CSE-321 Programming Languages Polymorphism

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CSE-321 Programming LanguagesPolymorphism
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• POSTECH
• May 15, 2006

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Polymorphism

• The same piece of code can be reused for
  different types of objects
• parameteric polymorphism
• ad hoc polymorphism
• crafty polymorphism

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Parametric Polymorphism

• Operates on all types of objects in a uniform
  way.
• C templates
• The same C template is instantiated to
  different classes.
• cannot exploit specific properties of a given
  type.
• Java generics (J2SE 5.0)
• another name for polymorphism similar to C
  templates

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Ad hoc Polymorphism

• Different behavior depending on the type of
  objects it operates on
• Operator overloading
• operator in SML
• - 1 1
• val it 2 int
• - 1.0 1.0
• val it 2.0 real

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Outline

• Polymorphism V
• System F - syntax and reduction rules
• extension of the untyped ?-calculus with
  parametric polymorphism
• Crafty polymorphism
• System F - type system

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Type of

• Two tasks
• bind variable x to some type
• decide the type of the resultant expression
• Candidates (for the simply typed ?-calculus)

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Idea use "any type" ?

• Read ? as "any type"

expression
type
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Ambiguity
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How to distinguish between ? and ??
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Identity Function Again

• Let's apply the identity function to true.

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Type Application
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System F

• Impredicative Polymorphic ?-calculus

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Reduction Rules for System F
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Outline

• Polymorphism V
• System F - syntax and reduction rules V
• Crafty polymorphism
• extremely dangerous for programming
• System F - type system

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Polymorph in Warcraft II

• Permanent effect
• You may cast polymorph on your ally units!

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Polymorph in Warcraft III

• Temporary effect
• 60 seconds

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Polymorph in World of Warcraft?
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Outline

• Polymorphism V
• System F - syntax and reduction rules V
• Crafty polymorphism V
• System F - type system

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Composing Two Functions

• ? ! ? makes sense only after both ? and ? are
  declared.
• the order of elements in a typing context matters.

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Typing Contexts

• Ordered sets

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Valid or Invalid?
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Typing Rules
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Example
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Substitution Lemmas

• As usual, except

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Type Safety