Author Archives: Shin

The Windowing Technique for Longest Segment Problems

Reviewing Zantema’s “windowing” technique for computing the longest segment of the input that satisfies a suffix-closed predicate.

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Longest Segment Satisfying Suffix and Overlap-Closed Predicates

Translating Zantema’s work to Bird-Meertens style, to compute the longest consecutive segment of the input that satisfies a predicate that is suffix and overlap-closed.

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On a Basic Property for the Longest Prefix Problem

Giving a constructive proof for one of the essential properties in Hans Zantema’s Longest Segment Problems.

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Beamer Article Mode Does Not Save Paper?

Among all the features of Beamer I like is the article mode with which I can produce handouts. “It’s easier to read, and it saves paper!” I thought.

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No Inverses for Injective but Non-Surjective Functions?

“I cannot prove that if a function is injective, it has an inverse,” Hideki Hashimoto posed this question to me. Is it possible at all?

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Proof Irrelevance, Extensional Equality, and the Excluded Middle

I was puzzled by the fact stated in a number of places that axiom of choice, proof irrelevance, and extensional equality together entail the law of excluded middle.

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Algebra of programming in Agda: dependent types for relational program derivation

S-C. Mu, H-S. Ko, and P. Jansson. Algebra of programming in Agda: dependent types for relational program derivation. In Journal of Functional Programming, Vol. 19(5), pp. 545-579. Sep. 2009. [PDF]

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“General Recursion using Coinductive Monad” Got Right

Anton Setzer argued in his letter to the Agda mailing list that we should go back to a category theoretical view of codata, and Dan Doel soon successfully experimented the ideas.

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General Recursion using Coindutive Monad

It would be nice to if we could write the program and prove its termination separately. Adam Megacz published an interesting paper: A Coinductive Monad for Prop-Bounded Recursion. As a practice, I tried to port his code to Agda.

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Typed λ Calculus Interpreter in Agda

In a recent meeting I talked to my assistants about using dependent type to guarantee that, in an evaluator for λ calculus using de Bruin indices, that variable look-up always succeeds.

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