@MISC{Kotowicz_mmlidentifier:, author = {Jarosław Kotowicz and Beata Madras and Małgorzata Korolkiewicz}, title = {MML Identifier: UNIALG_1.}, year = {} }

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Abstract

The articles [5], [7], [6], [8], [2], [1], [4], and [3] provide the notation and terminology for this paper. For simplicity, we follow the rules: A denotes a set, x, y denote finite sequences of elements of A, h denotes a partial function from A ∗ to A, and n denotes a natural number. Let us consider A and let I1 be a partial function from A ∗ to A. We say that I1 is homogeneous if and only if: (Def. 1) For all x, y such that x ∈ domI1 and y ∈ domI1 holds lenx = leny. Let us consider A and let I1 be a partial function from A ∗ to A. We say that I1 is quasi total if and only if: (Def. 2) For all x, y such that lenx = leny and x ∈ domI1 holds y ∈ domI1. Let A be a non empty set. Observe that there exists a partial function from A ∗ to A which is homogeneous, quasi total, and non empty. We now state three propositions: (1) h is non empty iff domh � = /0. (2) Let A be a non empty set and a be an element of A. Then {εA} ↦− → a is a homogeneous