Definition.new_definition

STRUCTURE

SYNOPSIS

Declare a new constant and install a definitional axiom in the current theory.

DESCRIPTION

The function new_definition provides a facility for definitional extensions to the current theory. It takes a pair argument consisting of the name under which the resulting definition will be saved in the current theory segment, and a term giving the desired definition. The value returned by new_definition is a theorem which states 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 (name, c v_1 ... v_n = t), where c is not already a constant, declares the sequent ({},\v_1 ... v_n. t) to be a definition in the current theory, and declares c to be a new constant in the current theory with this definition as its specification. This constant specification is returned as a theorem with the form

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

and is saved in the current theory under name. Optionally, the definitional term argument may have any of its variables universally quantified.

FAILURE

new_definition fails if t contains free variables that are not in x_1, ..., x_m (this is equivalent to requiring \v_1 ... v_n. t to be a closed term). Failure also occurs if any variable occurs more than once in v_1, ..., v_n. Finally, failure occurs if there is a type variable in v_1, ..., v_n or t that does not occur in the type of c.

EXAMPLE

A NAND relation can be defined as follows.

   - new_definition (
       "NAND2",
       Term`NAND2 (in_1,in_2) out = !t:num. out t = ~(in_1 t /\ in_2 t)`);

   > val it =
       |- !in_1 in_2 out.
              NAND2 (in_1,in_2) out = !t. out t = ~(in_1 t /\ in_2 t)
       : thm

SEEALSO

new_specification, new_binder_definition, new_infixl_definition, new_infixr_definition, new_recursive_definition, Define