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Correspondence between Operational and Denotational Semantics
 Handbook of Logic in Computer Science
, 1995
"... This course introduces the operational and denotational semantics of PCF and examines the relationship between the two. Topics: Syntax and operational semantics of PCF, Activity Lemma, undefinability of parallel or; Context Lemma (first principles proof) and proof by logical relations Denotational ..."
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This course introduces the operational and denotational semantics of PCF and examines the relationship between the two. Topics: Syntax and operational semantics of PCF, Activity Lemma, undefinability of parallel or; Context Lemma (first principles proof) and proof by logical relations Denotational semantics of PCF induced by an interpretation; (standard) Scott model, adequacy, weak adequacy and its proof (by a computability predicate) Domain Theory up to SFP and Scott domains; non full abstraction of the standard model, definability of compact elements and full abstraction for PCFP (PCF + parallel or), properties of orderextensional (continuous) models of PCF, Milner's model and Mulmuley's construction (excluding proofs) Additional topics (time permitting): results on pure simplytyped lambda calculus, Friedman 's Completeness Theorem, minimal model, logical relations and definability, undecidability of lambda definability (excluding proof), dIdomains and stable functions Homepa...
Parallel PCF has a Unique Extensional Model
 In Proc. 6th IEEE Annual Symp. Logic in Computer Science
, 1991
"... We show that the continuous function model is the unique extensional (but not necessarily pointwise ordered) model of the variant of the applied typed lambda calculus PCF that includes the "parallel or" operation. 1 Introduction Several extensional models of the applied typed lambda calculus PCF ar ..."
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We show that the continuous function model is the unique extensional (but not necessarily pointwise ordered) model of the variant of the applied typed lambda calculus PCF that includes the "parallel or" operation. 1 Introduction Several extensional models of the applied typed lambda calculus PCF are known to exist, including: (i) The continuous function model, which is orderextensional (pointwise ordered) but not equationally fully abstract [Plo]. (A model is equationally fully abstract when terms are identified in the model exactly when they are operationally equivalent.) (ii) The stable function model, which is neither orderextensional nor equationally fully abstract [Ber][BCL]. (iii) The terminal object of the category of equationally fully abstract, extensional models, which is inequationally fully abstract and orderextensional [Mil][Sto2]. (A model is inequationally fully abstract iff one term is less than another in the model exactly when the first is operationally less defin...
Lambda Calculus
"... Recursive functions are representable as lambda terms, and de nability in the calculus may be regarded as a de nition of computability. This forms part of the standard foundations of computer science. Lambda calculus is the commonly accepted basis of functional programming languages � and it is folk ..."
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Recursive functions are representable as lambda terms, and de nability in the calculus may be regarded as a de nition of computability. This forms part of the standard foundations of computer science. Lambda calculus is the commonly accepted basis of functional programming languages � and it is folklore that the calculus is the prototypical functional language in puri ed form. The course investigates the syntax and semantics of lambda calculus both as a theory of functions from a foundational point of view, and as a minimal programming language. Synopsis Formal theory, xed point theorems, combinatory logic: combinatory completeness, translations between lambda calculus and combinatory logic � reduction: ChurchRosser theorem � Bohm's theorem and applications � basic recursion theory � lambda calculi considered as programming languages � simple type theory and pcf: correspondence between operational and denotational semantics � current developments. Relationship with other courses Basic knowledge of logic and computability in paper B1 is assumed.