## The Lazy Lambda Calculus (1990)

Venue: | Research Topics in Functional Programming |

Citations: | 239 - 3 self |

### BibTeX

@INPROCEEDINGS{Abramsky90thelazy,

author = {Samson Abramsky},

title = {The Lazy Lambda Calculus},

booktitle = {Research Topics in Functional Programming},

year = {1990},

pages = {65--116},

publisher = {Addison-Wesley}

}

### Years of Citing Articles

### OpenURL

### Abstract

Introduction The commonly accepted basis for functional programming is the -calculus; and it is folklore that the -calculus is the prototypical functional language in puri ed form. But what is the -calculus? The syntax is simple and classical; variables, abstraction and application in the pure calculus, with applied calculi obtained by adding constants. The further elaboration of the theory, covering conversion, reduction, theories and models, is laid out in Barendregt's already classical treatise [Bar84]. It is instructive to recall the following crux, which occurs rather early in that work (p. 39): Meaning of -terms: rst attempt The meaning of a -term is its normal form (if it exists). All terms without normal forms are identi ed. This proposal incorporates such a simple and natural interpretation of the -calculus as

### Citations

441 | Introduction to higher order categorical logic - Lambek, Scott - 1986 |

398 |
LCF considered as a programming language
- Plotkin
- 1977
(Show Context)
Citation Context ...emantics). The pure -calculus as ordinarily conceived is too schematic to qualify. A further indication of the same point is that studies such as Plotkin's \LCF Considered as a Programming Language&qu=-=ot; [Plo7-=-7] have not been carried over to the pure -calculus, for lack of any convincing way of doing do in the standard theory. This in turn impedes the development of a theory which integrates the -calculus ... |

341 | The mechanical evaluation of expressions - Landin - 1964 |

321 | Calculi for synchrony and asynchrony - Milner - 1983 |

229 | Domain theory in logical form
- Abramsky
- 1991
(Show Context)
Citation Context ... its \categorical" or \absolute" nature should lead us to suspect that we can use D to study the whole class of lts. The medium we will use for this purpose is a suitable domain logic in the=-= sense of [-=-Abr87b]. 17 5 A Domain Logic for Applicative Transition Systems Denition 5.1 The syntax of our domain logic L is dened by ::= t j ^sj ( !s) ? Denition 5.2 (Semantics of L) Given a quasi ats A, we de... |

172 | Elementary induction on abstract structures - Moschovakis - 1974 |

160 |
The lambda calculus, its syntax and semantics. North-Holland, revised edition
- Barendregt
- 1984
(Show Context)
Citation Context ..., with applied calculi obtained by adding constants. The further elaboration of the theory, covering conversion, reduction, theories and models, is laid out in Barendregt's already classical treatise =-=[Ba-=-r84]. It is instructive to recall the following crux, which occurs rather early in that work (p. 39): Meaning of -terms:srst attempt The meaning of a -term is its normal form (if it exists). All ter... |

146 |
a non-strict functional language with polymorphic types
- Turner, Miranda
- 1985
(Show Context)
Citation Context ...ommonly accepted foundation for functional programming; more precisely, for the lazy functional languages, which represent the mainstream of current functional programming practice. Examples: MIRANDA =-=[Tur85-=-], LML [Aug84], LISPKIT [Hen80], ORWELL [Wad85], PONDER [Fai85], TALE [BvL86]. But do these languages as dened and implemented actually evaluate terms to head normal form? To the best of my knowledge,... |

132 | A correspondence between ALGOL 60 and Churchâ€™s lambda-notation: Part I - Landin - 1965 |

130 | Lambda-calculus models of programming languages - Morris - 1968 |

120 |
A domain equation for bisimulation
- Abramsky
- 1991
(Show Context)
Citation Context ... canonical model; that Plotkin's ideas can be carried over to it in a very natural way; and that the theory we shall develop will run quite strikingly in parallel with our treatment of concurrency in =-=[Abr87a-=-]. The plan of the remainder of the paper is as follows. In the next section, we introduce the intuitions on which our theory is based, in the concrete setting of -terms. We then set up the axiomatic ... |

109 | Fully abstract models of typed lambda-calculi - Milner - 1977 |

108 | Recursive programming techniques - Burge - 1975 |

86 |
A compiler for lazy ML
- Augustsson
- 1984
(Show Context)
Citation Context ...ted foundation for functional programming; more precisely, for the lazy functional languages, which represent the mainstream of current functional programming practice. Examples: MIRANDA [Tur85], LML =-=[Aug84-=-], LISPKIT [Hen80], ORWELL [Wad85], PONDER [Fai85], TALE [BvL86]. But do these languages as dened and implemented actually evaluate terms to head normal form? To the best of my knowledge, not a single... |

75 |
Functional Programming: Application and Implementation
- Henderson
- 1980
(Show Context)
Citation Context ...r functional programming; more precisely, for the lazy functional languages, which represent the mainstream of current functional programming practice. Examples: MIRANDA [Tur85], LML [Aug84], LISPKIT =-=[Hen80-=-], ORWELL [Wad85], PONDER [Fai85], TALE [BvL86]. But do these languages as dened and implemented actually evaluate terms to head normal form? To the best of my knowledge, not a single one of them does... |

57 | Categories of partial maps - Robinson, Rosolini - 1988 |

43 |
Set-Theoretical Models of Lambda-calculus: Theories
- Longo
- 1983
(Show Context)
Citation Context ...verges under allsnite stages of evaluation for all arguments|the experimenter can always observe convergence (or \consume an innite -stream"). We can make some connections between the theory ` an=-=d [Lon-=-83], as pointed out to me by Chih-Hao Ong. Firstly, 2.7(ii) can be generalised to: The set of terms in 0 which are least in ` are exactly the PO 0 terms in the terminology of [Lon83]. Moreover, YK i... |

31 | The partial lambda calculus - Moggi - 1988 |

29 | Relating theories of the lambda-calculus - Scott - 1980 |

28 |
Lectures on predomains and partial functions. Notes for a course given at the Center for the Study of Language and Information
- Plotkin
- 1985
(Show Context)
Citation Context ...hould be is readily elicited from the denition of ats. The structure map ev : A * (A ! A) is partial; the standard approach to partial maps in domain theory (pace Plotkin's recent work on predomains [=-=Plo85]) is-=- to make them into total ones by sending undened arguments to a \bottom" element, i.e. changing the type of ev to A ! (A ! A)? : This suggests the domain equation D = (D ! D)? i.e. the denotation... |

16 | Continuity and E#ectivity in Topoi - Rosolini - 1986 |

8 |
Design and implementation of a simple typed language based on the lambda-calculus
- Fairbairn
- 1985
(Show Context)
Citation Context ...recisely, for the lazy functional languages, which represent the mainstream of current functional programming practice. Examples: MIRANDA [Tur85], LML [Aug84], LISPKIT [Hen80], ORWELL [Wad85], PONDER =-=[Fai85-=-], TALE [BvL86]. But do these languages as dened and implemented actually evaluate terms to head normal form? To the best of my knowledge, not a single one of them does so. Instead, they evaluate to w... |

7 |
An introduction to Orwell
- Wadler
- 1985
(Show Context)
Citation Context ...gramming; more precisely, for the lazy functional languages, which represent the mainstream of current functional programming practice. Examples: MIRANDA [Tur85], LML [Aug84], LISPKIT [Hen80], ORWELL =-=[Wad85-=-], PONDER [Fai85], TALE [BvL86]. But do these languages as dened and implemented actually evaluate terms to head normal form? To the best of my knowledge, not a single one of them does so. Instead, th... |

6 |
Functional programming and the language Tale
- Barendregt, Leeuwen
- 1985
(Show Context)
Citation Context ...the lazy functional languages, which represent the mainstream of current functional programming practice. Examples: MIRANDA [Tur85], LML [Aug84], LISPKIT [Hen80], ORWELL [Wad85], PONDER [Fai85], TALE =-=[BvL86-=-]. But do these languages as dened and implemented actually evaluate terms to head normal form? To the best of my knowledge, not a single one of them does so. Instead, they evaluate to weak head norma... |

4 |
Extended type structures and lambda models
- Coppo, Dezani-Ciancaglini, et al.
- 1984
(Show Context)
Citation Context ...= : The proof is again routine. Note the striking similarity of our program logic with type inference, in particular with the intersection type discipline and Extended Applicative Type Structures of [=-=CDHL-=-84]. The crucial dierence lies in the entailment relation , and in particular the fact that their axiom (in our notation) t (t ! t) ? is not a theorem in our logic; instead, we have the weaker ((!) ?... |

3 | revised edition - North-Holland - 1984 |

1 | Domain theory in logical form (extended abstract - Abramsky - 1987 |

1 | Jozef Koymans. Models of the lambda calculus - Peter - 1982 |

1 | Partial cartesian closed categories of eective objects - Moggi |

1 | Categories of partial morphisms and the lambda p -calculus - Moggi - 1986 |

1 | Domain theory in logical form. Submitted for publication - Abramsky - 1987 |

1 | Categories of partial morphisms and the lambdap-calculus - Moggi - 1986 |