LTT: a type-theoretic framework for foundational pluralism. Zhaohui Luo Dept of Computer Science Royal Holloway, Univ of London. Type theory and applications. Proof assistants based on TTs Agda (Sweden/Japan) and NuPRL (USA) implementing Martin-L öf’s type theory
Dept of Computer Science
Royal Holloway, Univ of London
ECC/UTT (Unifying Theory of dependent Types)
(C) Classical logic
(I) Impredicative definitions
We would have
Classical set theory/simple type theory, HOL/Isabelle
Martin-Löf’s TT, Agda/NuPRL
Weyl, Feferman, Simpson, …
Uniform foundational framework for formalisation to support pluralism?
Now, types for (i) and typed sets for (ii)!
LTT = LF + Logic-enriched TTs + Typed Sets
LTT = Logics + Types Logic Types
(Luo 2007, LNCS 4435.)
ElimT(C,c,f,0) = c
ElimT(C,c,f,succ(n)) = f(n,ElimT(C,c,f,n))
(cf, de Bruijn’s use of this terminology)
OO F ??
OO ITT Coq/Plastic/…