A new type typename is installed in the type system.

The handler argument is either a procedure or a structured type describing the new type.

If handler is a procedure, then a type call of the form $\mathrm{type}\left(\mathrm{expr}\,\mathrm{typename}\right)$ results in a call to $\mathrm{handler}\left(\mathrm{expr}\right)$. Additional arguments can be passed to handler from a type call of the form $\mathrm{type}\left(\mathrm{expr},\mathrm{typename}\left(\mathrm{arg1},\mathrm{arg2},...\right)\right)$, which results in the call $\mathrm{handler}\left(\mathrm{expr},\mathrm{arg1},\mathrm{arg2},...\right)$. The handler argument, if it is a procedure, must return either true or false; no other return value is acceptable. It must also be prepared to handle any argument sequence that is passed to it.

If the handler argument is a structured type, then the type test is defined by the structured type interpreter as though the structured type were used directly in a call to type.

The AddType command returns NULL.

$\mathrm{TypeTools}\left[\mathrm{AddType}\right]\left(\mathrm{tff}\,'\left\{\mathrm{identical}\left(\mathrm{FAIL}\right)\,\mathrm{identical}\left(\mathrm{false}\right)\,\mathrm{identical}\left(\mathrm{true}\right)\right\}'\right)$

$\mathrm{type}\left(\mathrm{FAIL}\,'\mathrm{tff}'\right)$

$\mathrm{true}$

$\mathrm{type}\left(\left[\mathrm{true}\,\mathrm{false}\right]\,'\mathrm{list}\left(\mathrm{tff}\right)'\right)$

$\mathrm{true}$

$\mathrm{TypeTools}\left[\mathrm{AddType}\right]\left(\mathrm{integer7}\,t\mapsto \mathrm{evalb}\left(t::\mathrm{integer}\mathbf{and}\mathrm{irem}\left(t\,7\right)=0\right)\right)$

$\mathrm{type}\left(4\,'\mathrm{integer7}'\right)$

$\mathrm{false}$

$\mathrm{type}\left(28\,'\mathrm{integer7}'\right)$

$\mathrm{true}$

TypeTools[AddType]( pair, proc( expr, elementtype := anything )
    type( expr, [ elementtype, elementtype ] )
end proc ):

$\mathrm{type}\left(\left[2\,x\right]\,'\mathrm{pair}'\right)$

$\mathrm{true}$

$\mathrm{type}\left(\left[2\,x\right]\,'\mathrm{pair}\left(\mathrm{integer}\right)'\right)$

$\mathrm{false}$

$\mathrm{type}\left(\left[2\,3\right]\,'\mathrm{pair}\left(\mathrm{integer}\right)'\right)$

$\mathrm{true}$