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Most Recent Entries] [Calendar View]. Below are the 20. Most recent journal entries recorded in r6research. Wednesday, December 30th, 2015. From Van Laarhoven Isomorphisms in one shot. Forall; f, g : Functor. (g a → f b) → g s → f t. Is isomorphic to the type. S → a)×(b → t). The Van Laarhoven representation of isomorphisms uses this representation of a pair of function to capture the notion of an isomorphism. Given a value of type. Forall; f, g : Functor. (g a → f b) → g s → f t. What if I told you that.

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Most Recent Entries] [Calendar View]. Below are the 20. Most recent journal entries recorded in r6research. Wednesday, December 30th, 2015. From Van Laarhoven Isomorphisms in one shot. Forall; f, g : Functor. (g a → f b) → g s → f t. Is isomorphic to the type. S → a)×(b → t). The Van Laarhoven representation of isomorphisms uses this representation of a pair of function to capture the notion of an isomorphism. Given a value of type. Forall; f, g : Functor. (g a → f b) → g s → f t. What if I told you that.

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https://r6research.livejournal.com

Most Recent Entries] [Calendar View]. Below are the 20. Most recent journal entries recorded in r6research. Wednesday, December 30th, 2015. From Van Laarhoven Isomorphisms in one shot. Forall; f, g : Functor. (g a → f b) → g s → f t. Is isomorphic to the type. S → a)×(b → t). The Van Laarhoven representation of isomorphisms uses this representation of a pair of function to capture the notion of an isomorphism. Given a value of type. Forall; f, g : Functor. (g a → f b) → g s → f t. What if I told you that.

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A new case for the pointed functor class: r6research

http://r6research.livejournal.com/28338.html

A new case for the pointed functor class. There has been some debate for some time as to whether there should be a superclass for. Natural law: - fmap f . pure = pure . f class Functor f = Pointed f where pure : a - f a. The charge laid against this class is that there are no laws for this single function beyond the single law that is naturally implied. Compare this to a more reasonable class. What if I told you that. Are in fact the same class? Theorem 1. If we define. Theorem 2. If we define. Fmap (id ...

2

Prisms!: r6research

http://r6research.livejournal.com/27071.html

Shachaf taught me prisms today! Here is what I learned. A prism is dual to the notion of lens. A lens lets you access a field of a record by letting you get and set its value. A prism lets you access a component of a sum by letting you beget and match the component. Lenses are composable, letting you access fields inside deeply nested records. Prisms are composable, letting you access components of deep hierarchy of sums. Type is an abstract representation of. Exist;c. a b×c. Exist;c. a b c. I am not yet...

3

A Representation Theorem for Second-Order Pro-functionals: r6research

http://r6research.livejournal.com/27858.html

A Representation Theorem for Second-Order Pro-functionals. LANGUAGE RankNTypes, TupleSections #-}. The title of this post does not actually make sense; it is a joke based on the title of a recently published paper of Jaskelioff and myself. Here I will show that the same deduction found in that paper can be applied to the profunctor representation of lenses and other optics. This came out of some recent discussions I had with Bartosz Milewski. As usual, by two applications of Yoneda we have. The case for ...

4

Grate: A new kind of Optic: r6research

http://r6research.livejournal.com/28050.html

Grate: A new kind of Optic. James Deikun (known as xplat on freenode) and I discovered a new kind of Optic today. If not discovered, then at least characterized it. We know that lenses correspond to optics over strong profunctors, and prisms correspond to optics over choice profuctors. The open question was, what corresponds to optics over closed profuctors? Forall; P:Closed. P a b - P s t. From the last post. We saw that this is isomorphic to the free closed profunctor generated by. We can modify the.

5

Lenses Are Exactly the Coalgebras for the Store Comonad: r6research

http://r6research.livejournal.com/23705.html

Lenses Are Exactly the Coalgebras for the Store Comonad. The store comonad (better known as the costate comonad) can be defined as. Data Store b a = Store (b - a) b. With the following comonadic operations. Given this we can define a lens (aka a functional reference) as follows. Type Lens a b = a - Store b a. A lens can be used as an accessor to a field of a record, though they have many uses beyond this. Above we create a lens to access the name field of this. However, we expect the. Extract . l = id.

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r6research's Journal

Most Recent Entries] [Calendar View]. Below are the 20. Most recent journal entries recorded in r6research. Wednesday, December 30th, 2015. From Van Laarhoven Isomorphisms in one shot. Forall; f, g : Functor. (g a → f b) → g s → f t. Is isomorphic to the type. S → a)×(b → t). The Van Laarhoven representation of isomorphisms uses this representation of a pair of function to capture the notion of an isomorphism. Given a value of type. Forall; f, g : Functor. (g a → f b) → g s → f t. What if I told you that.

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