Hi Bill,

on 21/3/14 6:19 AM, Bill Richter <rich...@math.northwestern.edu> wrote:

> ...
>
> T = ((λxbool . x) = (λxbool . x))
>
> So it looks to me that HOL Light is defining Tom's primitive = in terms of
> the Ocaml =.  Is that correct?  And maybe that just means that the HOL
Light
> primitive = is "represented" in Ocaml as the ordinary =?

No, not at all.  The above is defining the constant 'T'.  The constant '='
does not have a definition in HOL Light, or in any of the HOL
axiomatisations.  We have to start somewhere with entities that don't have
definitions but are just declared.  In HOL Light's axiomatisation, the only
such entities are the 'bool' and 'fun' type constants and the '=' constant
(the other axiomatisations also have the '==>' and '?' constants).  In the
logic, the meaning of such entities is not captured in definitions, but
instead "drops out" from the aggregation of the axioms and primitive
inference rules.

Best,

Mark.

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