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\DOC define_finite_type
\TYPE {define_finite_type : int -> thm}
\SYNOPSIS
Defines a new type of a specified finite size.
\DESCRIBE
The call {define_finite_type n} where {n} is a positive integer defines a new
type also called simply `{n}', and returns a theorem asserting that its
universe has size {n}, in the form:
{
|- (:n) HAS_SIZE n
}
\noindent where {(:n)} is the customary HOL Light printing of the universe set
{UNIV:n->bool}.
\FAILURE
Fails if {n} is zero or negative, or if there is a type of the same name
(unless it was also defined by the same call for {define_finite_type}, which is
perfectly permissible), or if the names of the type constructor and destructor
functions are already in use:
{
mk_auto_define_finite_type_n:num->n
dest_auto_define_finite_type_n:32->num
}
\EXAMPLE
Here we define a 32-element type, perhaps useful for indexing the bits of a
word:
{
# define_finite_type 32;;
val it : thm = |- (:32) HAS_SIZE 32
}
\USES
In conjunction with Cartesian powers such as {real^3}, where only the size of
the indexing type is relevant and the simple name {n} is intuitive.
\SEEALSO
define_type, new_type_definition.
\ENDDOC
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