Abstract Syntax and Variable Binding for Linear Binders

We apply the theory of binding algebra to syntax with linear binders. We construct a category of models for a linear binding signature. The initial model serves as abstract syntax for the signature. Moreover it contains structure for modelling simultaneous substitution. We use the presheaf category on the free strict symmetric monoidal category on 1 to construct models of each binding signature. This presheaf category has two monoidal structures, one of which models pairing of terms and the other simultaneous substitution.

[1]  Gordon D. Plotkin,et al.  An axiomatisation of computationally adequate domain theoretic models of FPC , 1994, Proceedings Ninth Annual IEEE Symposium on Logic in Computer Science.

[2]  Gordon D. Plotkin,et al.  Towards a mathematical operational semantics , 1997, Proceedings of Twelfth Annual IEEE Symposium on Logic in Computer Science.

[3]  Peter W. O'Hearn.  A Model for Syntactic Control of Interference , 1993, Math. Struct. Comput. Sci..

[4]  A. Joyal.  Une théorie combinatoire des séries formelles , 1981 .

[5]  Eugenio Moggi,et al.  Computational lambda-calculus and monads , 1989, [1989] Proceedings. Fourth Annual Symposium on Logic in Computer Science.

[6]  B. Day.  On closed categories of functors , 1970 .

[7]  Christopher Strachey,et al.  The varieties of programming language , 1972 .

[8]  Andrew M. Pitts,et al.  A new approach to abstract syntax involving binders , 1999, Proceedings. 14th Symposium on Logic in Computer Science (Cat. No. PR00158).

[9]  Masahito Hasegawa.  Logical Predicates for Intuitionistic Linear Type Theories , 1999, TLCA.

[10]  A. J. Power,et al.  Enrichment through variation , 1997 .

[11]  Andrew Barber,et al.  Dual Intuitionistic Linear Logic , 1996 .

[12]  John McCarthy,et al.  Towards a Mathematical Science of Computation , 1962, IFIP Congress.

[13]  de Ng Dick Bruijn.  Lambda calculus notation with nameless dummies, a tool for automatic formula manipulation, with application to the Church-Rosser theorem , 1972 .

[14]  Gordon D. Plotkin,et al.  Abstract syntax and variable binding , 1999, Proceedings. 14th Symposium on Logic in Computer Science (Cat. No. PR00158).

[15]  Peter W. O'Hearn,et al.  Algol-Like Languages: v. 2 , 1996 .

[16]  G. M. Kelly,et al.  A universal property of the convolution monoidal structure , 1986 .

[17]  Peter W. O'Hearn,et al.  From Algol to polymorphic linear lambda-calculus , 2000, JACM.

[18]  Philippa Gardner,et al.  From Action Calculi to Linear Logic , 1997, CSL.

[19]  A. Joyal.  Foncteurs analytiques et espèces de structures , 1986 .