C. Borralleras and A. Rubio. A monotonic higher-order semantic path ordering. In Proc. LPAR '01, LNAI 2250, pages 531--547, 2001.  Home/Search   Document Details and Download   Summary   Related Articles   Check

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C. Borralleras and A. Rubio. A Monotonic Higher-Order Semantic Path Ordering. Proc. of 8th Int. Conf. on Logic for Programming, Artificial Intelligence and Reasoning (LPAR'01) LNAI 2250:531--547, 2001.

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C. Borralleras and A. Rubio. A Monotonic Higher-Order Semantic Path Ordering. Proc. of 8th Int. Conf. on Logic for Programming, Artificial Intelligence and Reasoning (LPAR'01) LNAI 2250:531--547, 2001.

....to two examples in Section 6. Some conclusions and possible extensions are given in Section 7. The reader is expected to be familiar with the basics of term rewrite systems [DJ90] and typed lambda calculi [Bar92] Due to the lack of room we have provided almost no proofs. All them can be found in [BR00]. 2 Preliminaries 2.1 Types, Signatures and Terms We consider terms of a simply typed lambda calculus generated by a signature of higher order function symbols. The set of types Tis generated from the set VT of type variables (considered as sorts) by the constructor for functional types in ....

....we are assuming that t is computable and hence strongly normalizing by Property 1. Note that in the assumtion of Property 5 we are only using the first component of the induction ordering. By using both components, we can improve the computable closure, as done in [JR99] adding new cases (see [BR00] for details) Lemma 3. hospo is well founded. The proof is done by showing that tfl is computable for every typed term t and computable substitution fl, by induction on the size of t and using Property 4.5 and Lemma 2. Note that for the empty substitution fl we have that all typed terms are ....

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C. Borralleras and A. Rubio. A monotonic higher-order semantic path ordering. Available at www.lsi.upc.es/~albert/papers.html, 2000.

.... In this case we stop applying the definition of the closure when we arrive at a bound variable or at reachable subterm (through equivalent types) of an argument of the left hand side term (this use of subterms in the closure is not included in the definition given in this paper, it can be found in [BR00] in Section 7) With this strategy we will get the following constraints, denoting by I the constraint on I and by Q the constraint on Q . I : map(F; I [ map(F; cons(x; xs) I cons( F; x) map(F; xs) ps( I [ ps(cons(x; xs) I cons(x; ps(map(y:x y; xs) Q : map(F; cons(x; ....

C. Borralleras and A. Rubio. A monotonic higher-order semantic path ordering. Available at www.lsi.upc.es/~albert/papers.html, 2000.

....outlined in section 6. Some conclusions and possible extensions are given in section 7. The reader is expected to be familiar with the basics of term rewrite systems [DJ90] and typed lambda calculi [Bar90,Bar92] Due to the lack of room we have provided almost no proofs. All them can be found in [BR00]. 2 Preliminaries 2.1 Types, Signatures and Terms Given a set S of sort symbols of a fixed arity, denoted by s : n , and a set S 8 of type variables, the set T S 8 of polymorphic types is generated from these sets by the constructor for functional types: T S 8 : s(T n S 8 ) j ff j ....

....this example all rules except the last one are included in MHOSPO. In the following section we will add a last improvement to HOSPO, which will allow us to prove the last rule. Due to the lack of room, we only provide, in each example, the ingredients of MHOSPO which are needed to prove it (see [BR00] for details) 16 Example 5 Let S = fBool; Nat : List : g, S 8 = fff; fi; flg and F = f0 : N at; s : Nat N at; le : Nat Theta Nat Bool; T rue; F alse : Bool; gcd; minus : Nat Theta Nat N at; if : Bool Theta Nat Theta Nat N at; List(ff) cons : ff Theta List(ff) ....

C. Borralleras and A. Rubio. A monotonic higher-order semantic path ordering. Available at www.lsi.upc.es/~albert/papers.html, 2000.

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C. Borralleras and A. Rubio. A monotonic higher-order semantic path ordering. In Proc. LPAR '01, LNAI 2250, pages 531--547, 2001.

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