Comments for for the few of us.

Comment on Tail-Recursive, Linear-Time Fibonacci by Shin

Shin — Sat, 12 Jul 2008 22:55:01 +0000

Thanks! I will correct them now.

Comment on Tail-Recursive, Linear-Time Fibonacci by Daniel

Daniel — Sat, 12 Jul 2008 20:01:34 +0000

I think I’ve spotted two typos: In the definition of the fusioned fib2 there’s a fold instead of a foldN. Later there’s gfib instead of a gib.

But nice read, indeed, for I’ve been thinkering around with such small multi-recursive problems lately.

Comment on Agda Exercise: Proving that Mergesort Returns Ordered Lists by Shin

Shin — Tue, 27 May 2008 10:03:13 +0000

newsh (sorry for the late response),

I think OList is a sorted list. Consider xs : OList 0. If xs is Nil, it is sorted. If xs equals, say, Cons 3 0≤3 ys, the tail ys must have type OList 3. Thus ys is lower-bounded by 3, not 0.

Comment on Agda Exercise: Proving that Mergesort Returns Ordered Lists by newsh

newsh — Thu, 15 May 2008 04:30:35 +0000

I think this only proves that the resulting list has a lower bound. You can construct arbitrary (unordered) lists of type (OList 0). The only restriction is that all elements are >= 0 (which is true by the definition of >=).

Comment on Deriving a Virtual Machine by Dave

Dave — Sun, 30 Mar 2008 20:53:04 +0000

After a quick skim of the Igarashi paper, I think the difference is they produce linear Compt terms — and it’s this linearization of the initial tree-structured term that prevents eval from trivializing to the identity.

Comment on Constructing List Homomorphism from Left and Right Folds by Tiempo finito y logarítmico » Tercer teorema de homomorfismo

Tiempo finito y logarítmico » Tercer teorema de homomorfismo — Sun, 10 Feb 2008 02:59:53 +0000

[...] Constructing List Homomorphism from Left and Right Folds (Shin-Cheng Mu, Institute of Information Science, Taiwan) explora el problema de encontrar op a partir de () y e. [...]

Comment on Deriving a Virtual Machine by MigMit

MigMit — Tue, 25 Dec 2007 11:12:22 +0000

Correction: “that’s all it does”

Comment on Deriving a Virtual Machine by MigMit

MigMit — Tue, 25 Dec 2007 09:52:04 +0000

Sorry, but… I don’t see the point. Let’s look at our data types:

Isn’t that exactly the same thing (up to renaming of constructors)? Moreover, if we identify this two types, then eval seems to be an identity - OK, it forces almost everything, but that’s all id does. I don’t see, why you call id a “compiler”.

Comment on S Combinator is Injective, with Proofs by Charles Stewart

Charles Stewart — Tue, 11 Dec 2007 12:17:59 +0000

I’ve posted this observation as a story on LtU.

Comment on S Combinator is Injective, with Proofs by Shin

Shin — Thu, 06 Dec 2007 01:50:51 +0000

lf,

Yes, I know about Djinn! In fact when I thought I found a general way to invert functions, I was merely constructing a term having the right type. After my talk, one of the audience fired up Djinn and showed me how it can be done. It must be one of my worst talks..

Frank Atanassow,

Oh, I’ve probably omitted too many steps. The reasoning goes like this:


   (∀ y ∈ A -> B : P)
≡  (∀ y : y ∈ A -> B ⇒ P)
⇒   { since (∃ b : y = K b) ⇒ (y ∈ A -> B) }
   (∀ y : (∃ b : y = K b) ⇒ P)
≡    { since (∃ b : Q) ⇒ P ≡ (∀ b : Q ⇒ P) }
   (∀ y : (∀ b : y = K b ⇒ P))
≡  (∀ b : P[(K b)/y])

Chris Rathman,

Thanks! I will have a read. The team I used to work with was also working on bidirectionality and I have to read that paper anyway…