Your definition of reliability seems different to how people use the word. I think most would consider a program that was statically checked, but often produces a wrong result as less reliable than a dynamically checked program that produces the right result.
>My argument is that in the totality of possible errors, statically typed programs have provably LESS errors and thus are definitionally MORE reliable than untyped programs. I am saying that there is ZERO argument here, and that it is mathematical fact. No amount of side stepping out of the bounds of the metric "reliability" will change that.
Making such broad statements about the real world with 100% confidence should already raise some eyebrows. Even through the lens of math and logic, it is unclear how to interpret your argument. Are you claiming that sum of all possible errors in all runnable programs in a statically checked language is less than sum of all possible errors in all runnable programs in an equivalent dynamically checked language? Both of those numbers are infinity, although i remember from school that some infinities are greater than others, I'm not sure how to prove that. And if such statement was true, how does it affect programs written in the real world?
Or is your claim that a randomly picked program from the set of all runnable statically checked programs is expected to have less errors than randomly picked program from the set of all runnable dynamically checked programs? Even this statement doesn't seem trivial, due to correct programs being rejected by type checker.
If your claim is about real world programs being written, you also have to consider that their distribution among the set of all runnable programs is not random. The amount of time, attention span and other resources is often limited. Consider the act of twisting an already correct program in various ways to satisfy the type checker, Consider the time lost that could be invested in further verifying the logic. The result will be much less clear cut, more probabilistic, more situation-dependent etc.
>My argument is that in the totality of possible errors, statically typed programs have provably LESS errors and thus are definitionally MORE reliable than untyped programs. I am saying that there is ZERO argument here, and that it is mathematical fact. No amount of side stepping out of the bounds of the metric "reliability" will change that.
Making such broad statements about the real world with 100% confidence should already raise some eyebrows. Even through the lens of math and logic, it is unclear how to interpret your argument. Are you claiming that sum of all possible errors in all runnable programs in a statically checked language is less than sum of all possible errors in all runnable programs in an equivalent dynamically checked language? Both of those numbers are infinity, although i remember from school that some infinities are greater than others, I'm not sure how to prove that. And if such statement was true, how does it affect programs written in the real world?
Or is your claim that a randomly picked program from the set of all runnable statically checked programs is expected to have less errors than randomly picked program from the set of all runnable dynamically checked programs? Even this statement doesn't seem trivial, due to correct programs being rejected by type checker.
If your claim is about real world programs being written, you also have to consider that their distribution among the set of all runnable programs is not random. The amount of time, attention span and other resources is often limited. Consider the act of twisting an already correct program in various ways to satisfy the type checker, Consider the time lost that could be invested in further verifying the logic. The result will be much less clear cut, more probabilistic, more situation-dependent etc.