Douglas J. Howe. Equality in lazy computation systems. In Proceedings of LICS '89, pages 193-203, 1989.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....on CCS [35] we prove that the equational theory is sound with respect to Morris style contextual equivalence [38, 44] Following methods by Gordon, Abramsky and others [2, 11, 15 17, 19] we specify a notion of applicative bisimilarity for the region calculus. With a proof technique due to Howe [24,25], recasted to typed functional programming languages by Gordon [15] we show that bisimilarity is a congruence for our region calculus. We use this result to prove that bisimilarity equals contextual equivalence and includes the equational theory. Plotkin [44] simpli ed Morris style contextual ....

.... f e ) and therefore by re exivity that f g B e implying R d 7 Bisimilarity is Compatible In this section, we prove that bisimilarity obeys a congruence property, more speci cally, we show that the bisimilarity relation is compatible. We use a technique due to Howe [24, 25], which has been re casted to typed functional languages by Gordon [15 17] The key idea is to de ne the notion of compatible extension, a compatible relation which we prove to coincide with the open extension of similarity. The compatible extension . of . is inductively de ned as the least ....

Douglas Howe. Equality in lazy computation systems. In LICS1989 [29], pages 198-203.

....at higher types. Given this success, it is important to see how broad the scope of the approach initiated in [1, 4] actually is. In this paper, we consider the lazy calculus [2, 6] This calculus, and certain associated notions such as applicative simulation, have been quite widely influential [8, 11, 13, 14, 17, 19, 22]. In [6] a syntactic construction of a fully abstract model for the basic sequential language was given, and the canonical denotational model was shown to be fully abstract for a certain parallel extension of the language. However, the problem of giving a direct, syntax free, purely semantic ....

D. J. Howe. Equality in lazy computation systems. In Proceedings, Fourth Annual Symposium on Logic in Computer Science, pages 198--203. IEEE Computer Society Press, 1989.

....work on CCS [33] we prove that the equational theory is sound with respect to Morris style contextual equivalence [35, 41] Following methods by Gordon, Abramsky and others [2, 11, 16 19] we specify a notion of applicative bisimilarity for the region calculus. With a proof technique due to Howe [24, 25], re casted to typed functional programming languages by Gordon [16] we show that bisimilarity is a congruence for our region calculus. We use this result to prove that bisimilarity equals contextual equivalence and includes the equational theory. Plotkin [41] simplified Morris style contextual ....

....1 ) #, #. Since Clean(S s (#) we can apply Lemma 30, from which the claim follows. 27 7 Bisimilarity is Compatible In this section, we prove that bisimilarity obeys a congruence property, more specifically, we show that the bisimilarity relation is compatible. We use a technique due to Howe [24, 25], which has been re casted to typed functional languages by Gordon [16 18] The key idea is to define the notion of compatible extension, a compatible relation which we prove to coincide with the open extension of similarity. The compatible extension of # is inductively defined as the least ....

Douglas J. Howe. Equality in lazy computation systems. In Proc. of the 4th Annual Symposium on Logic in Computer Science, pages 198--203, Pacific Grove, CA, June 1989. IEEE Computer Society Press.

....work on CCS [33] we prove that the equational theory is sound with respect to Morris style contextual equivalence [35, 41] Following methods by Gordon, Abramsky and others [2, 11, 16 19] we specify a notion of applicative bisimilarity for the region calculus. With a proof technique due to Howe [24, 25], re casted to typed functional programming languages by Gordon [16] we show that bisimilarity is a congruence for our region calculus. We use this result to prove that bisimilarity equals contextual equivalence and includes the equational theory. Plotkin [41] simpli ed Morris style contextual ....

....1 ) Since Clean(S s ( we can apply Lemma 30, from which the claim follows. 27 7 Bisimilarity is Compatible In this section, we prove that bisimilarity obeys a congruence property, more speci cally, we show that the bisimilarity relation is compatible. We use a technique due to Howe [24, 25], which has been re casted to typed functional languages by Gordon [16 18] The key idea is to de ne the notion of compatible extension, a compatible relation which we prove to coincide with the open extension of similarity. The compatible extension of . is inductively de ned as the least ....

Douglas J. Howe. Equality in lazy computation systems. In Proc. of the 4th Annual Symposium on Logic in Computer Science, pages 198-203, Paci c Grove, CA, June 1989. IEEE Computer Society Press.

....to those of LISP 1.5. We can think of O as a tiny higher order imperative language, with an applicative syntax making it a fragment of ML. We adopt CCS style bisimilarity as the natural operational equivalence on O programs. Our first theorem is congruence of bisimilarity, via Howe s method [14], justifying operationally based equational reasoning about O programs. The denotational semantics is specified in two stages. First, we give a denotational semantics to a metalogic M in the category CPPO of cppos and Scott continuous functions. Second, we give a formal translation of the types ....

....Nonetheless, just as in CCS, the availability of co induction means a great deal can be achieved simply using operational methods, provided that is a congruence. This is our first main result, which we can be proved via an adaptation of Howe s method; similar proofs can be found elsewhere [10, 12, 14]. Theorem 1. Bisimilarity is a congruence. In PCF like languages, we often define two programs p and q to be observationally equivalent iff there is no program context C such that C[p] converges and C[q] diverges, and vice versa. This is inappropriate for our calculus because (unlike in CCS, ....

Douglas J. Howe. Equality in lazy computation systems. In 4th LICS, 1989.

....is as a tool for proving actions contextual preordered. Therefore we have to show that the simulation preorders are included in the contextual preorders. By the basic context lemma (6.10) it suffices to prove that they are included in the experimental preorders. A more standard path, due to Howe [15], is to show the simulation preorders to be precongruences as in the proof of lemma 5.1 and consequently included in the contextual preorders. Given the basic context lemma, our approach is considerably simpler. Mason, Smith, and Talcott follow a similar route in [18] 32 Proof: m = ....

D. J. Howe. Equality in lazy computation systems. In 4th Annual Symposium on logic in computer science. IEEE, 1989. 44

....is also a simulation then it is a bisimulation. Normally bisimulation is defined on a language to define operational equivalence in that language. Then congruence is a desirable result, so replacing sub programs by operational equivalents yields an operationally equivalent program (Howe s method [11] is one approach to proving congruence) We are using bisimulation in a more general sense, to show that a graph of one language and its equivalent in another language have the same operational behaviour. We do not discuss the corresponding generalised form of congruence but if the sub graphs we ....

D. J. Howe. Equality in lazy computation systems. In Proc. 4th Annual Symposium on Logic in Computer Science, pages 198--203. IEEE Computer Society, Los Alamitos, CA., 1989.

....sound with respect to Morris style contextual equivalence [31, 36] using bisimulation, a proof method originating from work on CCS [29] Following methods by Gordon, Abramsky and others [2, 11, 15 18] we specify a notion of bisimilarity for the region calculus. With a proof technique due to Howe [21,22], re casted to typed functional programming languages by Gordon [15] we show that bisimilarity is a congruence for our region calculus. This forms the basis to prove that bisimilarity equals contextual equivalence and includes the operational theory. Plotkin [36] simpli ed Morris style ....

....= 2 S s ( 1 ) S s ( 2 ) we can apply lemma 26, from which the claim follows. 6 Bisimilarity is compatible In this section, we will prove that bisimilarity obeys a congruence property, more speci cally, we will show that the bisimilarity relation is compatible. We use a technique due to Howe [21, 22], which has been re casted for bisimilarity by Gordon [15 17] The key idea is to de ne the notion of compatible extension, a compatible relation which we will prove to coincide with the open extension of similarity. The compatible extension of . is the least well formed typed relation, which is ....

Douglas J. Howe. Equality in lazy computation systems. In Proc. of the 4th Annual Symposium on Logic in Computer Science, pages 198-203, Pacic Grove, CA, June 1989. IEEE Computer Society Press.

....system. Intr# ducing the concept of a pr#. Cx F4I system as the extensible str#nsible par# of anexpr#. Cx system, thepr#CF4 t paper alsotr#oC the open endedness of types. The concept of an evaluation system agener#aC 5.F.C of an untyped # calculus was intr# duced by Howe. In [23, 24, 10, 25], he used theappr#54 h of Plotkin [39] and Kahn [26] toextr#jI a simple butfair#j gener# oper# .4 kC str#.4 tur# fr## Mar#.4 kC of sinfor#jI descr#ICx . of the evaluation ofter#4 [33, 34] and ther#I y developed the concept of a structured lazy evaluation system, which is essentially the same as ....

....systems [28]ar# also developments d Paraphrased. 37 fr#r Aczel s wor# Wear# also indebted to Howefor the definition of bisimulationlikepr #.jFC equivalences andfor the pr# of that theyar# congr#4 Cx. The completenessr#mpletenes is, ML is complete with r#th ect to# C wasfir#I sketched in [23]; however# it was shown onlyfor somer#eC jF C class of L containing a specific collection of typeconstr#x4j4 I Inother wor#kk apr# of sketch was given based on a case by case analysis of sever#C basic typeconstr#x4F F Clar#r#x4F was not givenfor how each new typeincor# or#or# into ITT should ....

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D. J. Howe, "Equality in lazy computation systems," in Proc. 4th IEEE Symp. on 64 Logic in Computer Science, 1989, pp. 198--203.

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Douglas J. Howe. Equality in lazy computation systems. In Proceedings of LICS '89, pages 193-203, 1989.

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Douglas J. Howe. Equality in lazy computation systems. In Proceedings of LICS '89, pages 193--203, 1989.

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Douglas J. Howe. Equality in lazy computation systems. In Proceedings of LICS '89, pages 193--203, 1989.

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Howe, D. J., Equality in lazy computation systems, in: Proceedings of the Fourth Annual Symposium on Logic in Computer Science (1989), pp. 198--203. URL citeseer.ist.psu.edu/howe89equality.html

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D. J. Howe. Equality in lazy computation systems. In Fourth annual symposium on Logic In Computer Science, pp. 198--203. IEEE, 1989.

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D. J. Howe. Equality in lazy computation systems. In Fourth annual symposium on Logic In Computer Science, pages 198--203. IEEE, 1989.

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Howe, D.J.: Equality in lazy computation systems. In: Proceedings of the 4th IEEE Symposium on Logic in Computer Science. (1989) 198--203

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D. J. Howe. Equality in lazy computation systems. In Proceedings of the 4th IEEE Symposium on Logic in Computer Science, pages 198-203, 1989.

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Douglas J. Howe. Equality in lazy computation systems. In Proceedings of the IEEE Symposium on Logic in Computer Science, pages 198-203, Asilomar Conference Center, Paci c Grove, California, June 1989. IEEE, IEEE Computer Society Press.

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D. Howe. Equality in lazy computation systems. In LICS '89 [47], pages 198--201. (pp. 32, 33, 106)

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D. J. Howe. Equality in lazy computation systems. In Proceedings of the 4th IEEE Symposium on Logic in Computer Science, pages 198--203, 1989.

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D. J. Howe. Equality in Lazy Computation Systems. In Proc. 4th Annual Symp. on Logic in Computer Science, Asilomar, 1989 (IEEE Computer Society Press, Washington, 1989) pp 198--203.

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Douglas Howe. Equality in lazy computation systems. In Proc. LICS '89, pages 198--203. IEEE Computer Society Press, 1989.

No context found.

D. J. Howe. Equality in lazy computation systems. In Proceedings of the 4th IEEE Symposium on Logic in Computer Science, pages 198-203, 1989.

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D. J. Howe. Equality in lazy computation systems. In Proc. 4th Ann. Symp. Logic in Comput. Sci., Pacific Grove, CA, U.S.A., 1989. IEEE Comput. Soc. Press.

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D. J. Howe. Equality in lazy computation systems. In Proc. 4th Ann. Symp. Logic in Comput. Sci., Pacific Grove, CA, U.S.A., 1989. IEEE Comput. Soc. Press.

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