lambda-list - a deftype lambda list.

declaration - a declare expression; not evaluated.

documentation - a string; not evaluated.

form - a form.

The meaning of the new type specifier is given in terms of a function which expands the type specifier into another type specifier, which itself will be expanded if it contains references to another derived type specifier.

The newly defined type specifier may be referenced as a list of the form (name arg₁ arg₂ ...) . The number of arguments must be appropriate to the lambda-list. If the new type specifier takes no arguments, or if all of its arguments are optional, the type specifier may be used as an atomic type specifier.

The argument expressions to the type specifier, arg₁ ... arg_n, are not evaluated. Instead, these literal objects become the objects to which corresponding parameters become bound.

The body of the deftype form (but not the lambda-list) is implicitly enclosed in a block named name, and is evaluated as an implicit progn, returning a new type specifier.

The lexical environment of the body is the one which was current at the time the deftype form was evaluated, augmented by the variables in the lambda-list.

Recursive expansion of the type specifier returned as the expansion must terminate, including the expansion of type specifiers which are nested within the expansion.

The consequences are undefined if the result of fully expanding a type specifier contains any circular structure, except within the objects referred to by member and eql type specifiers.

Documentation is attached to name as a documentation string of kind type.

If a deftype form appears as a top level form, the compiler must ensure that the name is recognized in subsequent type declarations. The programmer must ensure that the body of a deftype form can be evaluated at compile time if the name is referenced in subsequent type declarations. If the expansion of a type specifier is not defined fully at compile time (perhaps because it expands into an unknown type specifier or a satisfies of a named function that isn't defined in the compile-time environment), an implementation may ignore any references to this type in declarations and/or signal a warning.

 (defun equidimensional (a)
   (or (< (array-rank a) 2)
       (apply #'= (array-dimensions a))))   EQUIDIMENSIONAL
 (deftype square-matrix (&optional type size)
   `(and (array ,type (,size ,size))
         (satisfies equidimensional)))   SQUARE-MATRIX