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The focus of my work is on the development and application of type theory as the language of computation. As the name implies, the central organizing principle of type theory is the concept of a type. For example, familiar tree and graph structures may be viewed as instances of the general concept of an inductive type, infinitary data structures such as streams of values may be viewed as coinductive types, and language features such procedures or objects may be viewed as instances of the general concept of a function. A beauty of type theory is that it provides a rich framework that accounts not only for the computational aspects of programming, but also the reasoning involved in ensuring that a program behaves correctly. The main tool is the propositions-as-types principle in which specifications, or propositions, are identified with types, and proofs are identified with programs. A proof, after all, is a step-by-step procedure for transforming assumptions into conclusions; it is, therefore, a program that takes assumptions as inputs and produces proofs as outputs. The theorem statement is a specification, or type, of this input-output behavior. Another beauty is that type theory connects directly to the language of mathematics through the concept of a category, a very general kind of algebraic structure. Types correspond to structures, such as topological spaces, and programs correspond to structure-preserving mappings between them. This provides a pathway for integrating the language of mathematics with the language of programming.
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论文共 35 篇作者统计合作学者相似作者
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CALCOpp.1:1-1:2, (2023)
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PROCEEDINGS OF THE ACM ON PROGRAMMING LANGUAGES-PACMPLno. POPL (2018): 1-30
Sigplan Noticesno. 1 (2017): 680-693
ACM SIGPLAN NOTICESno. 1 (2017): 706-718
Practical Foundations for Programming Languagespp.291-298, (2012)
Electronic Notes in Theoretical Computer Scienceno. 1 (2011): 263-289
POPLpp.27-38, (2010)
Scheduling deterministric parallel programs (2009)
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semanticscholar(2009)
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