(I need sleep, Ackermann is actually very easy to show as decreasing using lexicographic order).
Yeah, if you know that the recursive function always terminates, then you know that each recursive call makes the set of remaining steps strictly smaller.
When you want to prove termination, then it is exactly what you need to show (that the remaining work does get smaller, no cycles).
This probably is supposed to hint at a termination order. If a call to a recursive function terminates, then it it often (not always) possible to identify an ordering relation among the arguments of the call and the argument of the recursive call(s) within.
Though, there is also the Ackermann function... so for some recursive functions it is not be as easily seen why they would terminate.
Type theories are formal logic languages. People use formal logic for all sorts of things but mathematics has the longest history. This is where people first defined formal languages and assigned meaning (mathematical meaning.)
Starting from simply typed lambda calculus ("simple type theory", also "higher order logic"), one can make various extensions that make the logic language more expressive. The lambda cube is a way to systematically organize the space of type theories.
Interestingly, the theory has become very relevant for type systems of normal programming languages. Milner invented ML as "meta language" for helping with logic and theorem proving, but it was used widely and today everyone expects generics to work more or less as in System F polymorphic lambda calculus.
I understand the criticism to be targeted at the "web3" idea, which is assumed to be about the infrastructure for decentralized applications.
What is possible to implement is less relevant than what is likely to get implemented: here the clients (read: the app on the mobile) and their means of accessing the decentralized goodness matters.
The argument as I understand it is: if access/usage to whatever decentralized goods is always mediated by the old centralized approach (you have to ask the server whether the transaction is valid) then you trust the operators of the servers and those folks have the option of making "everything" (access to those services/goods) faster & better.
It is like the "last mile" problem where a company may well operate a global network but have no setup to act as ISP for end consumers, which is left to mediator. This is compatible with "web2" (https vpns etc) but the "web3" answer seems to be missing.
The problem is that benefits of well-thought out incentive systems evaporate when access is mediated. If every dapp comes with its own mobile client and app-specific servers to address this, there is nothing decentralized about it.
If this is to appeal to a community, there has to be some kind of incentive for that community to add their comments (content) to this site. What is it? Reputation?
In general, it could be appealing to have an open, established process for gathering public feedback on articles. It seems a scientific community would rather have their own version set up, where they could also curate content (rather than browse by category).
Also CS, my interpretation of "what makes science work" is a little different and I would argue that - despite a lot of foundations and techniques being shared in research papers - this field more than any other is constraining the free circulation and application of knowledge.
The equivalent to those biomedical industry players are the big tech who develop closed source and push the edge in some area. They will publish but that does not mean you can replicate any of it.
Software is also fragmented, crippled by IP lawsuits, patent trolls and so on. This does inhibit ability of society to benefit from software since it depends on the private sector to sort things out. The PhDs go and build businesses to "make the science work" in that sense.
The ideal of detached pursuit of knowledge is not a complete fiction (despite the hyperbole), but it does remain an ideal that can only be approximated.
I understood the criticism directed at the value of papers as instruments of knowledge sharing. The argument is not that papers are completely useless in terms of knowledge sharing but that this pure purpose of dissemination is largely overshadowed by considerations of carreer, prestige, funding or any interest other than knowledge sharing.
This is the world we live in. A scientist is a person that needs to make a living and is subject to various constraints.
The reason that there is little money to be made is that society hasn't found a way to set up the scientific process in such a way that the constraints would value the increase in public domain knowledge higher than the incentives to hold some knowledge back.
Part of this may stem from leaving specialized knowledge to academia while letting only companies reap the monetary rewards of putting the knowledge to use. Society benefits only indirectly (better drugs, machines, etc) but industry players will rather shield knowledge and adapt its representation to their own needs.
"A bowl is meant to stay being a bowl, it’s not supposed to turn into a plate or a vase, or to become square, or bigger or smaller. While the target is static, the world is dynamic, which is what makes it break."
This is lucid analogy since many times in software, people think the target (goal) is static, or static enough.
Sometimes though, there might be pressure to make the bowl bigger, smaller, into a plate, a vase and attach a straw, all at the same time.
Prolog was the first kind of logic programming that existed. It opened the door to a world but as a language and depending on the domain, it can be considered to have numerous deficiencies.
Constraints liberate. A datalog program for example can be considered a very restricted prolog program, but it is guaranteed to terminate and there are alternative evaluation strategies that can be very efficient.
It is true that tools can be emulated (RedHat doing podman as a docker replacement, with same flags) but it is also work.
I wonder whether in the Cloud world, the fan factor is a sign of credibility in a market that is looking for tooling that works across cloud providers.
Yeah, if you know that the recursive function always terminates, then you know that each recursive call makes the set of remaining steps strictly smaller.
When you want to prove termination, then it is exactly what you need to show (that the remaining work does get smaller, no cycles).