Practical Foundations of Mathematics
paultaylor.eu
Practical Foundations of Mathematics
1–10 of 24 posts
Re: Practical Foundations of Mathematics
#2A someone interested in programming language theory, this book looks very interesting. Unfortunately the HTML is incomplete and very hard to read, and the book itself is quite expensive.
Re: Practical Foundations of Mathematics
#3I think the author assumes u know how to apply a practical foundation. We need another book here.
Re: Practical Foundations of Mathematics
#4I think the author assumes u know how to apply a practical foundation. We need another book here.
https://news.ycombinator.com/item?id=20168936 probably will do the trick?
Re: Practical Foundations of Mathematics
#5>The logical calculus is easier to execute than any of the techniques of mathematics itself, yet only in 1934 did Gerhard Gentzen set it out in a natural way. Even now, mathematics students are expected to learn complicated (epsilon, delta)-proois in analysis with no help in understanding the logical structure of the arguments. Examiners fully deserve the garbage that they get in return.
With an opening like that how can I not read the rest of the book?
This actually touches on some work I've been doing the past week - arbitrary term rewriting to test how reliable a given LLM is when it needs to reason about symbolic manipulation. Everything is dynamically generated to avoid the usual problem of memorising every validation set every llm seems to suffer from.
Re: Practical Foundations of Mathematics
#6Looking at the table of contents, this seems like a really odd title. In what sense is this practical and a foundation for mathematics?
Re: Practical Foundations of Mathematics
#7Looking at the table of contents, this seems like a really odd title. In what sense is this practical and a foundation for mathematics?
> In what sense is this practical and a foundation for mathematics?
in a strong computational sense
Re: Practical Foundations of Mathematics
#8Looking at the table of contents, this seems like a really odd title. In what sense is this practical and a foundation for mathematics?
> In what sense is this practical and a foundation for mathematics? in a strong computational sense
Ah, now it makes sense, thanks! I was misinterpreting "of" as "for".
Re: Practical Foundations of Mathematics
#9I think the author assumes u know how to apply a practical foundation. We need another book here.
The practical application of these foundations is the field of programming language theory. At least that is the application I know of.
Whether programming language theory is practical or not depends, I think, on your attitude to programming languages. For example, if you think C is a masterpiece of clean and elegant design I suspect you won't have much time for programming language theory. If you think C is riddled with mistakes, then you will find solutions in programming language theory.
Re: Practical Foundations of Mathematics
#10I think the author assumes u know how to apply a practical foundation. We need another book here.
The practical application of these foundations is the field of programming language theory. At least that is the application I know of. Whether programming language theory is practical or not depends, I think, on your attitude to programming languages. For example, if you think C is a masterpiece of clean and elegant design I suspect you won't have much time for programming language theory. If you think C is riddled…
You do understand how a mathematical Theory (a set of true propositions made by relating operations i.e. from axioms and inference rules) and a Model (a set of elements with all the operations defined and where all the propositions are true) are related, i presume?
PLT is not one theory but a set of theories from which you are free to pick and choose any subset you would like to model in your language's abstract machine and syntax/semantics.
C simply chose a "minimal theory" and there is nothing wrong with that.