Are type abstraction values and universal types not for non functions, but only for functions?

In Types and Programming Languages by Pierce, Chapter 23 Universal Types has a summary of System F in the following figure, in particular, “type abstraction values” and their types “universal types”.

In all the examples I have seen so far in the chapter, in particular Section 23.4 Examples, (not sure if I miss any example):

  • all the type abstraction values are parametrically polymorphic functions, by allowing the types of their arguments to have any type, and
  • all the universal types, i.e. the types of type abstraction values, are types of parametrically polymorphic functions.

Are type abstraction values and their universal types not for non functions, but only for functions?

More specifically, in any type abstraction value, say $ \lambda X.t$ , must $ t$ have a function type, not a non-function type?

In Section 23.4 Examples, values of base types and of recursive types are type abstraction values, because their definitions in the section are functions by Church encodings.

Thanks.

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Can a Great Old One warlock use the Awakened Mind feature as a universal translator for Suggestion spells? [duplicate]

This question already has an answer here:

  • Can awakened mind be used with suggestion? 1 answer
  • Can Awakened Mind let you affect creatures that don’t share your language with spells that require them to understand you? [duplicate] 1 answer

Warlocks with the Great Old One patron start out with a universal translator that works on one target within 30 feet – the Awakened Mind feature (PHB, p. 110):

Starting at 1st level, your alien knowledge gives you the ability to touch the minds of other creatures. You can communicate telepathically with any creature you can see within 30 feet of you. You don’t need to share a language with the creature for it to understand your telepathic utterances, but the creature must be able to understand at least one language.

This “universal translator” ability appears to be just as powerful as the 3rd level spell “Tongues,” and possibly more so in limited situations because it is always on.

A warlock can also get suggestion as a 2nd-level spell:

You suggest a course of activity (limited to a sentence or two) and magically influence a creature you can see within range that can hear and understand you.

So it seems to me that a Great Old One warlock who speaks only Common could get within 30 feet of a goblinoid who speaks only Goblin, and communicate telepathically with Awakened Mind while speaking suggestion as a 2nd level spell. The goblinoid can hear the voice, and the goblinoid can understand the telepathy.

However, I suspect that some DMs would rule that the Warlock must be able to be understood just from the spoken words and not from any additional telepathy.

Does this work? Can a Great Old One warlock use Awakened Mind as a universal translator for Suggestion spells?

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How to resolve error creating universal data connection file (.udcx)?

Trying to follow along to create a Data Connection Library but run into the following error:

The specified location does not exist or could not be opened. Choose a data connection library on a server running Microsoft SharePoint Server and specify a valid filename.

I was able to create the SharePoint Data Connection Library. Then I move to the To create a new data connection file in InfoPath section. I get to step 7 and encounter the error before I can finish.

I have my dataconnectionlibrary Data Connection that I just created highlighted.

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I click Convert to Connection File button. Then as instructed, I put the address of the SharePoint Data Connection Library in followed by a chosen filename then the .udcx extension.

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I hit OK, and at first, it looks like it’s going to work, like everything’s normal:

enter image description here.

Nope:

enter image description here.

This happens no matter which Connection link type I choose (Relative to the site collection OR Centrally managed connection library). This happens no matter where I specify to put the file; I can Browse to my own Documents folder and it still gives me this error.

Looking for any kind of help on this one. Trying to create the Data Connection Library due to 5566 error trying to auto populate user info with GetUserProfileByName using SOAP in InfoPath form. Is there a workaround, a different way to create the .udcx file? This is so frustrating, running into error after error just trying to auto-populate a Person Picker control.

What is the gsettings schema for Settings > Universal Access > Sounds Keys

look I’m using Ubuntu 19.04 and currently trying to enable the sound keys from a command line but not sure where to look for the schema. At first, I thought it was gsettings set org.gnome.desktop.sound event-sounds "true" but I don’t think that was it. I’ve tried to browse for it throughout dconf-editor but still has no idea where it’s at; not to mention googled for the information many times. Thanks in advance!

infinite fold tensor product of universal enveloping algebra

Let $ \mathfrak a$ be a Lie algebra graded by the abelian semigroup $ S$ , then the universal enveloping algebra $ U(\mathfrak a)$ of $ \mathfrak a$ is $ S \sqcup \{0\}$ graded. I have the following questions.

  1. What is the definition of infinite fold tensor product ($ U(\mathfrak a)^{\otimes \infty}$ ) of $ U(\mathfrak a)$ and is this also $ S \sqcup \{0\}$ graded?
  2. If so, how to express the grade spaces of this infinite tensor product in terms of grade spaces of $ U(\mathfrak a)$ ?
  3. Is it a good notation $ U(\mathfrak a)^{\otimes \infty}$ ?

Thank you.

Which of the known alternative set theories is nearest in structure to this theory with a universal set and the complement of Russell set?

Before I’ll present the exposition of this theory, I’ll speak a little bit about the Mereological concept it is meant to catpure.

The idea is to work in Atomic General Extensional Mereology “AGEM”, one can think of it easily as a theory about collections of atoms, where atoms are indivisible objects, i.e. objects that do not have proper parts. The relation is an atomic part of is defined as:

$ \sf Definition:$ $ x P^a y \iff atom(x) \land x P y$ .

where $ P$ stands for “is a part of”, and atom(x) is defined as:

$ atom(x) \iff \not \exists y (y P x \land y \neq x)$

This atomic part-hood relation can be regarded, conceptually speaking, as an instance of set membership relation.

Now the following theory is a try to define a set theory by a strategy of mimicking properties of this atomic part-hood relation with the background theory being AGEM.

Notation: let $ \phi^{P^a}$ denote a formula that only use the binary relation $ P^a$ or otherwise the equality relation, as predicate symbols. The notation $ \phi^{\in|P^a}$ denotes the formula obtained by merely replacing each occurrence of the symbol $ “P^a”$ in $ \phi^{P^a}$ by the symbol $ “\in”$ .

Comprehension axiom schema: if $ \phi^{\in|P^a}(y)$ doesn’t have the symbol $ x$ occurring free, then all closures of:

$ $ \forall A [\exists x \forall y (y \ P^a \ x \leftrightarrow \phi^{P^a}(y)) \to \exists x \forall y (y \in x \leftrightarrow \phi^{\in|P^a}(y))]$ $

are axioms.

In order to complete this theory we add axioms of Extensionality, Empty set and Singletons:

Extensionality: $ \forall xy [\forall z (z \in x \leftrightarrow z \in y) \to x=y]$ .

Empty set: $ \exists x \forall y (y \not \in x)$

Singletons:: $ \forall A \exists x \forall y (y \in x \leftrightarrow y=A)$

This theory has a universal set, also has a set of all sets that are in themselves, however it doesn’t have complements; axioms of Set union and Power are there. There are separation axioms for formulas $ \phi^{\in|P^a}$ where $ \phi^{P^a}$ holds of at least one object. Similarily replacement axioms are granted if $ \phi^{P^a}$ formula replace atoms with atoms and of course is non empty.

The trick is that all formulas of the form $ x \not \in x$ , $ \exists x_1,..,x_n: \neg (x_1 \in x_2 \land…\land x_n \in x_1)$ ; $ x \text { is well founded }$ , $ x \text{ is a von Neumann ordinal }$ , etc.. all of those won’t have their $ \phi^{P^a}$ corresponding formulas hold of mereological atoms and so cannot be used in comprehension because there do not exist an object that has no atomic parts, since we are already working in AGEM.

Question: if one attempts to prove the consistency of this theory, which of the known alternative set theories have in some sense the nearest structure to this theory, other than positive set theory?

Can the “$” symbol be safely considered as universal when making a graphic depicting money?

Want to get a sense of any best practices of using the “$ ” dollar sign in the context of an image in order to depict a universal idea of money.

UPDATE: My task was to create an icon/graphic used in an e-commerce checkout process which depicted the idea of an ‘invoice’. It had to make sense in a global context (not just USD). Here is the exploration I had done: enter image description here

And here is the icon I ended up picking (without a symbol): enter image description here

Thanks for all the insights and weigh-ins everyone offered. VERY helpful!

Make Universal Clipboard fast and reliable

For me, the Universal Clipboard feature of Continuity has always been a bit spotty, but with newer hardware, it has become somewhat more reliable.

The problem is getting it to work consistently. I’ve read the Apple Support document, Use Universal Clipboard to copy and paste between your Apple devices which unfortunately is hopelessly simplistic.

Yes, I have Bluetooth, Wi-Fi, and Handoff enabled, and all of my devices are correctly signed into the same iCloud account. Other Continuity features (Handoff, notably) appear to be working just fine.

However, what I consistently experience now, between my iPad Pro 11” and my iPhone XS, is this: When I try to copy on one device and paste it on another, what happens is that it won’t work at all the first time, and then if I repeat the paste, the device on which I’m pasting will display an alert “Pasting from … ”, I’ll have to wait about 5 seconds, and then the text will be correctly pasted.

Previously I had seen this message appear when pasting a rather large text (say a page), but now it occurs repeatedly even when I’m only pasting only a few words. This is, however, not the case between the iOS devices and my 2018 MacBook Pro running macOS Mojave 10.14.5.

I’ve posted about this earlier — with different (older) hardware:

  • Is there any way to make Universal Clipboard in High Sierra reliable?

In the past, the most reliable fix for the Universal Clipboard not working at all — as reported on various sites — was to sign all devices out of iCloud account, restart, and log in to iCloud again on all devices. Yet as noted above, Universal Clipboard is working to some extent for me, while signing out of iCloud and signing in again is not as easy as it seems — many settings have to be re-established.

Are these sorts of problems par for the course with the Universal Clipboard? or is there a clear way to get it working quickly and reliably? All of my devices are running the latest versions of system software (macOS Mojave 10.14.5 and iOS 12.13.1).