Re: [Haskell-beginners] Avoid Case Analyses

Without speaking to the point of whether case analysis introduces unnecessary complication, I think truncate is a poor choice of example to demonstrate this idea. As Mike deftly demonstrated we can write a simple constant-time function which implements floor, while Roger's final version is a non-intuitive time-inefficient linear search over the integers. Perhaps a more complicated problem would better demonstrate Richard Bird's quotation, however, in general I think case analysis is a very useful tool when it illuminates the problem (as in a function over a recursive data structure (see treeInsert on http://learnyouahaskell.com/making-our-own-types-and-typeclasses)). -- Patrick On Mon, Oct 8, 2012 at 6:30 AM, Mike Meyer wrote:

On Sun, 7 Oct 2012 09:47:32 +0000 "Costello, Roger L." wrote:

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Hi Folks,

"Programs that avoid case analyses are clearer and simpler than those that use case analyses."

I'm not convinced. Here's the critical bits:

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Let's take a less trivial example. We will implement the floor function. Although Haskell already has a built-in floor function, it will be instructive to see how floor :: Float -> Integer can be programmed. The program will be developed in a systematic manner, starting with a specification for floor.

After implementing floor without case analyses, we will then compare it against an implementation that uses cases analyses.

A nice straw man implementation.

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It is tempting to plunge immediately into a case analysis, considering what to do if x is positive, what to do if x is negative, and, possibly, what to do if it is zero.

Right, this is the natural way to do it with case analysis.

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Add the definitions for decrease, upper, and lower:

floor x = searchFrom 0 where searchFrom = decrease . upper . lower lower = until (<=x) decrease upper = until (>x) increase decrease n = n - 1 increase n = n + 1

Notice that this implementation of function floor does not use case analyses. The program is surprisingly short, owing mainly to the absence of a case analysis on the sign of x.

Compare that with a version that uses case analyses:

floor x | x < 0 = lower 0 | x > 0 = (decrease . upper) 0 | x == 0 = 0 where lower = until (<=x) decrease upper = until (>x) increase decrease n = n - 1 increase n = n + 1 [...] The case analysis version is longer and arguably more complex.

Let's see - you constructed a set of primitives specifically designed to avoid case analysis, and when you use those to create a solution that is only "arguably more complex". Would you let me get away with arguing that an imperative solution was better if I forced you to use imperative primitives in a functional version?

If you follow that original case analysis urge, you get this version:

floor x = truncate x - if x < 0 then 1 else 0

Clearly shorter and less complex than any either of your two versions. Further, it actually, doesn't include any more case analysis, as it has the same "if" that is hidden in the "until" primitive in the version without case analysis.

http://www.mired.org/ Independent Software developer/SCM consultant, email for more information.

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