[TYPES] semantics of `quote'
Thomas Streicher
streicher at mathematik.tu-darmstadt.de
Fri Jul 14 08:11:53 EDT 2006
Does anyone know of a reference to work on (denotational) semantics of
`quote' constructs in functional languages like LISP?
Probably there is nothing like that since the operational evaluation rule
quote M -> "M" (where "M" is e.g. a Goedel number for M)
induces an onservational equivalence coinciding with syntactic equality.
Well, there should be variants if quote is call-by-value where the meaning
of quote M is a Goedel number of the weak head normal form of M.
More generally, one might ask for quote constructs \libqu where
\libqu M -> "N" such that M and N have the same denotation (whatever this is).
The reason why I am asking this on TYPES is that languages with (a kind of)
quote seem to be necessary for constructing realizabilty models of Martin-Loef
type theory validating Church's Thesis
(\Pi f : N \to N) (\Sigma e : N) (\Pi n:N) {e}(n) = f(n)
a question brought up recently by M.Maietti and G. Sambin.
My impression is that a quote construct seems to be incompatible with
the \xi-rule
M = N
-------------
\x.M = \x.N
Best regards, Thomas
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