Polymorphic System I

System I is a simply-typed lambda calculus with pairs, extended with an equational theory obtained from considering the type isomorphisms as equalities. In this work we propose an extension of System I to polymorphic types, adding the corresponding isomorphisms. We provide non-standard proofs of subject reduction and strong normalisation, extending those of System I.

[1]  Pablo Arrighi,et al.  A System F accounting for scalars , 2009, 0903.3741.

[2]  Thierry Coquand,et al.  The Calculus of Constructions , 1988, Inf. Comput..

[3]  Claude Kirchner,et al.  Theorem Proving Modulo , 2003, Journal of Automated Reasoning.

[4]  Alejandro D'iaz-Caro,et al.  Extensional proofs in a propositional logic modulo isomorphisms , 2020, Theor. Comput. Sci..

[5]  Jonghyun Park,et al.  Mechanizing Metatheory Without Typing Contexts , 2013, Journal of Automated Reasoning.

[6]  Gilles Dowek,et al.  Typing Quantum Superpositions and Measurement , 2016, TPNC.

[7]  Herman Geuvers,et al.  Pure Type Systems without Explicit Contexts , 2010, LFMTP.

[8]  Gérard Boudol,et al.  Lambda-Calculi for (Strict) Parallel Functions , 1994, Inf. Comput..

[9]  Alexandre Miquel,et al.  Realizability in the Unitary Sphere , 2019, 2019 34th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS).

[10]  Antonio Bucciarelli,et al.  A relational semantics for parallelism and non-determinism in a functional setting , 2012, Ann. Pure Appl. Log..

[11]  J. Girard,et al.  Proofs and types , 1989 .

[12]  Gilles Dowek,et al.  Proof Normalisation in a Logic Identifying Isomorphic Propositions , 2015, FSCD.

[13]  Lionel Vaux The algebraic lambda calculus , 2009, Math. Struct. Comput. Sci..

[14]  Roberto Di Cosmo Review of Isomorphisms of Types:: from λ-calculus to information retrieval and language design , 1997 .

[15]  Gilles Dowek,et al.  Non determinism through type isomorphism , 2012, LSFA.

[16]  Gilles Dowek,et al.  Lineal: A linear-algebraic Lambda-calculus , 2017, Log. Methods Comput. Sci..

[17]  ADOLFO PIPERNO,et al.  A FILTER MODEL FOR CONCURRENT -CALCULUS MARIANGIOLA DEZANI-CIANCAGLINI AND UGO DE'LIGUORO DIPARTIMENTO DI INFORMATICA UNIVERSIT , 1998 .

[18]  Michele Pagani,et al.  Linearity, Non-determinism and Solvability , 2010, Fundam. Informaticae.

[19]  Gilles Dowek,et al.  Proof normalization modulo , 1998, Journal of Symbolic Logic.

[20]  Jacques Garrigue,et al.  The typed polymorphic label-selective λ-calculus , 1994, POPL '94.

[21]  Mikael Rittri,et al.  Retrieving Library Identifiers via Equational Matching of Types , 1990, CADE.

[22]  Pablo E. Martínez López,et al.  Isomorphisms considered as equalities: Projecting functions and enhancing partial application through an implementation of λ+ , 2015, IFL '15.

[23]  Benoît Valiron,et al.  The Vectorial Lambda-Calculus , 2013, ArXiv.

[24]  Ugo de'Liguoro,et al.  Non deterministic extensions of untyped-calculus , 1995 .