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A Syntactic Approach to Type Soundness
 INFORMATION AND COMPUTATION
, 1992
"... We present a new approach to proving type soundness for Hindley/Milnerstyle polymorphic type systems. The keys to our approach are (1) an adaptation of subject reduction theorems from combinatory logic to programming languages, and (2) the use of rewriting techniques for the specification of the la ..."
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Cited by 634 (25 self)
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We present a new approach to proving type soundness for Hindley/Milnerstyle polymorphic type systems. The keys to our approach are (1) an adaptation of subject reduction theorems from combinatory logic to programming languages, and (2) the use of rewriting techniques for the specification of the language semantics. The approach easily extends from polymorphic functional languages to imperative languages that provide references, exceptions, continuations, and similar features. We illustrate the technique with a type soundness theorem for the core of Standard ML, which includes the first type soundness proof for polymorphic exceptions and continuations.
The Intrinsic Normal Cone
 Invent. Math
, 1997
"... We suggest a construction of virtual fundamental classes of certain types of moduli spaces. Contents 0 ..."
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Cited by 353 (9 self)
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We suggest a construction of virtual fundamental classes of certain types of moduli spaces. Contents 0
Dependent Types in Practical Programming
 In Proceedings of ACM SIGPLAN Symposium on Principles of Programming Languages
, 1998
"... Programming is a notoriously errorprone process, and a great deal of evidence in practice has demonstrated that the use of a type system in a programming language can effectively detect program errors at compiletime. Moreover, some recent studies have indicated that the use of types can lead to si ..."
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Cited by 341 (38 self)
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Programming is a notoriously errorprone process, and a great deal of evidence in practice has demonstrated that the use of a type system in a programming language can effectively detect program errors at compiletime. Moreover, some recent studies have indicated that the use of types can lead to significant enhancement of program performance at runtime. For the sake of practicality of typechecking, most type systems developed for general purpose programming languages tend to be simple and coarse, and this leaves ample room for improvement. As an advocate of types, this thesis addresses the issue of designing a type system for practical programming in which a notion of dependent types is available, leading to more accurate capture of program invariants with types. In contrast to developing a type theory with dependent types and then designing upon it a functional programming language, we study practical methods for extending the type systems of existing programming languages with dep...
Stability structures, motivic DonaldsonThomas invariants and cluster transformations
, 2008
"... ..."
Formal certification of a compiler backend, or: programming a compiler with a proof assistant
 IN PROC. 33RD ACM SYMPOSIUM ON PRINCIPLES OF PROGRAMMING LANGUAGES (POPL ’06
, 2006
"... This paper reports on the development and formal certification (proof of semantic preservation) of a compiler from Cminor (a Clike imperative language) to PowerPC assembly code, using the Coq proof assistant both for programming the compiler and for proving its correctness. Such a certified compile ..."
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Cited by 289 (16 self)
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This paper reports on the development and formal certification (proof of semantic preservation) of a compiler from Cminor (a Clike imperative language) to PowerPC assembly code, using the Coq proof assistant both for programming the compiler and for proving its correctness. Such a certified compiler is useful in the context of formal methods applied to the certification of critical software: the certification of the compiler guarantees that the safety properties proved on the source code hold for the executable compiled code as well.
Braid group actions on derived categories of coherent sheaves
 DUKE MATH. J
, 2001
"... This paper gives a construction of braid group actions on the derived category of coherent sheaves on a variety X. The motivation for this is M. Kontsevich’s homological mirror conjecture, together with the occurrence of certain braid group actions in symplectic geometry. One of the main results is ..."
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Cited by 261 (8 self)
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This paper gives a construction of braid group actions on the derived category of coherent sheaves on a variety X. The motivation for this is M. Kontsevich’s homological mirror conjecture, together with the occurrence of certain braid group actions in symplectic geometry. One of the main results is that when dim X ≥ 2, our braid group actions are always faithful. We describe conjectural mirror symmetries between smoothings and resolutions of singularities which lead us to find examples of braid group actions arising from crepant resolutions of various singularities. Relations with the McKay correspondence and with exceptional sheaves on Fano manifolds are given. Moreover, the case of an elliptic curve is worked out in some detail.
HiLog: A foundation for higherorder logic programming
 JOURNAL OF LOGIC PROGRAMMING
, 1993
"... We describe a novel logic, called HiLog, and show that it provides a more suitable basis for logic programming than does traditional predicate logic. HiLog has a higherorder syntax and allows arbitrary terms to appear in places where predicates, functions and atomic formulas occur in predicate calc ..."
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Cited by 247 (42 self)
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We describe a novel logic, called HiLog, and show that it provides a more suitable basis for logic programming than does traditional predicate logic. HiLog has a higherorder syntax and allows arbitrary terms to appear in places where predicates, functions and atomic formulas occur in predicate calculus. But its semantics is firstorder and admits a sound and complete proof procedure. Applications of HiLog are discussed, including DCG grammars, higherorder and modular logic programming, and deductive databases.
ON EPIMORPHISMS AND MONOMORPHISMS OF HOPF ALGEBRAS
, 2009
"... We notice that for a Hopf algebra H, its antipode S is both an epimorphism and a monomorphism from H to H op,cop in the category of Hopf algebras over a field. Together with the existence of Hopf algebras with noninjective or nonsurjective antipode, this proves the existence of nonsurjective epi ..."
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Cited by 10 (1 self)
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surjective epimorphisms and noninjective monomorphisms in the category of Hopf algebras. Using Schauenburg’s free Hopf algebra with a bijective antipode on a Hopf algebra and its “dual ” universal construction, we then show that one can even find examples of nonsurjective (noninjective) epis (resp. monos) of Hopf
TIL: A TypeDirected Optimizing Compiler for ML
 IN ACM SIGPLAN CONFERENCE ON PROGRAMMING LANGUAGE DESIGN AND IMPLEMENTATION
, 1995
"... We describe a new compiler for Standard ML called TIL, that is based on four technologies: intensional polymorphism, tagfree garbage collection, conventional functional language optimization, and loop optimization. We use intensional polymorphism and tagfree garbage collection to provide specializ ..."
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Cited by 235 (39 self)
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We describe a new compiler for Standard ML called TIL, that is based on four technologies: intensional polymorphism, tagfree garbage collection, conventional functional language optimization, and loop optimization. We use intensional polymorphism and tagfree garbage collection to provide
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