## An ideal model for recursive polymorphism (1986)

Venue: | Information and Control |

Citations: | 1 - 0 self |

### BibTeX

@ARTICLE{Macqueen86anideal,

author = {David Macqueen and Gordon Plotkin and Ravi Sethi},

title = {An ideal model for recursive polymorphism},

journal = {Information and Control},

year = {1986},

pages = {95--130}

}

### OpenURL

### Abstract

types

### Citations

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- Milner
- 1978
(Show Context)
Citation Context ...denoted by X °. The cpos we consider arc called domains; they have a countable number of finite elements. 3 6.2. Ideals. Type expressions will bc interpreted using certain subsets of V, called ideals =-=[13, 21, 22, 11]-=-. Recall from the summary at the end of Section 6 that we think of a type as a collection of structurally similar values. The structural distinctions that types are meant to capture satisfy the follow... |

977 | A machine-oriented logic based on the resolution principle - Robinson - 1965 |

381 |
Principal type-schemes for functional programs
- Damas, Milner
- 1982
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Citation Context ...uction rule for typing lambda abstractions ,~,x:~y k e : 'r The rules for the usual type constructs, including universal quantification, are fairly standard, following those of Hindley [8] and Milner =-=[13, 4]-=-. The rules for existential quantification are novel, but are beyond the scope of this paper. To deal with recursive type expressions, we add the following two rules that correspond respectively to "u... |

378 | Towards a theory of type structure - Reynolds - 1974 |

358 | The Art of Computer Programming, Volume 1: Fundamental Algorithms, 2nd ed - Knuth - 1973 |

149 |
The Principal Type-Scheme of an Object in Combinatory Logic
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- 1969
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Citation Context ...owing -- introduction rule for typing lambda abstractions ,~,x:~y k e : 'r The rules for the usual type constructs, including universal quantification, are fairly standard, following those of Hindley =-=[8]-=- and Milner [13, 4]. The rules for existential quantification are novel, but are beyond the scope of this paper. To deal with recursive type expressions, we add the following two rules that correspond... |

136 | Lambda-calculus Models of Programming Languages - Morris - 1968 |

135 |
Continuous lattices
- Scott
- 1972
(Show Context)
Citation Context ... V to V, the produc~ of V with itself, the sum of V with itself, and a value wrong standing for (dynamic) type-errors. The mathematics needed to solve equations like (6.1) is due essentially to Scott =-=[20]-=-. Details may be found m many places, such as [17]. Solutions to equations like (6.1) are particular partially ordered sets: a complete partial order (cpo) (D,_L-) consists of a set D and a partial or... |

103 |
les opérations dans les ensembles abstraits et leur application aux équations intégrales
- Banach, Sur
- 1920
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Citation Context ...inite element is taken to be the first place it appears in the chain. 6.5. Unique fixed points. In order to find ideals satisfying such equations as I = I F;I IN we use the Banach Fixed-Point Theorem =-=[2]-=-. A (uniformly) contractive map f:X -. Y of metric spaces is one such that there is a real number 0<~r<l such that for all x and x' in X, we have d(f(x),f(x')) <~ rd(x), and it is non-expansive if thi... |

87 | Processes and the denotational semantics of concurrency - Bakker, Zucker - 1982 |

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35 | Concrete domains
- Kahn, Plotkin
- 1993
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Citation Context ...V with itself, and a value wrong standing for (dynamic) type-errors. The mathematics needed to solve equations like (6.1) is due essentially to Scott [20]. Details may be found m many places, such as =-=[17]-=-. Solutions to equations like (6.1) are particular partially ordered sets: a complete partial order (cpo) (D,_L-) consists of a set D and a partial order r- on D, such that (i) there is a least elemen... |

26 | An Investigation of a Programming Language with a Polymorphic Type Structure - McCracken - 1979 |

23 | A linear algorithm for testing equivalence of finite automata - Hopcroft, Karp - 1971 |

4 |
A higher order polymorphic type system for applicative languages
- MacQueen, Sethi
- 1982
(Show Context)
Citation Context ...denoted by X °. The cpos we consider arc called domains; they have a countable number of finite elements. 3 6.2. Ideals. Type expressions will bc interpreted using certain subsets of V, called ideals =-=[13, 21, 22, 11]-=-. Recall from the summary at the end of Section 6 that we think of a type as a collection of structurally similar values. The structural distinctions that types are meant to capture satisfy the follow... |

3 |
On list structures and their use in the programming of unification
- Morris
- 1978
(Show Context)
Citation Context ...ng it. in this way, the appropriate type can bc found for the Y combinator. (Such an algorithm has been implemented for Scheme, which is a dialect of Lisp 1231.) Algorithms for "circular" unification =-=[15]-=- can readily be adapted from algorithms for testing the equivalence of (1) finite automata and (2) linked lists with cycles [10, Section 2.3.5, Exercise 111. The almost linear algorithm for testing I ... |

3 |
Data types as objects
- Shamir, Wadge
- 1977
(Show Context)
Citation Context ...denoted by X °. The cpos we consider arc called domains; they have a countable number of finite elements. 3 6.2. Ideals. Type expressions will bc interpreted using certain subsets of V, called ideals =-=[13, 21, 22, 11]-=-. Recall from the summary at the end of Section 6 that we think of a type as a collection of structurally similar values. The structural distinctions that types are meant to capture satisfy the follow... |

3 | C.: Private communication - Wand, Weidenbach - 2012 |

1 |
Metric interpretations of finite trees and semantics of nondeterministic rccursive programs
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- 1980
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Citation Context ... larger expression hx.xx.t Sincc the type ofx is s = s--,t, xx has type t, hx.xx has type s = s--,t, and the type of (hx.xx)(hx.xx) is I. Two remarks provide some perspective on the above discussion. =-=(1)-=- Since there arc no constraints on the type variable t, the above discussion applies with any type expression substituted for t. Thus, (hx.xx)(hx.xx) has type ~r for any type expression tr. Since the ... |

1 | An approach to compile-time type checking - Henderson - 1977 |

1 | Automatic assignment of concrete type schemes to programs," unpublished - Morris - 1977 |

1 |
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