Dynamic Semantics and Type-checking of Tuple
				  by
			    Jianbing Chen

			       Abstract

In this paper, we address some issues in the multiple dispatch
language Tuple.  Specifically, the purpose and basic ideas of the
language Tuple, our implementation in Haskell of the dynamic semantics
and type checking, and the soundness proof of it's static type system
are presented. The program for the dynamic semantics looks like the
denotional semantics of the language. And the program for type
checking resembles the type inference rules in logic.

Keywords:  Tuple language, single dispatch, multiple dispatch, 
multimethods, subtype, type checking, semantic prototype, tuples.

1997 CR Categories:
D.3.1 [Programming Languages] Formal Definitions and Theory --- semantics;
D.3.2 [Programming Languages] Languages Classifications ---
       object-oriented languages;
D.3.3 [Programming Languages] Languages Constructs and Features ---
	abstract data types, control structures, procedures, functions,
 	and subroutines;
D.3.m [Programming Languages] Miscellaneous --- multimethods,
	single dispatch, multiple dispatch, type systems;
F.3.2 [Logics and Meanings of Programs] Semantics of Programming Languages ---
	denotational semantics;
F.3.3 [Logics and Meanings of Programs]	Studies of Program Constructs ---
       control primitives, type structure.