new_specification :
{name:string, sat_thm:thm,
 consts:{const_name:string, fixity:fixity} list} -> thm

SYNOPSIS

Introduces a constant or constants satisfying a given property.

DESCRIBE

The ML function new_specification implements the primitive rule of constant specification for the HOL logic. Evaluating:

   new_specification {name=name, sat_thm = |- ?x1...xn. t,
                      consts = [{const_name = "c1", fixity = f1}, ...,
                                {const_name = "cn", fixity = fn}]}

simultaneously introduces new constants named c1,...,cn satisfying the property:

   |- t[c1,...,cn/x1,...,xn]

This theorem is stored, with name name, as a definition in the current theory segment. It is also returned by the call to new_specification The fixities f1, ..., fn are values which determine the parsing status of the new constants. Typical fixity values are Prefix, Binder, Infixl n, Infixr n, Suffix n, TruePrefix n or Closefix.

FAILURE

new_specification fails if the theorem argument has assumptions or free variables. It also fails if the supplied constant names c1, ..., cn are not distinct. Finally, failure occurs if some ci does not contain all the type variables that occur in the term ?x1...xn. t.

USES

new_specification can be used to introduce constants that satisfy a given property without having to make explicit equational constant definitions for them. For example, the built-in constants MOD and DIV are defined in the system by first proving the theorem:

   th |- ?MOD DIV.
         !n. (0 < n) ==>
             !k. ((k = (((DIV k n) * n) + (MOD k n))) /\ ((MOD k n) < n))

and then making the constant specification:

   - val DIVISION = 
        new_specification
            {name = "DIVISION",
             consts = [{fixity = Infixl 650, const_name = "MOD"},
                       {fixity = Infixl 600, const_name = "DIV"}],
             sat_thm = th};

This introduces the constants MOD and DIV with the defining property shown above.

SEEALSO  new_definition,   new_binder_definition,   new_infixl_definition,   new_infixr_definition,   Define