An optimization using the foldr fusion law

Because I find this exercise ([1]) very instructive, I want to show you how the foldr fusion law can be used to derive an efficient program from a very inefficient one. This note will let you see some important points:… Continue Reading →

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Re: the mean example explained in detail

In this post I’ll discuss in detail an example found in “Real World Haskell” ([1]) and “Thinking Functionally with Haskell” ([2]). The point of this post is to explain in detail some important functional transformations from an inefficient program to… Continue Reading →

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How do you find a function that…

In this post we’ll deal only with finite lists. Questions regarding partial and infinite lists are left as an exercise for the reader. Sometimes we have to answer questions like: I have something that looks like a functional equation, but… Continue Reading →

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Some simple derivations of recursive functions

The following are some personal notes on how a study of classical mathematical notations can help us to derive algorithms. The functions obtained in this way are simple enough to understand and clarify the technique used. As an aside, I… Continue Reading →

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Heuristic guidance from equational reasoning

Working through the exercises¬†of Richard Bird (Thinking Functionally with Haskell), I found a particular one that can be used to illustrate how equations can give us heuristic guidance in solving particular functional problems. The same pattern of thought will be… Continue Reading →

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Monoids and their efficiency in practice

As we observed in the post about equational reasoning (An exercie in equational reasoning), constructing algorithms based on laws can help us gain a lot in efficiency. Let’s introduce a little theory first. A monoid is a pair (M,o) where… Continue Reading →

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Cartesian product of lists

One of the patterns of problem solving in programming is the Exhaustive Search. This is simply saying that to find a solution to a specific problem, you have to search all the possible solutions and validate them based on some… Continue Reading →

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The living mathematics

We all know how mathematics is viewed by the non-mathematician nowadays: a body of knowledge full of formulas and incomprehensible symbols. It’s a point of view that most high-school teachers promote and, in this way, they make mathematics a sterile… Continue Reading →

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An exercise in equational reasoning

This is an exercise found in the very good book of Richard Bird,¬†Thinking Functionally with Haskell. It is a good example of how a certain method of thinking can help us to reason about programs in functional programming. The method… Continue Reading →

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CodeEval Challenge – Correct Algorithm for Self Describing Numbers

In this post I’ll show you how you can practically apply formal methods to obtain a correct algorithm to solve a problem. The chosen problem is a challenge posted on CodeEval: Self Describing Numbers Simply put, a self describing number… Continue Reading →

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