S. Kahrs, -rewriting, PhD thesis, Universitat Bremen, 1991. (in German)  Home/Search   Document Not in Database   Summary   Related Articles   Check

....form is usually regarded as a trivial change of notation. This is less obvious in presence of a powerful type discipline and higher order terms. In [528] it is proved that currying preserves confluence of arbitrary term rewriting systems. This is based on an earlier proof of the same result in [523], but a more thorough proof was devised to counter [548] where the opposite result is claimed and the construction of a counter example is given. It has now been established that the original result in [523] was right and the counter example was wrong. The calculus provides a convenient framework ....

....arbitrary term rewriting systems. This is based on an earlier proof of the same result in [523] but a more thorough proof was devised to counter [548] where the opposite result is claimed and the construction of a counter example is given. It has now been established that the original result in [523] was right and the counter example was wrong. The calculus provides a convenient framework in which one can formally represent and reason about functional programs. In [373] some work has been done on the use of expansion reduction systems reasoning about terms, in particular using categorical ....

S. Kahrs. -rewriting. PhD thesis, Universitat Bremen, 1991. \Phi.

....fi reduction in calculus. Application is here expressed by the binary function symbol . 12 Extracting the reduction relation It requires some subtlety to extract from the rewrite rules the actual rewrite relation that they generate. First we define substitutes (we adopt this name from Kahrs [Kah91]) Definition 12.1 Let t be a term. 1) Let (x 1 ; x n ) be an n tuple of pairwise distinct variables. Then the expression (x 1 ; x n ) t is an n ary substitute. We use as a meta lambda to distinguish it from the one of calculus. 2) The variables x 1 ; x n occurring ....

S. Kahrs. -rewriting. PhD thesis, Universitat Bremen, 1991.

....in any special way; there is no need to freeze variables or to adjust indices. Eliminating most the inefficiencies of the naive approach requires techniques known from the implementation of first order TRSs. However, when I applied such techniques in an implementation of rewriting (see [5]; rewriting systems also require the right hand sides of rules to be simple) the second order patterns had no impact on the approach at all. This observation generalises to arbitrary CRSs. We are interested in the rewrite relation of a CRS as such, not just in the relation that relates terms ....

Stefan Kahrs. -rewriting. PhD thesis, Universitat Bremen, 1991. (in German).

....common to both proofs, and in section 5 we instantiate this abstract proof with the data particular to the problem of currying. The general idea behind the technique is that for certain properties of terms there are associated cofinal reduction strategies. This result first appeared in my thesis (Kahrs, 1991). At the time, I did not bother to publish it separately, because the proof was rather tedious and the result appeared to me as being too predictable to justify such complications. I rapidly changed my mind when I came across a technical report by Kennaway, Klop, Sleep and de Vries (1993) on the ....

Kahrs, S. (1991). -rewriting. PhD thesis, Universitat Bremen. In German.

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S. Kahrs, -rewriting, PhD thesis, Universitat Bremen, 1991. (in German)

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S. Kahrs. -rewriting. PhD thesis, Universitat Bremen, Jan. 1991.

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