B.Courcelle: Fundamental properties of infinite trees, Theoretical Computer Science, 25, pp. 95169, 1983.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....when their infinite expansions (obtained by unfolding recursion) form equivalent infinite trees. Recursive type definitions describe finite graphs with type operators at the nodes, hence it is possible to test the condition above in finite time, without actually generating infinite structures [Courcelle 83] 5.7. Mutable types Imperative programming is based on the notion of a mutable global store, together with constructs for sequencing the operations affecting the store. Mutability interacts very nicely with subtyping and polymorphism 2 , showing that the functional style approach ....

B.Courcelle: Fundamental properties of infinite trees, Theoretical Computer Science, 25, pp. 95-169, 1983.

....a model for data structures, program schemes and program executions. As early as 1976, Grard Huet proposed an algorithm for unifying in nite terms, that is solving equations in that algebra [11] Bruno Courcelle has studied the properties of in nite trees in the scope of recursive program schemes [8, 9]. Alain Colmerauer has described the execution of Prolog II, III and IV programs in terms of solving equations and disequations in that algebra [4 6, 1] Michael Maher has introduced and justi ed a complete theory of the algebra of in nite trees [12] Among others, he has shown that in this ....

Courcelle B., Fundamental Properties of Innite Trees, Theoretical Computer Science, 25(2), pp. 95169, March 1983.

....used to reason about pointers in ML [Tof90, MT91] where one needs to use coinduction which is di cult to mix with usual term structure. Alternatively the condition is also similar to the de nition of rational trees which are known to be implementable in a nite setting as cyclic graphs [Cou83] but with that approach we loose the possibility of observing the cycles. succ a Figure 1: Graph of succ(succ( Our solution is the special symbol . called back pointer used to give a representation of cyclic graphs as terms. Occurring as a leaf in a term, a is a reference to an ....

B. Courcelle. Fundamental Properties of Innite Trees. Theoretical Computer Science, 25:95169, 1983.

.... n (t 1 )6= n (t 2 )g otherwise where n (t) denotes the truncation at height n of the tree t. Now by adding to T [X] all the limits of Cauchy sequences of terms, we obtain the set T 1 [X] of nite and in nite terms and (T 1 [X] d) is a complete metric space (for more details, see [6]) The distance d can be extended to ground atoms and the new Herbrand base considered is the metric completion of At ; written At 1 ; Now, the operator T P is both continuous and # continuous and the main results coming from [1] are expressed as follows. Given a derivation: R ....

B. Courcelle. Fundamental properties of innite trees. Theoretical Computer Science, 25(2):95169, 1983.

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B.Courcelle: Fundamental properties of infinite trees, Theoretical Computer Science, 25, pp. 95169, 1983.

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B.Courcelle: Fundamental properties of infinite trees, Theoretical Computer Science, 25, pp. 95- 169, 1983.

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B.Courcelle: Fundamental properties of infinite trees, Theoretical Computer Science, 25, pp. 95169, 1983.

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