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From: john skaller <skaller@us...>  20110510 10:41:43

On 10/05/2011, at 7:45 PM, Rhythmic Fistman wrote: > > Ok, cool. So when I'm implementing such a thing in c++, what the hell > do I call the class? Or classes, because I often derive these things > from an abstract base class. I can't bring myself to call them > "factories", but now I've got more creators than genesis. You must > have some insight into this because you generate this stuff. God is the creator, e has many names you can choose from :)  john skaller skaller@... 
From: Rhythmic Fistman <rfistman@gm...>  20110510 09:45:58

On 8 May 2011 17:55, john skaller <skaller@...> wrote: > > On 08/05/2011, at 10:31 PM, Rhythmic Fistman wrote: > >> You take a function f:a>b and wrap a up to get a new function with no >> arguments, like this: >> >> g:1>b? > > It's a closure, or a specialisation, or perhaps even a projection. > > Basically you're taking some domain a and a function > > k: c > a > > and composing them: > > g (x) = f ( k (x) ) > > or just > > g = f . k (in forward notation) > > In your case you picked > > k: 1 > a > > so the composition is g: 1 > b Ok, cool. So when I'm implementing such a thing in c++, what the hell do I call the class? Or classes, because I often derive these things from an abstract base class. I can't bring myself to call them "factories", but now I've got more creators than genesis. You must have some insight into this because you generate this stuff. class thing_that_returns_b : public things_that_return_b { a A; private: // pure virtual in things_that_return_b virtual b g() { // use a to create a b } }; > >> >> Is that 1 standard notation? > > In category theory, yes. 1 is "unit", a canonical type with 1 value. > In Felix that value is (), the empty tuple. In set theory, any set > > {x} > > is a unit (singleton). Note this is not the same as 0, aka void, > the type with NO values, or the empty set. In practice I don't see the difference. () seems like no values to me. 
From: john skaller <skaller@us...>  20110508 15:56:31

On 08/05/2011, at 10:31 PM, Rhythmic Fistman wrote: > You take a function f:a>b and wrap a up to get a new function with no > arguments, like this: > > g:1>b? It's a closure, or a specialisation, or perhaps even a projection. Basically you're taking some domain a and a function k: c > a and composing them: g (x) = f ( k (x) ) or just g = f . k (in forward notation) In your case you picked k: 1 > a so the composition is g: 1 > b > > Is that 1 standard notation? In category theory, yes. 1 is "unit", a canonical type with 1 value. In Felix that value is (), the empty tuple. In set theory, any set {x} is a unit (singleton). Note this is not the same as 0, aka void, the type with NO values, or the empty set. A function f: 1 > A is sometime called an "constant function" because it picks out a single element from A. For example: twenty: 1 > Z given by twenty () = 20 A function v: 0 > A is sometimes called the characteristic function of A, since it is THE unique function from the empty set to A. > I picked it up from Felix. In Felix, 0,1,2,3,4 .. etc are sums of n units eg 2 = 1 + 1 aka "bool", a type with two values. Unfortunately + is not associative: the type 2 + 1 is not equal to 3 (although they're isomorphic). Similarly tuple formation * isn't associative: (1,(2,3)) != (1,2,3) != ((1,2),3) BTW the names of values of a unit sum in Felix are like case 0 of 2 (aka "false") case 1 of 2 (aka "true") You can find these definitions in the library. Note case numbers are unfortunately zero origin, there's no case 2 of 2 even though that reads better ;( For symmetry with C arrays.  john skaller skaller@... 
From: Rhythmic Fistman <rfistman@gm...>  20110508 12:31:34

You take a function f:a>b and wrap a up to get a new function with no arguments, like this: g:1>b? Is that 1 standard notation? I picked it up from Felix. 