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Abstract: This paper introduces a new higher-order typed constructive predicate logic for fixpoint computations, which exploits the categorical semantics of computations introduced by Moggi [8] and contains a strong version of Martin-Lof's `iteration type' [11]. The type system enforces a separation of computations from values. The logic contains a novel form of fixpoint induction and can express partial and total correctness statements about evaluation of computations to values. The constructive nature... (Update)
Context of citations to this paper: More
.... requirement that ensures this is the existence of a fixed point object, using definitions and reults due to Crole, Pitts and Mulry [3, 16]. The structure of the paper is as follows. Section 2 reviews some of the elementary properties of initial algebras, terminal coalgebras,...
.... (B Omega C) l R R TA T l T (A Omega B Omega C) These have been used by Moggi [30] and Crole and Pitts [8] to model computation types which represent lifting, non determinism, side effects, continuations, etc. If the monoidal category C is symmetric...
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Tail Recursion Through Universal Invariants - Barry Jay Lfcs (1993) (Correct)
Programming Metalogics with a Fixpoint Type - Crole (1992) (Correct)
Partial Computations in Constructive Type Theory - Smith (1991) (Correct)
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0.6: Evaluation Logic - Pitts (1990) (Correct)
0.1: Fixed Points and Extensionality in Typed Functional Programming.. - Howard (1992) (Correct)
0.1: On Fixpoint Objects and Gluing Constructions - Crole (1997) (Correct)
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0.2: A Sound Metalogical Semantics for Input/Output Effects - Crole, Gordon (1994) (Correct)
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6: Computational lambda-calculus and monads - Moggi - 1989
5: Introduction to Higher Order Categorical Logic (context) - Lambek, Scott - 1986
4: The category-theoretic solution of recursive domain equations (context) - Smyth, Plotkin - 1982
BibTeX entry: (Update)
R.L. Crole and A.M. Pitts. New foundations for fixpoint computations. In Fifth Annual IEEE Symposium on Logic in Computer Science, pages 489--497, 1990. http://citeseer.ist.psu.edu/crole90new.html More
@incollection{ crole90new,
author = "Roy L. Crole and Andrew M. Pitts",
title = "New Foundations for Fixpoint Computations",
booktitle = "Proceedings 5th Ann.\ {IEEE} Symp.\ on Logic in Computer Science, Philadelphia, {PA}, {USA}, 4--7 June 1990",
publisher = "IEEE Computer Society Press",
address = "Washington, DC",
pages = "489--497",
year = "1990",
url = "citeseer.ist.psu.edu/crole90new.html" }
Citations (may not include all citations):359 Introduction to Higher Order Categorical Logic (context) - Lambek, Scott - 1986
306 LCF considered as a programming language (context) - Plotkin - 1977
266 Information and Computation (context) - Coquand, Huet et al. - 1988
87 Notions of Computations and Monads - Moggi - 1989
65 Sequential Algorithms and Functional Programming (context) - Curien, Combinators - 1986
46 Oxford University Press (context) - Dummett, Intuitionism - 1977
43 Logic and Computation (context) - Paulson - 1987
33 Algebraic Specification of Data Types: A Synthetic Approach (context) - Lehmann, Smyth - 1981
24 Denotational semantics with partial functions (context) - Plotkin - 1985
15 A type-theoretic alternative to CUCH (context) - Scott - 1969
10 Cat'egories et Machines (context) - Lafont - 1988
2 th Annual Symposium on Logic in Computer Science (context) - Moggi, lambda-calculus et al. - 1989
1 translated and with appendices by P (context) - Girard, Types et al. - 1989
1 LFCS Technical Report (context) - Moggi, lambda-calculus - 1988
1 Martin-Lof 's Type Theory as a Programming Logic (context) - Nordstrom - 1986
1 Notes on the domain theoretic interpretation of type theory (context) - Martin-Lof - 1983
The graph only includes citing articles where the year of publication is known.
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On the Observable Properties of Higher Order Functions that.. - Pitts, Stark (1993) (Correct)
Existential Types: Logical Relations and Operational Equivalence - Pitts (1998) (Correct)
Categorical Logic - Pitts (2001) (Correct)
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