F. Pottier. A versatile constraint-based type inference system. Nordic Journal of Computing, 7(4), 2000.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....of k 1 and the argument of k 2 correspond, the rst argument of k 1 being forgotten in the subtype relationship. From a formal point of view, it is simpler (and more general) to express the relationship between arguments by working with a structure of labeled terms. In the formalism of Pottier [6], each argument of a constructor is indicated by a label instead of a position. Moreover, positive and negative labels are distinguished in order to express the covariance or the contravariance of arguments w.r.t. the subtyping relation. So let L and L be two disjoint countable sets of labels, ....

....uS exists, then a(uS) s2S a(s) 3. for all S K, if tS exists, then a(tS) s2S a(s) 4. for all k 1 Kk 2 , there exists k s.t. k 1 Kk Kk 2 and a(k) a(k 1 ) a(k 2 ) Conditions 1, 2, 3 express the coherence of labels w.r.t. the order relation and are similar to the ones found in [6] for lattices. Condition 4 is speci c to quasilattices, its purpose is to forbid signatures like k 1 ( Kk 2 ( which do not induce a quasi lattice structure for types. For example, if k 3 and k 4 are not comparable, then k 2 (k 3 ) and k 2 (k 4 ) have common lower bounds, like k 1 (k 3 ) and ....

[Article contains additional citation context not shown here]

F. Pottier. A versatile constraint-based type inference system. Nordic Journal of Computing, 7(4):312-347, November 2000.

....row unification and is very inefficient. However, there are a number of efficiently implemented type inference algorithms available that should be fairly straightforward to adapt to our system. Good starting points would be the system of Henglein and Rehof [18] the Wallace framework of Pottier [28], and the soft typing implementation of Wright [38] The Wallace framework is probably the most advanced of these, it provides conditional constraints, rows, and subtyping. However, it only supports polymorphic lets at the top level. 6 Related Work 6.1 Alternative Type Inference Algorithms Lee ....

....on constraints, but rather by flow labels inferred by a flow analysis. 6.3 Row Types Remy and Wand [36, 30, 31] introduce row types, the heart of our approach, for modeling record and variant types. They give sound and complete type inference algorithms for their respective systems. Pottier [28] considers type inference for constrained type systems with subtyping. His constraint logic includes conditional constraints and rows, which clearly subsumes the facilities required for inferring multivocal types. The system is phrased as an instance of the HM(X) framework [25] which provides the ....

Francois Pottier. A versatile constraint-based type inference system. Nordic Journal of Computing, 7(4):312--347, November 2000.

....to polymorphic variants [16, 5] and objects with rst class (dynamic) messages [12] All these systems were proposed as extensions of the Hindley Milner type system [10] with growing degrees of complexity. A recent trend is to simplify these type systems by moving to a constraint based framework [13, 11, 18, 15]. This indeed greatly improved the understanding of the various systems, as they can all be described as particular instances of the HM(X) framework, on various constraint domains. However, the switch to a constraint system also means that A preliminiary version of this paper has been presented ....

....a message is dispatched between methods whose result types di er. Such a mechanism was rst proposed by Aiken et al. in the context of soft typing for dynamically typed languages [1] Pottier reformulated it as an instance of the HM(X) framework, calling it accurate analysis of pattern matching [15]. In both cases, the type of the result is described by a conditional type, depending on the input. Moreover, they use global inclusion constraints to deal with the problem, while we use only local ones. Concretely, we add a new cases construct, which has the same syntax as function , but allows ....

[Article contains additional citation context not shown here]

F. Pottier. A versatile constraint-based type inference system. Nordic Journal of Computing, 7(4):312-347, Nov. 2000.

....can naturally be extended to deal with the whole ML programming language, including # INRIA, BP 105, F 78153 Le Chesnay Cedex, France. references [Pot01] exceptions and variant or record datatypes. It also has been used as the basis of type systems for some advanced programming constructs [Pot00], or to describe static analyses [PS03] However, all these extensions are orthogonal to the treatment of polymorphism which remains in the ML tradition. Besides, Odersky and Laufer [OL92] proposed an extension of the ML language with existential quantification in algebraic data types, which ....

....solver for structural subtyping written in Objective Caml. It would be an interesting question to design algorithms for solving constraints generated by HM## (X) which handle other forms of subtyping. We considered the case of non structural subtyping where the set of types forms a lattice, as in [Pot00]. Limiting quantification bounds to be conjunctions of inequalities between universally quantified variables, we believe it is possible to solve the constraints generated by HM## (X) s inference algorithm by considering these variables as new symbols in the types lattice as Skolem types and ....

Francois Pottier. A versatile constraintbased type inference system. Nordic Journal of Computing, 7(4):312--347, November 2000. URL: http://pauillac.inria.fr/~fpottier/ publis/fpottier-njc-2000.ps.gz.

....can naturally be extended to deal with the whole ML programming language, including INRIA, BP 105, F 78153 Le Chesnay Cedex, France. references [Pot01] exceptions and variant or record datatypes. It also has been used as the basis of type systems for some advanced programming constructs, e.g. [Pot00], or to describe static analyses, e.g. PS03] However, all these extensions are orthogonal to the treatment of polymorphism which remains in the ML tradition. Besides, Odersky and La ufer [OL92] proposed an extension of the ML language with existential quanti cation in algebraic data types, ....

....solver for structural subtyping written in Objective Caml. It would be an interesting question to design algorithms for solving constraints generated by HM98 (X) which handle other forms of subtyping. We considered the case of non structural subtyping where the set of types forms a lattice, as in [Pot00]. Limiting quanti cation bounds to be conjunctions of inequalities between universally quanti ed variables, we believe it is possible to solve the constraints generated by HM98 (X) s inference algorithm by considering these variables as new symbols in the types lattice as Skolem types and to ....

Francois Pottier. A versatile constraintbased type inference system. Nordic Journal of Computing, 7(4):312-347, November 2000. URL: http://pauillac.inria.fr/~fpottier/ publis/fpottier-njc-2000.ps.gz.

....can naturally be extended to deal with the whole ML programming language, including INRIA, BP 105, F 78153 Le Chesnay Cedex, France. references [Pot01] exceptions and variant or record datatypes. It also has been used as the basis of type systems for some advanced programming constructs, e.g. [Pot00], or to describe static analyses, e.g. PS03] However, all these extensions are orthogonal to the treatment of polymorphism which remains in the ML tradition. Besides, Odersky and La ufer [OL92] proposed an extension of the ML language with existential quanti cation in algebraic data types, ....

....solver for structural subtyping written in Objective Caml. It would be an interesting question to design algorithms for solving constraints generated by HM98 (X) which handle other forms of subtyping. We considered the case of non structural subtyping where the set of types forms a lattice, as in [Pot00]. Limiting quanti cation bounds to be conjunctions of inequalities between universally quanti ed variables, we believe it is possible to solve the constraints generated by HM98 (X) s inference algorithm by considering these variables as new symbols in the types lattice as Skolem types and to ....

Francois Pottier. A versatile constraint-based type inference system. Nordic Journal of Computing, 7(4), 2000.

....Previous works have shown how to integrate it into languages such as the simply typed calculus, ML or Haskell. It appears as the basis of many type systems for object oriented languages, e.g. 1] and it allows designing ne grained type systems for advanced programming constructs, e.g. [2]. It may also be used for extending standard type systems in order to perform some static analysis, such as detection of uncaught exceptions [3] data [4] or information [5] ow analyzes. In all cases, subtyping consists of a partial order on types and a subsumption rule that allows every ....

....a super type t . Let 1 and 2 be two schemes of the same kind. 1 is more general than 2 (we write: 1 4 2 ) if and only if for every assignment , J 2 K . They are equivalent ( 1 2 ) if and only if 2 4 1 and 1 4 2 hold. Lemma 4. Let 1 = 8 [ 1 ] and 2 = 8 [ 2 ]: be two schemes. If 1 j= 2 then 2 4 1 . satisfying 1 such that = and ( t. Because 1 j= 2 , satis es 2 too. We conclude that t 2 J 2 K 4.3 Rewriting systems A rewriting rule is a triple of three constraints R = 0 j 0 considered modulo conversion of free ....

[Article contains additional citation context not shown here]

Pottier, F.: A versatile constraint-based type inference system. Nordic Journal of Computing 7 (2000) 312-347 url: http://pauillac.inria.fr/~fpottier/ publis/fpottier-njc-2000.ps.gz.

....Previous works have shown how to integrate it into languages such as the simply typed calculus, ML or Haskell. It appears as the basis of many type systems for object oriented languages, e.g. 1] and it allows designing ne grained type systems for advanced programming constructs, e.g. [2]. It may also be used for extending standard type systems in order to perform some static analysis, such as detection of uncaught exceptions [3] data [4] or information [5] ow analyzes. In all cases, subtyping consists of a partial order on types and a subsumption rule that allows every ....

....of the same kind. 1 is more general than 2 (we write: 1 4 2 ) if and only if for every assignment , J 2 K J 1 K . They are equivalent ( 1 2 ) if and only if 2 4 1 and 1 4 2 hold. In particular, if 1 and 2 are equivalent constraints then the schemes 8 [ 1 ] and 8 [ 2 ]: are equivalent too. 4.3 Rewriting systems A rewriting rule is a triple of three constraints R = 0 j 0 considered modulo conversion of free variables. We de ne the reduction associated to R as the smallest congruence (for and 9. R such that 0 R 0 . A rewriting system is a ....

[Article contains additional citation context not shown here]

Pottier, F.: A versatile constraint-based type inference system. Nordic Journal of Computing 7 (2000) 312-347

....is Pre if one argument has type Pre at and the other has type Abs at ; it is Abs if both arguments have type Abs at ; the operation is ill typed otherwise. The difficulty is not in the quantification over , which is dealt with by rows, but in the fact that this definition is by cases. In [11], I suggested addressing this issue using conditional constraints, a concept whose origin can be traced back to Reynolds [15] Non structural subtyping constraints can be solved in cubic time [6] In fact, McAllester s theorem [4] allows establishing that possibly conditional subtyping ....

....two kinds of types, plain types and field types. The record type constructor f g forms a plain type out of a row of field types. The constructor Pre forms a field type out of a plain type. Abs and Pre are made incomparable, because that is required to assign a sound type to record concatenation [1, 11], but they do have a common supertype field , so width subtyping is present. If we take a look ahead at the syntax of terms and at the sorting and kinding restrictions, defined in Section 2.3, we find that this ground signature gives rise to the following grammar of terms, where ranges over ....

[Article contains additional citation context not shown here]

Francois Pottier. A versatile constraint-based type inference system. Nordic Journal of Computing, 7(4):312--347, November 2000.

No context found.

F. Pottier. A versatile constraint-based type inference system. Nordic Journal of Computing, 7(4), 2000.

No context found.

F. Pottier. A versatile constraint-based type inference system. Nordic Journal of Computing, 7(4):312--347, November 2000.

No context found.

Fran cois Pottier. A versatile constraint-based type inference system. Nordic Journal of Computing, 7(4):312347, November 2000.

No context found.

Pottier, F.: A versatile constraint-based type inference system. Nordic Journal of Computing 7 (2000)

No context found.

Fran cois Pottier. A versatile constraint-based type inference system. Nordic Journal of Computing, 7(4):312--347, November 2000. url: http: //pauillac.inria.fr/~fpottier/publis/fpottier-njc-2000.ps.gz.

No context found.

F. Pottier. A versatile constraint-based type inference system. Nordic Journal of Computing, 7(4):312-347, Nov. 2000.

No context found.

F. Pottier. A versatile constraint-based type inference system. Nordic Journal of Computing, 7(4), 2000.

No context found.

F. Pottier. A versatile constraint-based type inference system. Nordic Journal of Computing, 7(4):312-347, Nov. 2000.

No context found.

F. Pottier. A versatile constraint-based type inference system. Nordic Journal of Computing, 7(4):312--347, Nov. 2000.

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