## lambda calculation: equivalent terms in call by name but not in call by value

When working on the lambda calculation without type, I am asked to give two terms that are equivalent in semantics of call by name but not in call by value.

Call $$text {fls} = lambda x. λ and. and$$ Y $$Omega = ( lambda x. X x) ( lambda x. X x)$$ . They proposed to look at these terms:

$$text {fls} ( lambda x. Omega)$$ which in both semantics is reduced to $$lambda and. and$$

$$text {fls} ( lambda x. Omega x)$$ which on call by name is reduced to $$lambda and. and$$ but in the value call "diverges when evaluating the argument for $$text {fls}$$".

I don't see how they diverge, except if I guess $$text {eta}$$-conversion that was not assumed in my course. On top of that, I don't see how one can diverge and evaluate the argument for $$text {fls}$$. Does this make sense to you?

Apart

I proposed the terms $$( lambda f. Omega)$$ Y $$( lambda t. lambda f. f) Omega$$ I think this is a valid example …

The notion of equivalence:

The notion of equivalence that I am using is behavioral equivalence (see Pierce's TAPL book for more details). The definition says that for any sequence of values ​​to which my terms apply, I should have the same observation: the two results diverge or Results do not diverge.

A separate notion is that of call by value or call by name, which are some standard evaluation strategies for lambda terms.

## Equivalent formulations of the compactness theorem for first-order logic

I have to prove that the following three formulations of the compactness theorem in first-order logic are equivalent:

1. $$Gamma$$ It is satisfactory if every finite $$Gamma_0 subseteq Gamma$$ It is satisfactory. (The standard definition)
$$( forall Gamma_0 subseteq Gamma: | Gamma_0 | < infty land sat ( Gamma_0)) implies sat ( Gamma)$$

2. For any formula $$varphi$$Yeah $$Gamma models varphi$$, then $$Gamma_0 models varphi$$ for something finite $$Gamma_0 subseteq Gamma$$.
$$forall varphi: Gamma models varphi implies exist Gamma_0 subseteq Gamma: | Gamma_0 | < infty land Gamma_0 models varphi$$

3. Yes $$Gamma$$ It is unsatisfactory, so there is something finite $$Gamma_0 subseteq Gamma$$ such that $$Gamma_0$$ It is unsatisfactory.
$$lnot sat ( Gamma) implies exist Gamma_0 subseteq Gamma: | Gamma_0 | < infty land lnot sat ( Gamma_0)$$

In general I would proceed with $$(1) implies (2) implies (3) implies (1)$$.

as $$(A implies B) implies ( lnot B implies lnot A)$$ this follows directly from 3

But for the other implications, I'm pretty caught

## Homotopia theory: what is an example of \$ infty \$ -posts not equivalent to pulleys at a Grothendieck site?

My question is as in the title: Does anyone have an example (assuming there is one) of a $$infty$$-positions known to be not equivalent to pulleys at a Grothendieck site.

A $$infty$$-topos it's like in Higher Topos Theory (HTT) 6.1.0.4: a $$infty$$-category that is an accessible location to the exact left of preheaves in a small $$infty$$-category.

A Grothendieck site it's a small $$infty$$-category $$mathcal {C}$$ equipped with the $$infty$$-category variant of the classical notion of a Grothendieck topology $$mathcal {T}$$, as in HTT 6.2.2: a collection of sieves (sub-objects $$U to j (C)$$ of representative presheaves in $$mathcal {C}$$) satisfying some axioms. Sheaves in $$( mathcal {C}, mathcal {T})$$ they are presheaves of $$infty$$-groupoids in $$mathcal {C}$$ which are local for sieves in $$mathcal {T}$$. Such forms a complete subcategory $$mathrm {Shv} ( mathcal {C}, mathcal {T})$$ of the $$infty$$-category of presheaves.

Note: The question Examples of \$ ( infty, 1) \$ – topoi that are not given as rollers in a Grothendieck topology seems to be superficially equivalent to this. In practice, it is not exactly the same. As the answers to that question show, many interesting $$infty$$-Topoi exists that can be described without reference to any Grothendieck site. But it is still conceivable that there is a suitable site.

Also note: any $$infty$$-topos $$mathcal {X}$$ it can be obtained as an accessible location to the exact left of some $$mathrm {Shv} ( mathcal {C}, mathcal {T})$$ regarding an appropriate class of $$infty$$connected morphisms (HTT 6.2.2, 6.5.3.14), for example, the class of hypercovers. However, this does not immediately prevent $$mathcal {X}$$ be equivalent to $$mathrm {Shv} ( mathcal {C} & # 39 ;, mathcal {T} & # 39;)$$ for some other Grothendieck site $$( mathcal {C} & # 39 ;, mathcal {T} & # 39;)$$.

## linux – Windows equivalent to \$ in unix commands

I am following a documentation and running some commands at the Windows 10 command prompt.

I have executed the first two commands using setx, since setx is the equivalent of Windows to export and when I try the third command `\$OPENAI_LOGDIR` not detected correctly Can anyone help with the equivalent of this in Windows?

commands

``````export OPENAI_LOG_FORMAT='stdout,log,csv,tensorboard'
export OPENAI_LOGDIR=path/to/tensorboard/data

tensorboard --logdir=\$OPENAI_LOGDIR
``````

Thank you

## MySQL select takes 0.2 seconds; The equivalent UPDATE takes 1.5 minutes!

This query runs in 0.2 seconds and finds 9 rows:

``````SELECT S.id, S.frame, S.active,
GF.groupNum, GF.frameDesc
FROM skus S
INNER JOIN group_frames GF ON (GF.frame = S.frame)
WHERE GF.groupNum = 204 AND GF.frameDesc LIKE '%lumbar%';
``````

This query runs on 1.5 minutes and update the same 9 rows:

``````UPDATE skus S
INNER JOIN group_frames GF ON (GF.frame = S.frame)
SET S.active = 0, S.updated_by=101355, updated_at = NOW()
WHERE GF.groupNum = 204 AND GF.frameDesc LIKE '%lumbar%';
``````

… while this incredibly pirate version runs in 0.5 seconds and updates the same rows:

``````UPDATE skus S SET S.active = 0, S.updated_by=101355, updated_at =
NOW() WHERE S.id IN (   SELECT id FROM (    SELECT S1.id    FROM skus S1
INNER JOIN group_frames GF ON (GF.frame = S1.frame)
WHERE GF.groupNum = 204 AND GF.frameDesc LIKE '%lumbar%' ) S3)
``````

(using a dummy internal query to beat the query optimizer complaining that the same table is used in a FROM clause)

Why the hell did the second consultation take so long?

## What is the equivalent of Shift + Solve in 9860GII graphing calculators?

How to solve a variable in the middle without isolating it?

## Formal languages: for arbitrary grammar RR (1) \$ G \$, is there an LL grammar (1) equivalent to \$ G & # 39; \$?

A similar term could not be found, here I coin the noun RR(From right to left, rightmost derivation) as an opposite concept of LL.

The question is inspired by an interesting example of grammar. $$G$$:
$$S rightarrow S S + | a$$
Obviously it is a RR language (1). After some time to explore, I find an equivalent grammar LL (1):
$$begin {array} {l} S rightarrow to A \ A → S + A | epsilon end {array}$$

So there seems to be a path to a more generalized conclusion. Consider arbitrary grammar RR (1), is there an equivalent grammar LL (1) $$G & # 39;$$, where equivalent means, medium $$L (G) = L (G & # 39;)$$?

## Navigation – Including a specific link & # 39; Home & # 39; when a site & # 39; Home & # 39; is equivalent to another function

I am designing a blog site where the `Home` The page is a list of blog posts.

In this situation, is there any investigation into the validity of the use of a `Home` navigation link that takes you to the list of blog posts and no including a `Blog` navigation item?

I think this would be acceptable as if the user were in the `Home` page you can see what it contains and if you have navigated to a publication, you know `Home` will take them back to where they came from and I hope I remembered that `Home` Contains a list of publications. But eager to see if there is any contrary investigation.

The alternatives I am considering are not to include a specific `Home` link and simply use `Blog` (using a logo to return to `Home`) but I would worry that this does not indicate enough how to go home unless the logo looks stylistically like a button.

Steve Krug is interested in using the site identification as a back-to-start link, which is fair, but also recommends (but does not insist) on having a `Home` navigation link. I see that Facebook includes a home link in the main browser and this link to `news feed` to the left of navigation. Amazon doesn't seem to include a start link anymore.

Or finally to include both a `Home` Y `Blog` link, but I don't like duplication since I think it can cause confusion if a user `Home` page clicks `Blog` and see is the same content. Also, I can only indicate one active page, so having two links seems like an incorrect approach.

## Inverse matrix[m1 m2] not equivalent to inverse[m2] Reverse[m1], m1, m2 are 3×3 matrices, why?

I would like to use Mathematica to show that $$(AB) -1 = B -1 A -1$$

used to

```m1 = {{a, b, c}, {d, e, f}, {g, h, i}} m2 = {{j, k, l}, {m, n, o}, {p, q, r}} Simplify(Inverse(m1 m2)) Simplify(Inverse(m2) Inverse(m1))```

and I find that the two expressions are not the same. I have also tried

`Inverse(m1 m2) == Inverse(m2) Inverse(m1)`

that does not produce True

However, when I try `Transpose(m1 m2) == Transpose(m1) Transpose(m2)` The output is true. Why? How can i fix this?

p.s: the result for the expression `Simplify(Inverse(m1 m2))` It is too long, therefore, I am not publishing it.

## Deep learning: is there an equivalent of word2vec for images?

I wonder if it would be possible to create dense vector representations for an image, similar to how I could create an embedded word with an algorithm like Word2Vec.

I understand that there are some big differences between text and image data, specifically the fact that word2vec uses the context of the word to train, but I hope to find a similar counterpart for the images.

If a simplistic example of w2v (from GitHub Gist from Allison Parrish) is:

``````            | cuteness (0-100) | size (0-100) |
|–––––––––––|––––––––––––––––––|––––––––––––––|
| kitten    |        95        |     15       |
| tarantula |         8        |      3       |
| panda     |        75        |     40       |
| mosquito  |         1        |      1       |
| elephant  |        65        |     90       |
``````

And another example being `king - man + woman = queen`

Is there any analogue (or way to create some kind of analogue) for the images in which I could get something in general along these lines (with some invented numbers):

``````                             | amount of people | abstract-ness |
| in image (0-100) |    (0-100)    |
|––––––––––––––––––––––––––––|––––––––––––––––––|–––––––––––––––|
| Starry Night               |         0        |       75      |
| Mona Lisa                  |         1        |        9      |
| American Gothic            |         2        |        7      |
| Garden of Earthly Delights |        80        |       50      |
| Les Demoiselles d'Avignon  |         5        |       87      |
``````

or `(starry night) - (landscape) + (man) = (van Gogh self portrait)` or `= (abstract self portrait)` or something in general in that regard.

These may not be the best examples, but just to recap, I am looking for some kind of algorithm to create an abstract n-dimensional representation learned for an image that can be grouped or compared with vectors that represent other images.