Term rewriting systems provide a framework in which it is possible to specify and program in a traditional syntax (oriented equations). Interaction nets, on the other hand, provide a graphical syntax for the same purpose, but can be regarded as being closer to an implementation since the reduction process is local and asynchronous, and all the operations are made explicit, including discarding and copying of data. Our aim is to bridge the gap between the above formalisms by showing how to understand interaction nets in a term rewriting framework. This allows us to transfer results from one paradigm to the other, deriving syntactical properties of interaction nets from the (well-studied) properties of term rewriting systems; in particular concerning termination and modularity.
|
1483
|
The Definition of Standard ML
– Milner, Tofte, et al.
- 1990
|
|
731
|
Inductive-Data-Type Systems
– Blanqui, Jouannaud, et al.
- 2001
|
|
583
|
Term rewriting systems
– Klop
- 1992
|
|
418
|
Termination of rewriting
– Dershowitz
- 1987
|
|
317
|
The polyadic -Calculus: a tutorial
– Milner
- 1991
|
|
218
|
CML: A higher-order concurrent language
– Reppy
- 1991
|
|
150
|
Interaction nets
– Lafont
- 1990
|
|
93
|
The geometry of optimal lambda-reduction
– Gonthier, Abadi, et al.
- 1992
|
|
91
|
Natural termination
– Dershowitz, Hoot
- 1995
|
|
83
|
Term graph rewriting
– Barendregt, Eekelen, et al.
- 1987
|
|
76
|
Counterexamples to termination for the direct sum of term writing systems
– Toyama
- 1987
|
|
49
|
From proof-nets to interaction nets
– Lafont
- 1995
|
|
47
|
On termination of the direct sum of term rewriting systems
– Rusinowitch
- 1987
|
|
43
|
De Vries. Transfinite Reduction in Orthogonal Term Rewriting Systems
– Kennaway, Klop, et al.
- 1995
|
|
33
|
Completeness of combinations of constructor systems
– Middeldorp, Toyama
- 1991
|
|
29
|
Termination for the Direct Sum of Left-Linear Term Rewriting Systems
– Toyama, Klop, et al.
- 1989
|
|
27
|
Modular termination of term rewriting systems revisited
– Fern'andez, Jouannaud
- 1995
|
|
27
|
Geometry of interaction 1: Interpretation of system F
– Girard
- 1989
|
|
22
|
The Geometry of Implementation
– Mackie
- 1994
|
|
20
|
Combinatory Reduction Systems, volume 127 of Mathematical Centre Tracts. CWI
– Klop
- 1980
|
|
20
|
Combinatory representation of mobile processes
– Honda, Yoshida
- 1994
|
|
18
|
Optimality and Concurrency in Interaction Systems
– Laneve
- 1993
|
|
18
|
The geometry of interaction machine
– Mackie
- 1995
|
|
15
|
Strong Normalization of Typeable Rewrite Systems
– Bakel, Fernandez
- 1994
|
|
15
|
Completeness of hierarchical combinations of term rewriting systems
– Rao
- 1993
|
|
14
|
Rewrite Proofs and Computations
– Jouannaud
- 1995
|
|
14
|
De Vries. On the adequacy of graph rewriting for simulating term rewriting
– Kennaway, Klop, et al.
- 1994
|
|
10
|
Combinators for interaction nets
– Gay
- 1995
|
|
9
|
The Algebraic Theory of Interaction Nets
– Banach
- 1995
|
|
9
|
Implementing term rewrite languages
– Kennaway
- 1990
|
|
7
|
Type Assignment and Termination of Interaction Nets
– Fern'andez
- 1998
|
|
6
|
From term rewriting to generalised interaction nets
– Fern'andez, Mackie
- 1996
|
|
5
|
Modularity in noncopying term rewriting
– Kurihara, Ohuchi
- 1995
|
|
5
|
A -evaluator based on interaction nets
– Mackie
- 1995
|
|
4
|
Non-copying term rewriting and modularity of termination
– Kurihara, Ohuchi
|
|
4
|
A refinement of strong sequentiality for term rewriting systems with constructors
– Thatte
- 1987
|
|
3
|
Action calculi II: ��-nets with boxes and replication
– Milner
- 1993
|
|
2
|
Interaction nets and term rewriting systems (extended abstract
– Fern'andez, Mackie
- 1996
|
|
2
|
editors. Theory and Formal Methods of Computing 94
– Hankin, Mackie, et al.
- 1995
|
|
