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Well Java didn't add lambdas to write make-counter, it was map and fold that got them envious. In fact, IIUC mathematically make-counter is first-order, countin

by willtim 10y ago

Well Java didn't add lambdas to write make-counter, it was map and fold that got them envious. In fact, IIUC mathematically make-counter is first-order, counting the nesting of funtion types. In other words, I don't understand why many describe it as a HOF at all. Map and fold are second order. Callcc, ignoring its Scheme implementation as a macro, would be third order. One could argue that the second order argument to callcc is strategy, with the continuation being the strategy.

qwertyuiop924 10y ago
Call/cc isn't a macro. It's actually a special form, although in CPS-based schemes, it could probably be implemented as a function if there was a lower level continuation primitive. And semantically, a continuation is pretty much never a strategy. As for make-counter not being higher-order, that's just not true. A higher-order function takes and/or returns a function. make-counter returns a function: it's higher-order.
- willtim 10y ago
  No its disputed, for the reasons I gave. But I've already accepted that many regard make-counter to be a HOF. I was careful and said make-counter is not a second-order HOF, which Strategy is. Callcc can be implemented as a function, no continuation primitives needed. Haskell has examples in its libraries. Lastly, regarding semantics, I see no difference between Strategy and a second-order HOF. Yes the scope of Strategy is supposed to much more limited, but I don't see value in this. I concede that others might do.
  - willtim 10y ago
    Having thought about this further, I think it is probably only correct of me to talk about the "order" of "functionals" as in functions to scalars in mathematics. The term "rank" is better suited here. Category theory supports the popular definition of higher-order function and gives a different meaning to "order". So make-counter is rank-1 but still higher-order. Apologies for the previous post.

by willtim 10y ago

qwertyuiop924 10y ago

Call/cc isn't a macro. It's actually a special form, although in CPS-based schemes, it could probably be implemented as a function if there was a lower level continuation primitive. And semantically, a continuation is pretty much never a strategy. As for make-counter not being higher-order, that's just not true. A higher-order function takes and/or returns a function. make-counter returns a function: it's higher-order.

willtim 10y ago
No its disputed, for the reasons I gave. But I've already accepted that many regard make-counter to be a HOF. I was careful and said make-counter is not a second-order HOF, which Strategy is. Callcc can be implemented as a function, no continuation primitives needed. Haskell has examples in its libraries. Lastly, regarding semantics, I see no difference between Strategy and a second-order HOF. Yes the scope of Strategy is supposed to much more limited, but I don't see value in this. I concede that others might do.
- willtim 10y ago
  Having thought about this further, I think it is probably only correct of me to talk about the "order" of "functionals" as in functions to scalars in mathematics. The term "rank" is better suited here. Category theory supports the popular definition of higher-order function and gives a different meaning to "order". So make-counter is rank-1 but still higher-order. Apologies for the previous post.