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APLAS 2019
Sun 1 - Wed 4 December 2019 Bali, Indonesia
Mon 2 Dec 2019 16:00 - 16:30 at Bali Room - Semantics Chair(s): Atsushi Igarashi

We present new proofs—formalized in the Coq proof assistant—of the correspondence among call-by-need and (various definitions of) call-by-name evaluations of lambda-calculus with mutually recursive bindings.

For non-strict languages, the equivalence between the high-level specification (call-by-name) and the actual implementation (call-by-need) is of foundational interest. A particular milestone is Launchbury’s natural semantics of call-by-need evaluation and proof of its adequacy with respect to call-by-name denotational semantics, which are recently formalized in Isabelle/HOL by Breitner (2018). Equational theory by Ariola et al. is another well-known formalization of call-by-need. Mutual recursion is especially challenging for their theory: reduction is complicated by the traversal of dependency (the “need” relation), and the correpondnence of call-by-name and call-by-need reductions becomes non-trivial, requiring sophisticated structures such as graphs or infinite trees.

In this paper, we give arguably simpler proofs solely based on (finite) terms and natural semantics, which are easier to handle for proof assistants (Coq in our case). Our proofs can be summarized as follows: (1) we prove the equivalence between Launchbury’s call-by-need semantics and heap-based call-by-name natural semantics, where we define a sufficiently (but not too) general correspondence between the two heaps, and (2) we also show the correspondence among three styles of call-by-name semantics: (i) the natural semantics used in (1); (ii) closure-based natural semantics that informally corresponds to Launchbury’s denotational semantics; and (iii) conventional substitution-based semantics.

Mon 2 Dec
Times are displayed in time zone: (GMT+08:00) Beijing, Chongqing, Hong Kong, Urumqi change

15:30 - 17:00: Research Papers - Semantics at Bali Room
Chair(s): Atsushi IgarashiKyoto University, Japan
aplas-2019-papers15:30 - 16:00
Beniamino AccattoliInria & Ecole Polytechnique, Claudia FaggianIRIF, Giulio GuerrieriUniversity of Bath
aplas-2019-papers16:00 - 16:30
Masayuki MizunoTohoku University , Eijiro SumiiTohoku University
aplas-2019-papers16:30 - 17:00
Kosuke MurataKyushu Institute of Technology , Kento EmotoKyushu Institute of Technology