Normal interface

macro: (amb expr ...) => <top>

In the form (amb) the expression always fails.

If the expression has any parameters, the first one of them is evaluated and the result is returned. If a subsequent occurrence of amb fails, though, backtracking may cause the second of the given expressions to be selected for evaluation, then the third and so forth until the whole program does not fail if at all possible.

The backtracking mechanism is described along with the amb-failure-continuation parameter below.

macro: (amb/random expr ...) => <top>

Works like amb but the parameters are not selected in sequence but randomly. None of them is selected more than once, though.

macro: (amb-find expr #!optional failure-value) => <top>

Evaluates expr returning its value if successful (possibly after backtracking).

If expr cannot be evaluated successfully and the expression tree is exhausted, failure-value is evaluated and the result is returned instead. If no failure-value is specified, an exception occurs. See the amb-failure-continuation parameter below for a description of the exception.

macro: (amb-collect expr) => <list>

Evaluates expr and performs backtracking repeatedly until all possible values for it have been accumulated in a list, which is returned.

macro: (amb-assert ok?) => <void>

Evaluates ok? and fails if it is #f.

Additional stuff exported by amb-base

parameter: amb-failure-continuation

Seen in a global context, the amb operator transforms the whole program that contains it into a depth first search for return values from amb forms that will not cause failure.

This is realized using a backtracking system that invokes previously stored continuations whenever an amb expression fails. The amb-failure-continuation parameter is the status variable for this system.

At the start of the program, or when no further backtracking options are available, this is set to a procedure of no arguments that throws an exception of the composite (exn amb) kind (except when a amb-collect statement is being processed, where the parameter will point to a procedure signalling amb-collect that there are no more backtracking options available).

In all other cases this parameter is set to a procedure of no arguments that causes backtracking to the next possible alternative in the "tree".

If you want to restrict the scope of backtracking to something smaller than the whole past program, use amb-find or amb-collect which restore this parameter to its original value when they are done evaluating the expressions they were given.

procedure: (amb-thunks <list of procedures>) => <top>

The backend of amb. amb wraps all its parameters into thunks and passes a list of them into this procedure, amb/random shuffles the list first.

procedure: (amb-find-thunk <procedure> #!optional <procedure>) => <top>

The backend of amb-find. amb-find wraps its parameters into thunks and passes them into this procedure.

procedure: (amb-collect-thunk <procedure>) => <list>

The backend of amb-collect. amb-collect wraps its parameter into a thunk and passes it into this procedure.