading

171
00:10:36,720 --> 00:10:40,380
issues so what you see here in this type
some as type

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numb a double arrow

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00:10:43,620 --> 00:10:47,960
list a to a so what this means

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is that some doesn't take

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alleged values have to pay for any a

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but only values of Taipei

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that

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are in this numb Kalash

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00:11:01,680 --> 00:11:04,730
or N if you think about

180
00:11:04,730 --> 00:11:08,999
and object orientation it only takes a
list of

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00:11:08,999 --> 00:11:12,290
value of type A that implemented in
phnom

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interface okay so I you see this
notation here numb

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a arrow double arrow got roughly

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if your job I receive sharp or PHP
programmer

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ya at CBS plus programmer think of this

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as you know restricting the values are

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on which this can work job you have the
same thing if you have a

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00:11:36,339 --> 00:11:39,379
generic function you can restrict

189
00:11:39,379 --> 00:11:42,540
the values by requiring

190
00:11:42,540 --> 00:11:46,819
that the types implement the shirt and
interface in c-sharp you can do the same

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00:11:46,819 --> 00:11:48,300
thing in

192
00:11:48,300 --> 00:11:52,160
you can most languages allowed as and
has got no

193
00:11:52,160 --> 00:11:56,569
exception alright SoCon takes a list

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and readers it into a value but they can

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only do that when values in the list

196
00:12:03,189 --> 00:12:06,509
support numb class Gordon um interface

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00:12:06,509 --> 00:12:10,939
okay

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00:12:10,939 --> 00:12:14,100
so in this case we can do chum of
integers

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00:12:14,100 --> 00:12:18,069
then in that case agent and we know

200
00:12:18,069 --> 00:12:21,639
that integers and our number so

201
00:12:21,639 --> 00:12:25,689
that's fine we will see what this number
lies in a tournament like basically says

202
00:12:25,689 --> 00:12:28,439
that you can do addition and
multiplication and so on

203
00:12:28,439 --> 00:12:32,860
second one here is a unless the
floating-point numbers

204
00:12:32,860 --> 00:12:36,889
I can sum them as well but here

205
00:12:36,889 --> 00:12:40,079
we get it I para de las 10 year we get
it i pair

206
00:12:40,079 --> 00:12:43,759
because here we have a list of
characters and

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00:12:43,759 --> 00:12:47,300
characters don't support dunno interface

208
00:12:47,300 --> 00:12:51,410
our game show characters are not an
instanceof the number loss

209
00:12:51,410 --> 00:12:55,699
and Haskell speak and has clashed

210
00:12:55,699 --> 00:13:00,379
the b-sides nominee several type classes
you can define your own type classes we

211
00:13:00,379 --> 00:13:02,269
will see how to do that later

212
00:13:02,269 --> 00:13:04,160
and in this case

213
00:13:04,160 --> 00:13:07,860
the numb class says that you have

214
00:13:07,860 --> 00:13:11,029
addition K what that means is that

215
00:13:11,029 --> 00:13:14,460
the type of addition takes

216
00:13:14,460 --> 00:13:18,790
value of type A readers a function that
takes another value

217
00:13:18,790 --> 00:13:21,910
Taipei and then burned returns a value
of type A

218
00:13:21,910 --> 00:13:26,290
but it's not only for that's not for all
values of k

219
00:13:26,290 --> 00:13:29,589
only values in the number clash
similarly

220
00:13:29,589 --> 00:13:32,820
when you want to compared to values for
equality

221
00:13:32,820 --> 00:13:37,080
they have to be in the EQ class showing
here you see

222
00:13:37,080 --> 00:13:40,310
that the equality operator as type

223
00:13:40,310 --> 00:13:43,820
EQ okay double arrow a arrow

224
00:13:43,820 --> 00:13:46,890
a arable and finally

225
00:13:46,890 --> 00:13:50,510
there's the type of values that you can
compare

226
00:13:50,510 --> 00:13:54,660
so the order types and their less than
has type

227
00:13:54,660 --> 00:13:57,959
or no pay arrow a RA arable

228
00:13:57,959 --> 00:14:01,940
okay so here are some

229
00:14:01,940 --> 00:14:05,510
exercises the exercises and you

230
00:14:05,510 --> 00:14:09,800
you will do an on the website so I wont
give you

231
00:14:09,800 --> 00:14:12,880
and the answers right now but their

232
00:14:12,880 --> 00:14:17,400
actual sizes will be on the website but
I'll walk you through this exercise

233
00:14:17,400 --> 00:14:22,529
an out to get you familiar showed the
question is like one ish the type

234
00:14:22,529 --> 00:14:28,070
of an the value of their lists

235
00:14:28,070 --> 00:14:31,100
it three characters AB and C

236
00:14:31,100 --> 00:14:34,480
and so on and so on show and

237
00:14:34,480 --> 00:14:38,459
please doing these exercises biggest day
well I make sure

238
00:14:38,459 --> 00:14:42,180
that you understand the idea of types
that we

239
00:14:42,180 --> 00:14:45,310
an explained in this lecture

240
00:14:45,310 --> 00:14:49,190
and many are a couple of more

241
00:14:49,190 --> 00:14:52,529
in complicated exercises an

242
00:14:52,529 --> 00:14:56,380
where you don't get a value and you have
to compute the type

243
00:14:56,380 --> 00:14:59,410
but you get a function and now you have
to

244
00:14:59,410 --> 00:15:03,640
a computer died function I'm and the
trick here

245
00:15:03,640 --> 00:15:07,320
and this is a.m. and well I'm going to

246
00:15:07,320 --> 00:15:10,329
you know the secret I'm going to reveal
to you

247
00:15:10,329 --> 00:15:13,100
is that you can use GHz

248
00:15:13,100 --> 00:15:17,380
to check your answers show you're doing
the exercises don't go I got

249
00:15:17,380 --> 00:15:20,420
try them out randomly let you do it

250
00:15:20,420 --> 00:15:23,800
open up GATT and used a go long time

251
00:15:23,800 --> 00:15:27,470
and functionality to do these exercises

252
00:15:27,470 --> 00:15:30,480
okay so you you you are

253
00:15:30,480 --> 00:15:34,750
sure that you can score a hundred
percent on every one of them

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00:15:34,750 --> 00:15:39,150
so thank you and happy hacking so use GC

255
00:15:39,150 --> 00:15:43,990
to do your exercises and and if you
don't use haskell

256
00:15:43,990 --> 00:15:48,340
and but another language make sure that
you're also using

257
00:15:48,340 --> 00:15:51,840
your compiler to check your tight okay

258
00:15:51,840 --> 00:15:55,600
because we as humans should not do this
type checking

259
00:15:55,600 --> 00:15:58,740
that's why we have computers to do that
for us

260
00:15:58,740 --> 00:16:01,230
thank you very much and see you next
week