Are there any techniques or metrics to define or measure how

Question

Are there any techniques or metrics to define or measure how specific or generic something is That something could be a function or class in a programming language an algorithm or even something less formally defined like a component in a UI framework I m familiar with some measures of complexity like counting dependencies or cyclomatic complexity which seems somewhat related Appreciate any pointers to papers or articles about this even if they just define how something is more or less specific or generic than something else to support a hypothesis that is totally unrelated

duncanawoods · Answer

I m not sure what how specific or general would actually mean for a class If you get a really precise definition then you have probably defined how to measure it too

duncanawoods · Answer

It reminds me a bit of <https en wikipedia org wiki Chomsky hierarchy> the main technique for e g proving something is turing powerful is to show an isomorophism to a known system with proven properties

stevekrouse · Answer

In BV s ladder of abstraction the number of parameters in functional abstraction is the measure of abstraction

duncanawoods · Answer

Interesting The types involved feel like a huge factor for measuring generalisation specialisation e g `add a ushort b ushort` `add a int b int ` `add a double b double ` `add a any b any ` `add lt T gt a T b T ` `add lt T gt list T `

duncanawoods · Answer

I am reading An Introduction to General Systems Thinking right now and it is discussing how to measure the relative generality of scientific laws Weinberg claims that that laws should properly be defined as conditional if so He says that the fewer if so clauses the more general the law Applying this to code instead of looking inside the code for it s generality look outside at the context in which it can be used i e how many caveats are there about when it can or cannot be used

stevekrouse · Answer

Variables are also know as degrees of freedom

duncanawoods · Answer

Number of variables parameters doesn t seem like a good measure when we can just encode any number of variables into a goedel number

stevekrouse · Answer

Good point

stevekrouse · Answer

I feel like you re onto something with the types thread

stevekrouse · Answer

Can t we measure the length of the godel number

Tim Swast · Answer

The first thing that comes to my mind is <https en wikipedia org wiki Kolmogorov complexity> but you kind of want the inverse Given a parameterized definition what is the size of the space it covers

Joshua Horowitz · Answer

ya ll getting silly with this complexity theory fuss

Joshua Horowitz · Answer

FWIW it seems like the best way to think about specific vs general isn t as a quantitative measure but as a comparative relation X is more general than Y if there s a nice mapping from situations where you d use Y to situations where you could use X instead This is analogous to the concept of reducing problems in complexity theory egg on my face for talking smack about CT 5 minutes ago

Joshua Horowitz · Answer

There s a lot of wiggle room in that definition and rightfully so For instance is a Turing machine more general than ANY computational artifact Well yeah kind of Although the mapping from your function to the Turing machine will basically involve programming the function into the Turing machine so that s not that nice of a mapping

Joshua Horowitz · Answer

Two examples of particularly nice mappings Passing the exact same parameters along typecast into a more general type So `add a double b double ` is more general than `add a int b int ` Passing the exact same parameters along with a few extra parameters So `join list delimiter ` is more general than `joinWithCommas list `

Joshua Horowitz · Answer

But as the mapping becomes more and more complex writing wrapper code to adapt a library to a different style of API etc it becomes less and less nice and it becomes less and less clear that one artifact is more general than the other