Formalising Foundations in Dependent Type Theories

See Vladimir Voevodsky - What if Current Foundations of Mathematics are Inconsistent. 

Subscribe to Formalization Seminar Cambridge.

Subscribe to ItaLean Conference. 

The state of the art three years ago:

Subscribe to Lean Prover Community. 

I came here because I heard this talk by Simon Willerton last week and he seems to be able to interpret some ideas like extanaturality from higher category theory into 2-category theory, but I am not sure about that: he doesn't say that's what he's done, it's just how it seems to me. 

Subscribe to Topos Institute. 

Comments

Post a Comment

Popular posts from this blog

Steven Johnson - So You Think You Know How to Take Derivatives?

Image
A derivative is linearisation, and differential calculus is essentially linear algebra, ...  See  Freya Holmér - Why Can't You Multiply Vectors?  and  Freya Holmér on Continuity of Splines . See also the MIT OCW page:  Matrix Calculus For Machine Learning And Beyond  (Alan Edelman, Steven G. Johnson) Subscribe to The Julia Programming Language . Alan Edelman talking about expressing mathematics as computer code. The idea is that you can use computer languages to communicate mathematical ideas precisely to other people. See my comments about functional programming languages here:  https://prooftoys.org/ian-grant/hm/ Subscribe to TEDx Talks .
Read more

Tensor Fields and Simplicial Complexes

Image
Listening to Freya Holmér last night I started to get glimmers of an idea I had long ago about how to represent vector spaces in computational processes using this recursive abstract type :  abstype 'a point = POINT   of {getx :  'a vector,       diff :  'a point -> 'a point,       move :  'a point -> 'a point,       scale : 'a -> 'a point,       proj :  'a point -> 'a} with    fun new i (op +) (op -) (op * ) dot =    let fun self x =  POINT       {getx = x,        move = fn (POINT pr) =>           (self (x + (#getx pr))),        diff = fn (POINT pr) =>          self (x - (#getx pr)),        scale = fn i =>          (self (x * i)),        proj = fn (POINT pr) =>     ...
Read more

Hitachi HD44780U LCD Display Fonts

Image
I finally got the bit-mapped fonts from the Hitachi "1602" display :  Here's some JavaScript: const HD44780U01ASCII=[ [],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[], [],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ], [4, 4, 4, 4, 0, 0, 4, 0, 0, 0, ], [10, 10, 10, 0, 0, 0, 0, 0, 0, 0, ], [10, 10, 31, 10, 31, 10, 10, 0, 0, 0, ], [4, 15, 20, 14, 5, 30, 4, 0, 0, 0, ], [24, 25, 2, 4, 8, 19, 3, 0, 0, 0, ], [12, 18, 20, 8, 21, 18, 13, 0, 0, 0, ], [12, 4, 8, 0, 0, 0, 0, 0, 0, 0, ], [2, 4, 8, 8, 8, 4, 2, 0, 0, 0, ], [8, 4, 2, 2, 2, 4, 8, 0, 0, 0, ], [0, 4, 21, 14, 21, 4, 0, 0, 0, 0, ], [0, 4, 4, 31, 4, 4, 0, 0, 0, 0, ], [0, 0, 0, 0, 12, 4, 8, 0, 0, 0, ], [0, 0, 0, 31, 0, 0, 0, 0, 0, 0, ], [0, 0, 0, 0, 0, 12, 12, 0, 0, 0, ], [0, 1, 2, 4, 8, 16, 0, 0, 0, 0, ], [14, 17, 19, 21, 25, 17, 14, 0, 0, 0, ], [4, 12, 4, 4, 4, 4, 14, 0, 0, 0, ], [14, 17, 1, 2, 4, 8, 31, 0, 0, 0, ], [31, 2, 4, 2, 1, 17, 14, 0, 0, 0, ], [2, 6, 10, 18, 31, 2, 2, 0, 0,...
Read more