​coda

​prelude

intermission

N2O,KVS,BPE and Erlang System Description

Calculus of Inductive Constructions and Action Semigroup

Properties of Replicated Chain Storage, etc.

intro

OSI and Unikernels

OSI Stack

Unikernels

Lisp Machines

Smalltalk-80

Singularity

MirageOS

HaLVM

LING

OSv

netbsd/rump

Voxoz  Synrc  Spawnproc

N2O 1.2K
KVS 1.2K
SHEN 220
NITRO 2.6K
MQS 288

BPE 625
FORMS 290
UPL 6K
LDAP 730
XA 2.2K

MAD 1K
FS 190
ACT 175

VZ 200

* — Lines of code

Lean/HoTT 10K

Prelude

CiC

 Axiom> ⊦ * : □

    R1> ⊦ * ↝ * : * 
    R2> ⊦ □ ↝ * : *
    R3> ⊦ * ↝ □ : □ 
    R4> ⊦ □ ↝ □ : □

∀ := Π x:A, B x
∃ := Σ x:A, B x
∧ := +

∨ := *
U := Prop : Type.{1} : Type.{2} ...

// *⟶*,a:A ⤂ f a

// rec induction

// rec coinduction

// <a:A,b:B a>

record app (P S : Type) :=
       (action  : P → S → S)​
       (spawn   : P → S)
       (run     : S → P)

action — effect handler
     P — protocol
     S — state

Semigroup Action

Π,Σ — provers

F*

Coq

Idris

Lean

Agda

CoInductive Structures, Type Classes

Polymorphic Stuctures, Type Classes

Type Classes

Type Classes

Type Classes, CoInductive Structures

Types and Effects

exception : rise
       io : read, write
    state : get, put
     comm : send, recv

      rnd : next

(action  : P → Eff P )​

Effects Encoding

Matija Pretnar
Gordon Plotkin
Andrej Bauer

eff-lang.org

Extensible Effects: an alternative to Monad Transformers

Oleg Kiselyov 

idris-lang.org

Edwin Brady

Linearizability

Transaction Logs
Chain Replication
Time Debugger
Statistics

Composing and Pipelining

Exe Model

Lean Network Proof

λ {A: Type.{1}}

  (a: A), a

1 #NS 0 A
2 #NS 1 a
1 #US 0
1 #ES 1
2 #EV 0
3 #EL #BD 2 2 2
4 #EL #BI 1 1 3

Notable:
Morte.Turtorial

Intermission

Intermission

definition ids   := option N
record container := (top: ids) (size: N)
record iterator  := (id: ids)
                    (next: ids) (prev: ids) 

Effects Persistence

Storage

record kv :=
       (get:   iterator → kvs)
       (put:   iterator → kvs)
       (index: iterator → kvs)

      record store extends app kvs container :=
             (sup: list container)
             (tab: list table)
             (tx:  iterator → container → container)

definition kvs := add + remove + reduce +
                  ok  + error  + io

Process

FS2

A scalaz-stream combinator library for Apache Camel, Akka Persistence and Akka Stream

Erlang

Open-source telecommunication platform created in Ericsson.

record task  := (name: string)
record event := (name: string)
record flow  := (source: task) (target: task)
record process extends iterator :=
       (env: list iterator)
       (tax: prod (prod (list task) (list flow))
                  (list event))

record proc extends app bpe process :=
       (sup: list process)

Specification

​Coda

Full-Stack Erlang

N2O Protocol

KVS

Packet Commands Transactions

> mnesia:activity(transaction, fun() ->
     kvs:append(#user{id=
     kvs:next_id("user",1)}) end).

[{get,container,_},
 {get,top,_},
 {put,iterator,_},
 {put,prev,_},
 {put,next,_},
 {put,container,_}].

KVS

> kvs:config(user).

[#in{l=902, r=infinity, name=user6, last=user2},
 #in{l=704, r=901,      name=user5, last=user2},
 #in{l=502, r=703,      name=user4, last=user2},
 #in{l=301, r=501,      name=user3, last=user},
 #in{l=200, r=300,      name=user2, last=user},
 #in{l=1,   r=199,      name=user,  last=user}]​

Chain Consistency
Link Atomic Txs
Record Versioning
Table Rotation
Distributed XA

N2O/BPE DSL

N2O Remote

BPE BPMN2