The function (backchain goal rules facts) tries to prove a goal given a set of rules and facts. goal is a symbol (atom or propositional variable). facts is a list of atoms that are known to be true. rules is a list of rules of the form (conclusion prem1 ... premn ); each rule states that the conclusion is true if all of the premises are true. For example, the rule A &and B &rarr C would be written (c a b).
backchain works as follows: if the goal is known to be a fact, return true. Otherwise, try rules to see if some rule has the goal as conclusion and has premises that are true (using backchain).
(defun backchain (goal rules facts) (or (member goal facts) (some #'(lambda (rule) (and (eq (car rule) goal) (every #'(lambda (subgoal) (backchain subgoal rules facts)) (cdr rule)))) rules)) )
> (backchain 'e '((c a b) (e c d)) '(a b d)) T
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