Outline of a proof theory of parametricity (1991) [21 citations — 0 self]
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@INPROCEEDINGS{Mairson91outlineof,author = {Harry G. Mairson},
title = {Outline of a proof theory of parametricity},
booktitle = {Proc. 5th International Symposium on Functional Programming Languages and Computer Architecture},
year = {1991},
pages = {313--327},
publisher = {Springer-Verlag}
}
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Abstract:
Reynolds ' Parametricity Theorem (also known as the Abstraction Theorem), a result concerning the model theory of the second order polymorphic typed-calculus (F 2), has recently been used by Wadler to prove some unusual and interesting properties of programs. We present a purely syntactic version of the Parametricity Theorem, showing that it is simply an example of formal theorem proving in second order minimal logic over a first order equivalence theory on-terms. We analyze the use of parametricity in proving program equivalences, and show that structural induction is still required: parametricity is not enough. As in Leivant's transparent presentation of Girard's Representation Theorem for F 2, we show that algorithms can be extracted from the proofs, such that if a-term can be proven parametric, we can synthesize from the proof an "equivalent " parametric-term that is moreover F 2-typable. Given that Leivant showed how proofs of termination, based on inductive data types and structural induction, had computational content, we show that inductive data types are indeed parametric, hence providing a connection between the two approaches. 1
