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Partial polymorphic type inference and higherorder unification
 IN PROCEEDINGS OF THE 1988 ACM CONFERENCE ON LISP AND FUNCTIONAL PROGRAMMING, ACM
, 1988
"... We show that the problem of partial type inference in the nthborder polymorphic Xcalculus is equivalent to nthorder unification. On the one hand, this means that partial type inference in polymorphic Xcalculi of order 2 or higher is undecidable. On the other hand, higherorder unification is oft ..."
Abstract

Cited by 80 (8 self)
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We show that the problem of partial type inference in the nthborder polymorphic Xcalculus is equivalent to nthorder unification. On the one hand, this means that partial type inference in polymorphic Xcalculi of order 2 or higher is undecidable. On the other hand, higherorder unification is often tractable in practice, and our translation entails a very useful algorithm for partial type inference in the worder polymorphic Xcalculus. We present an implementation in AProlog in full.
Mechanically Verifying the Correctness of an Offline Partial Evaluator
, 1995
"... We show that using deductive systems to specify an offline partial evaluator allows its correctness to be mechanically verified. For a mixstyle partial evaluator, we specify bindingtime constraints using a naturaldeduction logic, and the associated program specializer using natural (aka "deducti ..."
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Cited by 12 (3 self)
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We show that using deductive systems to specify an offline partial evaluator allows its correctness to be mechanically verified. For a mixstyle partial evaluator, we specify bindingtime constraints using a naturaldeduction logic, and the associated program specializer using natural (aka "deductive") semantics. These deductive systems can be directly encoded in the Elf programming language  a logic programming language based on the LF logical framework. The specifications are then executable as logic programs. This provides a prototype implementation of the partial evaluator. Moreover, since deductive system proofs are accessible as objects in Elf, many aspects of the partial evaluation correctness proofs (e.g., the correctness of bindingtime analysis) can be coded in Elf and mechanically verified. This work illustrates the utility of declarative programming and of using deductive systems for defining program specialization systems: by exploiting the logical character of definit...
A Hybrid Linear Logic for Constrained Transition Systems
, 2009
"... Linear implication can represent state transitions, but real transition systems operate under temporal, stochastic or probabilistic constraints that are not directly representable in ordinary linear logic. We propose a general modal extension of intuitionistic linear logic where logical truth is ind ..."
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Cited by 2 (0 self)
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Linear implication can represent state transitions, but real transition systems operate under temporal, stochastic or probabilistic constraints that are not directly representable in ordinary linear logic. We propose a general modal extension of intuitionistic linear logic where logical truth is indexed by constraints and hybrid connectives combine constraint reasoning with logical reasoning. The logic has a focused cutfree sequent calculus that can be used to internalize the rules of particular constrained transition systems; we illustrate this with an adequate encoding of the synchronous stochastic picalculus. We also present some preliminary experiments of direct encoding of biological systems in the logic. 1
A Logic for Constrained Process Calculi with Applications to Molecular Biology
, 2009
"... Linear implication can represent state transitions, but real transition systems operate under temporal, stochastic or probabilistic constraints that are not directly representable in ordinary linear logic. We propose a general modal extension of intuitionistic linear logic where logical truth is ind ..."
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Linear implication can represent state transitions, but real transition systems operate under temporal, stochastic or probabilistic constraints that are not directly representable in ordinary linear logic. We propose a general modal extension of intuitionistic linear logic where logical truth is indexed by constraints and hybrid connectives combine constraint reasoning with logical reasoning. The logic has a focused cutfree sequent calculus that can be used to internalize the rules of particular constrained transition systems; we illustrate this with an adequate encoding of the synchronous stochastic picalculus that has been used to encode a number of biochemical reaction systems. We also discuss direct encodings of biochemical reactions in suitable (temporal and stochastic) fragments of the logic. 1
Axiomatizing the Quote
"... We study reflection in the Lambda Calculus from an axiomatic point of view. Specifically, we consider various properties that the quote �· � must satisfy as a function from Λ to Λ. The most important of these is the existence of a definable left inverse: a term E, called the evaluator for �·�, that ..."
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We study reflection in the Lambda Calculus from an axiomatic point of view. Specifically, we consider various properties that the quote �· � must satisfy as a function from Λ to Λ. The most important of these is the existence of a definable left inverse: a term E, called the evaluator for �·�, that satisfies E�M � = M for all M ∈ Λ. Usually the quote �M � encodes the syntax of a given term, and the evaluator proceeds by analyzing the syntax and reifying all constructors by their actual meaning in the calculus. Working in Combinatory Logic, Raymond Smullyan [12] investigated which elements of the syntax must be accessible via the quote in order for an evaluator to exist. He asked three specific questions, to which we provide negative answers. On the positive side, we give a characterization of quotes which possess all of the desired properties, equivalently defined as being equitranslatable with a standard quote. As an application, we show that Scott’s coding is not complete in this sense, but can be slightly modified to be such. This results in a minimal definition of a complete quoting for Combinatory Logic.