## Behavioural Inverse Limit λ-Models (2003)

### BibTeX

@MISC{Dezani-Ciancaglini03behaviouralinverse,

author = {Mariangiola Dezani-Ciancaglini and Silvia Ghilezan and Silvia Likavec},

title = {Behavioural Inverse Limit λ-Models},

year = {2003}

}

### OpenURL

### Abstract

We construct two inverse limit λ-models which completely characterise sets of terms with similar computational behaviours: the sets of normalising, head normalising, weak head normalising λ-terms, those corresponding to the persistent versions of these notions, and the sets of closable, closable normalising, and closable head normalising λ-terms. More precisely, for each of these sets of terms there is a corresponding element in at least one of the two models such that a term belongs to the set if and only if its interpretation (in a suitable environment) is greater than or equal to that element. We use the finitary logical description of the models, obtained by defining suitable intersection type assignment systems, to prove this.