Note that, in the interaction net literature, it is pretty common to introduce graphical notation without corresponding textual counterparts. See the works of Lafont, Lamping, Asperti, Guerrini, and many others [1]. (However, the textual calculus can be absolutely crucial for formal proof.)
The absence of proofs and benchmarks undermines the paper for me as well. I find it absolutely critical to demonstrate how the approach works in comparison with already established software, such as BOHM [2].
Parallel beta reduction not being elementarily recursive is not a thing to address, nor a thing one can address. Lamping's abstract algorithm already performs the minimal amount of work to reduce a term -- one cannot improve it further.
From my understanding, the paper aims to optimize the bookkeeping overhead present in earlier implementations of optimal reduction. However, as I said, the absence of formal/empirical evidence of correctness and extensive benchmarks makes the contributions of the paper debatable.
Comments
Note that, in the interaction net literature, it is pretty common to introduce graphical notation without corresponding textual counterparts. See the works of Lafont, Lamping, Asperti, Guerrini, and many others [1]. (However, the textual calculus can be absolutely crucial for formal proof.)
The absence of proofs and benchmarks undermines the paper for me as well. I find it absolutely critical to demonstrate how the approach works in comparison with already established software, such as BOHM [2].
Parallel beta reduction not being elementarily recursive is not a thing to address, nor a thing one can address. Lamping's abstract algorithm already performs the minimal amount of work to reduce a term -- one cannot improve it further.
From my understanding, the paper aims to optimize the bookkeeping overhead present in earlier implementations of optimal reduction. However, as I said, the absence of formal/empirical evidence of correctness and extensive benchmarks makes the contributions of the paper debatable.
[1] https://github.com/etiamz/interaction-net-resources
[2] https://github.com/asperti/BOHM1.1