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?


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) 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,, 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?


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.frame,,
  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:

  INNER JOIN group_frames GF ON (GF.frame = S.frame)
SET = 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 = 0, S.updated_by=101355, updated_at =
NOW() WHERE IN (   SELECT id FROM (    SELECT    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.

Thanks for your help!