Mark Lillibridge. Translucent Sums: A Foundation for Higher-Order Module Systems. PhD thesis, Pittsburgh, PA, May 1997.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....languages [34, 2] has been particularly influential. Much effort has gone into the design of modular programming mechanisms for the ML family of languages, notably Standard ML [23] and Objective Caml [27] Numerous extensions and variations of these designs have been considered in the literature [21, 18, 28, 31, 5]. Despite (or perhaps because of) these substantial efforts, the field has remained somewhat fragmented, with no clear unifying theory of modularity having yet emerged. Several competing designs have been proposed, often seemingly at odds with one another. These decisions are as often motivated ....

....or hidden , abstract type within a scope requires that the types of the externally visible components avoid mention of the abstract type. This avoidance problem is often a stumbling block for module system design, since in most expressive languages there is no best way to avoid a type variable [9, 18]. 1.2 A Type System for Modules The type system proposed here takes into account all of these design issues. It consolidates and harmonizes design elements that were previously seen as disparate into a single framework. For example, rather than regard generativity of abstract types as an ....

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Mark Lillibridge. Translucent Sums: A Foundation for Higher-Order Module Systems. PhD thesis, Carnegie Mellon University, Pittsburgh, PA, December 1996.

....Mod is a module language expression and Expr a core language expression. Closure conversion then requires that an environment slot be allocated for the free module identifier s, leading to the need for first class modules. This potentially has some unpleasant consequences. For example Lillibridge [22] has demonstrated that type checking is undecidable for a type system with first class modules. The source of this undecidability is a subtype relation between modules that allows fields to be made private, and allows type definitions to be made opaque. There is no such subtype relation in the ....

Mark Lillibridge. Translucent Sums: A Foundation for Higher-Order Module Systems. PhD thesis, Carnegie-Mellon University, Pittsburgh, PA, May 1997. Technical Report CMU-CS-97-122.

....These expressions can refer to imported components via their associated internal variables. This explicit distinction between names and internal variables allows internal variables to be renamed by a conversion, while external names remain immutable, thus making projection by name un ambiguous [17, 2, 19]. The notation xi i Xi denote the unique surjective, finite map such that for all i 6 I, xi) Xi. It is valid only if for all i,j I, if j, then xi xj. Then dom( denotes xi I i 6 I and cod( denotes Xi I i 6 I . Xi i El, and Xi i Tii are defined in the same way. The notions of free and ....

M. Lillibridge. Translucent sums: a foundation for higher-order module systems. PhD thesis, School of Computer Science, Carnegie Mellon University, 1997.

....of languages [31, 2] has been particularly influential. Much e#ort has gone into the design of modular programming mechanisms for the ML family of languages, notably Standard ML [20] and Objective Caml [24] Numerous extensions and variations of these designs have been considered in the literature [18, 16, 26, 28, 5]. Despite (or perhaps because of) these substantial e#orts, the field has remained somewhat fragmented, with no clear unifying theory of modularity having yet emerged. Several competing designs have been proposed, often seemingly at odds with one another. These decisions are as often motivated by ....

....or hidden , abstract type within a scope requires that the types of the externally visible components avoid mention of the abstract type. This avoidance problem is often a stumbling block for module system design, since in most expressive languages there is no best way to avoid a type variable [6, 16]. 1.2 A Type System for Modules The type system proposed here takes into account all of these design issues. It consolidates and harmonizes design elements that were previously seen as disparate into a single framework. For example, rather than regard generativity of abstract types as an ....

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Mark Lillibridge. Translucent Sums: A Foundation for Higher-Order Module Systems. PhD thesis, Carnegie Mellon University, Pittsburgh, PA, December 1996.

....abbreviations in the context (Rule 30) can be seen to preserve decidability. Roughly speaking one can always first inline the abbreviations and then test for equivalence as in the previous case. It is not obvious how to extend the proof to include Rule 31 in a simple fashion. Lillibridge [Lil97] gives a complex argument for the decidability of constructor equivalence in a related system (without records of constructors) We conjecture an analogous argument would apply for our system. 7.1.2 Dynamic Semantics We define two states to be equivalent, written ( Delta#oe#E#phrase) ....

Mark Lillibridge. Translucent Sums: A Foundation for Higher-Order Module Systems. PhD thesis, School of Computer Science, Carnegie Mellon University, 1997. Available as CMU Technical Report CMU-CS-97-122.

....These papers give an involved syntactic translation, which, in this author s opinion, do little to clarify the semantics of Standard ML presented in [43, 44] Furthermore, there is currently no proof that this translation is faithful to the original semantics. The thesis of Lillibridge [33] develops the meta theory of a drastically simplified type theory that is presented as a kernel version of the translucent sum calculi underlying [18, 53, 22] Given the size of both the source and target languages, there probably never will be. 52 2.3.3.2 Leroy s Modules Historically, the ....

....rigid stratification between the core and modules. He only briefly 55 mentions the possibility of first class modules, and observes that removing the distinction between the core and modules is incompatible with applicative functors. Similar observations apply to Harper, Lillibridge and Stone s [18, 33, 53, 22] proposals: in these systems, the amalgamation of the core and modules languages means that the invariants needed to support applicative functors are violated. Leroy s stratification between core and modules ensures that both the subtyping relation on module types and typing relation on modules is ....

[Article contains additional citation context not shown here]

Mark Lillibridge. Translucent Sums: A Foundation for Higher-Order Module Systems. PhD thesis, School of Computer Science, Carnegie Mellon University, May 1997.

....of languages [33, 2] has been particularly influential. Much e#ort has gone into the design of modular programming mechanisms for the ML family of languages, notably Standard ML [22] and Objective Caml [26] Numerous extensions and variations of these designs have been considered in the literature [20, 17, 27, 30, 5]. Despite (or perhaps because of) these substantial e#orts, the field has remained somewhat fragmented, with no clear unifying theory of modularity having yet emerged. Several competing designs have been proposed, often seemingly at odds with one another. These decisions are as often motivated by ....

....or hidden , abstract type within a scope requires that the types of the externally visible components avoid mention of the abstract type. This avoidance problem is often a stumbling block for module system design, since in most expressive languages there is no best way to avoid a type variable [8, 17]. 1.2 A Type System for Modules The type system proposed here takes into account all of these design issues. It consolidates and harmonizes design elements that were previously seen as disparate into a single framework. For example, rather than regard generativity of abstract types as an ....

[Article contains additional citation context not shown here]

Mark Lillibridge. Translucent Sums: A Foundation for Higher-Order Module Systems. PhD thesis, Carnegie Mellon University, Pittsburgh, PA, December 1996. 22

....languages [34, 2] has been particularly influential. Much effort has gone into the design of modular programming mechanisms for the ML family of languages, notably Standard ML [23] and Objective Caml [27] Numerous extensions and variations of these designs have been considered in the literature [21, 18, 28, 31, 5]. Despite (or perhaps because of) these substantial efforts, the field has remained somewhat fragmented, with no clear unifying theory of modularity having yet emerged. Several competing designs have been proposed, often seemingly at odds with one another. These decisions are as often motivated ....

....or hidden , abstract type within a scope requires that the types of the externally visible components avoid mention of the abstract type. This avoidance problem is often a stumbling block for module system design, since in most expressive languages there is no best way to avoid a type variable [9, 18]. 1.2 A Type System for Modules The type system proposed here takes into account all of these design issues. It consolidates and harmonizes design elements that were previously seen as disparate into a single framework. For example, rather than regard generativity of abstract types as an ....

[Article contains additional citation context not shown here]

Mark Lillibridge. Translucent Sums: A Foundation for Higher-Order Module Systems. PhD thesis, Carnegie Mellon University, Pittsburgh, PA, December 1996.

....These expressions can refer to imported components via their associated internal variables. This explicit distinction between names and internal variables allows internal variables to be renamed by # conversion, while external names remain immutable, thus making projection by name unambiguous [19, 2, 21]. Due to late binding, a virtual (defined but not frozen) component of a mixin is both imported and exported by the mixin: it is exported with its current definition, but is also imported so that other exported components refer to its final value at the time the component is frozen or the mixin ....

M. Lillibridge. Translucent sums : a foundation for higher-order module systems. PhD thesis, School of Computer Science, Carnegie Mellon University, 1997.

....form of the symmetry and transitivity properties for logical equivalence, our initial attempts to use more traditional Kripke logical relations (with worlds being pairs of contexts) were unsuccessful. Other researchers have considered lambda calculi with more interesting equivalences. Lillibridge [10] considered a language in which equivalence depends on the typing context. He eliminates the context sensitivityby tagging each path with its enclosing typing context, and then gives a rewriting strategy for this tagged system. Curien and Ghelli [5] gave a proof of decidability of term equivalence ....

Mark Lillibridge. Translucent Sums: A Foundation for HigherOrder Module Systems. PhD thesis, School of Computer Science, Carnegie Mellon University, 1997. Available as CMU Technical Report CMU-CS-97-122.

....form of the symmetry and transitivity properties for logical equivalence, our initial attempts to use more traditional Kripke logical relations (with worlds being pairs of contexts) were unsuccessful. Other researchers have considered lambda calculi with more interesting equivalences. Lillibridge [10] considered a language in which equivalence depends on the typing context. He eliminates the context sensitivity by tagging each path with its enclosing typing context, and then gives a rewriting strategy for this tagged system. Curien and Ghelli [5] gave a proof of decidability of term ....

Mark Lillibridge. Translucent Sums: A Foundation for HigherOrder Module Systems. PhD thesis, School of Computer Science, Carnegie Mellon University, 1997. Available as CMU Technical Report CMU-CS-97-122.

....These expressions can refer to imported components via their associated internal variables. This explicit distinction between names and internal variables allows internal variables to be renamed by conversion, while external names remain immutable, thus making projection by name unambiguous [17, 2, 19]. The notation x i i2I 7 X i denote the unique surjective, nite map such that for all i 2 I , x i ) X i . It is valid only if for all i; j 2 I , if i 6= j, then x i 6= x j . Then dom( denotes fx i j i 2 Ig and cod( denotes fX i j i 2 Ig. X i i2I 7 E i , and X i i2I 7 T i are ....

M. Lillibridge. Translucent sums : a foundation for higher-order module systems. PhD thesis, School of Computer Science, Carnegie Mellon University, 1997.

....t val f : t t end if S is a structure having signature SIG, the type theory must ensure that S.t is interchangeable with int in any code having access to S. The standard account of sharing in type theory was developed independently by Harper and Lillibridge, under the name translucent sums [6, 13], and by Leroy, under the name manifest types [10] and extended in Leroy [11] These type theories provide a facility for stating type abbreviations in signatures and (importantly) ensure the correct propagation of type information resulting from those abbreviations. Exactly what is meant by ....

....derived without using that rule. If this aim is achieved, any singleton kinds remaining within the constructors are not used (in any essential way) and can simply be erased, resulting in valid constructors and derivations in the singleton free system. 2 As an aside, in the module based accounts [6, 13, 10, 11] it is impossible to discover that the module analogues of these types are equal because comparisons can be made only on expressions in named form. Naming the expressions ff:T:ff and ff:T:int obscures the possible connection between them, which depends essentially on their actual code. In the ....

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Mark Lillibridge. Translucent Sums: A Foundation for Higher-Order Module Systems. PhD thesis, Carnegie Mellon University, School of Computer Science, Pittsburgh, Pennsylvania, May 1997.

....system can only be used by type theory experts. 6.3 Related issues in programming languages 6.3. 1 Syntactic approaches Our work has been much inspired by SML like module systems [Mac84, Tof96] Especially important to us were Harper and Lillibridge s theoretical work on translucent sums [HL94, Lil97] and Leroy s on manifest types [Ler94, Ler95] Their works both present variants of the SML module system which are more elegant and have better metatheoretical properties than the initial SML module system. For instance they allow true separate compilation since only the knowledge of the type of ....

Mark Lillibridge. Translucent Sums: A Foundation for HigherOrder Module Systems. PhD thesis, School of Computer Science, Carnegie Mellon University, May 1997.

....f : int int end] read file extension ) of NONE = handle error . SOME m = m.f(12) There are many problems with this approach. First, it requires first class modules; in the context of a rich type system, first class modules require a complicated formalization (e.g. Lillibridge [28]) with restrictions on expressiveness; as a result, in most ML variants (and TAL as well) modules are second class [17] 26] 30] Second, it requires a type passing semantics as the type passed to load 0 must be checked against the actual type of the module at run time. This kind of semantics ....

M. Lillibridge. Translucent Sums: A Foundation for Higher-Order Module Systems. PhD thesis, Carnegie Mellon University, School of Computer Science, Pittsburgh, Pennsylvania, May 1997.

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Mark Lillibridge. Translucent Sums: A Foundation for Higher-Order Module Systems. PhD thesis, Pittsburgh, PA, May 1997.

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Mark Lillibridge. Translucent Sums: A Foundation for Higher-Order Module Systems. PhD thesis, Pittsburgh, PA, May 1997.

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Mark Lillibridge. Translucent Sums: A Foundation for Higher-Order Module Systems. PhD thesis, School of Computer Science, Carnegie Mellon University, 1997. Available as CMU Technical Report CMU-CS-97-122.

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Lillibridge, M. 1997. Translucent sums: A foundation for higher-order module systems. Ph.D. thesis, Carnegie Mellon University, School of Computer Science, Pittsburgh, Pennsylvania.

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Mark Lillibridge. Translucent Sums: A Foundation for Higher-Order Module Systems. PhD thesis, School of Computer Science, Carnegie Mellon University, 1997. Available as CMU Technical Report CMU-CS-97-122.

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Mark Lillibridge. Translucent Sums: A Foundation for Higher-Order Module Systems. PhD thesis, School of Computer Science, Carnegie Mellon University, 1997. Available as CMU Technical Report CMU-CS-97-122.

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Mark Lillibridge. Translucent Sums: A Foundation for Higher-Order Module Systems. PhD thesis, Carnegie Mellon University, Pittsburgh, PA, December 1996.

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Mark Lillibridge. Translucent Sums: A Foundation for Higher-Order Module Systems. PhD thesis, Carnegie Mellon Univ., May 1997.

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Mark Lillibridge. Translucent Sums: A Foundation for HigherOrder Module Systems. PhD thesis, Carnegie-Mellon University, Pittsburgh, PA, May 1997. Technical Report CMU-CS-97122.

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Mark Lillibridge. Translucent Sums: A Foundation for Higher-Order Module Systems. PhD thesis, Carnegie Mellon University,School of Computer Science, Pittsburgh, Pennsylvania, May 1997.

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