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Abstract: This paper considers some theoretical and practical issues concerning the use of linear logic as a logical foundation of functional programming languages such as Haskell and SML. First I give an operational theory for a linear PCF: the (typed) linear - calculus extended with booleans, conditional and non-termination. An operational semantics is given which corresponds in a precise way to the process of fi-reduction which originates from proof theory. Using this operational semantics I define... (Update)
Context of citations to this paper: More
.... The basic proof method is covered in great detail by Pitts in [Pit95] and [Pit94] another example of this technique may be seen in [Bie97]. Below, the major points of Pitts proof (which uses a method developed by Howe) are given for the functional operational semantics....
.... such as PCFL [26] a functional language with IO [11] the Object calculus of Abadi and Cardelli [1, 12] and the linear calculus [3, 7]. The papers [20, 22, 27] discuss when variants of the standard theories apply. A key step towards turning these theoretical...
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0.3: The λμ-calculus: Function and Control - Bierman (1998) (Correct)
0.1: Conservative Extensions of Polymorphic PCF - Akama (1996) (Correct)
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6: Bisimilarity as a theory of functional programming (context) - Gordon - 1995
5: Operationally-based theories of program equivalence - Pitts - 1995
5: Equality in lazy computation systems - Howe - 1989
BibTeX entry: (Update)
G.M. Bierman. Observations on a linear PCF. Technical Report 412, Computer Laboratory, University of Cambridge, January 1997. http://citeseer.ist.psu.edu/bierman97observations.html More
@techreport{ bierman97observations,
author = "G. M. Bierman",
title = "Observations on a linear {PCF}",
number = "412",
year = "1997",
url = "citeseer.ist.psu.edu/bierman97observations.html" }
Citations (may not include all citations):982 Theoretical Computer Science (context) - Girard - 1987
359 The Implementation of Functional Programming Languages (context) - Jones - 1987
144 Full abstraction for PCF - Abramsky, Jagadeesan et al. - 1994
112 Bisimilarity as a theory of functional programming (context) - Gordon - 1995
94 Equality in lazy computation systems - Howe - 1989
60 A term calculus for intuitionistic linear logic - Benton, Bierman et al. - 1993
48 Operationally-based theories of program equivalence - Pitts - 1995
47 Lilac: A functional programming language based on linear log.. (context) - Mackie - 1994
38 Traced monoidal categories (context) - Joyal, Street et al. - 1994
20 Type theory and recursion (context) - Plotkin - 1993
17 Some notes on inductive and co-inductive techniques in the s.. (context) - Pitts - 1994
16 monads and the lambda calculus (context) - Benton, Wadler - 1996
14 A fully abstract translation between a -calculus with refere.. (context) - Ritter, Pitts - 1995
13 Research Institute for Mathematical Sciences (context) - Hashimoto, Ohori et al. - 1996
8 call-by-need and the linear lambda calculus (context) - Maraist, Odersky et al. - 1995
4 The Girard translation extended with recursion - uner - 1995
2 A classical linear -calculus - Bierman - 1996
1 Available as BRICS Technical Report DS (context) - uner, Approach et al. - 1996
1 The untyped linear -calculus (context) - Bierman - 1996
Documents on the same site (http://sunsite.doc.ic.ac.uk/ic.doc/theory/guests/BiermanGM/): More
A Classical Linear λ-calculus - Bierman (1997) (Correct)
Term Assignment for Intuitionistic Linear Logic.. - Benton, Bierman, de.. (1992) (Correct)
Intuitionistic Necessity Revisited - Bierman, de Paiva (1996) (Correct)
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