Hereditarily Sequential Functionals

In order to define models of simply typed functional programming languages being closer to the operational semantics of these languages, the notions of sequentiality, stability and seriality were introduced. These works originated from the definability problem for PCF, posed in [Sco72], and the full abstraction problem for PCF, raised in [Plo77].

[1]  Guo-Qiang Zhang Logic of Domains , 1991, Progress in Theoretical Computer Science.

[2]  Klaus Weihrauch,et al.  Type 2 Recursion Theory , 1985, Theor. Comput. Sci..

[3]  Robin Milner,et al.  Fully Abstract Models of Typed lambda-Calculi , 1977, Theor. Comput. Sci..

[4]  J. Ersov Theorie der Numerierungen II , 1973 .

[5]  Pierre-Louis Curien,et al.  Sequential Algorithms on Concrete Data Structures , 1982, Theor. Comput. Sci..

[6]  S. C. Kleene,et al.  Recursive functionals and quantifiers of finite types. II , 1959 .

[7]  S. C. Kleene Recursive Functionals and Quantifiers of Finite Types Revisited II , 1980 .

[8]  Bruce M. Kapron,et al.  Characterizations of the basic feasible functionals of finite type , 1989, 30th Annual Symposium on Foundations of Computer Science.

[9]  V. Yu. Sazonov Expressibility of functions in D. Scott's LCF language , 1976 .

[10]  Pierre-Louis Curien,et al.  Categorical Combinators , 1986, Inf. Control..

[11]  Gerard Berry,et al.  Theory and practice of sequential algorithms: the kernel of the applicative language CDS , 1986 .

[12]  G.D. Plotkin,et al.  LCF Considered as a Programming Language , 1977, Theor. Comput. Sci..

[13]  R. Platek Foundations of recursion theory , 1966 .

[14]  Matthias Felleisen,et al.  Observable sequentiality and full abstraction , 1992, POPL '92.

[15]  R. O. Gandy Computable Functionals of Finite Type I , 1967 .

[16]  S. C. Kleene Recursive functionals and quantifiers of finite types revisited. V , 1991 .

[17]  Pierre-Louis Curien Observable algorithms on concrete data structures , 1992, [1992] Proceedings of the Seventh Annual IEEE Symposium on Logic in Computer Science.