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A filter lambda model and the completeness of type assignment1

Published online by Cambridge University Press:  12 March 2014

Henk Barendregt ,
Mario Coppo  and
Mariangiola Dezani-Ciancaglini
Henk Barendregt
Affiliation:
Mathematisch Instituut, Utrecht, The Netherlands
Mario Coppo
Affiliation:
Istituto di Scienze dell'Informazione, Torino, Italy
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Extract

In [6, p. 317] Curry described a formal system assigning types to terms of the type-free λ-calculus. In [11] Scott gave a natural semantics for this type assignment and asked whether a completeness result holds.

Inspired by [4] and [5] we extend the syntax and semantics of the Curry types in such a way that filters in the resulting type structure form a domain in the sense of Scott [12]. We will show that it is possible to turn the domain of types into a λ-model, among other reasons because all λ-terms possess a type. This model gives the completeness result for the extended system. By a conservativity result the completeness for Curry's system follows.

Independently Hindley [8], [9] has proved both completeness results using term models. His method of proof is in some sense dual to ours.

For λ-calculus notation see [1].

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 48 , Issue 4 , December 1983 , pp. 931 - 940
Copyright
Copyright © Association for Symbolic Logic 1983

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Footnotes

1

Research partially supported by the Italian C.N.R. Grant 80.01917.97.

References

REFERENCES

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