AdvTPL13 - Sound Definition: Chapter 13 SOOLs Type System...

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1 W. Pelz 2003-09 1 Chapter 13 SOOL’s Type System is Safe (and Sound) W. Pelz 2003-09 2 Sound • Definition: – Translation is sound if the translation function T C [| [| |] |] preserves typing • Demonstration: – If two types in SOOL are subtypes, then their translations are subtypes in Λ P <: – If C , ε E:T in SOOL, then T C [| [| C , ε E:T |] |] will have type will have type T C [| [|T |] |] W. Pelz 2003-09 3 Definition 13.1.1[240] • If C is a type constraint system and ε is a static type environment for SOOL, then let T C [| ε |]={x: T C [| [|T |] | |] | (x:T ε }. • Similarly, if C is a type constraint system for SOOL, let T C [| C |]={v <: T C [| [|T |] | |] | (v <:T) C }. W. Pelz 2003-09 4 Lemma 13.1.2 [240] • Suppose C and C = C {t <:T} are both type constraint systems. Then for all type expressions S T C [|S|]= T C [|S|] • Proof: use induction on the complexity of the type expressions noting that T C [|t|]= T C [|t|] W. Pelz 2003-09 5 Lemma 13.1.3 [240] • Let C and C be type constraint systems such that C ′= C C ′′ . Let S be a type expression that contains no type identifiers introduced in C ′′ . Then T C [|S|]=

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This note was uploaded on 02/21/2011 for the course CS 542 taught by Professor Dr. thomas during the Spring '10 term at SUNY Buffalo.

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AdvTPL13 - Sound Definition: Chapter 13 SOOLs Type System...

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