Like VDM-SL, Z [Hayes93] [Spivey92] (pronounced "zed") is a specification language that allows both the specification of mathematical values and program modules. Like LSL, Z allows the definition of mathematical operators equationally (see [Spivey92], section 3.2.2). A Z schema is roughly comparable to an LSL trait. The main difference between Z and LSL is that in Z specifications can include state variables.

First, a more precise comparison is needed, because Larch is not a single language, but a family of languages (see above). Another problem with this comparison is that Larch has two tiers, but VDM-SL [Jones90] [ISO-VDM96] [Fitzgerald-Larsen98], Z [Hayes93] [Spivey92], and COLD-K [Feijs-Jonkers92] are all integrated languages, which mix aspects of both of the tiers of the Larch family.

By VDM, one means, of course, the specification language VDM-SL [Jones90] [ISO-VDM96] [Fitzgerald-Larsen98]. In comparison with LSL, in VDM-SL one can specify mathematical values (models) using constructs similar to those in denotational semantics and typed, functional programming languages.

Like Larch, COLD-K [Feijs-Jonkers92] makes more of a separation into mathematical and interface specifications, although all are part of the same language. The part of COLD-K comparable to LSL is its algebraic specifications (see [Feijs-Jonkers92], Chapters 2 and 3). In contrast to LSL, COLD-K does not use classical logic, and can specify partial functions. All COLD-K types have an "undefined" element, except the type of the Booleans.

The two "tiers" used in the Larch family of specification languages are LSL, which is called the bottom tier, and a behavioral interface specification language (a BISL), which is called the top tier. This specification of program modules using two "tiers" is a deliberate design decision (see [Wing83] and [Guttag-Horning93], Chapter 3).

A15 - You apparently are familiar with those speakers, or consider them a reference, or have formed some opinion about them. To get an idea of where I place the ORION you might read the Design of Loudspeakers page. The Sound Reproduction page explains my design priorities and the importance I give to the motto "True to the Original". The ORION was designed to work optimally in normal living spaces without any specific acoustic treatment other than your normal "stuff of life".

A good place to start is the Guttag and Horning's book [Guttag-Horning93]. (This book is sometimes called "the silver book" by Larchers.) Consider it required reading. If you find that all tough going, you might want to start with Liskov and Guttag's book [Liskov-Guttag86], which explains the background and motivates the ideas behind abstraction and specification. (See section 1.9 What is the use of formal specification and formal methods?, for more background.

According to Jim Horning (personal communication, January 20, 1998) and John Guttag (personal communication, March 28 1998): "The name was not selected at PARC (hence from the Sunset Western Garden Book), but at MIT. The project had been known informally there as 'Bicycle'." One day Mike Dertouzos [director of the MIT Laboratory for Computer Science] and John were talking on the phone.

Larch [Guttag-Horning93] may be thought of as an approach to formal specification of program modules. This approach is an extension of Hoare's ideas for program specification [Hoare69] [Hoare72a]. Its distinguishing feature is that it uses two "tiers" (or layers) [Wing83]. The top tier is a behavioral interface specification language (BISL), tailored to a specific programming language. Such BISLs typically use pre- and postcondition specifications to specify software modules.

The main difference between LSL and a Larch BISL is that in LSL one specifies mathematical theories of the operators that are used in the pre- and postcondition specifications of a Larch BISL. Thus LSL is used to specify mathematical models and auxiliary functions, and the a Larch BISL is used to specify program modules that are to be implemented in some particular programming language.

The following is adapted from a posting of Horning to the larch-interest mailing list on June 19, 1995, which was itself condensed from the preface of [Guttag-Horning93].) This project has been a long time in the growing. The seed was planted by Steve Zilles on October 3, 1973.

This question might mean one of several other more precise questions. These questions are discussed below. One question is: is there a Larch-style BISL for some particular object-oriented (OO) programming language? Yes, there are Larch-style BISLs for Modula-3 (see [Guttag-Horning93], chapter 6, and [Jones91]), Smalltalk-80 (see [Cheon-Leavens94]), and C++ (see [Leavens97] [Leavens96b]).

The Larch Shared Language (LSL) (see [Guttag-Horning93], Chapter 4, and [Guttag-Horning-Modet90]) is a language for specifying mathematical theories. LSL is a kind of equational algebraic specification language [Guttag75] [Guttag-Horning78] [Goguen-Thatcher-Wagner78] [Ehrig-Mahr85] [Futatsugi-etal85] [Mosses96] [Loeckx-Ehrich-Wolf96]. That is, specifications in LSL mainly consist of first-order equations between terms.

The Larch Prover (LP) [Garland-Guttag95] is a program that helps check and debug proofs. It is not geared toward proving conjectures automatically, but rather toward automating the tedious parts of proofs. It automates equational rewriting (proofs by normalization), but does not (by default) automatically try other proof techniques. aid the debugging of specifications (i.e.

Most forms of treatment including acupuncture, massage, ultrasound, medication, TENS, etc. have been used to treat pain and stimulate the healing processes. For the most part the effects of these treatments have been discouraging or provide only temporary relief as they do little more then mask the symptoms. Alleviating symptoms has generally and unfortunately become the accepted norm of treating most conditions.

The NPL and MozPL both attempt to strike a middle ground between promoting free source development by commercial enterprises and protecting free source developers. Like the GPL, they require that any and all changes to code covered by the license must be made publicly available. However, they also allow you to combine covered code with other code to create a larger work without requiring that other code to be covered by the license. This is similar to, but even less restrictive, than the LGPL.

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