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Higherorder Unification via Explicit Substitutions (Extended Abstract)
 Proceedings of LICS'95
, 1995
"... Higherorder unification is equational unification for βηconversion. But it is not firstorder equational unification, as substitution has to avoid capture. In this paper higherorder unification is reduced to firstorder equational unification in a suitable theory: the &lambda ..."
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Cited by 103 (13 self)
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Higherorder unification is equational unification for &beta;&eta;conversion. But it is not firstorder equational unification, as substitution has to avoid capture. In this paper higherorder unification is reduced to firstorder equational unification in a suitable theory: the &lambda;&sigma;calculus of explicit substitutions.
An Overview of the FLINT/ML Compiler
 In Proc. 1997 ACM SIGPLAN Workshop on Types in Compilation
, 1997
"... The FLINT project at Yale aims to build a stateoftheart systems environment for modern typesafe languages. One important component of the FLINT system is a highperformance typedirected compiler for SML'97 (extended with higherorder modules). The FLINT/ML compiler provides several new capa ..."
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Cited by 91 (17 self)
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The FLINT project at Yale aims to build a stateoftheart systems environment for modern typesafe languages. One important component of the FLINT system is a highperformance typedirected compiler for SML'97 (extended with higherorder modules). The FLINT/ML compiler provides several new capabilities that are not available in other typebased compilers: ffl typedirected compilation is carried over across the higherorder module boundaries; ffl recursive and mutable data objects can use unboxed representations without incurring expensive runtime cost on heavily polymorphic code; ffl parameterized modules (functors) can be selectively specialized, just as normal polymorphic functions; ffl new type representations are used to reduce the cost of type manipulation thus the compilation time. This paper gives an overview of these novel aspects, and a preliminary report on the current status of the implementation. 1 Introduction The FLINT project at Yale aims to build a stateofthear...
Implementing Typed Intermediate Languages
, 1998
"... Recent advances in compiler technology have demonstrated the benefits of using strongly typed intermediate languages to compile richly typed source languages (e.g., ML). A typepreserving compiler can use types to guide advanced optimizations and to help generate provably secure mobile code. Types, u ..."
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Cited by 64 (16 self)
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Recent advances in compiler technology have demonstrated the benefits of using strongly typed intermediate languages to compile richly typed source languages (e.g., ML). A typepreserving compiler can use types to guide advanced optimizations and to help generate provably secure mobile code. Types, unfortunately, are very hard to represent and manipulate efficiently; a naive implementation can easily add exponential overhead to the compilation and execution of a program. This paper describes our experience with implementing the FLINT typed intermediate language in the SML/NJ production compiler. We observe that a typepreserving compiler will not scale to handle large types unless all of its typepreserving stages preserve the asymptotic time and space usage in representing and manipulating types. We present a series of novel techniques for achieving this property and give empirical evidence of their effectiveness.
Unification via Explicit Substitutions: The Case of HigherOrder Patterns
 PROCEEDINGS OF JICSLP'96
, 1998
"... In [6] we have proposed a general higherorder unification method using a theory of explicit substitutions and we have proved its completeness. In this paper, we investigate the case of higherorder patterns as introduced by Miller. We show that our general algorithm specializes in a very convenient ..."
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Cited by 56 (14 self)
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In [6] we have proposed a general higherorder unification method using a theory of explicit substitutions and we have proved its completeness. In this paper, we investigate the case of higherorder patterns as introduced by Miller. We show that our general algorithm specializes in a very convenient way to patterns. We also sketch an efficient implementation of the abstract algorithm and its generalization to constraint simplification, which has yielded good experimental results at the core of a higherorder constraint logic programming language.
A SemiFunctional Implementation of a HigherOrder Logic Programming Language
 Topics in Advanced Language Implementation
, 1991
"... ions *) and varbind = Varbind of string * term (* Variable binders , Type *) In the implementation of the term language and the type checker, we have two constants type and pi. And, yes, type is a type, though this could be avoided by introducing universes (see [16]) without any changes to the code ..."
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Cited by 36 (0 self)
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ions *) and varbind = Varbind of string * term (* Variable binders , Type *) In the implementation of the term language and the type checker, we have two constants type and pi. And, yes, type is a type, though this could be avoided by introducing universes (see [16]) without any changes to the code of the unifier. As is customary, we use A ! B as an abbreviation for \Pix : A: B if x does not occur free in B. Also, however, \Pix : A: B is an abbreviation for the application pi A (x : A: B). In our formulation, then, the constant pi has type \PiA : type: ((A ! type) ! type). As an example consider a predicate constant eq of type \PiA : type: A ! A ! o (where o is the type of formulas as indicated in Section 9). The single clause eqAM M: correctly models equality, that is, a goal of the form eq AM N will succeed if M and N are unifiable. The fact that unification now has to branch can be seen by considering the goal eq int (F 1 1) 1 which has three solutions for the functional logic var...
A Notation for Lambda Terms I: A Generalization of Environments
 THEORETICAL COMPUTER SCIENCE
, 1994
"... A notation for lambda terms is described that is useful in contexts where the intensions of these terms need to be manipulated. This notation uses the scheme of de Bruijn for eliminating variable names, thus obviating ffconversion in comparing terms. This notation also provides for a class of terms ..."
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Cited by 33 (12 self)
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A notation for lambda terms is described that is useful in contexts where the intensions of these terms need to be manipulated. This notation uses the scheme of de Bruijn for eliminating variable names, thus obviating ffconversion in comparing terms. This notation also provides for a class of terms that can encode other terms together with substitutions to be performed on them. The notion of an environment is used to realize this `delaying' of substitutions. The precise mechanism employed here is, however, more complex than the usual environment mechanism because it has to support the ability to examine subterms embedded under abstractions. The representation presented permits a ficontraction to be realized via an atomic step that generates a substitution and associated steps that percolate this substitution over the structure of a term. The operations on terms that are described also include ones for combining substitutions so that they might be performed simultaneously. Our notatio...
A Proof Procedure for the Logic of Hereditary Harrop Formulas
 JOURNAL OF AUTOMATED REASONING
, 1993
"... A proof procedure is presented for a class of formulas in intuitionistic logic. These formulas are the socalled goal formulas in the theory of hereditary Harrop formulas. Proof search inintuitionistic logic is complicated by the nonexistence of a Herbrandlike theorem for this logic: formulas cann ..."
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Cited by 32 (12 self)
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A proof procedure is presented for a class of formulas in intuitionistic logic. These formulas are the socalled goal formulas in the theory of hereditary Harrop formulas. Proof search inintuitionistic logic is complicated by the nonexistence of a Herbrandlike theorem for this logic: formulas cannot in general be preprocessed into a form such as the clausal form and the construction of a proof is often sensitive to the order in which the connectives and quantifiers are analyzed. An interesting aspect of the formulas we consider here is that this analysis can be carried out in a relatively controlled manner in their context. In particular, the task of finding a proof can be reduced to one of demonstrating that a formula follows from a set of assumptions with the next step in this process being determined by the structure of the conclusion formula. An acceptable implementation of this observation must utilize unification. However, since our formulas may contain universal and existential quantifiers in mixed order, care must be exercised to ensure the correctness of unification. One way of realizing this requirement involves labelling constants and variables and then using these labels to constrain unification. This form of unification is presented and used in a proof procedure for goal formulas in a firstorder version of hereditary Harrop formulas. Modifications to this procedure for the relevant formulas in a higherorder logic are also described. The proof procedure that we present has a practical value in that it provides the basis for an implementation of the logic programming language lambdaProlog.
An Empirical Study of the Runtime Behavior of HigherOrder Logic Programs
 University of Pennsylvania. Available as
, 1992
"... this document are those of the author and should not be interpreted as representing the official policies, either expressed or implied, of the U.S. Government. ..."
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Cited by 29 (7 self)
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this document are those of the author and should not be interpreted as representing the official policies, either expressed or implied, of the U.S. Government.
A FineGrained Notation for Lambda Terms and Its Use in Intensional Operations
 Journal of Functional and Logic Programming
, 1996
"... We discuss issues relevant to the practical use of a previously proposed notation for lambda terms in contexts where the intensions of such terms have to be manipulated. This notation uses the `nameless' scheme of de Bruijn, includes expressions for encoding terms together with substitutions to ..."
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Cited by 25 (9 self)
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We discuss issues relevant to the practical use of a previously proposed notation for lambda terms in contexts where the intensions of such terms have to be manipulated. This notation uses the `nameless' scheme of de Bruijn, includes expressions for encoding terms together with substitutions to be performed on them and contains a mechanism for combining such substitutions so that they can be effected in a common structure traversal. The combination mechanism is a general one and consequently difficult to implement. We propose a simplification to it that retains its functionality in situations that occur commonly in fireduction. We then describe a system for annotating terms to determine if they can be affected by substitutions generated by external ficontractions. These annotations can lead to a conservation of space and time in implementations of reduction by permitting substitutions to be performed trivially in certain situations. The use of the resulting notation in the reduction...