Infinitary Combinatory Reduction Systems
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Infinitary Combinatory Reduction Systems. / Ketema, Jeroen; Simonsen, Jakob Grue.
I: Information and Computation, Bind 209, Nr. 6, 2011, s. 893-926.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
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TY - JOUR
T1 - Infinitary Combinatory Reduction Systems
AU - Ketema, Jeroen
AU - Simonsen, Jakob Grue
PY - 2011
Y1 - 2011
N2 - We define infinitary Combinatory Reduction Systems (iCRSs), thus providing the first notion of infinitary higher-order rewriting. The systems defined are sufficiently general that ordinary infinitary term rewriting and infinitary ¿-calculus are special cases. Furthermore,we generalise a number of knownresults fromfirst-order infinitary rewriting and infinitary ¿-calculus to iCRSs. In particular, for fully-extended, left-linear iCRSs we prove the well-known compression property, and for orthogonal iCRSs we prove that (1) if a set of redexes U has a complete development, then all complete developments of U end in the same term and that (2) any tiling diagram involving strongly convergent reductions S and T can be completed iff at least one of S/T and T/S is strongly convergent. We also prove anancillary result of independent interest: a set of redexes in an orthogonal iCRS has a complete development iff the set has the so-called finite jumps property.
AB - We define infinitary Combinatory Reduction Systems (iCRSs), thus providing the first notion of infinitary higher-order rewriting. The systems defined are sufficiently general that ordinary infinitary term rewriting and infinitary ¿-calculus are special cases. Furthermore,we generalise a number of knownresults fromfirst-order infinitary rewriting and infinitary ¿-calculus to iCRSs. In particular, for fully-extended, left-linear iCRSs we prove the well-known compression property, and for orthogonal iCRSs we prove that (1) if a set of redexes U has a complete development, then all complete developments of U end in the same term and that (2) any tiling diagram involving strongly convergent reductions S and T can be completed iff at least one of S/T and T/S is strongly convergent. We also prove anancillary result of independent interest: a set of redexes in an orthogonal iCRS has a complete development iff the set has the so-called finite jumps property.
U2 - 10.1016/j.ic.2011.01.007
DO - 10.1016/j.ic.2011.01.007
M3 - Journal article
VL - 209
SP - 893
EP - 926
JO - Information and Computation
JF - Information and Computation
SN - 0890-5401
IS - 6
ER -
ID: 37440995