Practical Programming with Substructural Types

481 Pages·2012·1.63 MB·English

by  Jesse A. Tov

Practical Programming with Substructural Types
A dissertation presented
by
Jesse A. Tov
to the Faculty of the Graduate School
of the College of Computer and Information Science
in partial fulfillment of the requirements for the degree of
Doctor of Philosophy
Northeastern University
Boston, Massachusetts
February, 2012

Abstract
Substructural logics remove from classical logic rules for reordering, duplica-
tion, or dropping of assumptions. Because propositions in such a logic may no
longer be freely copied or ignored, this suggests understanding propositions
in substructural logics as representing resources rather than truth. For
the programming language designer, substructural logics thus provide a
framework for considering type systems that can track the changing states of
logical and physical resources.
While several substructural type systems have been proposed and im-
plemented, many of these have targeted substructural types at a particular
purpose, rather than offering them as a general facility. The more general
substructural type systems have been theoretical in nature and too unwieldy
for practical use. This dissertation presents the design of a general purpose
language with substructural types, and discusses several language design
problems that had to be solved in order to make substructural types useful in
practice.
i

So design is a constant challenge to balance comfort with luxe, the
practical with the desirable.
—Donna Karan
iii

Acknowledgments
Thanks go first to my advisor, Riccardo Pucella, for his steady support and
guidance. His suggestions and criticism have improved this dissertation in
waystoonumeroustolist. Iamalsogratefultotherestofmythesiscommittee:
Mitchell Wand, from whom I learned to think like a semanticist; Matthew
Fluet, whose work prompted and shaped my own; and Matthias Felleisen,
whose example and high expectations are an inspiration.
I owe much gratitude to the faculty and the present and former students
at the Northeastern University College of Computer and Information Science,
who together create a collegial, intellectual environment that I am sad to
leave: Ahmed Abdelmeged, Jay Aslam, Dan Brown, Bryan Chadwick, Agnes
Chan, Stephen Chang, Will Clinger, Richard Cobbe, Ryan Culpepper, Christos
Dimoulas, Carl Eastlund, Felix Klock, Tony Garnock-Jones, Dave Herman,
Ian Johnson, Karl Lieberherr, Olin Shivers, Vincent St-Amour, Paul Stansifer,
Stevie Strickland, Asumu Takikawa, Sam Tobin-Hochstadt, Aaron Turon,
DavidVanHorn,andDimitrisVardoulakis. AlecHeller’sinsightsanddemands
for clarity have been especially valuable.
This journey began when Norman Ramsey first introduced me to the study
ofprogramminglanguagesasanacademicdiscipline,andforthatIamforever
grateful. I would also like to thank Henry Leitner, Radhika Nagpal, Margo
Seltzer, and Chris Thorpe, from whom I learned much about teaching; Chung-
chieh Shan, who first told me to listen to the types; and my colleagues at
FNMOC, Oleg Kiselyov and Andrew Pimlott.
Last but not in the least least, I would like to thank my family: Yaron,
Shoshanah, Sarah, Michael, Maryann, Lau, Evelyn, and my infinitely patient
wife, Elizabeth, without whom nothing is possible.
v
vi ACKNOWLEDGMENTS
This research was supported in part by AFOSR grant FA9550-09-1-0110.
Contents
Abstract i
Acknowledgments v
List of Figures xi
1 Practical Substructural Types 1
1.1 The Structure of This Dissertation . . . . . . . . . . . . . . . . 3
2 Background: Stateful Type Systems 5
2.1 Substructural Logics and λ Calculi . . . . . . . . . . . . . . . . 6
2.2 Typestate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.3 Region-Based Memory Management . . . . . . . . . . . . . . . 22
2.4 Session Types. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
3 Programming in Alms 39
3.1 Alms by Example . . . . . . . . . . . . . . . . . . . . . . . . . . 39
3.2 Syntax Matters . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
4 Expressiveness of Alms 59
4.1 Typestate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
4.2 Regions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
4.3 Session Types. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
4.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
5 A Model of Alms 97
vii
viii CONTENTS
5.1 Syntax and Semantics of aλ . . . . . . . . . . . . . . . . . . . 98
ms
5.2 Theoretical Results . . . . . . . . . . . . . . . . . . . . . . . . . 116
6 Implementation of Alms 123
6.1 Core Alms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
6.2 A Type Inference Algorithm . . . . . . . . . . . . . . . . . . . . 132
6.3 Solving Subtype Constraints. . . . . . . . . . . . . . . . . . . . 135
6.4 Solving Subqualifier Constraints . . . . . . . . . . . . . . . . . 146
7 Mixing Affine and Conventional Types 153
7.1 Related Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154
7.2 A Model of Affine Contracts . . . . . . . . . . . . . . . . . . . . 155
A
7.3 Type Soundness for F . . . . . . . . . . . . . . . . . . . . . . . 174
C
7.4 Implementing Affine Contracts . . . . . . . . . . . . . . . . . . 186
8 Substructural Types and Control 197
8.1 Related Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201
8.2 Syntax and Semantics of λURAL . . . . . . . . . . . . . . . . . . 203
8.3 Generic Control Effects in λURAL(C) . . . . . . . . . . . . . . . 211
8.4 The Generic Theory . . . . . . . . . . . . . . . . . . . . . . . . . 219
8.5 Example Control Effects . . . . . . . . . . . . . . . . . . . . . . 231
8.6 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242
9 Related Work and Design Rationale 245
9.1 Substructural Type Systems . . . . . . . . . . . . . . . . . . . . 245
9.2 The Spirit of ML . . . . . . . . . . . . . . . . . . . . . . . . . . . 250
9.3 From ILL to Alms . . . . . . . . . . . . . . . . . . . . . . . . . . 253
10 Conclusion 257
10.1 Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 257
10.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 258
A Proofs: A Model of Alms 263
A.1 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263
A.2 Principal Qualifiers . . . . . . . . . . . . . . . . . . . . . . . . . 268