groupoid.space
InfInfinity Language
http://www.groupoid.space/
Infinity Language
http://www.groupoid.space/
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Inf | groupoid.space Reviews
https://groupoid.space
Infinity Language
groupoid.space
Inf
http://groupoid.space/inf
AST Specification as Inductive Constructions. Inf Language is built on top of CoC pure type system, predicative universes and inductive constructions you may find in other MLTT provers like Lean, Coq, Idris, Agda, and F*. As algebraїс prover, Inf supports. Option [] : = #list I : = #identifier U : = *. O : = I ( O ) U O O O O ( I : O ) O λ ( I : O ) O L : = I L I A : = O A A ( L : O ) F : = F ( I : O ) () E : = O E data L : A := F E record L : A. Mdash; Macro Expansion. Mdash; Type Information Erasure.
Encoding
http://groupoid.space/enc
Categorical Semantics of Inductive Encodings. DATE: 1 MAY 2016. Let I = data List: (A:*) - * := (nil: () - List A) (cons: A - List A - List A). Record ListAlg: (A:*) - * := (X: *) (nil: () - X) (cons: A - X - X). Infix '=' := Setoid.Ob.Equ record ListMor: (A: *) - (x1 x2: ListAlg A) - * := (map: x1.X - x2.X) (okNil: Eq (map x1.nil) x2.nil) (okCons: (a: A) - (x: x1) - map x1.cons a x = x2.cons a (map x). Introduce connected points of List type. Def := Cat.mk () def := Cat.mk 𝟙. Category. The construc...
Om
http://groupoid.space/om
For typechecking and normalization. Language is a dependently typed lambda calculus, an extension of Barendregt' and Coquand Calculus of Constructions with the predicative hierarchy of indexed universes. There is no fixpoint axiom needed for the definition of infinity term dependance. Axioms and Inference Rules. All terms obey the. Ranking inside the sequence of. Universes, and the complexity. S = *{n}, n : nat A = *{i} : *{i 1} R = *{i} - *{j} : *{max i j}. I : = #identifier T : = I ( T ) T T λ I T.
Types
http://groupoid.space/types
Inductive Dependent Base Library. Inductive types are the dependent version of generalized algebraic data types used in ML. With inductive and coinductive types you can model polynomial higher order functors that define generic trees and their constructors. Two very basic and known inductions are over natural numbers and lists, we show them the more detailed description. Pointed Unary System is a category nat with the terminal object and a carrier. Nat, succ: nat nat]. The data type of. Is run-time versi...
Semantics
http://groupoid.space/semantics
Type judgement inference rules. DATE: 4 AUG 2016. Begin{equation} tag{sorts} dfrac {i : Nat} {Type i} end{equation}. Begin{equation} tag{axioms} dfrac {i: Nat} {Type i : Type {i 1} end{equation} $. Begin{equation} tag{rules} dfrac {i : Nat, j : Nat} {Type i rightarrow Type {j} : Type {max(i,j)} end{equation} $. Begin{equation} tag{subst} dfrac { pi 1 : A u:A π 2 : B} {[π 1/u] π 2 : B} end{equation}. Begin{equation} tag{$Id$-formation} dfrac {x:A b:A A:Type} {Id(A,a,b) : Type} end{equation}. Begin{equatio...
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5HT
http://5ht.co/index.html
Open Source Investment Portfolio. TL;DR The purpose of this document is to display investment landscape for business angels. It covers four GitHub organizations and their intellectual structure:. 1 Make full-stack certified software available to wider audience. For the true happiness of all sentient beings. 1 Create prototypes of full-stack parts in untyped languages (LISP or Erlang). 2 Avoid using C-like languages as much as possible (C, Go, JavaScript). Virtual Machines and Network Infrastructure.
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Inf
Mdash; Language with Dependent Types on top of Trusted λ Core with Changeable Encodings. And Extraction to Untyped Lambda Interpreter. 15 FEB 16 intro. 1 MAY 16 lambek encoding. 4 AUG 16 type judgment rules. 18 MAR 16 project status. 13 AUG 16 identities. 4 SEP 16 encoding. 2016—2017 Groupoid Infinity.
Ronald Brown, Emeritus Professor, web site: Topology, Groupoids, Grothendieck.
Bangor University, N. Wales, UK. Higher Dimensional Group Theory. Crossed Complexes and Homotopy Groupoids. BOOK - Topology and Groupoids. BOOK - Nonabelian Algebraic Topology. Higher Dimensional Group Theory. This book gives an account of algebraic topology at the border of homotopy and homology, capturing some nonabelian aspects in dimensions 1 and 2. A main intuition is to use subdivisions and, conversely, compositions, of cubes. Nonabelian Algebraic Topology - an example illustration. As the Presiden...
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