LEARN DEPENDENTLY- TYPED PROGRAMMING WITH IDRIS WHO I AM - - PowerPoint PPT Presentation

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LEARN DEPENDENTLY- TYPED PROGRAMMING WITH IDRIS WHO I AM - - PowerPoint PPT Presentation

Oct 31, 2022 336 likes •741 views

LEARN DEPENDENTLY- TYPED PROGRAMMING WITH IDRIS WHO I AM @puffnfresh Tiny contributor to Idris (18 commits) Played with dependent types for 2 years Been doing Idris for 6 months ASSUMPTIONS Small experience with Haskell

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LEARN DEPENDENTLY- TYPED PROGRAMMING

WITH IDRIS

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WHO I AM

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▸ @puffnfresh ▸ Tiny contributor to Idris (18 commits) ▸ Played with dependent types for 2 years ▸ Been doing Idris for 6 months

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ASSUMPTIONS

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▸ Small experience with Haskell ▸ Have an install of Idris (can be tricky)

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$ brew install ghc cabal-install $ cabal update $ cabal install alex $ cabal install idris

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OUTLINE

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  • 1. Overview of dependent types and Idris
  • 2. Work through exercises, I lead
  • 3. Work through exercises, I help
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MOTIVATION

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Bad news: most software canoot be reasoned about

— Paul Phillips

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▸ Curry-Howard; programs are proofs ▸ Let's make our proofs interesting ▸ Therefore let's use a powerful type system

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MISCONCEPTIONS

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▸ Idris is harder than Haskell ▸ Dependent types are hard

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DEPENDENT TYPES

EVERYTHING IS A TERM

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isIdris : Bool isIdris = True

  • ne : Nat
  • ne = if isIdris then S Z else Z

StringList : Type StringList = if isIdris then List Char else Int

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▸ Types and kinds are values in universes ▸ Types can depend on values ▸ Fref polymorphism, type constructors

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the : (t : Type) -> (x : t) -> t the _ a = a

  • ne : Nat
  • ne = the Nat Z
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id1 : {t : Type} -> (x : t) -> t id1 {t} a = a id2 : (x : t) -> t id2 a = a id3 : t -> t id3 a = a

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Option : Type -> Type Option = Maybe

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TOTALITY

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$ idris --total $ idris --warnpartial %default total total plusOne : Nat -> Nat plusOne Z = S Z plusOne (S n) = S (S n)

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I am often asked ‘how do I implement a server as a program in your terminating language?’

— Conor McBride

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I reply that I do not: a server is a coprogram in a language guarantefing livenest

— Conor McBride

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▸ We always make progress ▸ Watch out for the totality checker! ▸ Church-Rosser theorem ▸ Evaluation is really normalisation! ▸ Can still do it all!

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EQUALITY

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data (=) : a -> b -> Type where refl : x = x x : 1 = 1 x = refl y : 1 + 1 = 2 y = refl

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x : {a : Nat} -> a - a = Z x {a=Z} = refl x {a=S k} = x {a=k} y : {a : Nat} -> a - a = Z y {a} = replace {P = \x => (a - x = Z)} (plusZeroRightNeutral a) (minusPlusZero a Z)

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x : {a : Nat} -> a - a = Z x = ?xproof xproof = proof intros rewrite (minusPlusZero a Z) rewrite (plusZeroRightNeutral a) trivial

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▸ The problem of dependent types ▸ Values are unified ▸ Checked for syntactic/term equality

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WHY IDRIS?

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▸ LLVM, C, Java, JS backends ▸ FFI ▸ Lots of syntactic sugar ▸ Tactic rewriting ▸ Allows more lying/cheating ▸ REPL, editor modes, doc tools

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HOW TO IDRIS

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▸ Idris Tutorial ▸ Idris library docs ▸ Idris library source ▸ Beginning Haskell: a Project Based Approach

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LET'S GO

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▸ printf ▸ Equality proofs ▸ Verified algebra ▸ Vector filtering

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http://goo.gl/gfCJne