Lens : Smart setter for immutable data

A implementation of lens library in Perl

Transcript

1. 2014೥8݄29೔
   Lens : Smart setter for immutable data
   hiratara @ FreakOut
   

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2. immutable data
   package Talk;
   use Moo;
   has speaker => (
   is => ’ro’, requires => 1
   );
   has name => (
   is => ’ro’, requires => 1
   );
   

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3. Nested immutable data
   getter works well
   $schedule->talk->speaker->name;
   

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4. Nested immutable data
   setter won’t work well
   # Can’t write it
   $new_schedule =
   $schedule->talk->speaker
   ->name("hiratara");
   

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5. Nested immutable data
   Must copy and copy and copy ...
   $new_speaker = Speaker->new(
   name => "hiratara",
   age => $speaker->age,
   mail => $speaker->age,
   );
   $new_talk = Talk->new(
   title => $talk->title,
   speaker => $new_speaker,
   );
   $new_schedule = Schedule->new(
   talk => $new_talk,
   kind => $schedule->kind,
   );
   

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6. Ugly way to solve it
   Though, I hate mutable data.
   package Talk;
   use Moo;
   has speaker => (
   is => ’rw’, requires => 1
   );
   has name => (
   is => ’rw’, requires => 1
   );
   

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7. Ugly way to solve it
   

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8. Another way : use Lens
   Lens acts like an accessor
   # getter (will get ’hiratara’)
   (talk . speaker . name)->($schedule);
   # setter
   $new_schedule =
   (talk . speaker . name)->($schedule, ’hiratara’);
   

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9. What is Lens?
   • A library of Haskell
   • https://github.com/ekmett/lens/
   

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10. Let’s implement Lens
    Lens is “costate comonad coalgebra”. We
    have only to implement it.
    

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11. Let’s implement Lens
    Lens is “costate comonad coalgebra”. We
    have only to implement it.
    

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12. Category theory
    Send e-mail to hira.tara+kenron@gmail.com if
    you want to buy this
    

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13. What is co-
    co- means opposite or dual.
    

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14. This is monad
    M
    ηM //
    D
    D
    D
    D
    D
    D
    D
    D
    D
    D
    D
    D
    D
    D
    D
    D MM
    µ
    
    M
    Mη
    oo
    zzzzzzzz
    zzzzzzzz
    M
    MMM
    Mµ //
    µM
    
    MM
    µ
    
    MM
    µ
    // M
    

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15. comonad is a dual of monad
    W WW
    ϵW
    oo Wϵ // W
    W
    EEEEEEEE
    EEEEEEEE δ
    OO y
    y
    y
    y
    y
    y
    y
    y
    y
    y
    y
    y
    y
    y
    y
    y
    WWW WW
    Wδ
    oo
    WW
    δW
    OO
    W
    δ
    oo
    δ
    OO
    

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16. comonad in Perl
    package Comonad;
    sub counit;
    sub coflatten;
    sub map;
    sub coflat_map;
    

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17. The type of state monad
    (A × S)S
    

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18. The type of state monad
    (A × S)S ≃ (−S ◦ (− × S))(A)
    

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19. costate comonad
    The dual of state monad
    AS × S ≃ ((− × S) ◦ −S)(A)
    

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20. costate comonad in Perl
    package Comonad::Costate;
    use Moo;
    extends ’Comonad’;
    has func => (is => ’ro’);
    has state => (is => ’ro’);
    sub counit my $self = shift; $self->func
    

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21. costate comonad in Perl
    sub map {
    my ($self, $f) = @_;
    (ref $self)->new(
    func => _comp($f, $self->func),
    state => $self->state,
    );
    }
    

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22. costate comonad in Perl
    sub coflatten {
    my $self = shift;
    my $class = ref $self;
    my $self_func = $self->func;
    $class->new(
    func => sub {
    my $state = shift;
    $class->new(
    func => $self_func,
    state => $state,
    );
    },
    state => $self->state,
    );
    }
    

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23. algebra of monad M
    MMX Mh //
    µX
    
    MX
    h
    
    MX h // X
    X
    ηX //
    C
    C
    C
    C
    C
    C
    C
    C
    C
    C
    C
    C
    C
    C
    C
    C MX
    h
    
    X
    

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24. coalgebra of comonad W
    WWX WX
    Wh
    oo
    WX
    δX
    OO
    X
    h
    oo
    h
    OO X
    C
    C
    C
    C
    C
    C
    C
    C
    C
    C
    C
    C
    C
    C
    C
    C WX
    ϵX
    oo
    X
    h
    OO
    

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25. costate comonad coalgebra in Perl
    coalgebra => sub {
    my $data = shift;
    Comonad::Costate->new(
    func => sub {
    my $value = shift;
    (ref $data)->new(
    %$data,
    $field => $value,
    )
    },
    state => $data->$field,
    );
    },
    

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26. costate comonad coalgebra
    costate comonad coalgebra is the
    combination of setter and getter. This is Lens.
    A → (AS × S) ≃ (A → AS) × (A → S)
    • A → AS is setter
    • A → S is getter
    

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27. composition of Lenses
    package Lens;
    use overload (
    ’.’ => ’chain’, fallback => 1,
    );
    sub chain {
    my ($self, $other) = @_;
    Lens->new(
    coalgebra => sub {
    ...
    },
    );
    }
    

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28. Field lens
    sub lens ($) {
    my $field = shift;
    Lens->new(
    coalgebra => sub {
    my $data = shift;
    Comonad::Costate->new(
    func => sub {
    my $v = shift;
    (ref $data)->new(%$data, $field => $v)
    },
    state => $data->$field,
    );
    }
    );
    }
    

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29. Lens is more powerful
    $schedule =
    (talk . speaker . name)->($schedule, ’hiratara’);
    # Setter and Getter of a part of string
    $schedule =
    (talk . speaker . name . substr_lens(3, 2))
    ->($schedule, ’@’);
    # $schedule->talk->speaker->name will be "hir@ara"
    

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30. CONCLUSION
    • Lens is a good setter for immutable data
    • https://github.com/hiratara/p5-Lens
    To tell the truth, haskell’s lens implementation
    has the type:
    Let (−(V))V, −(S): SetSet → Set be functors
    (−(V))V ⇒ −(S)
    

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