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Exploring Predicative Polymorphic λ-Calculus: Concepts and Applications

This document delves into the intricacies of Predicative Polymorphic λ-Calculus, addressing key concepts such as Let-polymorphism and implicit polymorphism. We explore the distinctions between untyped and typed systems, examining examples of typable and untypable expressions. The content emphasizes the practical applications of polymorphism, acknowledging challenges in complete implementation. Referencing course notes and presentations, this resource serves as a concise guide for students and scholars interested in advanced type systems within functional programming paradigms.

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Exploring Predicative Polymorphic λ-Calculus: Concepts and Applications

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  1. Polymorphism CSED 321 CSE 정진웅

  2. Polymorphism • Predicative polymorphic λ-calculus • Let-polymorphism • Implicit polymorphism

  3. Predicative polymorphic λ-calculus Untyped Typed Untypable e’ Typable e ’ ’ e

  4. Predicative polymorphic λ-calculus • Untyped • λ x . x • Typed • λ x : int . x • λ x : bool . x

  5. Predicative polymorphic λ-calculus • Monotype • A ::= A →A | α • Polytype • U ::= A | ∀ α.U

  6. Predicative polymorphic λ-calculus • Polymorphism을 완벽하게 구현하지 못함 • Just polymorphism을 적용!

  7. Let-polymorphism • polytype을 typing하는 방법

  8. Let-polymorphism

  9. Let-polymorphism U Untyped Typable(with system F) Typable(with let-poly) Typable(with predictive-poly)

  10. Implicit polymorphism • untyped -> typed

  11. Implicit polymorphism

  12. References • Course note • 김봉준 선배’s PPT

  13. Thank you

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