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66
An Effective Theory of Type Refinements
, 2002
"... We develop an explicit two level system that allows programmers to reason about the behavior of effectful programs. The first level is an ordinary MLstyle type system, which confers standard properties on program behavior. The second level is a conservative extension of the first that uses a logic ..."
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Cited by 62 (5 self)
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We develop an explicit two level system that allows programmers to reason about the behavior of effectful programs. The first level is an ordinary MLstyle type system, which confers standard properties on program behavior. The second level is a conservative extension of the first that uses a logic of type refinements to check more precise properties of program behavior. Our logic is a fragment of intuitionistic linear logic, which gives programmers the ability to reason locally about changes of program state. We provide a generic resource semantics for our logic as well as a sound, decidable, syntactic refinementchecking system. We also prove that refinements give rise to an optimization principle for programs. Finally, we illustrate the power of our system through a number of examples.
Practical RefinementType Checking
, 1997
"... Refinement types allow many more properties of programs to be expressed and statically checked than conventional type systems. We present a practical algorithm for refinementtype checking in a calculus enriched with refinementtype annotations. We prove that our basic algorithm is sound and comple ..."
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Cited by 37 (1 self)
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Refinement types allow many more properties of programs to be expressed and statically checked than conventional type systems. We present a practical algorithm for refinementtype checking in a calculus enriched with refinementtype annotations. We prove that our basic algorithm is sound and complete, and show that every term which has a refinement type can be annotated as required by our algorithm. Our positive experience with an implementation of an extension of this algorithm to the full core language of Standard ML demonstrates that refinement types can be a practical program development tool in a realistic programming language. The required refinement type definitions and annotations are not much of a burden and serve as formal, machinechecked explanations of code invariants which otherwise would remain implicit. 1 Introduction The advantages of staticallytyped programming languages are well known, and have been described many times (e.g. see [Car97]). However, conventional ty...
Tridirectional Typechecking
, 2004
"... In prior work we introduced a pure type assignment system that encompasses a rich set of property types, including intersections, unions, and universally and existentially quantified dependent types. In this paper ..."
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Cited by 37 (9 self)
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In prior work we introduced a pure type assignment system that encompasses a rich set of property types, including intersections, unions, and universally and existentially quantified dependent types. In this paper
Tabled HigherOrder Logic Programming
 In 20th International Conference on Automated Deduction
, 2003
"... Elf is a general metalanguage for the specification and implementation of logical systems in the style of the logical framework LF. Based on a logic programming interpretation, it supports executing logical systems and reasoning with and about them, thereby reducing the effort required for each ..."
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Cited by 26 (11 self)
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Elf is a general metalanguage for the specification and implementation of logical systems in the style of the logical framework LF. Based on a logic programming interpretation, it supports executing logical systems and reasoning with and about them, thereby reducing the effort required for each particular logical system. The traditional logic programming paradigm is extended by replacing firstorder terms with dependently typed terms and allowing implication and universal quantification in the bodies of clauses. These higherorder features allow us to model concisely and elegantly conditions on variables and the discharge of assumptions which are prevalent in many logical systems. However, many specifications are not executable under the traditional logic programming semantics and performance may be hampered by redundant computation. To address these problems, I propose a tabled higherorder logic programming interpretation for Elf. Some redundant computation is eliminated by memoizing subcomputation and reusing its result later. If we do not distinguish different proofs for a property, then search based on tabled logic programming is complete and terminates for programs with bounded recursion. In this proposal, I present a prooftheoretical characterization for tabled higherorder logic programming. It is the basis of the implemented prototype for tabled logic programming interpreter for Elf. Preliminary experiments indicate that many more logical specifications are executable under the tabled semantics. In addition, tabled computation leads to more efficient execution of programs. The goal of the thesis is to demonstrate that tabled logic programming allows us to efficiently automate reasoning with and about logical systems in the logical f...
Structural Subtyping of NonRecursive Types is Decidable
, 2003
"... We show that the firstorder theory of structural subtyping of nonrecursive types is decidable, as a consequence of a more general result on the decidability of term powers of decidable theories. ..."
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Cited by 25 (6 self)
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We show that the firstorder theory of structural subtyping of nonrecursive types is decidable, as a consequence of a more general result on the decidability of term powers of decidable theories.
Semantic Types: A Fresh Look at the Ideal Model for Types
, 2004
"... We present a generalization of the ideal model for recursive polymorphic types. Types are defined as sets of terms instead of sets of elements of a semantic domain. Our proof of the existence of types (computed by fixpoint of a typing operator) does not rely on metric properties, but on the fact tha ..."
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Cited by 23 (2 self)
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We present a generalization of the ideal model for recursive polymorphic types. Types are defined as sets of terms instead of sets of elements of a semantic domain. Our proof of the existence of types (computed by fixpoint of a typing operator) does not rely on metric properties, but on the fact that the identity is the limit of a sequence of projection terms. This establishes a connection with the work of Pitts on relational properties of domains. This also suggests that ideals are better understood as closed sets of terms defined by orthogonality with respect to a set of contexts.
Lightweight object specification with typestates
 In ESEC/FSE13
, 2005
"... kevin.bierhoff @ cs.cmu.edu Previous work has proven typestates to be useful for modeling protocols in objectoriented languages. We build on this work by addressing substitutability of subtypes as well as improving precision and conciseness of specifications. We states that incorporates state refin ..."
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Cited by 23 (8 self)
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kevin.bierhoff @ cs.cmu.edu Previous work has proven typestates to be useful for modeling protocols in objectoriented languages. We build on this work by addressing substitutability of subtypes as well as improving precision and conciseness of specifications. We states that incorporates state refinement, method refinement, and orthogonal state dimensions. Union and intersection types form the underlying semantics of method specifications. The approach guarantees substitutability and behavioral subtyping. We designed a dynamic analysis to check existing objectoriented software for protocol conformance and validated our approach by specifying two standard Java libraries. We provide preliminary evidence for the usefulness of our approach.
Inference of UserDefined Type Qualifiers and Qualifier Rules
 In Proc. ESOP
, 2006
"... Abstract. In previous work, we described a new approach to supporting userdefined type qualifiers, which augment existing types to specify and check additional properties of interest. For each qualifier, users define a set of rules that are enforced during static typechecking of programs. Separately ..."
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Cited by 21 (4 self)
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Abstract. In previous work, we described a new approach to supporting userdefined type qualifiers, which augment existing types to specify and check additional properties of interest. For each qualifier, users define a set of rules that are enforced during static typechecking of programs. Separately, these rules are automatically validated with respect to a userdefined predicate that formalizes the qualifier’s intended runtime invariant. We instantiated this approach as a framework for userdefined type qualifiers in C programs, called CLARITY. In this paper, we extend our earlier approach by resolving two usability issues. First, we show how to perform qualifier inference in the presence of userdefined rules by generating and solving a system of conditional set constraints, thereby relieving users of the burden of explicitly annotating programs. Second, we show how to automatically infer rules that respect a given userdefined invariant, thereby relieving qualifier designers of the burden of manually producing such rules. We have formalized both qualifier and rule inference and proven their correctness. We have also extended CLARITY to support qualifier and rule inference, and we illustrate their utility in practice through experiments with several type qualifiers and opensource C programs. 1
Type Assignment for Intersections and Unions in CallbyValue Languages
"... We develop a system of type assignment with intersection types, union types, indexed types, and universal and existential dependent types that is sound in a callby value functional language. The combination of logical and computational principles underlying our formulation naturally leads to the c ..."
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Cited by 21 (9 self)
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We develop a system of type assignment with intersection types, union types, indexed types, and universal and existential dependent types that is sound in a callby value functional language. The combination of logical and computational principles underlying our formulation naturally leads to the central idea of typechecking subterms in evaluation order. We thereby provide a uniform generalization and explanation of several earlier isolated systems. The proof of progress and type preservation, usually formulated for closed terms only, relies on a notion of definite substitution.
On the theory of structural subtyping
, 2003
"... We show that the firstorder theory of structural subtyping of nonrecursive types is decidable. Let Σ be a language consisting of function symbols (representing type constructors) and C a decidable structure in the relational language L containing a binary relation ≤. C represents primitive types; ..."
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Cited by 18 (8 self)
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We show that the firstorder theory of structural subtyping of nonrecursive types is decidable. Let Σ be a language consisting of function symbols (representing type constructors) and C a decidable structure in the relational language L containing a binary relation ≤. C represents primitive types; ≤ represents a subtype ordering. We introduce the notion of Σtermpower of C, which generalizes the structure arising in structural subtyping. The domain of the Σtermpower of C is the set of Σterms over the set of elements of C. We show that the decidability of the firstorder theory of C implies the decidability of the firstorder theory of the Σtermpower of C. This result implies the decidability of the firstorder theory of structural subtyping of nonrecursive types.