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E-commerce taxation电子商务税务问题(英文论文)

Vierteljahrshefte zur Wirtschaftsforschung69. Jahrgang, Heft 4/2000, S. 657–678Taxation of E-Commerce:Persistent Problems and Recent DevelopmentsBy Stefan B a c h*, Markus H u b b e r t** and Walter Mül l e r**SummaryE-commerce on the Internet will create new demands on taxation. In the field of income and business taxation there exists a large potential for profit-shifting into low-tax countries, especially concerning trans-fers of immaterial goods and transfer pricing. In the long run, this can lead to a severe revenue shortfall. Turnover taxation/VAT raise problems if foreign suppliers sell electronic products or services to final consu-mers online. VAT should be charged in the country where the consumption takes place, which is currentlynot the case. Otherwise, distortions of competition and unjust effects of taxation will become more compre-hensive. This requires special technical solutions and closer international co-operation among taxation au-thorities. As a basic principle, e-commerce should not enjoy tax privileges. Rather, it should compete against the traditional economy on the basis of its specific advantages, which, on the other hand, shouldnot be impeded by undue taxation procedures.1. IntroductionThe widespread diffusion of information and communi-cation systems and the development of the Internet into a global “network of networks” are said to be the main driv-ers of the “new economy”. A level of reasonable access to electronic data networks has stimulated the emergence of “cyber business” and “electronic commerce” (e-com-merce), in particular on the world wide web (www), which represents an entirely new channel for moving goods and services globally. This opens up additional opportunities for new products and production schemes, trade and the international division of labour in general, because dis-tance plays a diminishing role.While business goes global electronically, taxation re-mains physically local, at least to a large extent. Tax ar-rangements are basically suited to those businesses and transactions related to home markets or conventional foreign trade. Correspondingly, tax authorities are bound by national borders. Yet as the ongoing debate about globalisation shows, it becomes difficult to tax interna-tional mobile services or production factors such as capi-tal and related services. Electronic business on the Internet may aggravate these problems as firms from all over the world may co-operate or even integrate to vir-tual enterprises. Problems in the field of indirect con-sumption taxation may arise when consumers go shop-ping abroad. This is particularly true if the production and distribution process including payments goes completely online: In the long run, the Internet promises to integrate separate media such as computer software, music, video and television into a comprehensive digital multimedia channel.Against this economic background, e-commerce will create new demands on taxation, regarding the adapta-tion of tax regulations, as well as its enforcement. This paper gives an overview on these topics. After describ-ing the basic economical and technical-institutional backgrounds (chapter 2) an overview on the crucial problems of e-commerce taxation is presented (chapter 3). Chapter 4 addresses issues of income taxation and chapter 5 deals with the problems on turnover taxation/ VAT. For illustrating the problems the text often refers to examples form the German tax system and international tax law.*Deutsches Institut für Wirtschaftsforschung, Berlin, email: sbach@diw.de**University of Kassel, email: hubbert@wirtschaft.uni-kassel.de, muellerw@wirtschaft.uni-kassel.deThe authors would like to thank Bert Kaminski, University of Hamburg, for his substantial and helpful comments. All remaining shortcomings are, of course, in our responsibility alone.6572. Economic Performance and Technical-InstitutionalBackgroundsSince the establishment of the www in 1993, the Internet1 has developed into a global medium for telecom-munication and information exchange within the space of just a few years. In contrast to long-established (propri-etary) business-related networks, its non-proprietary character has proved to be a crucial competitive advan-tage: There is no centralised ownership selecting access by requiring licences and imposing charges for its use. The www permits digitalised data of all types — docu-ments, pictures, video, music and language — to be trans-mitted in an interactive way. Increasingly, conventional electronic networks are adopting Internet standards. Us-ers (suppliers and consumers) from all over the world can get access to the net.E-commerce encompasses the following main areas:—Electronic networks change the paths used to transmit information in the context of traditional trade in goods and services. Rather than using traditional communica-tion channels (providing information through cata-logues and ordering by letter, telephone or fax), inter-action between supplier and purchaser occurs via the Internet, while the goods and services are delivered physically. This is expected to create a substantial po-tential for mail order business, mediation agencies and similar service-providers.—Computer programmes, and increasingly also music/ audio and pictures/videos, can be exchanged in digital form via the Internet, and downloaded to remote stor-age media. Conventional telecommunication medias such as telephone/fax, radio and television will increas-ingly be integrated into the Internet, and will be en-larged by new multimedia services, e.g. video confer-ences, Pay TV, music and video on-demand. New Internet-related products will be offered increasingly (for instance homepage designing). In so far, the whole distribution process is tied online as well as parts of the production process of the traditional economy. Another characteristic feature of such digital products is that they can be reproduced in unlimited numbers without loss of quality.—In addition, the Internet offers a significant potential for services provided by financial intermediaries (elec-tronic banking, trade in securities, electronic cash, in-surance), for advisory services and consultants (audi-tors, management consultants, accountants, software programming, tele-medicine) and for transactions with public institutions.The rapid diffusion of modern information and commu-nication technologies, particularly in the most developed economic regions, North America, Western Europe and Japan, has established the pre-conditions required for a broad-based use of electronic commerce.2 The frontrunners in Internet penetration are the U.S.A. and Canada with the Scandinavian countries leading in Eu-rope, where nearly half of the population have access to the Internet (table 1). Germany lags at present with only 20% of the population or 16 Mill. Internet users, but diffu-sion of Internet access is climbing strong upwards and in-creased by about 6 Mill. during the last year.3 Forecasts of e-commerce transactions show a dynamic rise in market volume, whereas the dominance of business to business (B2B) market is predicted to remain, while the business to consumer segment (B2C) will account for only a small proportion of total electronic commerce in the foreseeable future (figure 1). Private households mainly buy books, CDs, videos, computers, clothes, travel and financial ser-vices via the Internet.41Originating in the 1960s in the U.S.A., the Internet was initially developed as a computer network between government offices, re-search laboratories and academic institutions. Its extremely decentralised network architecture reflected strategic military considerations: even if some important parts of the network were to be disabled, communication could continue automatically via the remaining components in use.2An actual survey gives Coppel (2000).3GfK (2000).4See Ernst & Y oung (2000).T able 1Persons with Access to the Internet in Different CountriesSpring 2000CountryNumber% ofmill.population Western Europe91.812.8of which:Norway 2.249.6Sweden 4.246.0Finland 2.343.0Denmark 2.137.0United Kingdom18.030.0Netherlands 4.629.0Switzerland 1.825.0Austria 1.922.7Belgium 2.222.0Germany15.919.4Italy9.316.4Greece 1.716.0France9.015.3Spain 3.810.0USA126.046.0Canada13.643.0Australia 6.936.4South Korea13.027.0T aiwan 5.023.0Japan21.216.8Sources: Nua Internet Surveys (2000a)658Despite this dynamic development in Internet access, barriers to a broader diffusion of electronic commerce re-main, although they will be overcome to a large extent within the next years:—Currently the bandwidth available for private house-holds or small enterprises only permits the limited use of multimedia forms (particularly audio/video). In this area the technical parameters can be improved in the medium term, however, by rapidly developing new standards (ADSL) or, in addition, by upgrading cable television and electricity networks as well as mobile telecommunication systems (WAP, GRPS, UMTS).—The prices for local calls, the decisive area for the ac-cess to the Internet, are still relatively high in many Eu-ropean countries, in particular in Germany, compared to the U.S.A. However, as a result of the deregulation of telecom markets, competition will lead to lower tariffs and enhanced price differentiation related to user pro-files, e.g. flat tariffs that are independent of the time spent online.—Legally binding contracts are an essential precondition for electronic commerce to function without friction. In the case of transactions involving large sums, the risks concerning the creditworthiness of partners and, in the case of international business relations, differences in general property rights and other legal standards can be expected to play an important role. In the case of sales to private households, consumer protection stan-dards must be maintained. International agreements will be required in this area or existing regulations will have to be reformed.—Furthermore, questions relating to data security and measures to establish identity and authenticity still re-main a significant obstacle to the development of e-commerce. In particular, secure and reasonable elec-tronic mechanism for payments, especially for micro payments, are deemed to be an important pre-conditi-on for the extensive use of e-commerce by private households. However, wide-range improvements had been made in terms of technical standards and public regulations. Trust centres are established, which issue digital signatures, monitored by public authorities. Ad-vanced encryption technologies provide a high level of security when transmitting data, in particular if elec-tronic payments are involved.—Last but not least, empirical analysis have shown that the intensity of communication is largely determined by the regional and cultural closeness of the services of-fered. Linguistic barriers play an important role in this context. It can therefore be assumed that even in the longer run regional clusters will remain, in the face of the trend towards an ongoing globalisation of the economy. This will also apply to electronic commerce, unless differences in taxation systems and other legal and institutional parameters create incentives for spa-tial changes.3. Relevance of E-Commerce for Taxation —an Overview3.1 Problematic issuesExisting taxation systems have developed in an econo-mic environment characterised by the exchange of tan-gible goods and personal services. As global electronic information and communication networks become ever more comprehensive, value added is shifting in favour of intangible goods and electronically provided services, in which suppliers need not be present at the point of sale.659This makes new demands on taxation systems. Firstly, taxation norms will have to be adapted to the new eco-nomic-technological environment of e-commerce. Sec-ondly, the institutional and technical implications of cyber business have enormous repercussions for taxation pro-cedures, for instance regarding the monitoring and con-trol function of the tax authorities and the tax compliance including the obligation on taxpayers to co-operate with the authorities.For an overview of the taxation problems connected with the electronic new economy, one can, in a first step, distinguish between legal and illegal courses of action of taxpayers. Because of the technical and institutional char-acteristics of the Internet, such as—decentralisation, encoding and anonymity,—commerce without receipts and disintermediation,—infinite reproducibility of digital products, and the—absence of public authorities in the net,tax evasion becomes easy and bears low risk. The Trea-sury is frequently unable to enforce its tax claims or re-quires considerable expenses on staff and material to do so.5 The fiscal aim of a revenue-intensive tax collection and the aim of a just and equal taxation will therefore hardly be obtainable. Closely connected are distortions of competition between the old and the new economy, if con-siderable tax evasion in e-commerce leads to lower gross prices there, compared to traditional trade.For the systematisation of the taxation problems in the Internet one can, in a second step, distinguish between national and international transactions. The network forces economic globalisation, while fiscal sovereignty mainly remains on the national level.6 This leads to inter-nationally different tax systems, that, on the one hand, are in a competitive relationship as important location factors, but, on the other hand, need to be co-ordinated, in order to avoid an unwanted double-taxation in e-commerce as well as taxation shortfalls and competition distortions.A third and last clustering aspect relevant for the taxa-tion of e-commerce can be conducted with regard to the affected tax types. Among the taxes levied on the applica-tion of income (so-called indirect taxes) the tax enforce-ment of the special excise duties (on mineral oil, tobacco, coffee, alcohol and spirits, etc) seems to be less problem-atic within the European Union (EU), because of the sys-tem of connected tax stores and a rather small total num-ber of producers or wholesalers. Against this the turnover tax is much more important. This is due to the very broad basis of assessment and the correspondingly extremely high number of taxable suppliers and chargeable transac-tions in the net. Looking beyond the EU border line, tax enforcement problems might arise even with the excise duties on tobacco, coffee or spirits, but only if the Internet will be used by smugglers as an instrument for direct mar-keting.Besides the taxes on the use of income, there are the so-called direct taxes, that tax income generation. Among these are the income tax (in Germany consisting of the wages tax, assessed income tax and capital income tax), the corporation tax and other business taxes (in Germany the local business tax).7 For a regular collection of tax the legal status, the place of residence and the owners of a company or the identity and the place of residence of the taxable person must be known. Therefore, the anonymity of Internet transactions creates problems for tax collec-tion. But there are problems specific to Internet taxation even when considering legal tax behaviour, especially with internationally operating legal tax payers. Here, the determination of taxable profits and their distribution among the involved states are challenging.Figure 2Three Perspectives to Structurethe Taxation Problems in the Internet660When concentrating on the most interesting cases with regard to fiscal policy, international taxation must be at the centre of this study. In future, the arrangement of national taxes will have to orientate themselves on these international agreements. In the following, the structure is therefore orientated on the distinction of tax types and deals mainly with aspects of legal as well as illegal op-tions of tax arrangement in international e-commerce (chapters 4 and 5). Firstly, however, the handling of the relevant taxes on traditional cross-border transactions or, respectively, internationally paid factor incomes, will be explained (chapter 3.2),8 in order to allow the discus-sion of the concrete problems of Internet taxation after-wards.3.2 Traditional international taxationp r i n c i p l e s3.2.1 Income taxation between country of residenceand source country principleTaxes on income generation are usually levied accor-ding to the world income principle. This means, that a tax-able natural person or a taxable entity is to be assessed with its entire income, regardless of the place of genera-tion. This at least holds true for unlimitedly taxable per-sons or entities, i.e. taxpayers with a domestic place of residence or company headquarters, respectively (place of residence principle). Simultaneously, foreigners or for-eign companies are limitedly taxable for their domestic in-come (source country principle). Because of the co-exist-ence of place of residence and source country principle the danger of international double taxation9 of income realised abroad arises, unless the involved states agree on a distribution of the tax competence. To this end, for example, the Federal Republic of Germany has agree-ments on the prevention of international double taxation of income and capital (DTA) with 75 states in force.10 Therein, either the country of residence renounces the taxation of domestic company income generated abroad (exemption procedure) or the taxes already paid abroad under the source country principle reduce the domestic tax burden (imputation method). Even in cases where no DTA exists, unilateral measures of the several national tax laws take effect and help to eventually prevent or reduce a double taxation. Despite bilateral agreements and unilat-eral measures, yet there are cases of double taxation of international income flows.11However, the major problems with Internet taxation are not the remaining cases of international double taxation, but the imminent taxation shortfalls.12 Again, the above mentioned characteristics of e-commerce, and – under certain circumstances – the spatial mobility of a server computer as a taxable permanent establishment, allow taxable persons to attain a taxation shortfall by legal and illegal measures. The results are distortions of competi-tion, unfair tax impacts and loss of revenue as chapter 4 will show.3.2.2 Turnover tax between country-of-destination andcountry-of-origin principleAs a consumer levy, turnover tax is so designed as to fall on final consumer expenditure.13 In Germany, the rev-enue of the turnover tax currently (2000) exceeds DM 275 bill. per year. That’s the second highest (behind the in-come tax) tax yield compared to other taxes.14Normally, the so-called country of destination principle is applied on transboundary transactions. This is to guar-antee that the final consumer bears the same domestic turnover tax for all goods supplied and services rendered that he consumes in his country – regardless of the coun-try by which the good or service was provided. The ex-porter gets a rebate for the input tax paid by him at the border of the exporting country, so that the export itself is not charged with turnover tax. The import is subject to im-port turnover tax of the importing country (country of de-stination). The country of destination principle also applies for international mail-order selling.Within the EU, where check points at the internal EU borders no longer exist, the destination principle is realised through separate settlement. The intra-Commu-nity supply is not subject to turnover tax, but intra-Com-munity acquisition is. Accordingly, the purchasing com-8See also Kesti/Andersen (2000) for basics of European taxa-tion.9The term “international double taxation” is used when a tax object (in this case income) is simultaneously charged two similar taxes of two different states within one period.10See Bundesministerium der Finanzen (2000), 37.11For example by non-uniform definitions of place of residence or company headquarters or non-uniform delimitations of tax liabil-ity, e.g. by where the company and where its management is based. Finally, double taxation can also be the result of complicated legal forms or shareholding structures. Details on this in Schaumburg (1998), Part 3.12A taxation shortfall exists, when a tax object, that can be at-tributed to different states, is subject to a lesser tax burden than intended by the tax policy of the country of residence or the source country. Taxation shortfalls can be the result of legal or illegal tax arrangements or of calculation errors, loopholes in the law or con-flicts of qualification between the national tax laws.13Within the OECD countries the concept of a value-added tax (VAT) has prevailed against other systems and was established more or less homogeneously in the EU. The turnover tax is levied on all turnovers of enterprises on all stages of production and dis-tribution. The input tax (turnover tax on purchased input products, raw materials etc.) is refunded by the tax authorities. This system is called input tax deduction system and will be at the fore in this study. An older kind of turnover tax, with diminishing relevance, is the sales tax, only imposed on sales to non-tax payers (consum-ers). In the U.S.A. or Canada we still find the sales taxes on the states-level. However, most of the east European countries in tran-sition applied to the VAT-system, recently.14See OECD (1999), 147.661pany has to pay turnover tax in the country of destination. For control purpose, monthly reports of the companies are obligatory. All companies participating in the intra-EU trade were assigned a turnover tax identification number, which they have to communicate to their business part-ners. The regular turnover reports must contain the num-ber of the suppliers and the acquirers, as well as the total value of intra-EU turnover. All this information will, gener-ally, be exchanged between the tax authorities of the Member States.Exceptions from the country of destination principle exist within the EU for direct sales to travellers, who are charged the turnover tax valid in the respective country they are visiting (country of origin principle). This rule, in turn, does not apply to the sales of new vehicles (cars, boats, planes) to final consumers. They are charged the tax rate of their home country.Besides, within the EU the origin-principle is applied to mail order delivery to consumers, if the sales of the selling company do not exceed Euro 100 000 per year in the country of destination (threshold amount). Exceeding this amount makes the selling company taxable in the desti-nation country. The EU member states are allowed to lower that threshold to Euro 35000. In Germany the threshold amount is DM 200000.Finally the country of origin principle is generally ap-plied to “services” (Article 6 of 6th VAT Directive, Sec. 3 (9) German VAT Act). This is to take into account, that ser-vices usually are consumed right at the place of their pro-duction. However, in some cases of “services” (see Article 9 (2)(e) 6th VAT Directive, Sec. 3a (3), (4) German VAT Act) the destination principle is valid.The dominance of the country of destination principle, compared to the country of origin principle, concerning the taxation of cross-border turnovers is necessary for tax system reason. The destination principle generates com-petition neutrality since it guarantees that every product, regardless of its origin, is charged the same domestic tax rate in the country of destination. In other words, the rela-tive prices of competing products are not distorted. At the same time, we speak of capital export efficiency – a prop-erty preventing internationally different turnover tax rates from seriously influencing the entrepreneurial locational decision (capital export, direct investment). Finally, and that’s the crucial point, it is considered a merit of the coun-try of destination principle, to best reflect the character of the turnover tax as an excise duty, that is to be paid by the final consumer,15 since the country of destination usually is the country of consumption too.The criticism against the country of destination principle is that the administrative realisation within an integrated international market without border controls is very diffi-cult. Additionally, purchases of travellers can not be taxed according to the destination principle. Besides, for “ser-vices” the place of consumption, i.e. the country of desti-nation, is hard to determine or is identical with the country of origin. These three arguments in turn lead to the range of validity of the country of origin principle. With respect to the Internet, one have to face an increasing relevance of these three aspects:—there are no national borders within the Internet,—the net will foster the direct cross-border shopping of fi-nal consumers,—and a wide range of new Internet products can be inter-preted as services.Regarding these aspects, the leading question for chap-ter 5 of this study is how to keep the economically prefer-able destination principle the dominant one for taxing in-ternational transactions.4. Income Taxation of E-Commerce4.1R e s i d e n t o r n o n-r e s i d e n t t a x a t i o n?In principle, all seven types of income, i.e. income from business enterprise or income from renting and leasing (see Sec. 2 (1) German Income Tax Act — ITA) are sub-ject to resident or non-resident taxation in Germany. Re-garding taxes on income and profits in e-commerce, cross-border activities are, above all, of interest for inter-nationally operating enterprises if they can be carried out via the Internet.Referring to the cross-border activities mentioned above, a distinction must be made between outbound cases and inbound cases. The term inbound-investment means a foreign investor investing in Germany whereas the outbound case is defined as a German investor’s ac-tivities in a foreign country. Concerning sub-cases of in-bound and outbound activities, the question arises in which legal form these activities take place. Direct activi-ties as well as alternative permanent establishments, sub-sidiaries or, in some cases, subsidiary-partnerships have to be taken into consideration, whereby the latter alterna-tive, according its taxation assessment, will be taxed as a rule, either as a permanent establishment of the co-owner or as a legal entity and thus as a corporation.In principle, an outbound case is subject to resident taxation (see Sec. 1 (1) ITA, Sec. 1 (2) Corporate Income Tax Act — CTA — combined with Sec. 2 (1) ITA) if the si-tus or the company’s management is based or located in Germany. The terms situs and management of a corpora-tion are defined in Sec. 10 and 11 German Fiscal Code (FC). As to situs in Germany the definition of residence is15For details on the normative theory of individual tax types compare Reding/Müller, especially chapters two, seven and eight.662possible even for purely virtual corporations. Attributing or assigning the actual location of the management — espe-cially concerning exclusively virtual enterprises — is much more difficult. It is conceivable that such enterprises either dispense with a central place of the management or the duration of their residence is limited and therefore not assignable for the fiscal administration. In such cases, according to the German tax law, the fiscal authorities can refer to the place of residence in order to impose resident taxation. In cases involving tax treaties, e.g. Article 4 (3) OECD Model Tax Convention (OECD-MTC) it is mainly the place of management that is decisive and an unclearly defined location of the management may lead to a loop-hole in the law of the OECD-MTC, i.e. a condition not cov-ered by a treaty or agreement of the OECD-MTC and thus subject to double or reduced taxation.In the case of non-resident taxation of foreign enterpri-ses (inbound case), the entire enterprise with its global in-come is not subject to non-resident taxation, except for the income obtained under Sec. 49 ITA with an objective and factual nexus to the home country (principle of source, see Sec. 1 (4) ITA, Sec. 1, 2 CTA). In order to provide the re-quired relation to the home country and thus a separation of domestic and foreign income, the facts of the case must be ascertained under the special constituent facts regard-ing domestic income (Sec. 13–23 ITA). If such a factual re-lation to Germany exists, the foreign enterprise will be sub-ject to non-resident taxation and will be faced with fiscal jurisdiction in at least two countries. To avoid international double taxation, the application of the international double taxation treaties, as far as available, will have to be exam-ined. Types of income under Sec. 49 (1) ITA, concerning e-commerce, which may lead to non-resident taxation for for-eign enterprises, will be analysed below.4.2P r o b l e m s r e l a t e d t o i n c o m e q u a l i f i c a t i o no f e n t e r p r i s e s s u b j e c t t o n o n-r e s i d e n tt a x a t i o nIn particular the following types of income can result from Sec. 49 (1) ITA for enterprises developing cross-bor-der activities in the Internet:1)Income from business enterprise (Sec. 49 (1) 2 ITA);2)Income from renting and leasing (Sec. 49 (1) 6 ITA);3)Other income from the transfer of non-protectableknow-how (Sec. 4 49 (1) 9 ITA).The terms and conditions for one of these types of in-come will be examined as follows.4.2.1 Income from business enterprise in case of a permanent establishment or a permanent representativeThe terms and conditions for the income qualification of a foreign content provider as income from business enter-prise as defined under Sec. 49 (1) 2 a ITA require main-taining a permanent establishment or the appointment of a permanent representative. If the foreign content provider resides or is located in a country with which a tax treaty has been concluded — normally the case — both the Fis-cal Code and the particular tax treaty are applicable. Two basic questions are to be differentiated:a)Does it qualify as a permanent establishment or a per-manent representation according to national laws? If so, it is subject to taxation under German tax law.b)Is this also applicable under treaty legislation? Result-ing from the above, the question is whether taxation according to national tax legislation is also legal under treaty legislation.In this case no contradictions are to be expected, as the international double taxation treaties concluded with Ger-many require the establishment of a permanent establish-ment in order to subject domestic profits of a foreign en-terprise to non-resident taxation. However, attention must be paid to the fact that in practice German and interna-tional definition in many cases differ considerably from those of Sec. 5 OECD-MTC.4.2.1.1 Server Computer as permanent establishmentThe definition of a permanent establishment16 as a pre-requisite of a location-dependent business is stated in Sec. 12 (1) FC and is identical with the definition of Art. 5 OECD-MTC, which a permanent establishment define as a place in which business is entirely or partially con-ducted.17 The following constituent facts have to be ful-filled for a permanent establishment:18—There will be a business place;—It will be fixed spatially and temporally;—It will serve the business;—The enterprise will hold disposing power.The place of business is defined as an existing physical object and the sum of all items serving the business.19 Simple equipment will suffice, physical objects are of ma-jor importance.20 No special buildings are required for the place of business and need not necessarily be fit for per-sons.21 The Internet server suffices the criterion of physi-16See also Portner, R. (1999), 20–26.17See Wassermeyer (1999), Tz. 1.2.1.1; BFH (Federal Finance Court) vom 30.10.1996 (II R 12/92, Federal Tax Gazette. II 1997, S.12); see Strunk/Kaminski (2000), 15.18See OECD-MA-Kommentar, Ziff. 2 zu Art. 5 (1); Vogel, DBA, 3. A., Art. 5 Rz 20.19BFH vom 3.2. 1993, I R 128/73, Federal Tax Gazette II 1993, 462.20See OECD-MA Kommentar, Ziff. 4 zu Art. 5 Abs. 1.21See BFH vom 13.05.1958, I B 49/58 — U; Federal Tax Ga-zette II 1958, 379.663。

经济学研究范式的英文

经济学研究范式的英文Economic research paradigms have evolved significantlyover the years, reflecting the complexity and dynamism of the field. The paradigms serve as frameworks that guideeconomists in their quest to understand and explain economic phenomena.One of the earliest and most influential paradigms is the Classical Economics paradigm, which emerged during the Industrial Revolution. It was characterized by a belief inthe self-regulating market and the 'invisible hand' that guides economic activity towards societal welfare. This paradigm emphasized the importance of laissez-faire policies and minimal government intervention.In contrast, the Keynesian Economics paradigm, which gained prominence in the mid-20th century, shifted the focus towards the role of government in managing economic cyclesand addressing unemployment. Keynes argued that aggregate demand, rather than market forces alone, determined the level of economic activity.The Neoclassical Economics paradigm, which emerged in the late 19th century, introduced the concept of marginal utility and the importance of individual choice in economic decisions. This paradigm also emphasized the role of equilibrium in markets and the efficiency of market outcomes.Behavioral Economics, a more recent paradigm, challenges the traditional assumptions of rationality in economic agents. It incorporates insights from psychology to explain anomalies in decision-making that deviate from the predictions of standard economic models.Another significant development is the Post-Keynesian Economics paradigm, which extends Keynes' insights to include issues of income distribution, financial instability, and the role of money and credit in the economy.The Institutional Economics paradigm, meanwhile, focuses on the role of social institutions and their impact on economic behavior and outcomes. It emphasizes the importanceof historical context and the evolution of economic systems.Finally, the Ecological Economics paradigm addresses the interdependence of economic systems with the environment, advocating for sustainable development and the integration of ecological concerns into economic policy.Each of these paradigms offers a unique lens throughwhich to view and interpret economic events and trends. The diversity of these paradigms reflects the multifaceted nature of economics as a discipline and the ongoing quest for a more comprehensive understanding of economic processes.。

创新与经济增长

这项工作可以不被翻译或者全部或部分复制未经书面出版商的许可（施普林格科学+商业媒体公司，泉街233号纽约，(NY10013，USA），除了与审查或学术分析连接简单摘录。

用于用任何形式的信息存储和检索，电子适应，计算机连接软件，或由相同或不同的方法，现在已知的或以后开发的是被禁止的。

本出版物的商品名称，商标，服务标记，以及类似术语的，使用即使他们未标识为这样的，不应被视为表达意见，以无论它们是否是受所有权印在美利坚合众国第四章阻碍产业结构调整：生长罚4.1简介对于经济增长的解释普遍限于限制宏观经济学（罗默，1990;克鲁格曼，1991）的领域。

然而，不同的学术传统上将增长挂钩与工业组织挂钩，这可以追溯到至少熊彼特（1934年）。

根据本传统，表现在经济增长来衡量，是通过到行业结构最有效的利用程度稀缺资源。

但决定这个最佳结构有一在产业组织的专门领域的悠久传统对确定行业结构的决定因素。

早在1948年，布莱尔表示，技术是最重要的决定因素行业STRU〜真实存在。

“〜舍雷尔和Ross（1990）和钱德勒（1990年）扩大优化行业结构的决定因素包括其他因素以及底层技术。

多西（1988，第1157），在他的系统文献复习经济文学杂志，总结“各生产活动的特点是一个特定的分布的公司“。

当底层产业结构的决定因素是稳定，行业结构本身不会被预期发生变化,然而，在基本决定因的变化，预计将导致在最佳工业结构的改变。

当然，钱德勒（1990）和舍雷尔和Ross（1990）确定了最优行业的换档朝增加集中和浓度在整个第一三分之二上世纪结构变化的结果底层技术以及其他因素。

《2024年事件研究方法及其在金融经济研究中的应用》范文

《事件研究方法及其在金融经济研究中的应用》篇一一、引言事件研究方法（Event Study Methodology）是一种广泛应用于金融经济学领域的实证研究方法。

它主要关注特定事件对研究对象（如公司、市场或经济体）的影响，通过分析事件发生前后相关指标的变化，来评估事件的经济效应。

本文将详细介绍事件研究方法的基本原理、实施步骤及其在金融经济研究中的应用。

二、事件研究方法的基本原理事件研究方法基于有效市场假说，即市场是理性的，能够迅速对信息进行反应并调整资产价格。

当某一事件发生时，如公司公告、政策发布等，市场会迅速吸收这些信息，并反映在资产价格上。

事件研究方法通过比较事件发生前后资产价格的变化，来评估事件的经济效应。

三、事件研究方法的实施步骤1. 定义事件：明确研究的事件及其发生时间。

2. 选择样本：根据研究目的选择合适的样本，如公司、行业或市场。

3. 确定事件窗口：确定事件发生前后需要关注的时间段，即事件窗口。

4. 数据收集与处理：收集事件窗口内的相关数据，如股价、交易量、财务报告等，并进行必要的处理。

5. 估计正常水平：运用统计方法估计事件窗口内相关指标的正常水平，如正常收益率。

6. 计算异常值：比较实际值与正常水平的差异，计算异常值。

7. 解释与推断：根据异常值分析事件的经济效应，并进行必要的推断。

四、事件研究方法在金融经济研究中的应用1. 公司财务领域：事件研究方法广泛应用于公司财务领域，如公司并购、股权变动、股权激励等事件的股价反应及经济效应研究。

通过分析这些事件前后股价、交易量等指标的变化，可以评估事件对公司价值的影响。

2. 金融市场领域：在金融市场领域，事件研究方法用于研究政策变化、市场波动等对股票市场、债券市场、外汇市场等的影响。

例如，研究货币政策调整对股市波动的影响，以了解政策变化对市场运行的影响。

3. 宏观经济领域：在宏观经济领域，事件研究方法可用于研究经济政策、自然灾害等对经济增长、就业、物价等的影响。

国外怎么说数字火炬手原理

国外怎么说数字火炬手原理The concept of a digital torchbearer, as articulated in foreign contexts, refers to an innovative approach that harnesses digital technology to symbolize and propagate a specific message or ideal. This principle is based on the use of digital platforms and tools to create a virtual representation of a torchbearer, carrying the torch of a movement, idea, or event and passing it on to others through digital means.在国外，数字火炬手原理指的是一种创新方法，它利用数字技术来象征和传播特定的信息或理念。

该原理基于数字平台和工具的使用，创建火炬手的虚拟形象，通过数字手段传递运动、思想或事件的火炬，并将其传递给其他人。

The digital torchbearer serves as a virtual ambassador, leveraging the reach and interactivity of digital media to engage a wider audience. It allows individuals and organizations to participate in a global movement or initiative, even without physical proximity, by virtually carrying and passing the torch.数字火炬手作为虚拟代表，利用数字媒体的传播范围和交互性，吸引更广泛的受众参与。

估值37.5亿美元,看看这头独角兽的秘密账本(双语)

估值37.5亿美元，看看这头独角兽的秘密账本（双语）身处行业寒冬，多家业内公司选择主动公布财务数据展示实力，想从表现低迷的同行之中脱颖而出。

信息技术与网络网络安全业务公司Tanium最近也公布了数据。

风险资本数据库Pitchbook显示，私人投资者对Tanium最新估值为37.5亿美元。

Tanium首席执行官兼联合创始人奥利恩•辛达维向《财富》杂志独家透露了财务数据。

他说：“总有客户要求我们解释为什么三年、五年和十年内如何发展更大更好。

他们想先确认这项技术能持续存在，否则不愿投资并应用。

”辛达维分享了一些具体的数据，以显示Tanium的实力和苦苦挣扎的同行不一样。

他告诉《财富》，公司上一个财年“营业收入远超2亿美元”，同比增长70%。

他补充说，去年Tanium经常性收入增长80%以上，达到2.3亿美元左右。

辛达维还称：“营运现金流方面有大量现金流入。

”目前现金流规模超过2000万美元，比上年同期约增加了四倍。

由于现金流较大，Tanium持有现金也大量增加。

辛达维此前接受采访时透露，截至去年年末，公司的现金及现金等价物突破了3亿美元。

这一数据可能让潜在投资者满意，因为流动性没有迫切需求，但可能继续募集几轮私人投资，给员工兑现持股的选择。

辛达维说，Tanium去年第四季度已实现盈利，不过仍在积极投资开拓业务。

“我预计未来会保持盈利。

”“投资者已经厌烦投资不可能赚钱的企业，”辛达维称，“抢椅子游戏的音乐一结束，很多公司就玩不下去了。

”辛达维常提到客户留存率。

他说，去年平均来看，Tanium几乎没有客户流失，客户留存率几近100%。

他接着说，“客户续签率达到150%”，这意味着“假设去年一位客户在我们身上花了一美元，明年他会花1.5美元。

”具体到Tanium公司，高续签率通常表现为，客户购买了Tanium的核心产品后追加购买一些高价的“模块”或者功能，方便工程师管理IT基础设施。

辛达维最后谈到之前想让公司公开上市的愿望。

当代研究生英语第七单元 B课文翻译

价格的利润生物公司正在吞噬可改变动物DNA序列的所有专利。

这是对阻碍医学研究发展的一种冲击。

木匠认为他们的贸易工具是理所当然的。

他们买木材和锤子后，他们可以使用木材和锤子去制作任何他们所选择的东西。

多年之后来自木材厂和工具储藏室的人并没有任何进展，也没有索要利润份额。

对于那些打造明日药物的科学家们来说，这种独立性是一种罕见的奢侈品。

发展或是发现这些生物技术贸易中的工具和稀有材料的公司，对那些其他也用这些工具和材料的人进行了严格的监控。

这些工具包括关键基因的DNA序列，人类、动物植物和一些病毒的基因的部分片段，例如，HIV,克隆细胞，酶，删除基因和用于快速扫描DNA样品的DNA 芯片。

为了将他们这些关键的资源得到手，医学研究人员进场不得不签署协议，这些协议可以制约他们如何使用这些资源或是保证发现这些的公司可以得到最终结果中的部分利益。

许多学者称这抑制了了解和治愈疾病的进程。

这些建议使Harold得到了警示，Harold是华盛顿附近的美国国家卫生研究院的院长，在同年早期，他建立了一个工作小组去调查此事。

由于他的提早的调查，下个月出就能发布初步的报告。

来自安阿伯密歇根大学的法律教授，该工作组的主席Rebecea Eisenberg说，她们的工作组已经听到了好多研究者的抱怨，在它们中有一份由美国联合大学技术管理组提交的重量级的卷宗。

为了帮助收集证据，NIH建立了一个网站，在这个网站上研究者们可以匿名举报一些案件，这些案件他们相信他们的工作已经被这些限制性许可证严重阻碍了。

迫使研究人员在出版之前需要将他们的手稿展示给公司的这一保密条款和协议是投诉中最常见的原因之一。

另一个问题是一些公司坚持保有自动许可证的权利，该许可证是有关利用他们物质所生产的任何未来将被发现的产品，并且这些赋予他们对任何利用他们的工具所赚取的利润的支配权利的条款也有保有的权利。

Eisenberg说：“如果你不得不签署了许多这样的条款的话，那真的是一个大麻烦”。

欧版QE议案曝光量化宽松并非万能药

欧版QE议案曝光量化宽松并非万能药
佚名
【期刊名称】《中国对外贸易》
【年(卷),期】2015(000)002
【摘要】1月22日，据外媒报道称，欧洲央行行长马里奥·德拉吉（Mario Draghi）已经提出了一项总额最多可达1．1万亿欧元（约合1．3万亿美元）的债券购买计划，目的是寻求刺激欧元区通胀率回升。

【总页数】1页(P12-12)
【正文语种】中文
【中图分类】F835.163
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Deriving DAP Implementations of Numerical Mathematical Software through Automated Program Transformation1 James M.Boyle2,Maurice Clint,Stephen Fitzpatrick3,Terence J.Harmerboyle@,M.Clint,S.Fitzpatrick,T.Harmer@The Queen’s University of Belfast, Department of Computer Science, Belfast BT71NN,Northern Ireland.Mathematics and Computer Science Division, Argonne National Laboratory,Argonne IL60439,USA.July1992Technical Report1992/Jul-JMB.MC.SF.TJH,Computer Science,QUB,July1992.<URL:/pub/TechReports/1992/Jul-JMB.MC.SF.TJH/><URL:ftp:///pub/TechReports/1992/Jul-JMB.MC.SF.TJH.ps.gz>1IntroductionAtﬁrst sight,functional programming languages seem to be not at all appropriate for expressing solutions to numerical mathematical problems.On the one hand,there is a long-established tradition of expressing such algorithms in procedural languages;in fact,the earliest procedural languages,Fortran and Algol60, were speciﬁcally designed with numeric computations in mind.On the other hand,functional languages appear to be ill-suited to the speciﬁcation of computations that operate on data represented by arrays-a data structure that is the dominant one in mathematical software.If one sets aside these preconceptions,however,closer examination reveals that functional languages do have advantages for describing numerical computations.The general advantages of functional programming -naturalness of expression(in some problem areas),ease of proof,and clarity-are well known.When one uses functional programming in a numerical mathematical context,oneﬁnds that many numerical computations are more naturally expressed by using recursion than by using the iterative constructs which are often employed when using procedural languages.Nevertheless,these desirable features of functional speciﬁcations for numerical problems count for nothing if the speciﬁed computations cannot be executed efﬁciently.The very problems and algorithms for which the advantages of functional speciﬁcation are most important are those that require prodigious amounts of computation and for which even relatively minor inefﬁciencies cannot be tolerated.We have been investigating the generation of efﬁcient programs from functional speciﬁcations for a range of numerical algorithms.We have succeeded in using transformations to derive automatically a vectorizable implementation of a hyperbolic PDE algorithm whose performance is more efﬁcient than that of the handwritten program on the CRAY X-MP[8].We consider a functional speciﬁcations as just that-an abstract speciﬁcation of how to solve a problem, not a concrete program to be run in order to compute a solution.By adopting this point of view,we liberate the style of the functional speciﬁcation from any demands for efﬁcient execution.We can write the speciﬁcation in the style and with the techniques that produce the greatest degree of clarity,guarantee correctness and facilitate adaptability.We then address the question of efﬁciency during the process of creating an executable concrete implementation by automated program transformation.In this paper we describe recent work on deriving implementations tailored for execution on the AMT DAP computer.We apply the transformation methods in the derivation of an efﬁcient implementation of an eigenvalue algorithm.2Notation:A Functional Speciﬁcation LanguageFor our functional speciﬁcation language we use a(very)small subset of the language constructs available in Standard ML(SML)[12].The speciﬁcations that we express in this language are high-level.They are, however,algorithmic and,in fact,executable.Indeed,we occasionally execute them in speciﬁcation form in order to carry out rapid prototyping.2.1Primitive Vector and Matrix FunctionsWe provide a standard library of vector/matrix operations to facilitate the speciﬁcation of numerical math-ematical algorithms.The transformational derivation must provide an implementation for each primitive operation tailored for the hardware architecture in use.In the discussion below we give deﬁnitions of the vector functions;each has a natural analogue for matrix arguments.2.1.1Deﬁnition1:01where is a vector of elements of typeThe function is applied to two arguments:a vector(referred to as the base vector)and a function (referred to as the generating function)and produces a result vector.The result vector is of the same size as the base vector and each of its elements is obtained by applying the generating function to the index for that element.2.1.2Deﬁnition2:defFor many vector expressions the evaluation of the generating function for a particular index requires only the element of the base vector.(Such expressions have a generating function that can be written in the form,where the body of the inner abstraction has no occurrences of the function.)Such expressions occur frequently enough to justify the deﬁnition of a simpler form of called.2.1.3Deﬁnition3:01A function combines the elements of a vector by means of a binary function to produce a single mon examples of reductions are calculation of the sum of the elements of a matrix of numbers and conjunction of the elements in a boolean matrix.The function is applied to a base vector,a generating function,a(binary)reducing function and an initial value.The generating function is applied to each element in the vector and the values returned by the generating function are combined by the reducing function to form theﬁnal result.We deﬁne a simpler form of called that applies a function to the elements of a vector in the traditional manner.The function has the same relation to as does map to;that is,it is a shorthand notation for a frequently used operation.3The Parallel Orthogonal Transformation(POT)AlgorithmThe eigenvaluesΛand eigenvectors of a matrix of order n satisfy the equation:Λ,whereΛis a diagonal matrix with the eigenvalues1of as its diagonal elements.If is symmetric is guaranteed to be non-singular and is,in addition,orthogonal.The POT algorithm is based on the construction of a sequence of similar symmetric matrices as shown below:1.02.10where the sequence is con-structed as follows:3.04.Then lim and limΛ[10].The function orthonormalizes the columns of its non-singular matrix argument using the standard Gram-Schmidt method.The POT algorithm may be realised by a Standard ML function of the form:fun Pot(A:real Array,U:real Array):real Array*real Array= let B=multiplymatrix(transpose(U),multiplymatrix(A,U))inif(is_satisfactory(B))then(U,B)elsePot(A,orthogonalize(multiplymatrix(A,multiplymatrix(U,transform(B))),diagonal(B))end;This deﬁnition follows directly from the description of POT given above:if is sufﬁciently diagonal then the columns of and the diagonal elements of are the eigenvalues;otherwise a more accurate approximation to is derived and POT is applied using this new approximation.The operation transform produces from its matrix argument a matrix,,each column of which is an approximation to an eigenvector of.The components of are computed as follows:21242From this deﬁnition the SML function may be coded thus:fun Transform(M:real Array):real Array=let fun Calculate(M:real Array,i:int,j:int):real=let val d=element(M,j,j)-element(M,i,i)in2*element(M,i,j)/(d+sign(d)*sqrt(sqr(d)+4*sqr(element(M,i,j))))endingenerate(fn(i,j)=>if(i>j)then Calculate(M,i,j)else if i=j then 1.0else˜Calculate(M,j,i),M)end;A function is used to construct the transformation matrix from its argument matrix,.A local function deﬁnes the value of the th element of the transformation matrix.The generating function embodies the cases required by the algorithm speciﬁcation.A similar development may be used for the ortho function.We claim that we have not intentionally biased these deﬁnitions.Indeed,we would further claim that they represent a natural SML formulation of the algorithm speciﬁcation.4The AMT DAP510The DAP510has a two-dimensional(3232)array of processors which operate in a single instruction, multiple datastream mode.The instructions for the processor array are supplied by a scalar processor.The data for each processor can emanate from:The scalar processor which may broadcast scalar data;The local memories of the processors of the array.Hardware channels that permit nearest neighbour communication and the rapid duplication of a vector of values in the rows or columns of the array.4.1DAP FortranThe language in which we express ourﬁnal implementation is DAP Fortran,an extension to standard Fortran that allows the array processor to be used efﬁciently.DAP Fortran supports two types,scalar vector and scalar matrix,which are similar to one dimensional and two dimensional array,respectively,in standard Fortran,but supplies additional operations that use the processor array.Each element of a vector or matrix is manipulated by its own processor,but corresponding components of different vectors and different matrices share a processor.The size of vectors or matrices is limited only by the the amount of memory available,not by the size of the processor array.DAP Fortran subdivides a vector or matrix whose dimensions are larger than those of the processor array into sections each of which is the size of the array(if necessary,it pads the edges of the vector or matrix to make the size a multiple of the processor array size).The features of DAP Fortran that are important to us are:Componental functions-scalar functions applied to each element of a vector/matrix and scalar functions applied to corresponding elements of a pair of vector/matrices;these include simple arithmetic and logical operations.Applications of componental functions are evaluated in constant time.Aggregate functions which perform certain elementwise reductions on a vector/matrix.Such reductions can be performed in steps.V ector/matrix assignment.V ector/matrix assignment controlled by a boolean vector/matrix,or mask.The assignment affects only those elements of the variable for which the corresponding element of the mask is.Functions to create vector/matrix masks having elements arranged in certain commonly used patterns.Geometric functions to re-arrange the order of elements in a vector/matrix;for example,functions to form the transpose of a matrix or to reverse the order of elements in a vector.Extraction functions that return a vector with elements equal to the elements of a given row or column of a matrix.Masked extraction functions.To runn efﬁciently on the DAP,a program must be expressed almost entirely in terms of these features.5Deriving Efﬁcient Programs from Functional SpeciﬁcationsOf course,our goal is not simply to execute our functional speciﬁcations as ML programs,where execution can often be excruciatingly slow.POT has been designed with large matrices in mind and is interesting because it permits implementations tailored for execution on computers having novel advancedarchitectures [9,13,14,10].Efﬁcient ML implementations are not likely to be available for such computers.Naturally, the question to be posed is:how can we obtain,from functional speciﬁcations,programs that execute efﬁciently and exploit high-performance computers?Our answer is to use program transformations.We use the TAMPR program transformation system[3,4]to apply a sequence of sets of program trans-formations that produce an efﬁcient Fortran or C program from the higher-order functional speciﬁcation. Most of the transformations are basic;that is,they can be employed in the efﬁcient implementation of any functional speciﬁcation.These transformations form the framework for the derivation.(Used alone, they are highly effective[4].)We intersperse the basic set of transformation with a few sets of other transformations that perform either problem-domain-oriented or hardware-oriented optimizations.These transformations,few in number but powerful in effect,guide the derivation in the direction of producing code that will exploit the specialized hardware of the ADT DAP.It is transformations of this kind that we emphasize in this section;however,we begin with a brief overview of the basic transformations in order to provide a framework for the later discussion.5.1Sketch of the Transformational DerivationThe derivation of an efﬁcient implementation for the AMT DAP510consists of about12major trans-formational steps.Each of these steps belongs to one of three types:domain-dependent transformations that apply to matrix/vector problems(marked with a single bullet,in the list below);hardware-speciﬁc transformations that direct the derivation toward code that is efﬁcient on the DAP(marked with two bullets, below);and general purpose functional-to-procedural transformations,such as might be incorporated in a compiler for functional languages(marked by+,below).The major steps in the derivation are as follows:+Translating the ML speciﬁcation into a canonical form(standardization)+Unfolding abstract data types and non-recursive function deﬁnitions and simplifying+Reducing the complexity of storage usage(implementing reuse where possible)Converting expressions into applications of array processor functions+Performing common subexpression removalConverting applications of array processor functions that have componental equivalents in DAP Fortran into the DAP Fortran versions+Preparing the ML for transformation to Fortran+Eliminating tail recursion+Transforming the prepared ML to structured,recursive FortranImplementing the data-parallel conditional+Transforming recursive Fortran to non-recursive FortranEliminating common logical subexpressionsEach TAMPR transformation rule is literally a rewrite rule,having a pattern and a replacement each of which is speciﬁed in terms of the grammar of the programming language.Typically,fewer than ten of thesetransformation rules are required to implement each of the major steps in the derivation.However,these rules are applied many times;for this speciﬁcation,the entire derivation from ML to DAP Fortran requiresabout10000rewrites.Clearly,it is vital that TAMPR provides the ability to apply rules automatically.No one could afford to apply thousands of transformations by hand,or even to guide their application.A somewhat more detailed discussion of the basic transformation steps,including some example code fragments generated at various stages,is given in[4](see also an earlier version in[5]).5.2DAP-Speciﬁc TransformationsEarlier we deﬁned two primitive vector/matrix functions:and.A function produces a vector/matrix the value of each element of which is speciﬁed by a function argument of.A function produces a scalar value that is an aggregate of its vector/matrix argument.A function argument of speciﬁes the combining expression to be used when computing the aggregate value. These functions do not have equivalents in DAP Fortran:in order to implement an arbitrary or in DAP Fortran we must use an explicit loop where expressions involve manipulations of individual matrix elements.However,certain simple forms of and do have equivalents in DAPFortran(and in other languages for array processors).Also,to make the most effective use of the processor array the aim is to produce an implementation where whole vector/matrix manipulations are used rather than giving alternative manipulations expressed as a sequence of simple vector/matrix element operations. The strategy that the transformation set for the DAP adopts is to propagate functions into expressions until the function argument of each is a value that is either independent of the generation index,or is a vector/matrix element operation.This strategy aims to remove occurrences of vector/matrix operations and arises from the desire to realize computations as whole vector/matrix operations.The strategy requires an algebra that deﬁnes how a may be propagated into expressions.This propagation algebra has5rules:1.A applied to a function the value of which is the vector/matrix element at the generating index isreplaced by the vector/matrix-the identity;.2.A applied to a function the value of which is independent of the generating index is replaced by anfunction that creates a vector/matrix in which all the elements have that independent value;e.g.,22,where matrix is of order.3.A with a scalar generating function that has a componental equivalent is converted to that componentalequivalent.The arguments to which the componental function is applied must be vectors/matrices,so the is propagated inward and applied to the arguments of the componental function;e.g.,4.A of a conditional expression becomes an application of a data-parallel conditional-a function.The is propagated inwards to the limbs of the conditional and applied to the conditional guards and the guarded results.The function combines(s)the results to form a single composite result for the conditional expression.5.A for which an aggregate function is deﬁned is replaced by an application of that aggregate function. The transformation strategy uses the following6simpliﬁcations/optimizations:1.A with duplicate computation is optimized to remove the duplicated evaluation.For example,a maycreate a symmetric or anti-symmetric matrix.Thus,only the values in the lower(upper)triangle of the matrix need be calculated,with the values in the upper(lower)triangle of the matrix being copied from the lower(upper) triangle of the matrix.2.A the effect of which is a predeﬁned rearrangement of the elements of a vector/matrix is replaced byan application of the standard rearrangement function;e.g.creating the transpose of a matrix.3.A that is a predeﬁned vector part of a matrix is replaced by an application of a standard vectorextraction function;e.g.column of a matrix.4.A function the result of which is a boolean vector/matrix with values in a predeﬁned arrangementis replaced by an application of that standard arrangement function;e.g.the value in the diagonal elements of a matrix.5.A vector is moved outside of the scope of a matrix(this is possible only if the functionhas a componental equivalent).6.Expressions that are independent of/indices are moved outside the scope of the genera-tion/reduction.The transformations outlined above are not speciﬁc to the DAP or any other array processor architecture: they target the set of operations that may be implemented efﬁciently on architectures of this kind.They, therefore,deﬁne(partially)an abstract array processor architecture and the program that is the result of applying these transformation rules is reﬁned further(by transformation)to produce a program that executes (efﬁciently)on a particular array processor.5.3Deriving an Implementation for the Function of POTTo illustrate the use of the above transformations,we consider,in detail,the function from POT illustrating the translation from SML speciﬁcation to code tailored for execution on the AMT DAP. After unfolding and simplifying has the form:generate(lambda((i,j)if i>j then2*element(M,i,j)....else if i=j then1else if true˜(2*element(M,i,j)....),M)The is anti-symmetric,so this annotated as an expression(Optimization1): antisymmetric(generate(lambda((i,j),if i=j then1else if true then negative(quotient(...))),M)(Note:this implies that the function is free to compute the elements of the upper triangle;however, later transformations remove this apparent inefﬁciency)By algebra rule4(propagation through conditional expressions)this becomes:antisymmetric(join(if generate(lambda((i,j),i=j),M)thengenerate(lambda((i,j)1),M)else if generate(lambda((i,j)true),M)thengenerate(lambda((i,j),˜(2*....)),M)))Theﬁrst predicate of the corresponds with one of the pattern functions,the unit diagonal pattern;so simpliﬁcation rule4applies.The s in theﬁrst result expression and in the second conditional guard are independent of both generating indices,so algebra rule2applies.Thus we get:antisymmetric(join(if patdiag(n)expand(1,n,n)else if(expand(true,n,n))thengenerate(lambda((i,j),˜(2*...)))))where creates a matrix of size with each component having value.The˜o perator has a componental equivalent,so algebra rule3applies.negative(generate(lambda((i,j),2*....)))The is propagated into the expression until the remaining s have bodies whose forms are either,or.Theﬁrst two of these correspond to one of the extraction functions:(rule5).The third corresponds to the function (rule4).antisymmetric(join(if patdiag(n)then expand(matrix,1,n,n))else if(expand(true,n,n))thennegative(el_wise-quotient(el_wise-times(expand(2,n,n),b),el_wise-plus(el_wise-difference(expand(rows,diagonal(b),n),expand(cols,diagonal(b),n)),el_wise-times(join(if el_wise-less(el_wise-difference(expand(rows,diagonal(b),n),expand(cols,diagonal(b),n)),expand(matrix,0,n,n))then expand(-1,n,n)else expand(matrix,1,n,n)),el_wise-sqrt(el_wise-plus(el_wise-times(el_wise-difference(expand(rows,diagonal(b),n),expand(cols,diagonal(b),n)),el_wise-difference(expand(rows,diagonal(b),n),expand(cols,diagonal(b),n))),el_wise-times(expand(matrix,4,n,n),el_wise-times(b,b)))))))))Whereis the arithmetic product operation applied between all corresponding pairs of elements of two matrices(-it is not standard matrix multiplication).After common sub-expression elimination is perfromed the conversion of this DAP independent form to DAP Fortran may be undertaken.Those functions which have equivalent functions(or combinations of functions)in DAP Fortran are converted into their DAP Fortran forms.The program may then be processed by the standard functional language compiler transformations to produce the following code:g371598=patlowertri(n).and..not.patunitdiag(n)g371651=patlowertri(n)g371652=patunitdiag(n)g22(g371651.and.g371652)=1g371651(g371652)=.false.g371652=g371598g371597=matr(g371600,n)-matc(g371600,n)g371629=1g371629(g371597.eq.0)=0g371629(g371597.lt.0)=-1g22(g371651.and.g371652)=(-2*b)/(&g371597+g371629*sqrt(g371597*g371597+&4*(b*b)))g22(.not.patlowertri(n))=-tran(g22)The variable g22contains the transformation matrix.The resulting program may appear to be rather ugly, but it is not intended that this form should be read.The identiﬁer names are chosen for convenience rather than for understandability or readability.6Comparison with Hand-Crafted Versions of POTIn comparing the execution times for programs that execute on the AMT DAP it is necessary to distinguish two distinct Fortran Dialects in which a program may be written;namely Fortran-Plus[1]and Fortran-Plus Enhanced[2].A Fortran-Plus program must express array operations in a size that matches the size of the processor array in use.Therefore,for the DAP used in these experiments,array operations are expressed as operations on3232array.A Fortran-plus Enhanced program need not take account of the processor array size when an vector/matrix operation is used.The Fortran-Plus Enhanced language compiler will produce an implementation that expresses operations on arrays that are larger than the processor array size as a sequence of operations on processor array size sections of the array;hopefully,the compiler can do this with a degree of efﬁciency.It is possible to use a mixture of Fortran-Plus Enhanced features and the more primitive Fortran Plus language features in a program.In the discussion below:a fortran-Plus program is one that always expresses array operations in terms of the size of the processor array;and a Fortran-Plus Enhanced program does not take account of the processor array size in array operations.In Table1the execution time(for each iteration)4for the implementation of POT derived by automatic program transformation is shown together with times for two hand crafted versions-theﬁrst is written in Fortran-Plus and the other written in Fortran Plus Enhanced.These hand-crafted versions have been analysed in[11,14].A hand crafted Fortran-Plus version of POT is between12%and13%faster than a hand crafted Fortran-Plus Enhanced version.As reported in[11]the implementation produced by the Fortran-Plus Enhanced compiler for frequently occurring linear algebra operations(e.g.matrix product)is very efﬁcient but less so on more specialized operations(e.g.Gram-Schmidt orthogonalization).The hand crafted and automatically derived versions have execution times that are almost identical.In (very)large matrix examples the derived implementation is marginally slower than time for the hand crafted version(about).7ConclusionWe have shown that it is possible automatically to produce a highly efﬁcient implementation of a high-level functional speciﬁcation tailored for execution on the AMT DAP510.The functional speciﬁcation is not baised in ways that would permit its efﬁcient execution on a particular machine architecture,but is writtenin a way that gives a clear statement of the algorithm.Indeed,the functional speciﬁcation of POT may be used as the starting point for producing implementations tailored for execution on other machines(and will be used in this way in future research).The transformations used in producing the implementation discussed herein are not particular to this problem and are being applied to functional speciﬁcation for other algorithms where an implementation tailored for the DAP is required.However,there is still development work to be undertaken for this derivation: including tailoring the generated code for the compiler(such as producing sectioned array operations)and tailoring for particular data sets(such as sparse matrices or banded matrices).References[1]Fortran-Plus Language,AMT,man00202,1988.[2]Fortran-Plus Language 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Speciﬁcations,Paciﬁc Grove,CA,USA,13-16May,1991,B.M¨o ller,Ed.,North-Holland,Amsterdam,1991,pp.205-224[8]A Practical Functional Program for the CRAY X-MP,James M.Boyle and Terence J.Harmer,Preprint MCS-P159-0690,Argonne National Laboratory,Argonne,Illinois,July1990,(To appear in Journal of Functional Programming.)[9]Towards the construction of an eigenvalue engine,Clint M.et al,Parallel Computing,8,127-132,1988.[10]A Comparison of two Parallel Algorithms for the Symmetric Eigenproblem,Clint M.et al,Intern’l Journal ofComputer mathematics,15,291-302,1984.[11]Fortran-Plus v.Fortran-Plus Enhanced:A comparison for an Application in Linear Algebra,M.Clint et al,QUBTechnical Report,1991(submitted for publication).[12]Functional Programming using Standard ML,Wilst¨o m,A,Prentice Hall,London1987.[13]The parallel computation of eigenvalues and eigenvectors of large hermitian marices using the AMT DAP510,Weston J.et al,Concurrency Practice and Experience,V ol3(3),179-185,June1991.[14]Two algorithms for the parallel computation of eigenvalues and eigenvectors of large symmetric matrices usingthe ICL DAP,Weston J.,Clint M.,Parallel Computing,13,281-288,1990.。