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A "linear graph" is effectively a graph with no cycles in it, i.e. a basic tree. All hierarchies can be described using graphs, and hierarchy is a relationship

A "linear graph" is effectively a graph with no cycles in it, i.e. a basic tree. All hierarchies can be described using graphs, and hierarchy is a relationship between different things in that graph through some dominating aspect (whatever that might be). A "linear hierarchy" is a hierarchy with no overlapping parts, no cycles, and a unique way to traverse up the hierarchy, e.g. you father is your son is not allowed, a node cannot be part of multiple hierarchies, a node has two parents which share a common ancestor, etc. I am not sure why you brought up my "Value" definition, that was a little random. > Unless you equate the graphs with their traverses? I mostly am because data structures on their own without algorithms are useless things. Type systems try to encode information about the values effectively restricting what algorithms can do to them. Ownership semantics are another aspect of the type system of some languages which encodes a responsibility dependency graph to values. This means it explicitly restricts what data structures can be like _by default_. It encourages linear data structures, where the dependency between the values can be model through linear logic. This is why something as basic as a linked list is difficult to implement in languages designed around ownership semantics. It is of course possible but either requires restricting what the linked lists can do, or doing something to bypass the ownership semantics entirely.

Joker_vD 6y ago
> I am not sure why you brought up my "Value" definition, that was a little random. Because your definition of "Value" is uncontroversial and customary, unlike your definition of "linear graph"--I have met it in your article for the first time. Granted, my knowledge is limited but that's my point exactly: if you bother to introduce the most basic concepts that your readers are most likely already accustomed with, then also please introduce the advanced concepts that you're about to discuss. If you feel that it makes the article too long, maybe consider removing the trivial definitions of the basic concepts, but not the other way around. I don't want to come off sounding aggressive or rude, and in fact I've read some other articles on your site with great interest, but this particular one leaves a bit of a taste of a maths article written by a crackpot: it starts with talking about what is a number, what is addition, talks about how numbers can also be multiplied and divided, a-a-a-and then in a blink of an eye it goes into very remoted areas of the number theory which may not actually exist (at least Googling them doesn't show anything relevant). In fact, googling "linear hierarchy" suggests that it's a term from biology, and it doesn't describe a graph or a tree at all: "In a linear hierarchy, there is one individual who dominates all the other group members, a second who dominates all but the top individual, and so on, down to the last individual who dominates no one" (Ivan D. Chase, Kristine Seitz, "Aggression", in Advances in Genetics, 2011). So "linear hierarchy" is apparently a linear (or "total", as it's also called) order, and it's actually consistent with the customary definition of "linear data structure": the one that arranges it's elements in a sequence, so arrays and linked lists (in fact, those used to be called "linear lists", see Wirth's "Algorithms + Data Structures = Programs" from the seventies) are linear data structures, but trees and graphs are not. To sum it: your usage of the term "linear" seems to be novel, and so it's confusing for someone who hasn't met it already, and arguably most of the readers haven't, maybe define it, even at the expense of defining what a "value" or an "agent" is? Those words you use in their customary senses.
- gingerBill 6y ago
  > this particular one leaves a bit of a taste of a maths article written by a crackpot That gave me a good laugh! I do understand the issue and I am not a brilliant writer in this regard. I was trying to make it understandable to the average programmer but also be at least "correct", and I think I have kind of failed at both in this article. I wanted to make sure that the ideas I was trying to express made sense not just to me or in speech form, but in written form too. I added all those definitions, including "value", because I know so many people who use the terms "value" and "object" interchangeably and assume all values are "objects" in the OOP sense. So I wanted to make a distinction between the two, as I wanted to emphasize the object-ness as the key relationship, not the value-ness. I am quite interested in how people build mental models of things and how they think about programming in general, but there is very little on the topic currently. And ownership semantics (even the name alone) has a lot of implicit assumptions tagged along to it that I wanted to understand. In sum, "ownership" is the wrong word but oh well, silly history. And yes, "linear hierarchy" does come from biology. It does mean "linear order" in that sense. That is a much better way of explaining it succinctly. Interesting you brought up Wirth, since he is one of my idols and that book is absolutely amazing. I always recommend Wirth to beginners wanting to learn how to write compilers.

Joker_vD 6y ago

> I am not sure why you brought up my "Value" definition, that was a little random. Because your definition of "Value" is uncontroversial and customary, unlike your definition of "linear graph"--I have met it in your article for the first time. Granted, my knowledge is limited but that's my point exactly: if you bother to introduce the most basic concepts that your readers are most likely already accustomed with, then also please introduce the advanced concepts that you're about to discuss. If you feel that it makes the article too long, maybe consider removing the trivial definitions of the basic concepts, but not the other way around. I don't want to come off sounding aggressive or rude, and in fact I've read some other articles on your site with great interest, but this particular one leaves a bit of a taste of a maths article written by a crackpot: it starts with talking about what is a number, what is addition, talks about how numbers can also be multiplied and divided, a-a-a-and then in a blink of an eye it goes into very remoted areas of the number theory which may not actually exist (at least Googling them doesn't show anything relevant). In fact, googling "linear hierarchy" suggests that it's a term from biology, and it doesn't describe a graph or a tree at all: "In a linear hierarchy, there is one individual who dominates all the other group members, a second who dominates all but the top individual, and so on, down to the last individual who dominates no one" (Ivan D. Chase, Kristine Seitz, "Aggression", in Advances in Genetics, 2011). So "linear hierarchy" is apparently a linear (or "total", as it's also called) order, and it's actually consistent with the customary definition of "linear data structure": the one that arranges it's elements in a sequence, so arrays and linked lists (in fact, those used to be called "linear lists", see Wirth's "Algorithms + Data Structures = Programs" from the seventies) are linear data structures, but trees and graphs are not. To sum it: your usage of the term "linear" seems to be novel, and so it's confusing for someone who hasn't met it already, and arguably most of the readers haven't, maybe define it, even at the expense of defining what a "value" or an "agent" is? Those words you use in their customary senses.

gingerBill 6y ago
> this particular one leaves a bit of a taste of a maths article written by a crackpot That gave me a good laugh! I do understand the issue and I am not a brilliant writer in this regard. I was trying to make it understandable to the average programmer but also be at least "correct", and I think I have kind of failed at both in this article. I wanted to make sure that the ideas I was trying to express made sense not just to me or in speech form, but in written form too. I added all those definitions, including "value", because I know so many people who use the terms "value" and "object" interchangeably and assume all values are "objects" in the OOP sense. So I wanted to make a distinction between the two, as I wanted to emphasize the object-ness as the key relationship, not the value-ness. I am quite interested in how people build mental models of things and how they think about programming in general, but there is very little on the topic currently. And ownership semantics (even the name alone) has a lot of implicit assumptions tagged along to it that I wanted to understand. In sum, "ownership" is the wrong word but oh well, silly history. And yes, "linear hierarchy" does come from biology. It does mean "linear order" in that sense. That is a much better way of explaining it succinctly. Interesting you brought up Wirth, since he is one of my idols and that book is absolutely amazing. I always recommend Wirth to beginners wanting to learn how to write compilers.