Type theories, normal forms, and D∞-lambda-models
Information and Computation
Set-theoretical and other elementary models of the &lgr;-calculus
Theoretical Computer Science - A collection of contributions in honour of Corrado Bo¨hm on the occasion of his 70th birthday
Journal of Computer and System Sciences
Full abstraction in the lazy lambda calculus
Information and Computation
A complete characterization of complete intersection-type preorders
ACM Transactions on Computational Logic (TOCL)
Domains for Denotational Semantics
Proceedings of the 9th Colloquium on Automata, Languages and Programming
Applicative Information Systems
CAAP '83 Proceedings of the 8th Colloquium on Trees in Algebra and Programming
The Y-combinator in Scott''s Lambda-calculus Models
The Y-combinator in Scott''s Lambda-calculus Models
Behavioural inverse limit λ-models
Theoretical Computer Science - Logic, semantics and theory of programming
The Parametric Lambda Calculus: A Meta-Model for Computation (Texts in Theoretical Computer Science)
The Parametric Lambda Calculus: A Meta-Model for Computation (Texts in Theoretical Computer Science)
Compositional characterisations of λ-terms using intersection types
Theoretical Computer Science - Mathematical foundations of computer science 2000
A filter model for the λµ-calculus
TLCA'11 Proceedings of the 10th international conference on Typed lambda calculi and applications
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Filter models and (solutions of) recursive domain equations are two different ways of constructing lambda models. Many partial results have been shown about the equivalence between these two constructions (in some specific cases). This paper deepens the connection by showing that the equivalence can be shown in a general framework. We will introduce the class of disciplined intersection type theories and its four subclasses: natural split, lazy split, natural equated and lazy equated. We will prove that each class corresponds to a different recursive domain equation. For this result, we are extracting the essence of the specific proofs for the particular cases of intersection type theories and making one general construction that encompasses all of them. This general approach puts together all these results which may appear scattered and sometimes with incomplete proofs in the literature.