Giorgio Ghelli and Benjamin Pierce. Bounded existentials and minimal typing. Theoretical Computer Science, 193:75--96, 1998.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....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 ....

....= s # 1 (M 2 ) 2 [M 2 s] When M 2 is impure, this rule is more expressive than our typing rule, because the application can still occur. However, to exploit this rule, the type checker must find a non dependent supersignature that is suitable for application to M 2 . The avoidance problem [9, 18] is that there is no best way to do so. For example, consider the signature: # = T ] #s(s) s(s) To obtain a supersignature of # avoiding the variable s, we must forget that the first component is a constant function, and therefore we can only say that the second component is equal to the ....

Giorgio Ghelli and Benjamin Pierce. Bounded existentials and minimal typing. Theoretical Computer Science, 193:75-- 96, 1998.

....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 ....

....[M 2 s] s #1 (M 2 ) When M 2 is indeterminate, this rule is more expressive than our typing rule, because the application can still occur. However, to exploit this rule, the type checker must find a non dependent supersignature that is suitable for application to M 2 . The avoidance problem [6, 16] is that there is no best way to do so. For example, consider the signature: # = T ] s(s) s(s) Indeed, the transparent interpretation of datatypes, which exposes their representations, presents severe typing di#culties [4] 13 To obtain a supersignature of # avoiding the variable s, ....

Giorgio Ghelli and Benjamin Pierce. Bounded existentials and minimal typing. Theoretical Computer Science, 193:75--96, 1998.

....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 ....

....) # 2 [M 2 s] s #1 (M 2 ) When M 2 is impure, this rule is more expressive than our typing rule, because the application can still occur. However, to exploit this rule, the type checker must find a non dependent supersignature that is suitable for application to M 2 . The avoidance problem [8, 17] is that there is no best way to do so. For example, consider the signature: # = T ] s(s) s(s) To obtain a supersignature of # avoiding the variable s, we must forget that the first component is a constant function, and therefore we can only say that the second component is equal to ....

Giorgio Ghelli and Benjamin Pierce. Bounded existentials and minimal typing. Theoretical Computer Science, 193:75--96, 1998.

....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 ....

....= s s 1 (M 2 ) 2 [M 2 s] When M 2 is impure, this rule is more expressive than our typing rule, because the application can still occur. However, to exploit this rule, the type checker must find a non dependent supersignature that is suitable for application to M 2 . The avoidance problem [9, 18] is that there is no best way to do so. For example, consider the signature: s = T ] #s(s) s(s) To obtain a supersignature of s avoiding the variable s, we must forget that the first component is a constant function, and therefore we can only say that the second component is equal to the ....

Giorgio Ghelli and Benjamin Pierce. Bounded existentials and minimal typing. Theoretical Computer Science, 193:75-- 96, 1998.

....semantics of the type system becomes more challenging; recursive types also complicate the metatheory. OR, OE, and ORE work fine with the kernel F : subtyping rule for quantifiers. ORBE requires the full F : rule, leading to a substantial increase in the theoretical complexity of the calculus [Ghe95, Ghe93] and the loss of some pragmatically desirable properties such as decidability [Pie94] See [PS97] for more discussion of variants of this rule. The stronger rule is needed in ORBE to validate the usual subtyping rule for object types. Recall that, in F : bounded existential are ....

Giorgio Ghelli. Divergence of F type checking. Theoretical Computer Science, 139(1,2):131--162, 1995.

....alternatively, conditional systems provide a natural bridge between functional programming, based on equational semantics, and logicprogramming, based on Horn clauses. See [35] Narrowing [36, 37] is a linear restriction of paramodulation akin to the SLD strategy in Horn clause logic [2]. Whereas paramodulation uses both sides of an equation in the same way, narrowing is more directed unifying with left hand sides only thereby taking the direction of rewriting into account. In the conditional case, a rule l r : Gamma c may be applied to a goal t[s] if a nonvariable ....

.... to use directed goals of the form e z, similar to the equations in normal conditions, meaning that we are looking for a z that is the normal form of e [9] 5 Stream Programming The desirability of incorporating infinite structures in a functional logic language has been widely asserted [2, 30]. Unfortunately, we are presented with a tradeoff between the benefits of lazy evaluation of orthogonal, nonterminating rules and those of eager simplification with terminating, nonorthogonal rules. Starting from the lazy approach, one can allow some additional simplification rules. These rules ....

Pier Giorgio Bosco, Elio Giovannetti, and Corrado Moiso. Narrowing vs. SLD-resolution. Theoretical Computer Science, 59:3--23, 1988.

....semantics of the type system becomes more challenging; recursive types also complicate the metatheory. OR, OE, and ORE work fine with the Kernel Fun subtyping rule for quantifiers. ORBE requires the full F : rule, leading to a substantial increase in the theoretical complexity of the calculus [Ghe95, Ghe93] and the loss of some pragmatically desirable properties such as decidability [Pie94] See [PS97] for more discussion of variants of this rule. 14 Karl Crary has observed [personal communication] that it may be possible to ameliorate this deficiency in ORBE by introducing a single type ....

Giorgio Ghelli. Divergence of F type checking. Theoretical Computer Science, 139(1,2):131--162, 1995.

....quantified types is contravariant in their bounds and covariant in their bodies: Gamma 1 oe 1 Gamma; ff 1 oe 2 2 Gamma 8ff oe 1 : oe 2 8ff 1 : 2 (Sub All) B. C. Pierce 10 This rule deserves a closer look, since it causes considerable difficulties (cf. Section 6. 2 and (Ghelli, 1995; Pierce, 1994; Ghelli, 1993) Intuitively, it reads as follows: A type j 8ff 1 : 2 describes a collection of polymorphic values (functions from types to values) each mapping subtypes of 1 to instances of 2 . If 1 is a subtype of oe 1 , then the domain of is smaller than that of oe j ....

....time. 2.4.3. Fact: Curien and Ghelli] Gamma oe is derivable in F N iff the algorithm F N halts and returns true when given this statement as input. Unfortunately, the algorithm is not a decision procedure for the subtype relation. Indeed, this relation can be shown to be undecidable (Ghelli, 1995; Pierce, 1994) 3. The F Calculus We now introduce System F , an explicitly typed second order lambda calculus with bounded quantification and intersection types. F can roughly be characterized as the union of the concrete syntax and typing rules for the systems and F . To achieve a compact ....

Ghelli, G. 1995. Divergence of F Type Checking. Theoretical Computer Science, 139(1,2), 131--162.

....semantics of the type system becomes more challenging; recursive types also complicate the metatheory. OR, OE, and ORE work fine with the kernel F : subtyping rule for quantifiers. ORBE requires the full F : rule, leading to a substantial increase in the theoretical complexity of the calculus [Ghe95, Ghe93] and the loss of some pragmatically desirable properties such as decidability [Pie94] See [PS97] for more discussion of variants of this rule. The stronger rule is needed in ORBE to validate the usual subtyping rule for object types. Recall that, in F : bounded existential are ....

Giorgio Ghelli. Divergence of F type checking. Theoretical Computer Science, 139(1,2):131--162, 1995.

No context found.

G. Ghelli. Divergence of F type checking. Theoretical Computer Science, 139(1-2):131--162, 1995.

No context found.

G. Ghelli and B. Pierce. Bounded existentials and minimal typing. Theoretical Computer Science, 193(1-2):75--96, 1998.

No context found.

G. Ghelli. Divergence of F type checking. Theoretical Computer Science, 139(1-2):131--162, 1995.

....syntax and semantics have been investigated in detail, and they have formed the basis for a number of experimental language designs. Moreover, many ways of enriching these pure systems have been studied, including extensions with recursive types [AC93] extensible records [CM91] existential types [GP97], and type operators [Car90, CL91, PT94, HP95, PS94, Com94] However, one quite obvious extension has apparently never been considered in detail. Most presentations of Kernel Fun (and F ) include a type Top that is used, among other things, to recover ordinary unbounded quantification from ....

....or the guard of a case has type Bot. These cases must later be treated in the proof of subject reduction. 4. The algorithm for finding the smallest supertype of a given type that does not use a given type variable is actually somewhat simpler than the corresponding algorithm for Kernel Fun [GP97]. The following section introduces the syntax of the extended system formally. The remainder of the paper is broken into two main parts: Sections 3 and 4 develop the properties of subtyping, while Section 5 defines the typing relation and proves subject reduction. 2 Syntax Besides the addition ....

[Article contains additional citation context not shown here]

Giorgio Ghelli and Benjamin Pierce. Bounded existentials and minimal typing. Theoretical Computer Science, 1997. To appear.

....He published nine papers on refereed journals and twentyeight papers in international refereed conferences and workshops, coauthored with Antonio Albano, Luca Cardelli, Giuseppe Castagna, Richard Connor, Pierre Louis Curien, Giuseppe Longo, Benjamin Pierce, and many others. Selected Papers: [6, 12, 11, 31, 16]. Keywords Database programming languages, Type systems, Data models, Semistructured data, World Wide Web. ....

G. Ghelli and B. Pierce. Bounded existentials and minimal typing. Theoretical Computer Science, 193(1-2):75-96, 1998.

.... of complex databases in interrelated units, and for the de nition of external schemas [6, 17] The language has been implemented, and during this phase we studied the implementation of object with roles, the implementation of typechecking procedures, and the ecient use of persistent memory [26, 4, 28, 29, 16]. A view mechanism for object databases. The main contribution is a set of object viewing operations for the strongly typed database programming language Galileo 97, which supports objects with roles. These viewing operations are then used to give the semantics of a higher level mechanism to de ....

G. Ghelli. Divergence of F type checking. Theoretical Computer Science, 139(12) :131-162, 1995.

....the two systems differ above all in the treatment of existential bounded quantifiers. Existential quantifiers can be encoded in terms of universal ones, and the resulting subtyping rule turns out to be invariant in the bounds for the kernel fun version, and covariant for the full version [GP98] While the kernel fun version of the universal quantification is powerful enough for practical aims, the kernel fun version of existential quantification turns out to be weak in some specific situations. A typical example is given by the four different interpretations of object oriented ....

G. Ghelli and B. Pierce. Bounded existentials and minimal typing. Theoretical Computer Science, 193(1-2):75--96, 1998.

....not hold in pure F , but it is derivable in the extended system obtained by adding recursion and the two unfold rules to F . The limitation result shows that every non conservative F judgement makes the standard subtype checking algorithm diverge; this is very interesting since we know from [Ghe95] that only very special judgements diverge. We conjecture that the same limitation result can be proved for system F bounded too, but we leave this as an open problem. 10 PER semantics The semantic interpretation that we propose for system F bounded is obtained by adapting the semantics of ....

G. Ghelli. Divergence of F type checking. Theoretical Computer Science, 139(1-2):131--162, 1995.

.... than the full F variant where two polymorphic function types with different upper bounds for their type components are allowed to stand in the subtype relation under appropriate conditions; in the latter system, it can be shown that variables cannot always be eliminated in a most general way [GP97]. Formally, we write Gamma S V T for the relation T is the least supertype of S such that FV(T) V = and Gamma S V T for the dual relation T is the greatest subtype of S such that FV(T) V = The variable elimination by promotion relation can be computed as follows: Gamma ....

.... S V S 0 Gamma; X :A T V T 0 Gamma All(X :A)S T V All(X :A)S 0 T 0 (VD Fun 1) FV(A) V 6= Gamma All(X :A)S T V Bot (VD Fun 2) It is easy to check that, for each variable set V , V and V are total functions. These functions are similar to the ones used in [GP97], but somewhat simpler because of the presence of Bot in our type system. 3.2.1 Lemma [Soundness of variable elimination] 1. If Gamma S V T then FV(T) V = and Gamma S : T. 2. If Gamma S V T then FV(T) V = and Gamma T : S. Proof: By a straightforward simultaneous ....

Giorgio Ghelli and Benjamin Pierce. Bounded existentials and minimal typing. Theoretical Computer Science, 1997. To appear.

....Top V Top (VD Top) Bot V Bot (VD Bot) X 2 V X V Bot (VD Var 1) X = 2 V X V X (VD Var 2) S V U T V V All(X)S T V All(X)U V (VD Fun) It is easy to check that V and V are total functions, for any given set V . These functions are similar to the ones used in [GP97], but somewhat simpler because of the presence of Bot in our type system. 3.2.1 Lemma [Soundness] 1. If S V T then FV(T) V = and S : T. 2. If S V T then FV(T) V = and T : S. Proof: A simple simultaneous induction on the variable elimination derivations. Xi 3.2.2 Lemma ....

Giorgio Ghelli and Benjamin Pierce. Bounded existentials and minimal typing. Theoretical Computer Science, 1997. To appear.

....syntax and semantics have been investigated in detail, and they have formed the basis for a number of experimental language designs. Moreover, many ways of enriching these pure systems have been studied, including extensions with recursive types [AC93] extensible records [CM91] existential types [GP97], and type operators [Car90, CL91, PT94, HP95, PS94, Com94] However, one quite obvious extension has apparently never been considered in detail. Most presentations of Kernel Fun (and F ) include a type Top that is used, among other things, to recover ordinary unbounded quantification from bounded ....

....or the guard of a case has type Bot. These cases must later be treated in the proof of subject reduction. 4. The algorithm for finding the smallest supertype of a given type that does not use a given type variable is actually somewhat simpler than the corresponding algorithm for Kernel Fun [GP97]. The following section introduces the syntax of the extended system formally. The remainder of the paper is broken into two main parts: Sections 3 and 4 develop the properties of subtyping, while Section 5 defines the typing relation and proves subject reduction. 2 Syntax Besides the addition of ....

[Article contains additional citation context not shown here]

Giorgio Ghelli and Benjamin Pierce. Bounded existentials and minimal typing. Theoretical Computer Science, 1997. To appear.

No context found.

Giorgio Ghelli and Benjamin Pierce. Bounded existentials and minimal typing. Theoretical Computer Science, 1996. To appear.

....be proved by a unique derivation in normal form. There is a syntax directed algorithm (summarized by the rules in Appendix C) that discovers the minimal type for any typeable F term by constructing its normal form derivation [5] Although it fails to terminate on some pathological ill typed terms [8, 11], the algorithm is easy to implement and has been found to behave well in practice. 2.2 Encoded and Primitive Existentials in F The simplest way to add existential quantifiers to F is to regard them as syntactic sugar for combinations of universal quantifiers, using the standard encoding: Some ....

.... bounded quantifiers: Gamma; AS T U Gamma All (AS)T All (AS)U (All Sub KFun) Although this equal bounds rule seems semantically less natural than the one used in subsequent presentations of F , it yields a system with much simpler syntactic properties, including decidable subtyping [8]. The addition of bounded existential quantifiers to this fragment often called Kernel Fun is accomplished by adjoining the same introduction and elimination rules as before, but restricting the subtyping rule by analogy with the one for the universal quantifier: Gamma; AS T U Gamma ....

Giorgio Ghelli. Divergence of F type checking. Theoretical Computer Science, 139(1,2):131--162, 1995.

No context found.

Giorgio Ghelli and Benjamin Pierce. Bounded existentials and minimal typing. Theoretical Computer Science, 193:75--96, 1998.

No context found.

Giorgio Ghelli and Benjamin Pierce. Bounded existentials and minimal typing. Theoretical Computer Science, 193:75--96, 1998.

No context found.

Giorgio Ghelli. Divergence of F type checking. Theoretical Computer Science, 139(1,2):131--162, 1995.

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC