DTP '13Pub Date : 2013-09-24DOI: 10.1145/2502409.2502410
Nils Anders Danielsson
{"title":"Correct-by-construction pretty-printing","authors":"Nils Anders Danielsson","doi":"10.1145/2502409.2502410","DOIUrl":"https://doi.org/10.1145/2502409.2502410","url":null,"abstract":"A new approach to correct-by-construction pretty-printing is presented. The basic methodology is the one of classical (not necessarily correct) pretty-printing: users convert values to pretty-printer documents, and a general rendering algorithm turns documents into strings. The main novelty is that dependent types are used to ensure that, for each value, the constructed document is correct with respect to the value and a given grammar. Other parts of the development use well-established technology: the pretty-printer document interface is basically that of Wadler (2003), but with more precise types, and a single additional primitive combinator; and Wadler's rendering algorithm is used.\u0000 It is proved that if a given value is pretty-printed, and the resulting string parsed (with respect to the same, unambiguous grammar), then the original value is obtained. No guarantees are made about \"prettiness\".","PeriodicalId":205623,"journal":{"name":"DTP '13","volume":"56 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129836402","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}
DTP '13Pub Date : 2013-09-24DOI: 10.1145/2502409.2502414
Larry Diehl, T. Sheard
{"title":"Leveling up dependent types: generic programming over a predicative hierarchy of universes","authors":"Larry Diehl, T. Sheard","doi":"10.1145/2502409.2502414","DOIUrl":"https://doi.org/10.1145/2502409.2502414","url":null,"abstract":"Generic programming is about writing a single function that does something different for each type. In most languages one cannot case over the structure of types. So in such languages generic programming is accomplished by defining a universe, a data structure isomorphic to some subset of the types supported by the language, and performing a case analysis over this datatype instead. Such functions support a limitied level of genericity, limited to the subset of types that the universe encodes. The key to full genericity is defining a rich enough universe to encode all types in the language.\u0000 In this paper we show how to define a universe with a predicative hierarchy of types, encoding a finite set of base types (including dependent products and sums), and an infinite set of user defined datatypes. We demonstrate that such a system supports a much broader notion of generic programming, along with a serendipitous extension to the usefulness of user defined datatypes with existential arguments.","PeriodicalId":205623,"journal":{"name":"DTP '13","volume":"24 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115364895","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}
DTP '13Pub Date : 2013-09-24DOI: 10.1145/2502409.2502412
Neal Glew, Tim Sweeney, Leaf Petersen
{"title":"A multivalued language with a dependent type system","authors":"Neal Glew, Tim Sweeney, Leaf Petersen","doi":"10.1145/2502409.2502412","DOIUrl":"https://doi.org/10.1145/2502409.2502412","url":null,"abstract":"Type systems are used to eliminate certain classes of errors at compile time. One of the goals of type system research is to allow more classes of errors (such as array subscript errors) to be eliminated. Dependent type systems have played a key role in this effort, and much research has been done on them. In this paper, we describe a new dependently-typed functional programming language based on two key ideas. First, it makes no distinction between expressions, types, kinds, and sorts-everything is a term. The same integer values are used to compute with and to index types, such as specifying the length of an array. Second, the term language has a multivalued semantics-a term can evaluate to zero, one, multiple, even an infinite number of values. Since types are characterised by their members, they are equivalent to terms whose possible values are the members of the type, and we exploit this to express type information in our language. In order to type check such terms, we give up on decidability. We consider this a good tradeoff to get an expressive language without the pain of some dependent type systems. This paper describes the core ideas of the language, gives an intuitive description of the semantics in terms of set-theory, explains how to implement the language by restricting what programs are considered valid, and sketches the core of the type system.","PeriodicalId":205623,"journal":{"name":"DTP '13","volume":"53 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127859417","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}
DTP '13Pub Date : 2013-09-24DOI: 10.1145/2502409.2502413
Hsiang-Shang Ko, J. Gibbons
{"title":"Relational algebraic ornaments","authors":"Hsiang-Shang Ko, J. Gibbons","doi":"10.1145/2502409.2502413","DOIUrl":"https://doi.org/10.1145/2502409.2502413","url":null,"abstract":"Dependently typed programming is hard, because ideally dependently typed programs should share structure with their correctness proofs, but there are very few guidelines on how one can arrive at such integrated programs. McBride's algebraic ornamentation provides a methodological advancement, by which the programmer can derive a datatype from a specification involving a fold, such that a program that constructs elements of that datatype would be correct by construction. It is thus an effective method that leads the programmer from a specification to a dependently typed program. We enhance the applicability of this method by generalising algebraic ornamentation to a relational setting and bringing in relational algebraic methods, resulting in a hybrid approach that makes essential use of both dependently typed programming and relational program derivation. A dependently typed solution to the minimum coin change problem is presented as a demonstration of this hybrid approach. We also give a theoretically interesting \"completeness theorem\" of relational algebraic ornaments, which sheds some light on the expressive power of ornaments and inductive families.","PeriodicalId":205623,"journal":{"name":"DTP '13","volume":"2673 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114638423","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}
DTP '13Pub Date : 2013-04-02DOI: 10.1145/2502409.2502411
Guillaume Allais, Pierre Boutillier, Conor McBride
{"title":"New equations for neutral terms: a sound and complete decision procedure, formalized","authors":"Guillaume Allais, Pierre Boutillier, Conor McBride","doi":"10.1145/2502409.2502411","DOIUrl":"https://doi.org/10.1145/2502409.2502411","url":null,"abstract":"The definitional equality of an intensional type theory is its test of type compatibility. Today's systems rely on ordinary evaluation semantics to compare expressions in types, frustrating users with type errors arising when evaluation fails to identify two `obviously' equal terms. If only the machine could decide a richer theory! We propose a way to decide theories which supplement evaluation with `ν-rules', rearranging the neutral parts of normal forms, and report a successful initial experiment.\u0000 We study a simple λ-calculus with primitive fold, map and append operations on lists and develop in Agda a sound and complete decision procedure for an equational theory enriched with monoid, functor and fusion laws.","PeriodicalId":205623,"journal":{"name":"DTP '13","volume":"30 19 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116708984","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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