CS 792 Notes : Lecture 14

• P = {1, 2, 3, . . .} • Seq = {< n1, . . . , nk > | k > 0, n1, . . . , nk ∈ P}. p, q, r and s, possibly decorated, are metavariables ranging over Seq. • If p =< m1, . . . ,mk > and q =< n1, . . . , nl > then p ∗ q = 〈m1, . . . ,mk, n1, . . . , nl〉. • p ∗ 〈 〉 = 〈 〉 ∗ p = p for every p ∈ Seq. • p 6 q iff there is s such that p ∗ s = q. Definition 1.1 (Trees). T ⊆ Seq is a tree iff: 1. q ∈ T and p 6 q imply p ∈ T , 2. p∗ < n+ 1 >∈ T with n > 1 implies p∗ < n >∈ T . The subtree of T at node p is the tree Tp = {q | p ∗ q ∈ T }.