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Iterative function definitions in Coq
I’ve been playing with coq for a bit and have the following code:
Inductive reducible (A : Set) : Prop :=
true_red : forall (x y : A), x = y -> reducible A
| false_red : forall (x y : A), x \/ y -> reducible A.
I’m not sure if I can define inductively a function in this way or if I have to do it “by hand”. Is it even possible to use inductive function definitions in Coq?
A:
There are two things that are disputable here. First, whether you can write a recursive function in the form you’ve used. Coq has no type for the $\forall$ or $\exists$ quantifiers, and so (in your form) you’d be getting a syntax error. For example, let’s try to write the type of a function $f$ in your form:
Inductive reducible (A : Set) : Prop :=
true_red : forall (x y : A), x = y -> reducible A
| false_red : forall (x y : A), x \/ y -> reducible A.
Inductive f : reducible A -> Prop :=
refl : forall a, f true_red a
| cong a: forall b: forall (a’ b): forall a b’, a’ = a -> f (reducible_eq (a, a’) b’ -> reducible_eq a’ b -> reducible A) b.
There is no type for the $\forall$ quantifier in Coq, and so the type of this function is ambiguous, and the typechecker cannot figure out what $b’$ should be. Indeed, it is possible to make your function work by writing it like this instead:
Inductive reducible (A : Set) : Prop :=
true_red
https://colab.research.google.com/drive/1PDvvd9JCCLi9HpAUZFEM5UtwTjxKHIyv
https://colab.research.google.com/drive/1ENgK_IU1D-JHPq9iFg4NURZgR76337v9
https://colab.research.google.com/drive/1-S7bH9F569Vsz-22qZLdAhCCC-qekMgU
https://colab.research.google.com/drive/1mUfhD-24vlu56LiXh4SSgzAGMhcqKezf
https://colab.research.google.com/drive/1NJWp3YhY7OfkT_iEqR3XD6EMZjh92dGv
In Detail
amtlib.dll
Conclusion
A:
Your dll was created for a WinXP 64-bit system, if that’s the only system you are using and you are not able to use it in any other system, then I would strongly suggest to get the original dll, as if you create one yourself and it will work in your system, you can have it never break and not have to be afraid of it losing support any time.
On the flip side, if you’re able to use any system, then you might want to check if any software you use supports being able to patch dlls, but that is an entirely different matter.
Escritorio
Tuesday, February 7, 2010
After a disappointing start, I think I’m really getting into GTD. I think I can actually be productive after all.
It’s been a little stressful finding things in the form of tasks. Mainly as a result of my starting with GTD so late and not knowing my own personal rules, but I think it’s going pretty well.
I’m still in the habit of starting by figuring out where I’ll write my notes, bookmarks, stuff I want to read, etc. Then I get it all over in a single location. For example today I was in the library and realized I had some stuff that I wanted to read and a note on a particular book I wanted to order. I wanted the note to be at home so I left it in my notebok. I wanted the book in my to-read pile so I placed it there too. Then I decided to get dinner and return a phone call. I went to the library, found the book I wanted to get and ended up ordering it too. I then went to the movie theater and wondered how long it was going to take me to see Avatar, and how much I’d like it when I finally did see it. I went to the theater, ate the ticket out of my already packed lunch and enjoyed the movie. And I got to read my book too!
Then I had the usual Tuesday activity of working some from home, getting to work and returning calls and stuff on the way home. Then my husband walked in the door and asked if I wanted to go eat Chinese food before we watched a movie. I checked my list of stuff and realized I had nothing on that. By then it was 3:30 and I didn’t have to
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