Head Linear Reduction and Pure Proof Net Extraction

Abstract Proof net calculus introduced in Girard (1987) has been extended in the paradigm of Scott's domains equation D = D → D which generates a logical point of view for pure λ-calculus in Donos (1989). Methodologically speaking, in this paper the proof theoretic counterpart of Bohm's theorem given in Bohm (1968) for pure λ-calculus, is proposed as extension of the Curry-Howard paradigm. Technically 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 realizes managing and better understanding the procedure of extraction.

[1]  J. Krivine.  Lambda-calcul : types et modèles , 1990 .

[2]  Valeria C V de Paiva,et al.  Term Assignment for Intuitionistic Linear Logic , 1992 .

[3]  Jean-Yves Girard,et al.  Linear Logic , 1987, Theor. Comput. Sci..

[4]  Jean-Yves Girard,et al.  On the Unity of Logic , 1993, Ann. Pure Appl. Log..

[5]  Yves Lafont,et al.  Interaction nets , 1989, POPL '90.

[6]  Pasquale Malacaria,et al.  Some results on the interpretation of lambda -calculus in operator algebras , 1991, [1991] Proceedings Sixth Annual IEEE Symposium on Logic in Computer Science.

[7]  Henk Barendregt,et al.  The Lambda Calculus: Its Syntax and Semantics , 1985 .

[8]  Martín Abadi,et al.  Explicit substitutions , 1989, POPL '90.

[9]  Gianluigi Bellin,et al.  On the pi-Calculus and Linear Logic , 1992, Theor. Comput. Sci..

[10]  M. Nivat.  Fiftieth volume of theoretical computer science , 1988 .