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Tuesday, January 29, 2013. On safety and abstraction. Haskell does not have full-fledged dependent types. For example, there is no way to create naturals as a subset of integers. One way to sidestep this restriction is creating an abstract datatype. Define. Newtype Natural = N Integer. And add a collection of methods (addition, printing etc.). Clients can interact with this type only via these methods. They cannot construct a pathological value such as. Data Natural = Zero Succ Natural. The same thing ha...

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monoidal | monoidal.blogspot.com Reviews

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Tuesday, January 29, 2013. On safety and abstraction. Haskell does not have full-fledged dependent types. For example, there is no way to create naturals as a subset of integers. One way to sidestep this restriction is creating an abstract datatype. Define. Newtype Natural = N Integer. And add a collection of methods (addition, printing etc.). Clients can interact with this type only via these methods. They cannot construct a pathological value such as. Data Natural = Zero Succ Natural. The same thing ha...

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6 quotients

7 is equivalent to

8 since aa

9 what about rationals

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monoidal | monoidal.blogspot.com Reviews

https://monoidal.blogspot.com

Tuesday, January 29, 2013. On safety and abstraction. Haskell does not have full-fledged dependent types. For example, there is no way to create naturals as a subset of integers. One way to sidestep this restriction is creating an abstract datatype. Define. Newtype Natural = N Integer. And add a collection of methods (addition, printing etc.). Clients can interact with this type only via these methods. They cannot construct a pathological value such as. Data Natural = Zero Succ Natural. The same thing ha...

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monoidal.blogspot.com

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monoidal: September 2010

http://monoidal.blogspot.com/2010_09_01_archive.html

Wednesday, September 1, 2010. Consider the following two functions:. F : () - (). F = const (). G : () - (). Is there a way to write a function that tells them apart? Given an infinite loop, first will stop and the second will hang. But you can do better, give an exception and check if it was thrown:. Data TestException = TestException deriving (Show, Typeable). Test : - () - Bool. Test k = unsafePerformIO $ catch (k (throw TestException) `seq` return True). TestException - return False). Throw A throw B.

2

monoidal: May 2010

http://monoidal.blogspot.com/2010_05_01_archive.html

Tuesday, May 4, 2010. You're given diagrams of some Haskell types ordered by semantic order. Vertices are inhabitants of a datatype, and the lines point upwards, from less defined to more defined. (See Wikibooks. For an introduction and examples.) Your objective is to construct a type corresponding to the diagram, or show that is impossible. I've done the first one - it is obviously Bool. Good luck! Data Three = X Y Z. Data Four = A B C D. Data T = P Q Three R Four. Data NaturalsUp = S NaturalsUp. Create...

3

monoidal: July 2010

http://monoidal.blogspot.com/2010_07_01_archive.html

Thursday, July 29, 2010. Take (or imagine) a blank sheet of paper. This is a plane. You can put points and vectors on it. A vector connects two points, but it is "movable": if you can translate one vector into another, they are deemed equal. A vector doesn't really have a beginning - you can position it wherever you want. In this setting, some operations make sense, like. Vector point = point:. Position the vector at a point, and its end will be the result. Point - point = vector:. Vector vector = vector:.

4

monoidal: August 2009

http://monoidal.blogspot.com/2009_08_01_archive.html

Saturday, August 22, 2009. Some thoughts and exercises on folding. I assume you know what are foldl and foldr and have basic experience with them - you know how to express functions like sum, maximum using these folds. Here. Are some very nice diagrams showing fold and related functions. Compose : [a - a] - a - a. Compose [f1, f2, ., fn] = f1 . f2 . . . fn. Solution at the end. Aut = foldl ( state a - state & (a = 'x' a = 'y') True. But in general the behaviour can be quite complex. Convert : (a - b - [a...

5

monoidal: Kind polymorphism in action

http://monoidal.blogspot.com/2010/07/kind-polymorphism-in-action.html

Monday, July 26, 2010. Kind polymorphism in action. Is an experimental Haskell compiler that supports polymorphism on the kind level. This means that in. Data Eq a b = Eq (forall f. f a - f b). Eq is given kind. Eq : forall a . a - a - *. And both Eq Integer Char and Eq [] Maybe are valid types. Using kind polymorphism, it is possible to write sigfpe's From monoids to monads. Using a single type class. To talk about monoids, you need a category (mor), multiplication (mul) and a unit. One : mor unit m.

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monoidal.blogspot.com

monoidal

Tuesday, January 29, 2013. On safety and abstraction. Haskell does not have full-fledged dependent types. For example, there is no way to create naturals as a subset of integers. One way to sidestep this restriction is creating an abstract datatype. Define. Newtype Natural = N Integer. And add a collection of methods (addition, printing etc.). Clients can interact with this type only via these methods. They cannot construct a pathological value such as. Data Natural = Zero Succ Natural. The same thing ha...

monoidal.net

Benoît Valiron, Assistant Professor

Benoît Valiron, Assistant Professor. I have a full-time position of assistant professor at CentraleSupélec. Researchwise, I am member of the team MODHEL. I have two addresses (and two offices):. Dept Informatique, Bât Bréguet. 91190 Gif sur Yvette. Benoit (dot) valiron (at) centralesupelec (dot) fr. Laboratoire de Recherche en Informatique ( LRI. 13 (Bât. 650 - PCRI). Benoit (dot) valiron (at) lri (dot) fr. You can contact me through this domain name, using:. Benoit (dot) valiron (at) monoidal (dot) net.

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