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## Principal type schemes for the strict type assignment system (1993)

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Venue: | Logic and Computation |

Citations: | 37 - 21 self |

### Citations

1266 |
The Lambda Calculus, its Syntax and Semantics
- Barendregt
- 1984
(Show Context)
Citation Context ...ssignment systems for functional programming languages – that use the ‘untyped’-approach – are based on (extensions of) the Curry type assignment system [11, 12] for the pure, untyped lambda calculus =-=[5]-=-. For example, the functional programming language ML [19] is in fact an extended lambda calculus and its type system is based on Curry’s system. It is well known that in Curry’s system, the problem o... |

1064 | A theory of type polymorphism in programming
- Milner
- 1978
(Show Context)
Citation Context ...that use the ‘untyped’-approach – are based on (extensions of) the Curry type assignment system [11, 12] for the pure, untyped lambda calculus [5]. For example, the functional programming language ML =-=[19]-=- is in fact an extended lambda calculus and its type system is based on Curry’s system. It is well known that in Curry’s system, the problem of typeability Given a term , are there and such that : (i.... |

258 |
Combinatory Logic
- Curry, Feys
- 1958
(Show Context)
Citation Context ...ck consistency. Many of the now existing type assignment systems for functional programming languages – that use the ‘untyped’-approach – are based on (extensions of) the Curry type assignment system =-=[11, 12]-=- for the pure, untyped lambda calculus [5]. For example, the functional programming language ML [19] is in fact an extended lambda calculus and its type system is based on Curry’s system. It is well k... |

247 |
A filter lambda model and the completeness of type assignment
- Barendregt, Coppo, et al.
- 1983
(Show Context)
Citation Context ...ersity of Nijmegen, Toernooiveld 1, 6525 ED Nijmegen, The Netherlands. E-mail: steffen@cs.kun.nl Abstract We study the strict type assignment system, a restriction of the intersection type discipline =-=[6]-=-, and prove that it has the principal type property. We define, for a term , the principal pair (of basis and type). We specify three operations on pairs, and prove that all pairs deducible for can be... |

170 |
The system F of variable types: Fifteen years later
- Girard
- 1986
(Show Context)
Citation Context ...ymorphic functions’ in programming languages like ML. There exist type assignment systems for which it is uncertain whether or not this property holds. For example, in the polymorphic type discipline =-=[14]-=-, there is no known way to obtain the types ( . ) ( . ) and ( . ) ( . ) – both types for the lambda term – from a unique type. (See [13].) Moreover, there exists no type derivable for such that both t... |

116 |
The principal type scheme of an object in combinatory logic
- Hindley
- 1969
(Show Context)
Citation Context ...cipal type for . For Curry’s system the operation O consists entirely of substitutions, i.e. operations that replace type-variables by types. (Principal type schemes for Curry’s system are defined in =-=[15]-=-.) The existence of a principal type for a typeable lambda term shows an internal coherence between all types that can be assigned to . Since substitution is an easy operation, in Curry’s system the s... |

115 | Complete restrictions of the Intersection Type Discipline
- Bakel
- 1992
(Show Context)
Citation Context ...the term ( ), and although the lambda terms ( ) and (( )) are -equal, the principal type schemes for these terms are different. The intersection type discipline as presented in [9] (see also [6], and =-=[1]-=-) is an extension of Curry’s system that does not have these drawbacks. The extension to Curry’s system is essentially that terms and term-variables are allowed to have more than one type. Intersectio... |

112 |
Polymorphic type inference and containment
- Mitchell
- 1988
(Show Context)
Citation Context ...ction, whereas the latter is not. The main result proved for the strict system in [1] is that of completeness of type assignment without the -relation, by using inference type semantics as defined in =-=[20]-=- instead of the simple type semantics as defined in [16]. As stated above, if for the construction of a type inference system for an untyped functional programming language instead of Curry’s system a... |

106 | An extension of the basic functionality theory for the λ-calculus - Coppo, Dezani-Ciancaglini - 1980 |

65 | Principal type schemes for an extended type theory. Theoretical Computer Science - Rocca, Venneri - 1984 |

61 | Functional characters of solvable terms. Zeitschrift für Mathematische Logik und Grundlagen der Mathematik - Coppo, Dezani-Ciancaglini, et al. - 1981 |

51 |
Principal type schemes and λ-calculus semantics
- Coppo, Dezani-Ciancaglini, et al.
- 1980
(Show Context)
Citation Context ...e assignment system with intersection types is to be used, then such a system should at least have the principal pair property. There exists two of those systems for which this property is proved. In =-=[8]-=- principal type schemes are defined for a type assignment system that is a restriction of the system as presented in [9]. This system has as a disadvantage that it is not an extension of Curry’s syste... |

42 | An extension of the basic functionality theory for the -calculus - Coppo, Dezani-Ciancaglini - 1980 |

36 |
Principal type schemes and -calculus semantics
- Coppo, Dezani-Ciancaglini, et al.
- 1980
(Show Context)
Citation Context ...e assignment system with intersection types is to be used, then such a system should at least have the principal pair property. There exists two of those systems for which this property is proved. In =-=[8]-=- principal type schemes are defined for a type assignment system that is a restriction of the system as presented in [9]. This system has as a disadvantage that it is not an extension of Curry’s syste... |

35 |
Principal Type Scheme and Unification for Intersection Type Discipline
- Rocca, S
- 1988
(Show Context)
Citation Context ..., be the principal pair of . Then there exists a strict chain C such that C ( , ) = , . 2. ( ) is infinite. Then there exist a pair , ( ) and a strict chain C such that C ( , ) = , . Final remarks In =-=[21]-=- a unification semi-algorithm for intersection types is presented, together with a semi-algorithm PP that finds the principal type for every strongly normalizable lambda term. The unification algorith... |

30 |
A complete type inference algorithm for simple intersection types
- Coppo, Giannini
- 1992
(Show Context)
Citation Context ..., type assignment in this system is not decidable, but semi-decidable. This means of course that in an implementation of the strict system some restrictions have to be made, as is done for example in =-=[10]-=- and [2]. Limiting the notion of type assignment by restricting the situations in which the derivation rules can be applied (the technique used in [10]), or by limiting the structure of types (as is d... |

28 |
The Completeness Theorem for Typing λ-terms
- HINDLEY
- 1983
(Show Context)
Citation Context ...for the strict system in [1] is that of completeness of type assignment without the ≤-relation, by using inference type semantics as defined in [20] instead of the simple type semantics as defined in =-=[16]-=-. As stated above, if for the construction of a type inference system for an untyped functional programming language instead of Curry’s system a type assignment system with intersection types is to be... |

24 |
Combinatory Logic volume 1
- Curry, Feys
- 1968
(Show Context)
Citation Context ...ck consistency. Many of the now existing type assignment systems for functional programming languages – that use the ‘untyped’-approach – are based on (extensions of) the Curry type assignment system =-=[11, 12]-=- for the pure, untyped lambda calculus [5]. For example, the functional programming language ML [19] is in fact an extended lambda calculus and its type system is based on Curry’s system. It is well k... |

19 | Partial Intersection Type Assignment in Applicative Term Rewriting Systems
- Bakel
- 1993
(Show Context)
Citation Context ...example, take : : . Notice that , but we can not derive : : . (A notion of type assignment that is a minor variant of the strict system is presented in [3]. (A short version of this paper appeared as =-=[4]-=-.) This variant consists of replacing the type assignment rule ( E) of the strict system by one for ( ), also allowed only for term-variables. In this way a notion of type assignment is obtained that ... |

18 |
Filter models with polymorphic types
- Jacobs, Margaria, et al.
- 1992
(Show Context)
Citation Context ...g that the strict type assignment system has the principal pair property, we could have used the same technique as [18]. In that paper principal typings for the type assignment system as presented in =-=[17]-=- are studied. That system is a combination of the BCD-system and the polymorphic type discipline as presented in [14]. This combination can be seen as an extension of the BCD-system by adding the type... |

12 | Essential Intersection Type Assignment
- BAKEL
- 1993
(Show Context)
Citation Context ...es not hold: If : , and , then : . As a counter example, take : : . Notice that , but we can not derive : : . (A notion of type assignment that is a minor variant of the strict system is presented in =-=[3]-=-. (A short version of this paper appeared as [4].) This variant consists of replacing the type assignment rule ( E) of the strict system by one for ( ), also allowed only for term-variables. In this w... |

12 |
The completeness theorem for typing -terms
- Hindley
- 1983
(Show Context)
Citation Context ... for the strict system in [1] is that of completeness of type assignment without the -relation, by using inference type semantics as defined in [20] instead of the simple type semantics as defined in =-=[16]-=-. As stated above, if for the construction of a type inference system for an untyped functional programming language instead of Curry’s system a type assignment system with intersection types is to be... |

9 |
Della Rocca. Characterization of typings in polymorphic type discipline
- Giannini, Ronchi
- 1988
(Show Context)
Citation Context ...property holds. For example, in the polymorphic type discipline [14], there is no known way to obtain the types ( . ) ( . ) and ( . ) ( . ) – both types for the lambda term – from a unique type. (See =-=[13]-=-.) Moreover, there exists no type derivable for such that both types can be obtained from by substitution. Although frequently used as a basis for type assignment algorithms for functional programming... |

9 |
Une extension de la théorie des types
- SALLÉ
- 1978
(Show Context)
Citation Context ...at is closed under -equality: if : and , then : . The first type assignment system with intersection types was presented in [7]; the CDV-system with intersection types and is introduced in [9] and in =-=[23]-=-. The best-known intersection type assignment system is the BCD-system, as presented in [6], that is an extension of the CDV-system: there it is strengthened further by introducing a partial order rel... |

8 | Partial Intersection Type Assignment of Rank 2 in Applicative Term Rewriting Systems - Bakel - 1992 |

5 |
Principal Typing in a ∀∩-Discipline
- MARGARIA, ZACCHI
- 1995
(Show Context)
Citation Context ... [22] do not provide principal types for the strict type assignment system. In proving that the strict type assignment system has the principal pair property, we could have used the same technique as =-=[18]-=-. In that paper principal typings for the type assignment system as presented in [17] are studied. That system is a combination of the BCD-system and the polymorphic type discipline as presented in [1... |

2 | Principal Typing in a 8"-Discipline - Margaria, Zacchi - 1995 |

2 |
Filter Models with Polymorphic Types
- Zacchi
- 1992
(Show Context)
Citation Context ...g that the strict type assignment system has the principal pair property, we could have used the same technique as [18]. In that paper principal typings for the type assignment system as presented in =-=[17]-=- are studied. That system is a combination of the BCD-system and the polymorphic type discipline as presented in [14]. This combination can be seen as an extension of the BCD-system by adding the type... |