Re: [Haskell-beginners] Avoid Case Analyses

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

...

that use case analyses."

I'm not convinced.

I agree that the floor function is not a good one to demonstrate why case analysis should be avoided. But in general, freely thrown case analysis makes reasoning (especially the equational reasoning) about the program behaviour more difficult. This is one of the points of Bird's advice. Important point to note here is to capture patterns of different types of "case analysis" and abstract them out, so that you can make (equational) reasoning without having to do inordinate amount of brain gymnastics. Arbitrary case analysis (especially the one which you cannot turn into pattern matching, e.g. case that a part of a list doesn't contain a given element) makes giving formal proofs difficult, so what do you do? You try to look for a solution that avoids such a case analysis. Once you capture a particular type of case analysis as an abstraction, then only once you have to prove that thing. Later you are "free" to use them in other parts of program without having to worry about their behaviour. But, yes, if you don't have to reason about your programs formally, then you can throw in "case analysis" as per your wish; but then you can do "standard C" programming with pointers etc too. 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?

The "until" that you saw there has nothing that makes it imperative, it is purely functional. Damodar On Mon, Oct 8, 2012 at 4:00 PM, Mike Meyer wrote:

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

...

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:

...

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.

...

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.

...

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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