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Initiality for Typed Syntax and Semantics

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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


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InitialityforTypedSyntaxandSemanticsBenediktAhrensUniversitéNiceSophiaAntipolisSéminaireGdTSémantique,PPS,ParisDecember13,2011
ATranslationfromPCFtoLCCPFITypedLanguageIAbstractionApplicationFixpointOperatorArithmetic&LogicConsts.Translationsi:PCFLCsuluclaCadbmaLIdepytnUitcartsbAIAApbpsltircaacttiioonni(λx.M)=λx.i(M)i(M@N))=i(M)@i(N)i(Fix(f))=Θi(f)ori(Fix(f))=Yi(f)...
Translation,mathematicallyMathematicalstructureofChallenges:IvaryingtypesPCFLC?Icapturecompatibilitywithsubstitution+reductionMorepreciselyIPCFLC?yrogetacemosnimsihpromIxErtatsrcutnirutieaiolnCLotpscefiyidffrenetushcrtnalstaoisn
Translation,mathematicallyMathematicalstructureofChallenges:IvaryingtypesPCFLC?Icapturecompatibilitywithsubstitution+reductionMorepreciselyIPCFLCinitialmorphisminsomecategory?IxErtatsrcuuternoCLotpscefiyidffrenetushcrtnalstaoisn
Translation,mathematicallyMathematicalstructureofChallenges:IvaryingtypesPCFLC?Icapturecompatibilitywithsubstitution+reductionMorepreciselyIPCFLCinitialmorphisminsomecategory?IExtrastructureonLCtospecifydifferentsuchtranslations