CSE-321 Programming Languages Subtyping

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CSE-321 Programming LanguagesSubtyping
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• POSTECH
• May 14, 2007

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Key Features of Object-Oriented Languages

• Multiple representation
• different methods of the same name
• dynamic dispatch
• Encapsulation
• Only an object's own methods can see private
  data.
• Inheritance
• classes, subclasses, ...
• Subtyping
• interface, interface extension

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Outline

• Overview V
• Principle of subtyping
• Subtyping relations
• Coercion semantics

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Principle of Subtyping
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Examples
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Basic Rules

• Reflexivity and transitivity
• Rule of subsumption

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Subset Semantics for Subtyping

• Example
• 32-bit word for nat
• 32-bit word for int
• 64-bit word for float

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Outline

• Overview V
• Principle of subtyping V
• Subtyping relations
• Coercion semantics

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Setup
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Subtyping for Product Types
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Subtyping for Sum Types
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Subtyping for Function Types
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Subtyping for Reference Types
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You are all so gullible!
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Wrong Subtyping Rules!
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(No Transcript)
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(No Transcript)
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Subtyping for Function Types

• Covariant in return types B and B'
• Contravariant in argument types A and A'

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Dereferencing ref A
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Assigning to ref A
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Subtyping for Reference Types

• A B corresponds to dereferencing.
• B A corresponds to assigning a new value.
• Nonvariant (neither covariant nor contravariant)

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Subtyping for Array Types

• Array types extension of reference types
• Subtyping for array types in Java
• runtime overhead of dynamic tag-checks.

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Outline

• Overview V
• Principle of subtyping V
• Subtyping relations V
• Coercion semantics

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Coercion Semantics for Subtyping

• Example
• 32-bit word for int
• 64-bit word for float

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Coercion Subtyping Judgment
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Coherence

• All coercion functions for A B
• ) exhibit the same behavior.