A. J. Kfoury and J. B. Wells. New notions of reduction and nonsemantic proofs of fi-strong normalization in typed -calculi. In Proc. 10th Ann. IEEE Symp. Logic in Computer Sci., pages 311--321, 1995.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....(SN) Vid 89] also introduces reductions similar to those of [Reg 94] Furthermore, KTU 94] uses (and other reductions) to show that typability in ML is equivalent to acyclic semi unification. SF 92] uses a reduction which has some common themes to . Nederpelt 73] and [dG 93] use whereas [KW 95a] uses fl to reduce the problem of strong normalisation for fi reduction to the problem of weak normalisation for related reductions. KW 94] uses amongst other things, and fl to reduce typability in the rank 2 restriction of system F to the problem of acyclic semi unification. AFM 95] uses ....

Kfoury, A.J. and Wells, J.B., New notions of reductions and non-semantic proofs of fi-strong normalisation in typed -calculi, LICS, 1995.

....SN. Vid 89] also introduces reductions similar to those of [Reg 94] Furthermore, KTU 94] uses (and other reductions) to show that typability in ML is equivalent to acyclic semi unification. SF 92] uses a reduction which has some common themes to . dG 93] uses a restricted version of and [KW 95a] uses fl to reduce the problem of strong normalisation for fi reduction to the problem of weak normalisation for related reductions. KW 94] uses amongst other things, and fl to reduce typability in the rank 2 restriction of system F to the problem of acyclic semi unification. AFM 95] uses ....

Kfoury, A.J. and Wells, J.B., New notions of reductions and non-semantic proofs of fi-strong normalisation in typed -calculi, LICS, 1995.

.... Tiuryn, and Urzyczyn used (and other reductions) to show that typability in ML is equivalent to acyclic semi unification [KTU94] Sabry and Felleisen described a relationship between a reduction similar to and a particular style of CPS [SF93] De Groote [dG93] used and Kfoury and Wells [KW95b] used fl to reduce the problem of fi strong normalization to the problem of weak normalization (WN) for related reductions. Kfoury and Wells used and fl to reduce typability in the rank 2 restriction of system F to the problem of acyclic semi unification [KW94] Klop, Srensen, and Xi [Klo80, ....

....a = fi c; hence b = fi c. By confluence of fi, 9d 2 where b fi d, and c fi d. By Remark 1, b gfi d, and c gfi d. There are, as we mentioned in the introduction, various notions of generalized reduction. For other proofs of confluence of some of these notions, we refer the reader to [AFM 95, dG93, Kam96, KW95b, Klo80]. Finally, the following ensures the good passage of gfi reduction through ff gg and U k : Lemma 5 Let a; b; c; d 2 . The following hold: 1. If c gfi d, then U k (c) gfi U k (d) 2. If c gfi d, then affn cgg gfi affn dgg. 3. If a gfi b, then affn cgg gfi bffn cgg. 15 ....

[Article contains additional citation context not shown here]

A. J. Kfoury and J. B. Wells. New notions of reduction and nonsemantic proofs of fi-strong normalization in typed -calculi. In Proceedings of the 10th Annual IEEE Symposium on Logic in Computer Science, pages 311--321, Los Alamitos, CA, 1995. IEEE.

....( x: y:x :y)z)u (Rffi) z ) P ffi) x ) Qffi) y ) N Figure 2: normal forms in item notation for term A ( x: y:x :y)u)z, but not to write ( x: y:x :y)z)u fl ( y:x : x: y)z)u. Local transformations such as fl and began to appear in the literature around 1989. See [KW95a] for a summary. Regnier [Reg92] introduced the notion of a premier redex, which is similar to the redex based on y and Q above (which we call a generalized redex ) Later, he used and fl (and called the combination oe) to show that the perpetual reduction strategy finds the longest reduction ....

A. J. Kfoury and J. B. Wells. Addendum to "New notions of reduction and non-semantic proofs of fi-strong normalization in typed -calculi". Technical Report 95-007, Department of Computer Science, Boston University, 1995.

....and Applications 1995 stating that, for every pure type system, weak normalization implies strong normalization. The conjecture is also mentioned by Geuvers [11] and, in a less concrete form, by Klop. Nederpelt [19] Klop [18] Khasidashvili [17] Karr [15] de Groote [9] and Kfoury and Wells [16] present techniques to infer strong normalization from weak normalization. However, these techniques all infer strong normalization of fi reduction in a typed calculus from weak normalization of a more complicated notion of reduction in the typed calculus. Therefore, they do not apply directly ....

A.J. Kfoury and J. Wells. New notions of reduction and non-semantic proofs of fi-strong normalization in typed -calculi. Technical Report 94-01, Boston University Computer Science Department,

....(Harper and Lillibridge, 1993a) Hence, the weak normalisation theorem in F implies the strong normalisation theorem in it. 5. Related work and Conclusion Ideas of transforming strong normalisation into weak normalisation can also be found in Nederpelt (1973) Klop (1980) de Groote (1993) and Kfoury and Wells (1994). To some extent, our transformation T is related to the controlling erasure in the literature, which, in addition to contracting fi I redex, only reduces (x:y:u)v to y: x:u)v when u contain no free occurrences of x. In this way, the conservation theorem for K calculus can be called to establish ....

.... were first studied by Meyer and Wand (1985) and extended to polymorphic type systems by Harper and Lillibridge (1993a, 1993b) The formulation of transformation T makes use of continuations, which not only avoids introducing other uncommon reductions such as the ones used by de Groote (1993) and Kfoury and Wells (1994), but also reveals an intimate relation between types and normalisations. With some known results on typing properties in various typed calculi, we can readily claim that these systems are closed under transformation T . Therefore, it becomes unnecessary to complicate methods for the purpose of ....

Kfoury, A.J. and Wells, J.B., (1994), New notions of reduction and non-semantic proofs of fi- strong normalisation in typed -calculi, Tech. Rep. 94-104, Computer Science Department, Boston University.

....independently invented by Prawitz [Pra65] in proof theory. A detailed account of it can also be found in [And71] Several authors have invented between techniques to infer from this result strong normalisation of simply typed calculus and related systems, see [Ned73] Klo80] deGr93] and [KW94]. Another proof, using a different characterisation of strongly normalising terms is given in [RS95] Definition 6.6 The complexity com(T ) of a type T is defined as follows. com(T ) 0 if T is atomic; maxf1 com(T 0 ) com(T 1 )g if T = T 0 T 1 . Let the complexity com(t) of a simply ....

....arguments in our opinion are more involved in some cases. There exists a close similarity between . l relation and the perpetual strategies in [Bar76] and [BK82] Other ideas of transforming strong normalisation into weak normalisation can also be found in [Ned73] Klo80] deGr93] and [KW94]. l relation brings out inner fi redexes or their residuals by leftmost reductions and subterm relations. It is often easier to prove H(t) 1 than to prove S(t) 1 for given terms t. Perpetual strategies spot the crucial places where fi reductions may change the strong normalisability of a ....

A.J. Kfoury and J.B. Wells (1994), New notions of reduction and non-semantic proofs of fi-strong normalisation in typed -calculi, Tech. Rep. 94-104, Computer Science Department, Boston University.

....(SN) Vid 89] also introduces reductions similar to those of [Reg 94] Furthermore, KTU 94] uses (and other reductions) to show that typability in ML is equivalent to acyclic semi unification. SF 92] uses a reduction which has some common themes to . Nederpelt 73] and [dG 93] use whereas [KW 95a] uses fl to reduce the problem of strong normalisation for fi reduction to the problem of weak normalisation for related reductions. KW 94] uses amongst other things, and fl to reduce typability in the rank 2 restriction of system F to the problem of acyclic semi unification. AFM 95] uses ....

Kfoury, A.J. and Wells, J.B., New notions of reductions and non-semantic proofs of fi-strong normalisation in typed -calculi, LICS, 1995.

....is Strongly Normalising (SN) 35] also introduces reductions similar to those of [32] Furthermore, 23] uses (and other reductions) to show that typability in ML is equivalent to acyclic semi unification. 34] uses a reduction which has some common themes with . 29] and [11] use whereas [26] uses fl to reduce the problem of fi strong normalisation to the problem of weak normalisation for related reductions. 24] uses and fl to reduce typability in the rank 2 restriction of the 2nd order calculus to the problem of acyclic semi unification. 2] uses (called let C ) as a part of ....

A. Kfoury and J. Wells. New notions of reductions and non-semantic proofs of fi-strong normalisation in typed -calculi. LICS, 1995.

....[Vid 89] also introduces reductions similar to those of [Reg 94] Furthermore, KTU 94] uses (and other reductions) to show that typability in ML is equivalent to acyclic semi unification. SF 92] uses a reduction which has some common themes to . dG 93] uses a restricted version of and [KW 95a] uses fl to reduce the problem of strong normalisation for fi reduction to the problem of weak normalisation for related reductions. KW 94] uses amongst other things, and fl to reduce typability in the rank 2 restriction of system F to the problem of acyclic semi unification. AFM 95] uses ....

Kfoury, A.J. and Wells, J.B., New notions of reductions and non-semantic proofs of fi-strong normalisation in typed -calculi, LICS, 1995.

....is Strongly Normalising (SN) 37] also introduces reductions similar to those of [33] Furthermore, 22] uses (and other reductions) to show that typability in ML is equivalent to acyclic semiunification. 35] uses a reduction which has some common themes with . 30] and [11] use whereas [25] uses fl to reduce the problem of fi strong normalisation to the problem of weak normalisation (WN) for related reductions. 23] uses and fl to reduce typability in the rank 2 restriction of the 2nd order calculus to the problem of acyclic semi unification. 27, 38, 36, 26] use related ....

A.J. Kfoury and J.B. Wells. New notions of reductions and non-semantic proofs of fi-strong normalisation in typed -calculi. LICS, 1995.

....could guess from A itself the presence of the future redex. That is, looking at A itself, we see that fi is matched with ff and y is matched with x. This has been noted by many researchers and hence rules like ( x :N)PQ ( x :NQ)P have been introduced in many articles with different purposes [1, 4, 6, 8, 10, 11, 13, 15, 16, 18, 19, 20, 22] Such rules enable one to rewrite A so that both redexes become visible in A. Note that: A j ( fi : y : f :fy)ffx ( fi : y : f :fy)x)ff j B. These transformations are rather powerful in that they can group together terms with equal reductional behaviour. Let us give here this example: ....

....[10] uses (and other reductions) to show that typability in ML is equivalent to acyclic semi unification. 1 We are grateful to Joe Wells for enlightening discussions on this subject. 20] uses a reduction which has some common themes with . Nederpelt s thesis in [17] and [4] use whereas [13] uses fl to reduce the problem of fi strong normalization to the problem of weak normalization (WN) for related reductions. 11] uses and fl to reduce typability in the rank 2 restriction of the 2nd order calculus to the problem of acyclic semi unification. 15, 23, 21, 14] use related ....

A.J. Kfoury and J.B. Wells. New notions of reductions and non-semantic proofs of fi-strong normalisation in typed -calculi. LICS, 1995.

....[Vid 89] also introduces reductions similar to those of [Reg 94] Furthermore, KTU 94] uses (and other reductions) to show that typability in ML is equivalent to acyclic semi unification. SF 92] uses a reduction which has some common themes to . dG 93] uses a restricted version of and [KW 95a] uses fl to reduce the problem of strong normalisation for fi reduction to the problem of weak normalisation for related reductions. KW 94] uses amongst other things, and fl to reduce typability in the rank 2 restriction of system F to the problem of acyclic semi unification. AFM 95] uses ....

Kfoury, A.J. and Wells, J.B. (1995), New notions of reductions and non-semantic proofs of fi-strong normalisation in typed -calculi, LICS.

....we point out that this is a result which can be formulated in the first order Peano arithmetic. 5 Related Work The research on deriving strong normalisation (SN) from weak normalisation (WN) has lasted for at least thirty years. Nederpelt[21] Klop[17] Karr[16] de Groot[7] and Kfoury and Wells[20] have all invented techniques to infer SN from WN. Their techniques all require introducing some notions of reduction different from fi reduction, deriving strong fi normalisation from weak normalisation of these newly introduced notions of reduction. For example, Klop s technique amounts to ....

....a lot of administrative fi redexes introduced by CPS transformation [22] 6 Conclusion and Future Work We have demonstrated some applications of our technique. The reader is encouraged to verify that this technique also works on Gamma with Curry typing [19] Gamma with Church typing [20] and the calculi with positive recursive types [31] On the other hand, translation [ Delta] which exploits continuations, has troubles handling Curry typing [29] and is less robust than translation k Delta k. Besides, k Delta k in the author s opinion leads to much more ....

A.J. Kfoury and J.B. Wells (1994), New notions of reduction and nonsemantic proofs of fi-strong normalisation in typed -calculi, Tech. Rep. 94-104, Computer Science Department, Boston University.

....has the undesirable consequence that, even if one knows that a notion of reduction is weakly normalizing, one has to redo the weak normalization proof for the complicated notion of reduction to conclude strong normalization for the original notion of reduction. This is a non trivial process see [37] for comments on two such proofs which involves very different techniques for different calculi. For instance, for fi reduction in simply typed calculus one can extend the Turing Prawitz weak normalization proof to the complicated notion of reduction, but for second order typed calculus one ....

....with de Groote s technique since it resembles Klop s the most. The remaining techniques are then described in less detail. For more on the relationship between Klop s and Nederpelt s technique, see [41, II.4] For more on the relationship between de Groote s and Kfoury and Wells technique, see [37]. The notions of reduction discussed in this section have been considered in a number of other contexts [1, 33, 34, 35, 48, 57, 60, 71] see [37] 3.1. The technique by de Groote This subsection presents de Groote s [14] technique to reduce strong normalization for the systems in the cube [3] ....

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A.J. Kfoury and J. Wells. Addendum to "new notions of reduction and non-semantic proofs of fi-strong normalization in typed -calculi". Technical Report 95-007, Boston University Computer Science Department, 1995.

....derivations in predicate logic. Since weak normalization is sometimes easier to establish than strong normalization, it is natural to develop techniques to infer the latter from the former. Indeed, Nederpelt [43] Klop [38] Khasidashvili [37] Karr [35] de Groote [17] and Kfoury and Wells [36] have invented such techniques. However, these techniques all infer strong normalization of one notion of reduction from weak normalization of a more complicated notion of reduction. S rensen [56] and Xi [61] recently developed techniques which infer strong normalization of fi reduction in a typed ....

A.J. Kfoury and J. Wells. New notions of reduction and non-semantic proofs of fi-strong normalization in typed -calculi. In Proceedings of the Annual Symposium on Logic in Computer Science (LICS'95), pages 311--321. IEEE Computer Society Press, 1995.

....in every step of a certain fi reduction sequence. Prawitz [71] independently uses the same technique to prove weak normalization for reduction of natural deduction derivations in predicate logic. Nederpelt [63] Klop [55] Khasidashvili [54] Karr [52] de Groote [26] and Kfoury and Wells [53] have invented techniques to infer strong normalization from weak normalization. However, these techniques all infer strong normalization of one notion of reduction from weak normalization of a more complicated notion of reduction. S rensen [85] and Xi [91] recently developed techniques which ....

A.J. Kfoury and J. Wells. New notions of reduction and non-semantic proofs of fi-strong normalization in typed -calculi. Technical Report 94-014, Boston University Computer Science Department, 1994.

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A. J. Kfoury and J. B. Wells. Addendum to "New notions of reduction and non-semantic proofs of fi-strong normalization in typed - calculi". Tech. Rep. 95-007, Comput. Sci. Dept., Boston Univ., 1995.

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A. J. Kfoury and J. B. Wells. New notions of reduction and non-semantic proofs of fi-strong normalization in typed -calculi. Tech. Rep. 94-014, Comput. Sci. Dept., Boston Univ., 1994.

....SN. Vid 89] also introduces reductions similar to those of [Reg 94] Furthermore, KTU 94] uses (and other reductions) to show that typability in ML is equivalent to acyclic semi unification. SF 92] uses a reduction which has some common themes to . dG 93] uses a restricted version of and [KW 95a] uses fl to reduce the problem of strong normalisation for fi reduction to the problem of weak normalisation for related reductions. KW 94] uses amongst other things, and fl to reduce typability in the rank 2 restriction of system F to the problem of acyclic 33 semi unification. AFM 95] uses ....

Kfoury, A.J. and Wells, J.B. (1995), New notions of reductions and non-semantic proofs of fi-strong normalisation in typed -calculi, LICS.

....to 6 any function companion that might be in N . It is easy to show that T reduction is both confluent and strongly normalizing, so that repeated T reductions will eventually expose all implicit redexes. Let T nf denote the function such that T nf(M) is the (unique) T normal form of M . See [KW95] for a discussion of similar notions of reduction in the literature. There is a close connection with notions of generalized fi reduction which can contract the implicit redexes directly [Kam96, KRW98] Making all implicit redexes into explicit redexes serves two major purposes in System I k ....

A. J. Kfoury and J. B. Wells. Addendum to "New notions of reduction and non-semantic proofs of fi-strong normalization in typed -calculi". Tech. Rep. 95-007, Comp. Sci. Dept., Boston Univ., 1995.

.... [46] Kfoury, Tiuryn, and Urzyczyn use (and other reductions) to show that typability in ML is equivalent to acyclic semi unification [27] Sabry and Felleisen describe a relationship between a reduction similar to and a particular style of CPS [44] De Groote [13] uses and Kfoury and Wells [30] use fl to reduce the problem of fi strong normalisation to the problem of weak normalisation (WN) for related reductions. Kfoury and Wells use and fl to reduce typability in the rank 2 restriction of system F to the problem of acyclic semi unification [28] Klop, S rensen, and Xi [31, 47, 45] ....

....a = fi c, hence b = fi c. By confluence of fi, 9d 2 where b fi d and c fi d. By Remark 2.13, b gfi d and c gfi d. There are, as we mentioned in the introduction, various notions of generalised reduction. For other proofs of confluence of some of these notions, we refer the reader to [2, 13, 19, 30, 31]. Finally, the following ensures the good passage of gfi reduction through ff gg and U i k : Lemma 2.18. Let a; b; c; d 2 . The following hold: 1. If c gfi d then U i k (c) gfi U i k (d) 2. If c gfi d then affn cgg gfi affn dgg. 3. If a gfi b then affn cgg gfi bffn cgg. ....

[Article contains additional citation context not shown here]

A. J. Kfoury and J. B. Wells. New notions of reduction and non-semantic proofs of fi-strong normalization in typed -calculi. In Proc. 10th Ann. IEEE Symp. Logic in Computer Sci., pp. 311--321, 1995.

....y in the term A may be affected by the reducible pair of x and P . For example, it is fine to write ( x: y:x :y)z)u ( x: y:x :y)u)z but not to write ( x: y:x :y)z)u fl ( y:x : x: y)z)u. 1 Local transformations like fl and began to appear in the literature around 1989. See [29] for a summary) Regnier [41] introduces the notion of a premier redex which is similar to the redex based on y and Q above (which we call a generalised redex) Later, he uses and fl (and calls the combination oe) to show that the perpetual reduction strategy finds the longest reduction path ....

A. J. Kfoury and J. B. Wells. Addendum to "New notions of reduction and non-semantic proofs of fi-strong normalization in typed -calculi". Tech. Rep. 95-007, Comp. Sci. Dept., Boston Univ., 1995.

.... Tiuryn, and Urzyczyn used (and other reductions) to show that typability in ML is equivalent to acyclic semi unification [KTU94] Sabry and Felleisen described a relationship between a reduction similar to and a particular style of CPS [SF93] De Groote [dG93] used and Kfoury and Wells [KW95b] used fl to reduce the problem of fi strong normalization to the problem of weak normalization (WN) for related reductions. Kfoury and Wells used and fl to reduce typability in the rank 2 restriction of system F to the problem of acyclic semi unification [KW94] Klop, S rensen, and Xi [Klo80, ....

....c. By confluence of fi, 9d 2 where b fi d, and c fi d. By Remark 1, b gfi d, and c gfi d. There are, as we mentioned in the introduction, various notions of generalized reduction. For other proofs of confluence of some of these notions, we refer the reader to [AFM 95, dG93, Kam96, KW95b, Klo80] Proof of Theorem 1 2 Finally, the following ensures the good passage of gfi reduction through ff gg and U i k : Lemma 5 Let a; b; c; d 2 . The following hold: 1. If c gfi d, then U i k (c) gfi U i k (d) 2. If c gfi d, then affn cgg gfi affn dgg. 3. If a gfi b, then ....

[Article contains additional citation context not shown here]

A. J. Kfoury and J. B. Wells. New notions of reduction and nonsemantic proofs of fi-strong normalization in typed -calculi. In Proceedings of the 10th Annual IEEE Symposium on Logic in Computer Science, pages 311--321, Los Alamitos, CA, 1995. IEEE.

....fi Reduction x1.2 (Rffi) z ) P ffi) x ) Qffi) y ) N Figure 2: normal forms in item notation for term A ( x: y:x :y)u)z, but not to write ( x: y:x :y)z)u fl ( y:x : x: y)z)u. 2 Local transformations such as fl and began to appear in the literature around 1989. See [KW95a] for a summary. Regnier [Reg92] introduced the notion of a premier redex, which is similar to the redex based on y and Q above (which we call a generalized redex ) Later, he used and fl (and called the combination oe) to show that the perpetual reduction strategy finds the longest reduction ....

A. J. Kfoury and J. B. Wells. Addendum to "New notions of reduction and non-semantic proofs of fi-strong normalization in typed -calculi". Technical Report 95-007, Department of Computer Science, Boston University, 1995.

.... Calculi A. J. Kfoury kfoury cs.bu.edu Dept. of Computer Science Boston University J. B. Wells jbw cs.bu.edu Dept. of Computer Science Boston University March 31, 1995 Boston University Computer Science Department Technical Report 95 007 This addendum to our technical report of December 1994 [KW94b] has several purposes: 1. To clarify some statements about the focus and purpose of the paper which were written unclearly. 2. To add information on research by others on the notion of reduction which we call fl reduction and other similar transformations. 3. To discuss the closely related ....

A. J. Kfoury and J. B. Wells. New notions of reduction and non-semantic proofs of fi-strong normalization in typed -calculi. Tech. Rep. 94-014, Comput. Sci. Dept., Boston Univ., 1994.

....we have presented a simple algorithm for the Splitting Tagging transformation. We plan to develop and implement a more efficient algorithm. An important practical issue in compiling with types is controlling the size of the intermediate representations. Our current language, following the style of [15], duplicates terms when it duplicates types. Our language is convenient for specifying our framework, but for implementation a considerable size savings can be obtained by using a typed calculus with intersection and union types in the style of [31] Finally, we plan to study the interaction of ....

A. J. Kfoury and J. B. Wells. New notions of reduction and nonsemantic proofs of fi-strong normalization in typed -calculi. In Proc. 10th Ann. IEEE Symp. Logic in Computer Sci., pages 311--321, 1995.

....leading to that term, and since all reduction paths from a term with a normal form must eventually reach the normal form, this yields the desired result. For a further discussion of differences in how our method s are applied to various typed calculi, see the addendum to our technical report [KW95]. This addendum also contains a summary of other research into the fl and fi S notions of reduction and a comparison of both our and de Groote s methods with the earlier method of Klop. Acknowledgements. Pawel Urzyczyn spotted a wrong proof in the technical report and suggested many shorter ....

A. J. Kfoury and J. B. Wells. Addendum to "New notions of reduction and non-semantic proofs of fi-strong normalization in typed - calculi". Tech. Rep. 95-007, Comput. Sci. Dept., Boston Univ., 1995.

....be reduced to the question of normalization. Subsequent sections will then show for certain typed calculi that all typable terms have normal forms, implying that all typable terms are fi strongly normalizing. See the technical report version of the present paper for full details if necessary [KW94]. 3.1 fl Reduction and fl Normal Forms. Definition 3.1 fl reduction is the least reduction relation such that: x: y:N ) P ) Gamma fl (y: x:N )P ) We assume that x 6= y and y 62 FV(P ) using ff conversion if necessary. In a pictorial format, this reduction looks like this: x y N P ....

....is an innermost I redex, then order ffl (M ) order ffl (N ) Proof: Note that this proof follows ideas first presented in Turing s weak normalization proof for the simply typed calculus [Gan80a] We give here only the barest sketch of the proof. See the full technical report for details [KW94]. The residuals of any pre existing fi redexes (other than the one being reduced) retain the same order value, so for them we need only show they are not duplicated. The initial fi reduction step (of the reduction step) does not duplicate fi redexes because Delta is innermost. Also, any new ....

[Article contains additional citation context not shown here]

A. J. Kfoury and J. B. Wells. New notions of reduction and non-semantic proofs of fi-strong normalization in typed -calculi. Tech. Rep. 94-014, Comput. Sci. Dept., Boston Univ., 1994.

No context found.

A. J. Kfoury and J. B. Wells. New notions of reduction and nonsemantic proofs of fi-strong normalization in typed -calculi. In Proc. 10th Ann. IEEE Symp. Logic in Computer Sci., pages 311--321, 1995.

No context found.

A. Kfoury and J. Wells. New notions of reductions and non-semantic proofs of fi-strong normalisation in typed -calculi. LICS, 1995.

No context found.

Kfoury A.J. and Wells J., Addendum to `New notions of reduction and non-semantic proofs of fi-strong normalization in typed -calculi'. Report 95--007, Boston University, 1995.

No context found.

Kfoury A.J. and Wells J., Addendum to `New notions of reduction and non-semantic proofs of fi-strong normalization in typed -calculi'. Report 95-007, Boston University, 1995.

No context found.

A. J. Kfoury and J. B. Wells. Addendum to "new notions of reduction and non-semantic proofs of fi-strong normalization in typed -calculi". Technical Report 95--007, Boston University Computer Science Department, March 31 1995.

No context found.

A. J. Kfoury and J. B. Wells. New notions of reduction and non-semantic proofs of fi-strong normalization in typed -calculi. Technical Report 94--014, Boston University Computer Science Department, 1994. (See [KW95]).

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