Partial intersection type assignment in applicative term rewriting systems

Bakel, Steffen van

doi:10.1007/bfb0037096

Cited by 22 publications

(44 citation statements)

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“…We can look at such calculi also as extensions of the Curryfied Term Rewriting Systems (C uTRS) considered in [3,5,6], by adding λ-abstraction and a β-reduction rule. We assume the reader to be familiar with LC [10] and refer to [22,15] for rewrite systems.…”

Section: Term Rewriting Systems With β-Reduction Rulementioning

confidence: 99%

“…In this section we define a type assignment system for TRS+β, that can be seen as an extension of the intersection type assignment system presented in [3]. The LC-fragment of our type assignment system corresponds directly to the system presented in [4].…”

Section: Type Assignment In Trs+βmentioning

confidence: 99%

“…For example, in [3] a notion of type assignment for TRS has been developed. In particular, that paper considered systems in which it is possible to make hypotheses about the functional characterization of the function symbols in the signature of the TRS.…”

Section: Introductionmentioning

confidence: 99%

“…constant types) for TRS extended with application, λ-abstraction and β-reduction. This system is an extension of the type assignment systems for TRS presented in [3]. It exploits the power and generality of intersection types with ω (see, e.g., [11,2,4]), managing to type broad and meaningful sets of terms and rewrite rules.…”

Section: Introductionmentioning

confidence: 99%

“…The notion of intersection type assignment for TRS developed in [3,5,6] enables the study of the relation between semantics of reduction and type assignment in the framework of TRS. In [7] the notion of approximant and the related approximation model defined by Thatte [25] are used to show that every type that can be assigned to a term, can also be assigned to one of its approximants (provided the TRS satisfies certain conditions).…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Rewrite systems with abstraction and β-rule: Types, approximants and normalization

Bakel

Barbanera

Fernández

1996

Programming Languages and Systems — ESOP '96

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Section: Term Rewriting Systems With β-Reduction Rulementioning

confidence: 99%

Section: Type Assignment In Trs+βmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Rewrite systems with abstraction and β-rule: Types, approximants and normalization

Bakel

Barbanera

Fernández

1996

Programming Languages and Systems — ESOP '96

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Normalization Results for Typeable Rewrite Systems

Bakel

Fernández

1997

Information and Computation

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In this paper we introduce Curryfied Term Rewriting Systems, and a notion of partial type assignment on terms and rewrite rules that uses intersection types with sorts and ω. Three operations on typessubstitution, expansion, and lifting -are used to define type assignment, and are proved to be sound. With this result the system is proved closed for reduction. Using a more liberal approach to recursion, we define a general scheme for recursive definitions and prove that, for all systems that satisfy this scheme, every term typeable without using the type-constant ω is strongly normalizable. We also show that, under certain restrictions, all typeable terms have a (weak) head-normal form, and that terms whose type does not contain ω are normalizable.

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The Essence of Principal Typings

Wells¹

2002

Automata, Languages and Programming

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Let S be some type system. A typing in S for a typable term M is the collection of all of the information other than M which appears in the final judgement of a proof derivation showing that M is typable. For example, suppose there is a derivation in S ending with the judgement A M : τ meaning that M has result type τ when assuming the types of free variables are given by A. Then (A, τ) is a typing for M. A principal typing in S for a term M is a typing for M which somehow represents all other possible typings in S for M. It is important not to confuse this notion with the weaker notion of principal type often mentioned in connection with the Hindley/Milner type system. Previous definitions of principal typings for specific type systems have involved various syntactic operations on typings such as substitution of types for type variables, expansion, lifting, etc. This paper presents a new general definition of principal typings which does not depend on the details of any particular type system. This paper shows that the new general definition correctly generalizes previous system-dependent definitions. This paper explains why the new definition is the right one. Furthermore, the new definition is used to prove that certain polymorphic type systems using ∀-quantifiers, namely System F and the Hindley/Milner system, do not have principal typings.

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Partial intersection type assignment in applicative term rewriting systems

Cited by 22 publications

References 11 publications

Rewrite systems with abstraction and β-rule: Types, approximants and normalization

Rewrite systems with abstraction and β-rule: Types, approximants and normalization

Normalization Results for Typeable Rewrite Systems

The Essence of Principal Typings

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