Logical Types for Scheme Sam Tobin-Hochstadt PLT @ Northeastern - - PowerPoint PPT Presentation

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Logical Types for Scheme Sam Tobin-Hochstadt PLT @ Northeastern - - PowerPoint PPT Presentation

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Logical Types for Scheme Sam Tobin-Hochstadt PLT @ Northeastern University NEPLS, April 29, 2010 1 What do these languages have in common? COBOL Scheme Ruby Haskell 2 What do these languages have in common? COBOL

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Logical Types for Scheme

Sam Tobin-Hochstadt PLT @ Northeastern University NEPLS, April 29, 2010

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What do these languages have in common?

  • COBOL
  • Scheme
  • Ruby
  • Haskell

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What do these languages have in common?

  • COBOL [Komondoor 05]
  • Scheme [Tobin-Hochstadt 06]
  • Ruby [Furr 09]
  • Haskell [Vytiniotis 10]

New static checks

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What do these languages have in common?

  • COBOL [Komondoor 05]
  • Scheme [Tobin-Hochstadt 06]
  • Ruby [Furr 09]
  • Haskell [Vytiniotis 10]

Millions of lines of code

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Types for Existing Languages

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What’s Hard?

How programmers reason

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What’s Hard?

Simple Types How programmers reason

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What’s Hard?

Simple Types Reflection How programmers reason

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What’s Hard?

Simple Types Parametricity Reflection How programmers reason

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What’s Hard?

Simple Types Dependent Types Parametricity Reflection How programmers reason

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What’s Hard?

Simple Types Dependent Types Parametricity Reflection Generic Functions How programmers reason

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What’s Hard?

Simple Types Classes and Objects Dependent Types Parametricity Reflection Generic Functions How programmers reason

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Checking Existing Code

  • New static checking is valuable for existing code

Maintenance, Optimization, Trust

  • Work with existing idioms

Survey, Analyze, Design, Validate

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What Can We Learn?

  • New points in the design space

Ruby, Scheme, ...

  • New type system ideas

Occurrence Typing

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Occurrence Typing

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Simple Examples

#lang typed/scheme (: twice : Any -> Number) (define (twice x) (if (number? x) (* 2 x) 0))

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Simple Examples

#lang typed/scheme (: twice : Any -> Number) (define (twice x) (if (number? x) (* 2 x) 0)) Numberx

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Simple Examples

#lang typed/scheme (: twice : (U Number String) -> Number) (define (twice x) (if (number? x) (* 2 x) (* 2 (string-length x))))

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Simple Examples

#lang typed/scheme (: twice : (U Number String) -> Number) (define (twice x) (if (number? x) (* 2 x) (* 2 (string-length x)))) Numberx

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Logical Combination

#lang typed/scheme (: twice : (U Number String) -> Number) (: g : Any (U Number String) -> Number) (define (g x y) (cond [(or (number? x) (string? x)) (twice x)] [else 0]))

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Logical Combination

#lang typed/scheme (: twice : (U Number String) -> Number) (: g : Any (U Number String) -> Number) (define (g x y) (cond [(or (number? x) (string? x)) (twice x)] [else 0])) Numberx ∨ Stringx

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Logical Combination

#lang typed/scheme (: twice : (U Number String) -> Number) (: g : Any (U Number String) -> Number) (define (g x y) (cond [(or (number? x) (string? x)) (twice x)] [else 0])) Numberx ∨ Stringx (U Number String)x

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Logical Combination

#lang typed/scheme (: twice : (U Number String) -> Number) (: g : Any (U Number String) -> Number) (define (g x y) (cond [(and (number? x) (string? y)) (+ (twice x) (twice y))] [else 0]))

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Logical Combination

#lang typed/scheme (: twice : (U Number String) -> Number) (: g : Any (U Number String) -> Number) (define (g x y) (cond [(and (number? x) (string? y)) (+ (twice x) (twice y))] [else 0])) Numberx ∧ Stringy

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Logical Combination

#lang typed/scheme (: twice : (U Number String) -> Number) (: g : Any (U Number String) -> Number) (define (g x y) (cond [(and (number? x) (string? y)) (+ (twice x) (twice y))] [(number? x) (* 2 y)] [else 0]))

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Logical Combination

#lang typed/scheme (: twice : (U Number String) -> Number) (: g : Any (U Number String) -> Number) (define (g x y) (cond [(and (number? x) (string? y)) (+ (twice x) (twice y))] [(number? x) (* 2 y)] [else 0])) Numberx ∨ Stringy

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Logical Combination

#lang typed/scheme (: twice : (U Number String) -> Number) (: g : Any (U Number String) -> Number) (define (g x y) (cond [(and (number? x) (string? y)) (+ (twice x) (twice y))] [(number? x) (* 2 y)] [else 0])) Numberx ∨ Stringy , Numberx Stringy

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Logical Combination

#lang typed/scheme (: twice : (U Number String) -> Number) (: g : Any (U Number String) -> Number) (define (g x y) (cond [(and (number? x) (string? y)) (+ (twice x) (twice y))] [(number? x) (* 2 y)] [else 0])) (U Number String)y , Stringy Numbery

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Data Structures

#lang typed/scheme (: twice-car : (Pair Any Any) -> Number) (define (twice-car x) (if (number? (car x)) (* 2 (car x)) 0))

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Data Structures

#lang typed/scheme (: twice-car : (Pair Any Any) -> Number) (define (twice-car x) (if (number? (car x)) (* 2 (car x)) 0)) Number_car(x)

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Abstraction

#lang typed/scheme (: car-num? : (Pair Any Any) -> Boolean : Number @ car) (define (car-num? x) (number? (car x)))

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Abstraction

#lang typed/scheme (: car-num? : (Pair Any Any) -> Boolean : Number @ car) (define (car-num? x) (number? (car x)))

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Propositional Logic

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Judgments

Γ e : T ; φ1 | φ2

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Judgments

Γ e : T ; φ1 | φ2 e ::= n | c | (λ x : T . e) | (e e) | (if e e e)

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Judgments

Γ e : T ; φ1 | φ2 T ::= Number | (U T ...) | #t | #f | (x:T -> T : φ|φ)

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Judgments

Γ e : T ; φ1 | φ2 φ ::= T_π(x) | T_π(x) | φ1 ∨ φ2 | φ1 ∧ φ2 | φ1 ⊃ φ2

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Judgments

Γ e : T ; φ1 | φ2 φ ::= T_π(x) | T_π(x) | φ1 ∨ φ2 | φ1 ∧ φ2 | φ1 ⊃ φ2

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Judgments

Γ e : T ; φ1 | φ2 Γ ::= T_π(x) ...

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Judgments

Γ e : T ; φ1 | φ2 Γ ::= φ ...

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Judgments

Γ φ

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Judgments

Γ φ Numberx ∨ Stringy , Numberx Stringy

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Typing

(if e1 e2 e3)

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Typing

(if e1 e2 e3) Γ e1 : T1 ; φ_+|φ_-

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Typing

(if e1 e2 e3) Γ e1 : T1 ; φ_+|φ_- Γ,φ_+ e2 : T ; φ1_+|φ1_- Γ,φ_- e3 : T ; φ2_+|φ2_-

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Typing

(if e1 e2 e3) Γ e1 : T1 ; φ_+|φ_- Γ,φ_+ e2 : T ; φ1_+|φ1_- Γ,φ_- e3 : T ; φ2_+|φ2_-

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Typing

Γ (if e1 e2 e3) : T ; φ1_+∨φ2_+ | φ1_-∨φ2_- Γ e1 : T1 ; φ_+|φ_- Γ,φ_+ e2 : T ; φ1_+|φ1_- Γ,φ_- e3 : T ; φ2_+|φ2_-

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Typing

Γ (if e1 e2 e3) : T ; φ1_+∨φ2_+ | φ1_-∨φ2_- Γ e1 : T1 ; φ_+|φ_- Γ,φ_+ e2 : T ; φ1_+|φ1_- Γ,φ_- e3 : T ; φ2_+|φ2_-

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Typing

Γ (if e1 e2 e3) : T ; φ1_+∨φ2_+ | φ1_-∨φ2_- Γ e1 : T1 ; φ_+|φ_- Γ,φ_+ e2 : T ; φ1_+|φ1_- Γ,φ_- e3 : T ; φ2_+|φ2_-

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Typing

Γ x : T

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Typing

Γ x : T Γ Tx

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Try Typed Scheme

Installer and Documentation http://www.plt-scheme.org

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Try Typed Scheme

Installer and Documentation http://www.plt-scheme.org

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