D. Sands, From SOS rules to proof principles: An operational metatheory for functional languages, in Conference Record 24th ACM Symposium on Principles of Programming Languages, Paris, France, 1997, pp. 428--441.  Home/Search   Document Details and Download   Summary   Related Articles   Check

.... the fit between reasonable operational extensions for the language PCF [175] and Scott s original lattice model for it has been studied in [46] within the framework of SOS; ffl the derivation of proof rules for functional languages from their operational specifications has been investigated in [194], building upon the work in [8] cf. Sect. 5.4.5) These are only a few of the many interesting examples of applications of SOS that are not covered in this chapter. We hope that the reader will be tempted to explore them, and possibly to contribute to this fascinating research area. ....

D. Sands, From SOS rules to proof principles: An operational metatheory for functional languages, in Conference Record 24th ACM Symposium on Principles of Programming Languages, Paris, France, 1997, pp. 428--441.

....The proposed approach requires to distinguish two kinds of variables, terms, substitutions, etc. like in [17] A transition rule format is proposed for which a congruence result is given. The format concerned is virtually incomparable with the generalized panth format de ned in Section 4.2. In [33], which has been inspired by [26] another format, called the GDSOS format, is introduced. That format is more restrictive, but guarantees other properties which permit, for example, to use a kind of xed point induction. Higher order features of process calculi, and programming languages and ....

D. Sands. From SOS rules to proof principles: An operational metatheory for functional languages. In Symposium on Principles of Programming Languages, pages 428-441. ACM Press, 1997.

....the congruence of vertical bisimilarity with respect to recursion, as formulated in Rule R 24 of Table 6.5, is quite dicult to prove. The usual proof techniques for this kind of congruence property, such as the up to technique proposed in [20, 21] or Howe s technique used in functional calculi [17, 30], are not applicable to non re exive, non transitive relations like vertical bisimilarity. Furthermore, we have investigated alternative extensions of closed relations to open terms in [27] however, the resulting theory is neither developed far enough nor simple enough to apply here. For that ....

D. Sands. From SOS rules to proof principles: An operational metatheory for functional languages. In 24TH ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages. ACM, 1997. 45

....that the congruence of vertical bisimilarity with respect to recursion, as formulated in Rule R 26 of Table 5, is quite di#cult to prove. The usual proof techniques for this kind of congruence property, such as the up to technique proposed in [29, 30] or Howe s technique used in functional calculi [26, 40], are not applicable to non reflexive, non transitive relations like vertical bisimilarity. Furthermore, we have investigated alternative extensions of closed relations to open terms in [36] however, the resulting theory is neither developed far enough nor simple enough to apply here. For that ....

D. Sands. From SOS rules to proof principles: An operational metatheory for functional languages. In 24TH ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages, pages 428--441. ACM Press, 1997.

....[Abr87, Ong88, AO93] The internal choice operator in Section 12 is inspired by an operator introduced by De Nicola and Hennessy [DH87] in a CCS like process calculus. Studies of format of operators in concurrency include [DS85, BIM88, ABV94, GV92] and in functional languages [Blo90, How96, San97a] The L#vy Longo Trees were introduced by Longo [Lon83] where they were simply called trees developing an original idea by Levy [L#v76] They were called L#vy Longo Trees by Ong [Ong88] B#hm Trees are studied in depth in [Bar84] For models of the calculus, such as P , T , DA , D1 , and ....

D. Sands. From SOS rules to proof principles: An operational metatheory for functional languages. In Proc. 24th POPL, pages 428441. ACM Press, 1997.

....are a congruence [How96] Sands defines the Globally Deterministic SOS rule format (GDSOS) which guarantees the congruence property for small step evaluation in functional languages. He also establishes proof principles for reasoning about languages that can be expressed in this format [San97]. Weber and Bloom define rule format for defining languages similar to the calculus [WB96] Sangiorgi defines a rule format that extends the tyft tyxt rule format with calculus evaluation rules [San94] Howe showed that applicative bisimulation is a congruence for Sangiorgi s rule format ....

David Sands. From SOS rules to proof principles: An operational metatheory for functional languages. In 24th ACM Symposium on Principles of Programming Languages, Paris, France, January 1997. ACM Press.

.... semantics [2] or denotational semantics [10] but the use of structural operational semantics or natural semantics as a basis for the design of analysers has been advocated by several researchers recently [8, 13, 18, 17] A notion of Structural Operational Semantics format was introduced in [16] in order to establish a metatheory supporting general reasoning techniques. The broad objective of this paper is similar to ours (de ning semantics formats to achieve a level of factorisation over a class of programming languages) but the context is dioeerent: the format of [16] is dedicated to ....

....was introduced in [16] in order to establish a metatheory supporting general reasoning techniques. The broad objective of this paper is similar to ours (de ning semantics formats to achieve a level of factorisation over a class of programming languages) but the context is dioeerent: the format of [16] is dedicated to functional programming languages and the paper is concerned with the establishment of general proof techniques (like xed point induction) rather than program analysis. 13 One dioeerence comes from the fact that their slicing criterion is a program point rather than a function ....

D. Sands. From sos rules to proof principles: an operational metatheory for functional languages. In 24th Annual ACM Symposium on Principles of Programming Languages, POPL'97, Paris, France, January 1997.

....by recursion. Section 6 contains a comparison of this paper s results with, among others, the work on SOS formats by De Simone [7] Bloom, Istrail and Meyer [4] and Groote and Vaandrager [18] on contexts by Larsen and Xinxin [22] on bisimilarity in functional programming by Howe and others [20,16,32] and in higher order calculi by Sangiorgi [33] Due to lack of space, most of the proofs have been omitted; a full version is available as [30] 2 Conditional operational semantics In this section we recall the notions of term variables and open terms and we discuss their operational semantics. To ....

....our substitutive bisimilarity ( sb ) The difference mainly seems due to the fact that [33] takes the closed instance approach, defining bisimulation directly over closed terms only. Another field where bisimulation has recently gained a foothold is that of functional calculus: see, e.g. [16,20,32]. Again, the operational semantics and bisimilarity are defined over closed terms, and extended to open terms using the closed instance definition. Here, too, substitutivity is a necessary condition for bisimilarity to be a congruence. It would seem that in both settings described above, the ....

D. Sands. From SOS rules to proof principles: An operational metatheory for functional languages. In 24TH ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages. ACM, 1997.

....Finally, section 12 concludes, and we discuss of future avenues of research. 2. RELATED WORK Improvement theory and the improvement theorem were originally developed in the call by name setting [Sands 1991; Sands 1996] and generalised to a variety of call by name and call by value languages in [Sands 1997]. Whether this programme could be carried out in a call by need setting has long been an open question. An inspiration which gave us con dence in the possibility of a tractable improvement theory for call by need is the call by need lambda calculus presented by Ariola and Felleisen, and Maraist, ....

....to 3 Thanks to Stefan Blom for providing an example, and to Zena Ariola for pointing out an error in the use of an earlier formulation of our value copy rule. 18 A. K. Moran and D. Sands Scott induction for other languages may be found in e.g. Pitts 1997b; Smith 1991; Mason et al. 1996; Sands 1997; Lassen 1998] we present the rst such result for a call by need semantics. We will use the following mechanism to describe the syntactic unwindings of a recursive function. In the de nition, the f i are distinct, new variables. Definition 7. f 0 = V def = f 0 = f n 1 = V def = f ....

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Sands, D. 1997. From SOS rules to proof principles: An operational metatheory for functional languages. In Proc. POPL'97, the 24 th ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages (Jan. 1997). ACM Press.

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