Head Linear Reduction and Pure Proof Net Extraction

Mascari, G. F. and M. Pedicini, Head linear reduction and pure proof net extraction, Theoretical Computer Science 135 (1994) 111–137. Proof net calculus introduced in [10] has been extended in the paradigm of the Scott’s domains equation D = D → D which generates a logical point of view for pure λ-calculus in [7]. Methodologically speaking: in this paper the proof theoretic counterpart of the Böhm’s Theorem given in [6] for pure λ-calculus, is proposed as extention of the Curry-Howard paradigm. Tecnicallly speaking: as the extraction of a subterm using the β-reduction is possible also subnet extraction can be internalized by cut-elimination: using proof nets helps us to understand more deeply, and to handle in a better way the procedure of extraction.