R. Muller. M-LISP: A representation-independent dialect of LISP with reduction semantics. ACM Trans. on Prog. Langs. & Systs., 14(4), 1992.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....and standardization. At the same time, Plotkin proved that evaluation via rewriting was equivalent to evaluation via abstract machine. Subsequently, this approach has been applied to many systems, including systems with imperative features such as assignments and continuations (examples include [10, 11, 21, 3, 19, 12, 26, 17]) Warning 1.1 (Not Quite Same as Observational Equivalence) What we call meaning preservation is related to observational equivalence (sometimes called observational soundness [18] operational equivalence, consistency [25] etc. but is only the same for contextually closed rewriting systems. ....

R. Muller. M-LISP: A representation-independent dialect of LISP with reduction semantics. ACM Trans. on Prog. Langs. & Systs., 14(4), 1992. 18

....to various list constructors, the forward quote notation is an abbreviation for a simple quote expression. i.e. X is the same as (quote X) McCarthy invented quote expressions as a mechanism for representing the constants that appeared in his M expression language [6] Smith [11] and Muller [8] have both argued that that there is something suspect about McCarthy s quote. Both are worried that quote somehow confuses levels of representation and reference. They 9 When quasiquotation was migrated to MacLisp [9] X was chosen to mean a destructive version of splicing. They also thought ....

R. Muller. M-LISP: A representation-independent dialect of LISP with reduction semantics. ACM Transactions on Programming Languages and Systems, 14(4):589--616, Oct. 1992.

....of reflection was introduced by Smith [23, 24] to study programs that need to analyze, and potentially modify, their own behavior. Reflection has since received attention in different areas of computer science. In programming languages, it has been used as a tool in the study of interpreters [3, 16, 18, 33], the design of extensible programming languages [13] and polymorphism [26] In A.I. reflection has been used to study programs that must explain their own reasoning strategy [4, 15] In databases, Stemple et al. 25] applied reflection in the dynamic creation of data types in database ....

R. Muller. M-LISP: A representation-independent dialect of LISP with reduction semantics. ACM Transactions on Programming Languages and Systems, 14(4):589--616, 1992.

....not clear from the categorical analysis of multi stage computation [3] whether or not staging and monads can coexist fruitfully, and this question remains an open and interesting one. There has also been a number of related studies in the contexts of LISP and the untyped lambda calculus. Muller [24] studies the reduction semantics of LISP s quote and eval. Muller observes that his formulation of these constructs breaks confluence. The reason for this seems to be that his calculus distinguishes between s expressions and representations of s expressions. Muller proposes a closedness ....

Muller, R. M-LISP: A representation-independent dialect of LISP with reduction semantics. ACM Transactions on Programming Languages and Systems 14, 4 (Oct. 1992), 589--616.

....and the properties we expect them to enjoy. In doing so, we have identified a variety of subtleties related to multi stage programming, and provided solutions to a number of them. The results presented in this paper are based directly on Chapters 5 and 6 of the author s dissertation. Muller [17] studies the reduction semantics of quote and eval in the context of LISP. Muller observes that his formulation of these constructs breaks confluence. The reason for this seems to be that his calculus distinguishes between s expressions and representations of s expressions. Muller proposes a ....

Muller, R. M-LISP: A representation-independent dialect of LISP with reduction semantics. ACM Transactions on Programming Languages and Systems 14, 4 (Oct. 1992), 589--616.

....reasoning about programs at the source level. Danvy and Malmkjaer seem to have had a similar experience in their study of the reflective tower. Reduction Semantics and Equational Theories for Multi Level Languages Muller has studied the reduction semantics of quote and eval in the context of LISP [56]. Muller observed that his formulation of these constructs breaks confluence. The reason for this seems to be that his calculus distinguishes between s expressions and representations of s expressions. Muller proposes a closedness restriction in the notion of reduction for eval and shows that this ....

Muller, R. M-LISP: A representation-independent dialect of LISP with reduction semantics. ACM Transactions on Programming Languages and Systems 14, 4 (Oct. 1992), 589--616.

....example, in the full language map is de ned by (DEFINE map (LAMBDA op . LETREC ( loop (LAMBDA l . IF (null l) op (car l) loop (cdr l) loop) where the special forms are distinguished from applications by the presence of a symbolic constant in the function position. See [Mul90] for a discussion of special forms in M LISP. 2.3 Semantics In the following we generally adopt the terminology and notation of [Bar84] We use the symbol to denote the set of terms, the metavariables M , N , to range over terms, the metavariables x, y, to range over variables ....

R. Muller. Syntax macros in M-LISP: A representation independent dialect of LISP with reduction semantics. Technical Report CRCT TR-04-90, Harvard University, 1990.

....criteria. Let us call this subset 3R . For example, one well known and widely used representation is the encoding of the Godel number of a term as a Church numeral. For the sake of simplicity, we assume representations to be constants, and that these representations can be inductively specified [8]. Such a specification would permit recursive examination of terms. 3.2 The representation function We can now define a representation function f R : 3 3R that gives us the representation of any term in 3, based on our chosen representation scheme. It is well known that such a function is ....

....externally, and the reflective system cannot know of its implementation. We thus introduce two more reductions in our language. M fR (M ) # M f 01 R (M ) M is a representation Recall that the order of evaluation is now fixed, M may not be further reduced when applied to . Muller [8] has introduced such operations in the context of LISP and has shown how confluence can be preserved even when we relax the restrictions on the order of evaluation. 3.3 Turing Completeness and Evaluation Contexts The v calculus is a Turing Complete system. The corresponding rewriting evaluator ....

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Muller, R., M-LISP: A Representation-Independent Dialect of LISP with Reduction Semantics. ACM Transactions on Programming Languages and Systems, Vol. 14, 4, (1992).

....clarified. This issue is particularly explicit when specifying the behaviour of eval on internal representations of abstractions. In the present work we take a very liberal attitude and do evaluate internal representations of abstractions. Our definition of eval should be contrasted with those of Muller (Muller, 1992) and Smith (Smith, 1994) Throughout the paper we use freely standard notions and terminology from proof theory. For the sake of completeness however we briefly recall a few crucial concepts which will be extensively used in the sequel. We take a formal system to be a set of rule schemata of the ....

....To this aim, if an S symbol submitted to quote contains a lambda expression, the special symbol eval will process the resulting literal representation as if it contained a closure. Other semantical accounts of the behaviour of eval quote, can be found in the literature. For example, Muller, in (Muller, 1992), gives a complete coding of an input expression in terms of new syntactical operators. This is extremely natural in a setting in which the operational semantics is expressed as a term rewriting system, but it is awkward in an input output (big step) SOS setting, such as ours. Furthermore, in ....

Muller, R. 1992. M-LISP: A Representation-Independent Dialect of LISP with Reduction Semantics. ACM T.o.P.L.a.S. 14 (4): pp. 589--616.

....the ability of a Lisp program to manipulate expressions as data, it also make sure the data can be executed after a quick decoding making a true Lisp expression out of its quoted representation. This decoding is automatically done by the eval function. But, this behavior is considered anomalous [Mul92] and indeed it makes it difficult to manipulate the reified expressions. When Smith invented computational reflection and implemented it in Lisp, he was aware of this problem. He first proposed 2 Lisp to address issues related to structural reflection and the representation relationship between ....

....the metalevel data representation and the base level code representation. In 2 Lisp, no automatic decoding appears in the evaluation process. Instead, two primitives, UP and DOWN, help to mediate the metastructural hierarchy, and there is no other mean to remove quotes. More recently, Muller [Mul92] proposed M Lisp with a similar motivation. M Lisp is claimed to be a simpler, or rationalized, 2 Lisp. 3.1.2 3 Lisp and behavioral reflection Perhaps because the 2 Lisp solution to self reference was too complicated (according to Muller) Smith s work is much more famous for his second language ....

R. Muller. M-LISP: A Representation Independent Dialect of LISP with Reduction Semantics. ACM TOPLAS, 14(4):589--615, Oct. 1992.

....of a reflective facility that we know of: it has no types, no data, and no environments, and yet the reflection is powerful enough to make the resulting theory trivial. In this section we will discuss some of the consequences of this result. More conventional reflective languages, such as those of [15, 18, 3, 12], reify expressions as list structures, so the construction of distinguishing contexts is even easier, and the same results apply to these languages. Hence a variety of quite different reflective languages have the same equational theory. This suggests that the emphasis on equational theories in ....

Robert Muller. M-LISP: A representation-independent dialect of LISP with reduction semantics. ACM Transactions on Programming Languages and Systems, 14(4):589--616, October 1992.

.... issues such as the order of evaluation, the application ( A; F) x) would then be preceded by an unfolding operation where the apply function would be extracted from (A; F) and applied to the representation of A and x, e.g. F fR (A) fR (x) where fR is a suitable representation function [22], 20] The apply function would itself be an abstraction, and to stop the unfolding, one could provide a basic apply function, as in our model. The unfolding process could be expressed as a PRS with one rule to do the unfolding and a higher priority one to stop the unfolding on the basic apply ....

R. Muller. M-LISP: A Representation-Independent Dialect of LISP with Reduction Semantics. ACM TOPLAS, 14(4):589--615, October 1992.

....With this latter possibility, environments are immutable objects. If a variable already appears in the environment, it is left unchanged; otherwise it is adjoined with an uninitialized state. 1 Remember that quotations do not mention the value to be returned per se but rather describe it [Mul92]. This is obvious when looking at a Scheme to C compiler where quotations are turned into some C code to regenerate some value. Therefore there is no hidden sharing between levels. ffl env set sets the value of a variable within an environment to some value. Its result is unspecified. ffl run ....

R. Muller. M-LISP: A representation-independent dialect of LISP with reduction semantics. ACM Transactions on Programming Languages and Systems, 14, No. 4:589--615, 1992.

....semantics and the rewriting system. A proof of standardization is one way to do this. 2. The existing theoretical tools for the above task have proven dicult to use. In practice, standardization proofs have been carefully hand crafted for equational calculi intended for program reasoning [FF89, FH92, Mul92, AF97]. When proving standardization for a new language, it is a laborious task to adapt an existing proof to the new language. There are some general purpose tools from the rewriting community, but the programming language theorist has problems using them for various reasons: a) Some methods are too ....

.... something they call abstract standardization [KG96] and what they call relative standardization [GK] Standardization has been used extensively for validating the consistency of an operational semantics with a calculus by Plotkin, Felleisen, Ariola, Friedman, Hieb, Muller, and others not listed [Plo75, FF89, FH92, Mul92, AF97]. The method of Ariola and Felleisen depends on disjoint redexes having disjoint residuals. Higher order term rewriting has been presented in a number of di erent formalisms, including several variations on the format of CRS s [Klo80, Nip91, KvO95, Ken89, vR96, vO94, KvOvR93, Kha90, Tak93, Wol93] ....

R. Muller. M-LISP: A representation-independent dialect of LISP with reduction semantics. ACM Trans. on Prog. Langs. and Systs., 14(4):589-615, 1992.

....M with N when equation M = N is in the theory. In order to use this general approach, one must de ne both an operational semantics of a programming language and a calculus of fragments and then establish the appropriate connection between them. In [Plo75] and many subsequent studies (e.g. [FF89, FH92, Mul92]) the operational semantics and calculus are de ned independently and then connected via a standardization theorem for the calculus. More recently (e.g. AF97] it is common to start with the calculus, prove a standardization theorem for it and then simply de ne the operational semantics as a ....

....for the calculus. In either approach, a standardization theorem for the calculus is required. Unfortunately, the usual approach to proving standardization for calculi intended for program reasoning is somewhat unsatisfying. In practice, such proofs have been hand crafted for each calculus (e.g. [FF89, FH92, Mul92, AF97]) The usually ad hoc nature of such proofs means that proving standardization for a new language is a laborious and error prone task of adapting an existing proof to the new language. The Corresponding author. Voice: 1 617 552 3964. Fax: 1 617 552 2097. E mail: muller cs.bc.edu. This ....

[Article contains additional citation context not shown here]

R. Muller. M-LISP: A representation-independent dialect of LISP with reduction semantics. ACM Trans. on Prog. Langs. and Systs., 14(4):589-615, 1992.

....symbols and or literal strings are important for making macros readable, however, we have not included them here (and use object and pattern variables informally as constants) to keep the equations simple. Similarly, we are not addressing the problems of parsing the concrete syntax (but see [Car93, Mul89]) or problems of programmers specifying compile time computations over representations backquote. The algorithm will translate terms relative to an environment : j [A=v] that binds pattern variables v to values A. Environments have the following behavior: v) A=v 0 ] v) ....

R. Muller. M-LISP: A Representation Independent Dialect of LISP with Reduction Semantics. PhD thesis, Boston University, 1989.

....to be answered then is how LISP s various metalinguistic facilities are to be reintroduced in the new dialect. In this paper we consider the eval and reify operators, the latter is a non strict operator which converts its argument to its representation 2 . We consider syntax macros elsewhere [Mul90]. Although our main objective in this paper is to come to grips with the operational aspects of these metalinguistic facilities, we believe that it is also important to clear up the longstanding confusion about the source of LISP s metalinguistic power contrary to folklore, it is unrelated to ....

Robert Muller. Syntax macros in M-LISP: A representation independent dialect of LISP with reduction semantics. Technical Report CRCT-TR-04-90, Harvard University, 1990.

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R. Muller. M-LISP: A representation-independent dialect of LISP with reduction semantics. ACM Trans. on Prog. Langs. & Systs., 14(4), 1992.

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R. Muller. M-LISP: A representation-independent dialect of LISP with reduction semantics. ACM Trans. on Prog. Langs. & Systs., 14(4), 1992.

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