Parametric parameter passing-calculus

A -calculus is defined, which is parametric with respect to a set V of input values and subsumes all the different -calculi given in the literature, in particular the classical one and the call-by-value -calculus of Plotkin. It is proved that it enjoy the confluence property, and a necessary and sufficient condition is given, under which it enjoys the standardization property. Its operational semantics is given through a reduction machine, parametric with respect to both V and a set Vo of output values. © 2003 Elsevier Inc. All rights reserved.

[1]  Benjamin C. Pierce,et al.  Types and programming languages: the next generation , 2003, 18th Annual IEEE Symposium of Logic in Computer Science, 2003. Proceedings..

[2]  Luca Paolini,et al.  La chiamata per Valore e La valutazione pigra nel λ-calcolo , 1998 .

[3]  Mariangiola Dezani-Ciancaglini,et al.  A CUCH-machine: The automatic treatment of bound variables , 1972, International Journal of Computer & Information Sciences.

[4]  Ralph Loader.  Notes on Simply Typed Lambda Calculus , 1998 .

[5]  Furio Honsell,et al.  Final Semantics for untyped lambda-calculus , 1995, TLCA.

[6]  Simona Ronchi Della Rocca,et al.  Call-by-value Solvability , 1999, RAIRO Theor. Informatics Appl..

[7]  R. David.  Une preuve simple de résultats classiques en λ calcul , 1995 .

[8]  J. Roger Hindley,et al.  Introduction to combinators and λ-calculus , 1986, Acta Applicandae Mathematicae.

[9]  Jan Willem Klop,et al.  Combinatory reduction systems , 1980 .

[10]  Masako Takahashi,et al.  Parallel reductions in λ-calculus (revised version) , 1992 .

[11]  William C. Frederick,et al.  A Combinatory Logic , 1995 .

[12]  Simona Ronchi Della Rocca.  Operational semantics and extensionality , 2000, PPDP '00.

[13]  P. J. Landin.  The Mechanical Evaluation of Expressions , 1964, Comput. J..

[14]  Hugo Herbelin,et al.  The duality of computation , 2000, ICFP '00.

[15]  A. Church.  The calculi of lambda-conversion , 1941 .

[16]  C.-H. Luke Ong,et al.  Full Abstraction in the Lazy Lambda Calculus , 1993, Inf. Comput..

[17]  Luca Roversi,et al.  The call-by-value [lambda]-calculus: a semantic investigation , 1999, Math. Struct. Comput. Sci..

[18]  Furio Honsell,et al.  Operational, denotational and logical descriptions: a case study , 1992, Fundam. Informaticae.