Journal of Formalized Mathematics
Volume 5, 1993
University of Bialystok
Copyright (c) 1993 Association of Mizar Users

## On Defining Functions on Trees

Grzegorz Bancerek
Polish Academy of Sciences, Institute of Mathematics, Warsaw
Piotr Rudnicki
University of Alberta, Department of Computing Science, Edmonton

### Summary.

The continuation of the sequence of articles on trees (see [2], [3], [4], [5]) and on context-free grammars ([13]). We define the set of complete parse trees for a given context-free grammar. Next we define the scheme of induction for the set and the scheme of defining functions by induction on the set. For each symbol of a context-free grammar we define the terminal, the pretraversal, and the posttraversal languages. The introduced terminology is tested on the example of Peano naturals.

This work was partially supported by NSERC Grant OGP9207 while the first author visited University of Alberta, May--June 1993.

#### MML Identifier: DTCONSTR

The terminology and notation used in this paper have been introduced in the following articles [17] [10] [21] [19] [1] [23] [22] [8] [9] [6] [12] [14] [18] [15] [16] [7] [20] [13] [2] [3] [4] [5] [11]

#### Contents (PDF format)

1. Preliminaries
2. The set of parse trees
3. An example: Peano naturals
4. Properties of parse trees
5. The example continued
6. Tree traversals and terminal language

#### Bibliography

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Received October 12, 1993