Yes, multiplying graph adjacency matrices over a min-tropical semiring produces shortest paths. APL supports this syntactically, but how does it function in the real world? What if the matrices are extremely sparse, like almost all real world graphs are? Syntax is the easy the problem. The hard problem is having very sparse graphs with billions of nodes and many billions of edges. How is a square matrix going to deal with that? Sparse and hypersparse graph computing is hard, which is not syntactically relevant.
Python does not have this terse a syntax, but it gets very close with multiple bindings to the SuiteSparse GraphBLAS Hypersparse graph processing libraries, which intrinsically supports sparse graphs and a very large number of operators, including the tropical min/max ones. Suitesparse doesn't provide syntax (that's the easy part), it provides the hard part, sparse and hypersparse data structures and very complex dynamic, parallel graph processing optimizations including JIT compilation of GPU accelerated operations.
Here's a notebook that shows your shortest path example using Python and the GraphBLAS. While it's a trivial example, it can scale the the largest graphs possible to use today using SuiteSparse:
NB: I should clarify I'm not advocating for Python's syntax in particular vs APL, I'm saying that syntax is not the hard part of any particular problem, especially when it comes to sparse graphs. There are also other binding to GraphBLAS like Julia that are quite nice. I do appreciate that APL does elgantly permit the notion of graph operations with linear algebra.
Python does not have this terse a syntax, but it gets very close with multiple bindings to the SuiteSparse GraphBLAS Hypersparse graph processing libraries, which intrinsically supports sparse graphs and a very large number of operators, including the tropical min/max ones. Suitesparse doesn't provide syntax (that's the easy part), it provides the hard part, sparse and hypersparse data structures and very complex dynamic, parallel graph processing optimizations including JIT compilation of GPU accelerated operations.
Here's a notebook that shows your shortest path example using Python and the GraphBLAS. While it's a trivial example, it can scale the the largest graphs possible to use today using SuiteSparse:
https://github.com/Graphegon/pygraphblas/blob/main/demo/Intr...
NB: I should clarify I'm not advocating for Python's syntax in particular vs APL, I'm saying that syntax is not the hard part of any particular problem, especially when it comes to sparse graphs. There are also other binding to GraphBLAS like Julia that are quite nice. I do appreciate that APL does elgantly permit the notion of graph operations with linear algebra.