N. Dershowitz and Z. Manna. Proving termination with multiset orderings. Comm. ACM, 22:465--476, 1979. Home/Search Document Not in Database Summary Related Articles Check |
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....number of indices 1 i h such that C i is not trivial. De nition 5.8. The measure of a BHOUP (S; b) is a lexicographic one with the components 1 ; 2 ; 3 ; 4 ; 5 ; 6 : 1 = the multiset fb(x) j x 2 FV(S) b(x) ar(x)g. This component is ordered by the multiset ordering (see [DM79,BN98]) 2 = the multiset fb(x) ar(x) j x 2 FV(S) b(x) ar(x)g. This component is ordered by the multiset ordering. 3 = if there is a cycle in S, then minf (L) j L is a cycle in Sg; Otherwise, 1. 4 = the multiset fsize(t) j t is a top level term in S that is not a rst order variableg. ....
Nachum Dershowitz and Z. Manna. Proving termination with multiset orderings. Communications of the ACM, 22:465-476, 1979.
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....For a type = 1 ) 2 ) n ) o, de ne the arity of , ar( to be n. For with ar( 0 we shall write i for the type of the ith argument to and i;j for the type of the jth argument to i . A well founded order on types, based on the nested multiset ordering [4] can be de ned as follows. De nition 3.9 Let (o) fog, and ( f( i ) j i ar( g, if ar( 0. Then if ( ms ( where ms is the nested multi set ordering [4] over the single element o. Recall that this can be be de ned as the least relation satisfying: If M 6= o then o ms ....
....i;j for the type of the jth argument to i . A well founded order on types, based on the nested multiset ordering [4] can be de ned as follows. De nition 3.9 Let (o) fog, and ( f( i ) j i ar( g, if ar( 0. Then if ( ms ( where ms is the nested multi set ordering [4] over the single element o. Recall that this can be be de ned as the least relation satisfying: If M 6= o then o ms M . If M 6= M and 8x 2 M M :9y 2 M M:x ms y then M ms M . The following is then an instance of the general result in [4] Proposition 3.10 (Dershowitz and ....
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N. Dershowitz and Z. Manna. Proving termination with multiset orderings. Communications of the ACM, 22:465-476, 1979.
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N. Dershowitz and Z. Manna. Proving termination with multiset orderings. Comm. ACM, 22:465--476, 1979.
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N. Dershowitz and Z. Manna. Proving termination with multiset orderings. Communications of the ACM, 22(8):465--476, 1979.
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N. Dershowitz and Z. Manna. Proving termination with multiset orderings. Communications of the ACM, 22(8):465--476, 1979.
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N. Dershowitz and Z. Manna. Proving termination with multiset orderings. Communications of the ACM, 22(8):465--476, 1979.
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N. Dershowitz and Z. Manna. Proving termination with multiset orderings. Communications of the ACM, 22(8):465--476, 1979.
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N. Dershowitz and Z. Manna. Proving termination with multiset orderings. Communications of the ACM, 22(8):465--476, 1979.
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N. Dershowitz, Z. Manna, Proving termination with multiset orderings, Communications of the ACM 22 (8) (1979) 465--476.
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