Comments (4)
I think your second paragraph is right. There are no "universe variables" in the formal system of the book.
from book.
I'm not sure what you mean by "uniformly" introducing functions. There are certainly better ways to set up a theory of universes if you're going to implement it in a proof assistant, but I believe that in the Book the subscripts on universes are literally metatheoretic natural numbers, so they do have least upper bounds. The treatment of universes in the definition of things like function-types is, well, ambiguous, because it uses typical ambiguity, but I think the intent was that all types involved live in the same universe.
from book.
Thanks for the comment. To give a concrete example: if we have
Or maybe what I'm misunderstanding is the use of "variable indices", and a theorem involving them as in the book was meant to be a theorem schema involving every (metatheoretical) natural number.
That's what I meant by "uniformly" defining functions, doing so for every pair of variable indices, not just a pair of concrete ones. To be clear, I understand that metatheoretically we can show that we can do so for every concrete pair (and therefore all pairs), but, at least to me, one of the advantages of DTT was being able to internalize these sort of things through dependent protducts.
from book.
Thanks!
from book.
Related Issues (20)
- "term" vs "element" HOT 2
- Corollary 2.4.4. (use of naturality and whiskering) HOT 9
- Deducing propositional uniqueness for product types HOT 1
- Clarification of the proof of Lemma 6.2.9. (universal property of the circle) HOT 10
- The Cauchy real numbers satisfy the fundamental theorem of algebra and are not Cauchy complete in the rest of the constructive mathematics literature HOT 9
- Assumption that `A // R` is a set HOT 4
- Rules for universes in Appendix A.2 are incomplete HOT 3
- identity type usage HOT 19
- 自动驾驶更新笔记 Autopilot Updating Notes HOT 1
- Augment assumptions for Thm 5.4.4, 5.4.5, and 5.4.7 HOT 19
- Typos in proof of Lemma 10.3.12 HOT 5
- Use parentheses in the proof of Lemma 2.1.4(iii) HOT 3
- CI problem: "dubious ownership" HOT 1
- Provided Hashes in errata.pdf Not Found HOT 2
- Errata PDF unreadable
- Corollary 8.8.5 HOT 4
- Lemma 8.5.9 is missing a label
- Nightly builds pdfs are dead links HOT 8
- Exercise 7.3 could be made stronger
Recommend Projects
-
React
A declarative, efficient, and flexible JavaScript library for building user interfaces.
-
Vue.js
🖖 Vue.js is a progressive, incrementally-adoptable JavaScript framework for building UI on the web.
-
Typescript
TypeScript is a superset of JavaScript that compiles to clean JavaScript output.
-
TensorFlow
An Open Source Machine Learning Framework for Everyone
-
Django
The Web framework for perfectionists with deadlines.
-
Laravel
A PHP framework for web artisans
-
D3
Bring data to life with SVG, Canvas and HTML. 📊📈🎉
-
Recommend Topics
-
javascript
JavaScript (JS) is a lightweight interpreted programming language with first-class functions.
-
web
Some thing interesting about web. New door for the world.
-
server
A server is a program made to process requests and deliver data to clients.
-
Machine learning
Machine learning is a way of modeling and interpreting data that allows a piece of software to respond intelligently.
-
Visualization
Some thing interesting about visualization, use data art
-
Game
Some thing interesting about game, make everyone happy.
Recommend Org
-
Facebook
We are working to build community through open source technology. NB: members must have two-factor auth.
-
Microsoft
Open source projects and samples from Microsoft.
-
Google
Google ❤️ Open Source for everyone.
-
Alibaba
Alibaba Open Source for everyone
-
D3
Data-Driven Documents codes.
-
Tencent
China tencent open source team.
from book.