new_definition : term -> thm

SYNOPSIS

Declare a new constant and a definitional axiom.

DESCRIPTION

The function new_definition provides a facility for definitional extensions. It takes a term giving the desired definition. The value returned by new_definition is a theorem stating the definition requested by the user. Let v_1,...,v_n be tuples of distinct variables, containing the variables x_1,...,x_m. Evaluating new_definition `c v_1 ... v_n = t`, where c is a variable whose name is not already used as a constant, declares c to be a new constant and returns the theorem:

   |- !x_1 ... x_m. c v_1 ... v_n = t

Optionally, the definitional term argument may have any of its variables universally quantified.

FAILURE CONDITIONS

new_definition fails if c is already a constant or if the definition does not have the right form.

EXAMPLE

A NAND relation on signals indexed by `time' can be defined as follows.

  # new_definition
       `NAND2   (in_1,in_2) out <=> !t:num. out t <=> ~(in_1 t /\ in_2 t)`;;
  val it : thm =
    |- !out in_1 in_2.
           NAND2 (in_1,in_2) out <=> (!t. out t <=> ~(in_1 t /\ in_2 t))

COMMENTS

Note that the conclusion of the theorem returned is essentially the same as the term input by the user, except that c was a variable in the original term but is a constant in the returned theorem. The function define is significantly more flexible in the kinds of definition it allows, but for some purposes this more basic principle is fine.