Introduction Background Operations & observability Outro Intro to Prometheus With a dash of operations & observability Richard Hartmann & Frederic Branczyk @TwitchiH & @fredbrancz 2018-12-12 Richard Richard Hartmann & Frederic Branczyk @TwitchiH & @fredbrancz Intro to Prometheus Introduction Background Operations & observability Outro Who are we? Richard ”RichiH” Hartmann Swiss army chainsaw at SpaceNet SIG-Instrumentation lead Prometheus team member Richard Hartmann & Frederic Branczyk @TwitchiH & @fredbrancz Intro to Prometheus Introduction Background Operations & observability Outro Time split 1 1/3 Prometheus

Intro: SIG VMware what is the SIG and what’s going on right now Steve Wong, Fabio Rapposelli Co-chairs VMware SIG Engineers VMware Cloud Native Applications Business Unit December 11, 2018 2 Open API to Deploy Clusters On-Prem and in Public Clouds – Loc Nguyen & Kris Nova Tomorrow • 1:45pm – Intro: Cloud Provider SIG – Chris Hoge & Jago Macleod Thursday • 10:50am – Deep Dive: Cloud Provider

applys in sequence: lemma prop_comp (a b c : Prop) (hab : a → b) (hbc : b → c) : a → c := begin intro ha, apply hbc, apply hab, apply ha end Putting on our mathematician’s hat, we can verbalize the Below, the thin, large square brackets � � enclose optional syntax. intro(s) intro � name � intros � name1 . . . namen � The intro tactic moves the leading ∀-quantified variable or the leading assump- Basic Tactics 25 with the unprovable subgoal ⊢ false. We say that apply is unsafe. In contrast, intro always preserves provability and is therefore safe. exact ex act lemma-or-hypothesis The ex act

hpq : p ∧ q, have hp : p, from and.left hpq, have hq : q, from and.right hpq, show q ∧ p, from and.intro hq hp If you are reading the book online, you will see a button that reads “try it!” Pressing the hypothesis and obtain a proof of implies p q. We could render this as follows: constant implies_intro : Π p q : Prop, (Proof p → Proof q) → Proof (implies p q). This approach would provide us with a expression and.intro h1 h2 builds a proof of p ∧ q using proofs h1 : p and h2 : q. It is common to describe and.intro as the and-introduction rule. In the next example we use and.intro to create a proof

Introduction Intro 2.0 to 2.2.1 2.4 - 2.6 Beyond Outro Prometheus Deep Dive Monitoring. At scale. Richard Hartmann & Frederic Branczyk @TwitchiH & @fredbrancz 2018-12-12 Richard Hartmann & Frederic Frederic Branczyk @TwitchiH & @fredbrancz Prometheus Deep Dive Introduction Intro 2.0 to 2.2.1 2.4 - 2.6 Beyond Outro Who are we? Richard ”RichiH” Hartmann Swiss army chainsaw at SpaceNet Project lead for Richard Hartmann & Frederic Branczyk @TwitchiH & @fredbrancz Prometheus Deep Dive Introduction Intro 2.0 to 2.2.1 2.4 - 2.6 Beyond Outro Show of hands Who has heard of Prometheus? Who is considering

introducing the first two hypotheses. example (a b : Prop) : a → b → a ∧ b := by do eh1 ← intro `h1, eh2 ← intro `h2, skip The backticks indicate that h1 and h2 are names; we will discuss these below. the tactic to print the current goal: example (a b : Prop) : a → b → a ∧ b := by do eh1 ← intro `h1, eh2 ← intro `h2, target >>= trace, admit In this case, the output is a ∧ b, as we would expect. We can eh1 ← intro `h1, eh2 ← intro `h2, local_context >>= trace, admit This yields the list [a, b, h1, h2]. We already happen to have representations of h1 and h2, because they were returned by the intro tactic

Introduction Quick intro OpenMetrics Outro OpenMetrics Standing on the shoulders of Titans Richard Hartmann, RichiH@{freenode,OFTC,IRCnet}, richih@{fosdem,debian,richih}.org, @TwitchiH 2018-12-11 RichiH@{freenode,OFTC,IRCnet}, richih@{fosdem,debian,richih}.org, @TwitchiH OpenMetrics Introduction Quick intro OpenMetrics Outro ‘whoami‘ Richard ”RichiH” Hartmann Swiss army chainsaw at SpaceNet Currently RichiH@{freenode,OFTC,IRCnet}, richih@{fosdem,debian,richih}.org, @TwitchiH OpenMetrics Introduction Quick intro OpenMetrics Outro Prometheus What’s Prometheus? You can’t talk about OpenMetrics without mentioning

mk a b in a context where the expression can be inferred to be a pair, and ⟨h1, h2⟩ denotes and. intro h1 h2 in a context when the expression can be inferred to be a conjunction. The notation will nest left h2, show p ∧ q, from and.intro h1 h3 example (p q r : Prop) : p → (q ∧ r) → p ∧ q := assume : p, assume : q ∧ r, have q, from and.left this, show p ∧ q, from and.intro ‹p› this example (p q r : Prop) Prop) : p → (q ∧ r) → p ∧ q := assume h1 : p, assume h2 : q ∧ r, suffices h3 : q, from and.intro h1 h3, show q, from and.left h2 Lean also supports a calculational environment, which is introduced with

We can provide such an expression explicitly: example (a b : Prop) : a ∧ b → b ∧ a := λ h, and.intro (and.right h) (and.left h) We can use projections and anonymous constructors to express the proof assume h : a ∧ b, have ha : a, from and.left h, have hb : b, from and.right h, show b ∧ a, from and.intro hb ha You can write proofs incrementally using sorry to temporarily fill in any intermediate step b ∧ a := assume h : a ∧ b, have ha : a, from sorry, have hb : b, from sorry, show b ∧ a, from and.intro hb ha Lean notices that you are cheating, but will otherwise confirm that the proof is correct modulo