\DOC new_binder_definition
\TYPE {new_binder_definition : string * term -> thm}
\SYNOPSIS
Defines a new constant, giving it the syntactic status of a binder.
\DESCRIBE
The function {new_binder_definition} provides a facility for making
definitional extensions to the current theory by introducing a constant
definition. It takes a pair of arguments, consisting of the name under
which
the resulting theorem will be saved in the current theory segment and a
term
giving the desired definition. The value returned by
{new_binder_definition}
is a theorem which states the definition requested by the user.
Let {v1}, ..., {vn} be syntactically distinct tuples constructed from the
variables {x1,...,xm}. A binder is defined by evaluating
{
new_binder_definition (name, `b v1 ... vn = t`)
}
where {b} does not occur in {t}, all the free variables that
occur in {t} are a subset of {x1,...,xn}, and the type
of {b} has the form {(ty1->ty2)->ty3}. This declares {b} to be a new
constant with the syntactic status of a binder in the current theory, and
with
the definitional theorem
{
|- !x1...xn. b v1 ... vn = t
}
as its specification. This constant specification for {b} is saved
in the current theory under the name {name} and is returned as a theorem.
The equation supplied to {new_binder_definition} may optionally have any
of its
free variables universally quantified at the outermost level. The
constant {b}
has binder status only after the definition has been made.
\FAILURE
{new_binder_definition} fails if {t} contains free
variables that are not in any one of the variable structures {v1}, ...,
{vn} or
if any variable occurs more than once in {v1, ..., v2}. Failure also
occurs if
the type of {b} is not of the form appropriate for a binder, namely a
type of
the form {(ty1->ty2)->ty3}. Finally, failure occurs if there is a type
variable in {v1}, ..., {vn} or {t} that does not occur in the type of
{b}.
\EXAMPLE
The unique-existence quantifier {?!} is defined as follows.
{
- new_binder_definition
(`EXISTS_UNIQUE_DEF`,
Term`$?! = \P:(*->bool). ($? P) /\ (!x y. ((P x) /\ (P y)) ==>
(x=y))`);
> val it = |- $?! = (\P. $? P /\ (!x y. P x /\ P y ==> (x = y))) : thm
}
\COMMENTS
It is a common practice among HOL users to write a {$} before the
constant
being defined as a binder to indicate that it will have a special
syntactic
status after the definition is made:
{
new_binder_definition(name, Term `$b = ... `);
}
This use of {$} is not necessary; but after the definition
has been made {$} must, of course, be used if the syntactic status of {b}
needs to be suppressed.
\SEEALSO
Definition.new_definition, boolSyntax.new_infixl_definition,
boolSyntax.new_infixr_definition, Prim_rec.new_recursive_definition,
TotalDefn.Define.
\ENDDOC