CSE-321 Programming Languages
Let-polymorphism
박성우
POSTECH
May 22, 2006
System F
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Typing Rules
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Identity Function
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Outline
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System F V
Predicative polymorphic -calculus
Let-polymorphism
Value restriction
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Predicative Polymorphic -Calculus
• Sublanguage of System F
– decidable type reconstruction
System F
let-polymorphism
P.P. -calculus
undecidable
decidable
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Types in P.P. -Calculus
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Predicative Polymorphic -Calculus
A variable is assigned a monotype.
A type application uses a monotype.
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Typing Rules
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Polymorphic types in predicative
polymorphic -calculus are
USELESS!
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• Let's apply id to two different types bool and int.
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Outline
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System F V
Predicative polymorphic -calculus V
Let-polymorphism
Value restriction
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Let-binding
• let x = e in e'
– binds x to a polymorphic expression e.
– allows multiple occurrences of x in e'.
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Let-polymorphism
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Reduction of let-bindings
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Why not?
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다음 셋 영화의 공통점은?
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공통점?
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Outline
System F V
Predicative polymorphic -calculus V
Let-polymorphism V
Implicit polymorphism
– SML does not use let-polymorphism!
• Value restriction
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Implicit Polymorphism
• No type abstraction, no type application
• No type annotation in -abstraction
• An expression may have multiple types:
– x. x
• bool ! bool, int ! int, ..., 8. ! 
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Type System
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Example
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Outline
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System F V
Predicative polymorphic -calculus V
Let-polymorphism V
Implicit polymorphism V
Value restriction
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Prototypical Example
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Value Restriction
• Expression in the rule Gen must be a syntactic
value.
• If not, it must be used monomorphically.
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SML Example
- let val id = (fn y => y) (fn z => z) in id true end;
val it = true : bool
- let val id = (fn y => y) (fn z => z) in (id true, id 1) end;
stdIn:2.40-2.56 Error: operator and operand don't agree [literal]
operator domain: bool
operand:
int
in expression:
id 1
- let val id = (fn y => y) (fn z => z) in id end;
stdIn:1.1-1.46 Warning: type vars not generalized because of
value restriction are instantiated to dummy types (X1,X2,...)
val it = fn : ?.X1 -> ?.X1
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