In the paper "On a Theory of Computation and Complexity over the Real Numbers: NP Completeness, Recursive Functions and Universal machines" (BSS 1989), the authors, Lenore Blum, Mike Shub, and Steve Smale, generalize the notion of computability from the set of natural numbers to an arbitrary ordered ring. In particular they discuss the existence of a Universal Machine over such a ring and the "godel" number or "code" of machines defined on such a ring. In this short paper we wish to correct some minor error in their definition of a "code" of a machine.
{"title":"The representation of a program in the Blum-Shub-Smale theory of computation over an arbitrary ring","authors":"Hu Xiao-Long","doi":"10.1145/166589.166596","DOIUrl":"https://doi.org/10.1145/166589.166596","url":null,"abstract":"In the paper \"On a Theory of Computation and Complexity over the Real Numbers: NP Completeness, Recursive Functions and Universal machines\" (BSS 1989), the authors, Lenore Blum, Mike Shub, and Steve Smale, generalize the notion of computability from the set of natural numbers to an arbitrary ordered ring. In particular they discuss the existence of a Universal Machine over such a ring and the \"godel\" number or \"code\" of machines defined on such a ring. In this short paper we wish to correct some minor error in their definition of a \"code\" of a machine.","PeriodicalId":388781,"journal":{"name":"Bull. EATCS","volume":"45 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1993-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114193974","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1989-08-28DOI: 10.1007/3-540-51486-4_77
C. Jousselin, J. Moskowitz
{"title":"Memory and algebra","authors":"C. Jousselin, J. Moskowitz","doi":"10.1007/3-540-51486-4_77","DOIUrl":"https://doi.org/10.1007/3-540-51486-4_77","url":null,"abstract":"","PeriodicalId":388781,"journal":{"name":"Bull. EATCS","volume":"24 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1989-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134558973","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Miranda is an advanced functional programming system which runs under the UNIX operating system 1 . The aim of the Miranda system is to provide a modern functional language, embedded in a convenient programming environment, suitable both for teaching and as a general purpose programming tool. The purpose of this short article is to give a brief overview of the main features of Miranda. The topics we shall discuss, in order, are: Basic ideas The Miranda programming environment Guarded equations and block structure Pattern matching Currying and higher order functions List comprehensions Lazy evaluation and infinite lists Polymorphic strong typing User defined types Type synonyms
{"title":"An overview of Miranda","authors":"David Turner","doi":"10.1145/15042.15053","DOIUrl":"https://doi.org/10.1145/15042.15053","url":null,"abstract":"Miranda is an advanced functional programming system which runs under the UNIX operating system 1 . The aim of the Miranda system is to provide a modern functional language, embedded in a convenient programming environment, suitable both for teaching and as a general purpose programming tool. The purpose of this short article is to give a brief overview of the main features of Miranda. The topics we shall discuss, in order, are: Basic ideas The Miranda programming environment Guarded equations and block structure Pattern matching Currying and higher order functions List comprehensions Lazy evaluation and infinite lists Polymorphic strong typing User defined types Type synonyms","PeriodicalId":388781,"journal":{"name":"Bull. EATCS","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1986-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128920244","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1900-01-01DOI: 10.1142/9789812562494_0050
M. Bezem, T. Coquand
{"title":"Newman's lemma - a case study in proof automation and geometric logic, Logic in Computer Science Column","authors":"M. Bezem, T. Coquand","doi":"10.1142/9789812562494_0050","DOIUrl":"https://doi.org/10.1142/9789812562494_0050","url":null,"abstract":"","PeriodicalId":388781,"journal":{"name":"Bull. EATCS","volume":"20 12","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"120916097","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1900-01-01DOI: 10.1142/9789812562494_0005
M. Drmota, W. Szpankowski
{"title":"Analysis of Algorithms (AofA) Part II: 1998-2000 (\"Princeton-Barcelona-Gdansk\")","authors":"M. Drmota, W. Szpankowski","doi":"10.1142/9789812562494_0005","DOIUrl":"https://doi.org/10.1142/9789812562494_0005","url":null,"abstract":"","PeriodicalId":388781,"journal":{"name":"Bull. EATCS","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125846924","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A Foundation of Computable Analysis","authors":"K. Weihrauch","doi":"10.1007/BFb0052087","DOIUrl":"https://doi.org/10.1007/BFb0052087","url":null,"abstract":"","PeriodicalId":388781,"journal":{"name":"Bull. EATCS","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122313612","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1900-01-01DOI: 10.1007/springerreference_221624
P. S. D. Fenizio
{"title":"Artificial Chemistries","authors":"P. S. D. Fenizio","doi":"10.1007/springerreference_221624","DOIUrl":"https://doi.org/10.1007/springerreference_221624","url":null,"abstract":"","PeriodicalId":388781,"journal":{"name":"Bull. EATCS","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129300801","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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