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QUESTION
I was trying to recreate a simplified version of the natural numbers, for learning purposes (as it involves inductive definitions, recursive functions, etc...). In that process however, I got stuck in something that I thought would be very trivial.
Basically, I have a definition for natural numbers 'natt
' and a definition for the '<
' relation:
ANSWER
Answered 2021-May-12 at 22:34After some tips from user9716869, it's clear that my main problem was the lack of knowledge about the arbitrary
option in induction
. Using (induction _ arbitrary: _)
and (cases _)
(see the reference manual for details), the proofs are quite straight forward.
Since these are made for educational purposes, the following proofs are not meant to be concise, but to make every step very clear. Most of these could be vastly reduced if more automation is desired, and some can be done in one line (which I left as a comment below the lemma).
Note: In these proofs, we are using an implicit lemma about inductive types, their injectivity (which implies (Succ a = Succ b) ≡ (a = b)
and Zero ≠ Succ a
). Furthermore, (Succ a < Succ b) ≡ (a < b)
by definition.
First, we prove 2 useful lemmas:
a < b ⟹ b ≠ Zero
b ≠ Zero ⟷ (∃ b'. b = Succ b')
QUESTION
I would like to produce an HTML / JS page with reflex-dom (only client side, frontend). However, I use the singletons package (2.6) and it seems that it cannot be compiled with ghcjs or ghc 8.6.5 (singletons 2.5.1, broken-unpatched). Therefore, the reflex-platform solutions, reflex-stone or equivalent did not help me.
I saw that ghcjs 8.8 or 8.10 could be installed through haskell.nix, but I did not find how.
How can I do it? Or maybe, is there a way to use GHCJS (or reflex-platform solutions) with recent packages (that need ghc 8.8 or +)? Is there a way to use ghcjs-8.8 or 8.10 with the reflex-platform?
...ANSWER
Answered 2021-May-12 at 18:08First of all I would like to highlight that I'm not in any way related to GHC or GHCJS projects development, just another person who encountered similar issues, so take it with a grain of salt.
Currently GHCJS supports <= 8.6.5 out of the box. There is some development going on now and we will probably see officially supported 8.10 soon.
Meanwhile you can try to build the following branches on your own risk: 8.10 8.8
QUESTION
How do you wrap text around an image in HTML and CSS? I have an image and a text next to it, but it would not go below the image. how could I make text go around the image? What would be the best way for the text and image to looks when we view on a phone screen.
I cannot any useful way on the internet. I am quite new to html
Thank you.
here is my code bellow
...ANSWER
Answered 2021-May-09 at 22:34To make the time below the image, remove
QUESTION
I have define an odd like this:
...ANSWER
Answered 2021-May-01 at 08:29Your definition of odd
seems wrong. Is it not n+2
. Anyway our problem
is related to
How to prove a odd number is the successor of double of nat in coq?
QUESTION
I have the odd number definition as below:
...ANSWER
Answered 2021-Apr-30 at 22:40Standard induction let you jump from n
to n+1
. Here with your odd
function
you need to jump from n
to n+2
. So what is needed is a stronger induction. One way to do this is to prove:
QUESTION
I am using reflex-platform
with obelisk
.
This is my frontend code to get the current date
ANSWER
Answered 2021-Apr-24 at 23:41https://github.com/reflex-frp/reflex-dom/commit/93f0f4bd00e1dc871d193d7d53d5d7f2dbb518af
Looks like this was a bug, that has been fixed in reflex-dom
.
QUESTION
This question is better explained with an example. Suppose I want to prove the following lemma:
...ANSWER
Answered 2021-Apr-23 at 22:44You can introduce a concrete representation with the theorem int.abs_induct
. However, you almost never want to do that manually.
The general method of proving statements about quotients is to first state an equivalent theorem about the underlying relation, and then use the transfer tool. It would've helped if your example wasn't automatically discharged by automation... in fact, let's create our own little int
type so that it isn't:
QUESTION
I have an inductive type Env
that is a snoclist with multiple cons constructors
ANSWER
Answered 2021-Apr-20 at 16:26You could declare WfEnv
to be a morphism for the relation EnvEq
as follows:
QUESTION
I want to write a fixpoint definition that matches over a value inside a dependent type without proof-mode. The essential issue is that Coq won't use the match
to notice that the types are equivalent in a dependent type; I can force it in proof-mode, but I wonder if it's possible to do so without it.
I'm working on a project that involves lots of matrix operations. The matrices can be arbitrarily many dimensions (each of which is rectangular), so I wrote a definition to compute the type of the matrix:
...ANSWER
Answered 2021-Mar-30 at 14:12This is one of the major headaches of using dependent types in Coq. The solution is to rewrite linearize so that it returns a function after matching:
QUESTION
So I am extremely new to coding and I am doing this for my career school capstone project and I am running into a lot of problems. Mainly two: How to put the image above the content box? (even with a transparent background).
Here is my Code:
...ANSWER
Answered 2021-Mar-26 at 15:30Try this
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