Initiality for Typed Syntax and Semantics

Sophia Antipolis

Description

Initiality for Typed Syntax and Semantics Benedikt Ahrens Université Nice Sophia Antipolis Séminaire GdT Sémantique, PPS, Paris December 13, 2011

• operator arithmetic


• lambda calculus


• séminaire gdt


• application fixpoint


• logic consts


• benedikt ahrens

Sujets

• Antipolis
• Lambda calculus

Informations

• Publié par: pefav
• Nombre de lectures: 18
• Langue: English

Extrait

InitialityforTypedSyntaxandSemantics BenediktAhrens UniversitéNiceSophiaAntipolis SéminaireGdTSémantique,PPS,Paris December13,2011

ATranslationfromPCFtoLC CPF I TypedLanguage I Abstraction Application FixpointOperator Arithmetic& LogicConsts. Translationsi:PCF → LC suluclaCadbmaL I depytnU itcartsbA I A A p b p s l t i r c a a c t t i i o o n n i (λ x . M )=λ x . i ( M ) i(M@N))=i(M)@i(N) i ( Fix ( f ))=Θ � i ( f )
ori ( Fix ( f ))= Y � i ( f )
...

Translation,mathematically Mathematicalstructureof Challenges: I varyingtypes PCF → LC? I capturecompatibilitywithsubstitution+reduction Moreprecisely I PCF → LC?yrogetacemosnimsihprom I xErtatsrcut ni ru ti e ai o l nCLotpscefiyidffrenetushcrtnalstaoisn

Translation,mathematically Mathematicalstructureof Challenges: I varyingtypes PCF → LC? I capturecompatibilitywithsubstitution+reduction Moreprecisely I PCF → LCinitialmorphisminsomecategory? I xErtatsrcuuternoCLotpscefiyidffrenetushcrtnalstaoisn

Translation,mathematically Mathematicalstructureof Challenges: I varyingtypes PCF → LC? I capturecompatibilitywithsubstitution+reduction Moreprecisely I PCF → LCinitialmorphisminsomecategory? I ExtrastructureonLCtospecifydifferentsuchtranslations