This proposal for random numbers is not a literal transcription of the Common Lisp interface, but it uses the same concepts, and the text is a heavily edited version of the CLHS. I have added make-strong-random-source to what is in CL.
A random-source object is an encapsulation of the state information used by a pseudo-random number generator. Its state, which is implementation-dependent, can be printed out and successfully read back in by the same implementation, but might not function correctly as a random-source state in another implementation. Random-source objects are a disjoint type.
(make-random-source)
Constructs and returns a random-source object that has been randomly initialized by some implementation-defined means.
(make-strong-random-source)
Constructs and returns a random-source object whose state has been randomly initialized by some implementation-defined means. This may be the same as make-random-source, but should if possible use a truly random source of bits (such as /dev/random on certain systems) to initialize its state.
(make-random-source-from-state state)
Constructs and returns a random-source object whose state is a copy of state, so that mutating state does not affect the random-source object. It is an error to pass a mutated state object. The result will generate the same sequence of random numbers that the original random-source object would have generated as of the time random-source-state was invoked on it.
(random-source-state random-source)
Returns an implementation-specific object representing a copy of the state encapsulated by random-source. This object must be printable and rereadable. It must also be suitable for passing to make-random-source-from-state. Providing this mechanism makes it possible to save and reconstitute a random-source in a file or database, or to pass it across a network to an equivalent implementation. Mutating the result of this procedure does not affect random-source.
(copy-random-source random-source)
Constructs and returns a random-source object whose state is an independent copy of the state of random-source. Calling this procedure is equivalent to (make-random-source-from-state (random-source-state random-source), but potentially more efficient because it can avoid copying the state twice. The result and random-source will henceforth return the same sequence of values, allowing the same series of pseudo-random numbers to be generated many times within a single program.
(current-random-source [random-source])
A parameter that returns or sets the default random-source object. Its initial value must be a random-source object, but is implementation-dependent.
(random limit [random-source])
Returns a pseudo-random number that is a non-negative number less than limit. Limit must be an exact integer (in which case random returns an exact integer), or an inexact real number (in which case random returns an inexact real number).
If the random-source, which is modified by this function, encapsulates the internal state maintained by the random number generator. If not specified, the value of (current-random-source) is used.
An approximately uniform choice distribution is used. If limit is an integer, each of the possible results occurs with (approximate) probability 1/limit.