Syntactic considerations on recursive types

We study recursive types from a syntactic perspective. In particular, we compare the formulations of recursive types that are used in programming languages and formal systems. Our main tool is a new syntactic explanation of type expressions as functors. We also introduce a simple logic for programs with recursive types in which we carry out our proofs.

[1]  Andrew M. Pitts,et al.  Relational properties of recursively defined domains , 1993, [1993] Proceedings Eighth Annual IEEE Symposium on Logic in Computer Science.

[2]  D. Scott.  Identity and existence in intuitionistic logic , 1979 .

[3]  Roberto M. Amadio,et al.  Recursion over Realizability Structures , 1991, Inf. Comput..

[4]  Carl A. Gunter.  Semantics of programming languages: structures and techniques , 1993, Choice Reviews Online.

[5]  Martín Abadi,et al.  A PER model of polymorphism and recursive types , 1990, [1990] Proceedings. Fifth Annual IEEE Symposium on Logic in Computer Science.

[6]  Thierry Coquand,et al.  Inheritance as Implicit Coercion , 1991, Inf. Comput..

[7]  M. Fourman.  The Logic of Topoi , 1977 .

[8]  M. Beeson.  Formalizing constructive mathematics: Why and how? , 1981 .

[9]  Gordon D. Plotkin,et al.  The category-theoretic solution of recursive domain equations , 1977, 18th Annual Symposium on Foundations of Computer Science (sfcs 1977).

[10]  Marcelo P. Fiore.  Axiomatic domain theory in categories of partial maps , 1994 .

[11]  Luca Cardelli,et al.  Subtyping recursive types , 1991, POPL '91.

[12]  P. Freyd.  Algebraically complete categories , 1991 .

[13]  Peter J. Freyd,et al.  Recursive types reduced to inductive types , 1990, [1990] Proceedings. Fifth Annual IEEE Symposium on Logic in Computer Science.

[14]  Greg Nelson,et al.  Systems programming in modula-3 , 1991 .

[15]  Gordon D. Plotkin,et al.  Type theory and recursion , 1993, [1993] Proceedings Eighth Annual IEEE Symposium on Logic in Computer Science.

[16]  E. Moggi.  The partial lambda calculus , 1988 .

[17]  M. Beeson.  Foundations of Constructive Mathematics , 1985 .

[18]  Robin Milner,et al.  Edinburgh LCF , 1979, Lecture Notes in Computer Science.

[19]  Pawel Urzyczyn.  Positive Recursive Type Assignment , 1996, Fundam. Informaticae.

[20]  J. Hyland.  First steps in synthetic domain theory , 1991 .