Crumbling Abstract Machines

Beniamino Accattoli (1, 2) , Andrea Condoluci (3) , Giulio Guerrieri (4) , Claudio Sacerdoti Coen (5)

1 PARSIFAL - Proof search and reasoning with logic specifications
2 PARTOUT - Automatisation et ReprésenTation: fOndation du calcUl et de la déducTion
3 DISI - Dipartimento di Informatica - Scienza e Ingegneria [Bologna]
4 Department of Computer Science [Bath]
5 DISI - Department of Computer Science and Engineering [Bologna]

Extending the λ-calculus with a construct for sharing, such as let expressions, enables a special representation of terms: iterated applications are decomposed by introducing sharing points in between any two of them, reducing to the case where applications have only values as immediate subterms. This work studies how such a crumbled representation of terms impacts on the design and the efficiency of abstract machines for call-by-value evaluation. About the design, it removes the need for data structures encoding the evaluation context, such as the applicative stack and the dump, that get encoded in the environment. About efficiency, we show that there is no slowdown, clarifying in particular a point raised by Kennedy, about the potential inefficiency of such a representation. Moreover, we prove that everything smoothly scales up to the delicate case of open terms, needed to implement proof assistants. Along the way, we also point out that continuation-passing style transformations-that may be alternatives to our representation-do not scale up to the open case.

Mots clés: Abstract machine; Complexity; Explicit substitution; Lambda-calculus

Domaines: Logique en informatique [cs.LO]

Beniamino Accattoli, Andrea Condoluci, Giulio Guerrieri, Claudio Sacerdoti Coen. Crumbling Abstract Machines. PPDP 2019 - 21st International Symposium on Principles and Practice of Programming Languages, Oct 2019, Porto, Portugal. ⟨10.1145/3354166.3354169⟩. ⟨hal-02415766⟩