https://github.com/official-stockfish/fishtest/wiki/Fishtest...

  A . B : C :. D

  ((A B) C) D

What if you need to nest parentheses? Then you use more dots. A double dot (:) is like a single dot, but stronger. For example, we write ((1 + 2) × 3) + 4 as 1 + 2 . × 3 : + 4, and the double dot isolates the entire 1 + 2 . × 3 expression into a single sub-formula to which the + 4 applies.²

A dot can be thought of as a pair of parentheses, “) (”, with implicit parentheses at the beginning and end as needed.

In general the “direction” rule for interpreting a formula ‘A.B’ will be to first indicate that the center dot “works both backwards and forwards” to give first ‘A).(B’, and then the opening and closing parentheses are added to yield ‘(A).(B)’. The extra set of pairs of parentheses is then reduced to the formula (A.B).³

So perhaps one way of thinking about it is that more dots indicates more separation.

¹ https://plato.stanford.edu/entries/pm-notation/dots.html

² https://blog.plover.com/math/PM.html

³ https://plato.stanford.edu/entries/pm-notation/dots.html

See also https://plato.stanford.edu/entries/pm-notation/index.html and https://muse.jhu.edu/article/904086.

From what I understand of the C++ memory model (shared by C and Rust), this is not the definition of data race – a data race occurs when two or more threads access memory concurrently where at least one access is a write and the accesses are unsynchronized. However, synchronized accesses may not have a deterministic ordering, in which case a race condition occurs.

(Confusing as it may be, I believe this is standard terminology.)

(I find it baffling in the extreme that in many mainstream languages the convention is to write type annotations as “x: T”, both prima facie and because in those languages the notation then collides with field assignment!)

(The B language was implemented for the PDP-7 before the PDP-11, which are rather different machines. It’s sometimes suggested that the increment and decrement operators in C, which were inherited from B, are due to the instruction set architecture of the PDP-11, but this could not have been the case. Per Dennis Ritchie:¹

> Thompson went a step further by inventing the ++ and -- operators, which increment or decrement; their prefix or postfix position determines whether the alteration occurs before or after noting the value of the operand. They were not in the earliest versions of B, but appeared along the way. People often guess that they were created to use the auto-increment and auto-decrement address modes provided by the DEC PDP-11 on which C and Unix first became popular. This is historically impossible, since there was no PDP-11 when B was developed. The PDP-7, however, did have a few “auto-increment” memory cells, with the property that an indirect memory reference through them incremented the cell. This feature probably suggested such operators to Thompson; the generalization to make them both prefix and postfix was his own.

Another person puts it this way:²

> It's a myth to suggest C’s design is based on the PDP-11. People often quote, for example, the increment and decrement operators because they have an analogue in the PDP-11 instruction set. This is, however, a coincidence. Those operators were invented before the language [i.e. B] was ported to the PDP-11.

In any case, the PDP-11 usually gets all the love, but I want to make sure the other PDPs get some too!)

[1] https://www.bell-labs.com/usr/dmr/www/chist.html

[2] https://retrocomputing.stackexchange.com/questions/8869

This makes no sense to me – it’s not a feeling I can personally relate to. I’d like to raise kids because I’d enjoy getting to teach them and share things with them, but I don’t care whether they are my biological children or not.

So it’s something I’ve wondered about. The likely why makes sense, but I don’t really get the what.

In so many facets of our lives already, our wants are being manipulated for the benefit of others. And who am I to decide what is important? For things that involve other people, I’d rather make that decision collectively. I want the thoughts, opinions, and feelings of people who don’t possess or exercise charisma to have space and weight.

(Homepage) https://takoshell.org/index.html

(Differences from Xonsh) https://takoshell.org/xonsh.html

From what I recall, the size of a typical interword space is ⅓ of an em, and traditionally a bit more than this is inserted between sentences (but less than ⅔ of an em). The period itself introduces a fair amount of negative space, and only a skosh more is needed if any.

I think “cargo culting” in the popular sense means little more than that (whereas actual cargo culting is much more complex, as the featured article describes).

    U+00B7 MIDDLE DOT = midpoint (in typography); Georgian comma; Greek middle dot (ano teleia) • also used as a raised decimal point or to denote multiplication; for multiplication 22C5 is preferred

    U+22C5 DOT OPERATOR • preferred to 00B7 for denotation of multiplication

From the footnote on page 219 of Word by Word by Kory Stamper (formerly a lexicographer at Merriam-Webster):

> Here is the one thing that our pronunciation editor wishes everyone knew: those dots in the headwords, like at “co·per·nic·i·um,” are not marking syllable breaks, as is evident by comparing the placement of the dots with the placement of the hyphens in the pronunciation. Those dots are called “end-of-line division dots,” and they exist solely to tell beleaguered proof-readers where, if they have to split a word between lines, they can drop a hyphen.

I realize these questions may not even be posed sensibly; maybe the answer is as simple as, "the naturals are defined constructively here; of course they are the naturals and therefore are well-founded". As I said, it's been a while, so things are hazy in my mind.

Coq uses an inductive type like "N = 0 : N | S : N → N", and a first-order theory with integers axiomatized this way admits nonstandard models (whose prefixes are isomorphic to the naturals but have elements not reachable by repeated application of S, defeating infinite descent). But universal quantification in system F (inherited by the calculus of inductive constructions) corresponds to a fragment of second-order logic, where there is only one model (– the theory is categorical).

Is that right?