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Control Operators and Natural Numbers are Robin Adams

Summary: Control Operators and Natural Numbers are
Robin Adams
September 20, 2010
We work in a type theory that has both -operators, and a type of natural
numbers. Suppose we have a term iszero such that
iszero0 1
iszero(Sn) 0
In addition to the above, our type theory has the following reduction rules:
S(.n) .[S[]/]n (1)
iszero(.n) .[iszero[]/]n (2)
[].n [/]n (3)
where, for C[] a context, the term
is defined to be the result of replacing every subterm of the form []M with
(There may be other reduction rules, too; we do not care.)
Consider the term
M .[]S(.[]0)
Theorem 1 The term iszeroM is not confluent.


Source: Adams, Robin - Department of Computer Science, Royal Holloway, University of London


Collections: Computer Technologies and Information Sciences