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why chimera

为什么 chimera 这个项目是值得做的？

  • 因为 dependent type 与 logic programming 之间的关系。
  • 因为 constraint programming 我还没有探索过。

顶层不需要 compute 和 任意的 exp， 只需要 application 以及 method application。

code block 没必要支持空的 {}， 空的，和 { name } 留做 Record 的语法， 只有 { f(x) } 才是正常的 block 语法。

higher order relation

[higher order relation] We can support higher order relation by allowing a relation to take relations as arguments.

[array] Array(Number)(l1)

  • [maybe] use constraint to implement higher-order logic.
  • [maybe] when using relation as predicate, we should not overload Ap

forward chaining

a.k.a. bottom-up

  • Is Earley parser bottom-up? Can we do Earley parser using datalog?

play with forward chaining where we accumulate facts in some kind of database.

  • dialogue planning, dixon 2009
  • voting protocols, DeYoung 2011
  • operational semantic of PL, simmons 2012
  • modular robotics, goldstein 2012

datalog can be implemented using forward chaining

datalog stratification: https://en.wikipedia.org/wiki/Stratification_(mathematics)

tabling

lvars -- programming with fix points over lattices

If you implemented different things, and you find that you are using similar implementation techniques, maybe there are deep theoretical connections too.

search strategy

[complexity] analyze time complexity of our search strategy

[question] [complexity] how to analyze time complexity of relation automatically?

conflict directed clause learning

[maybe] [schedule control] control how pursue can return some extra information about how schedule the result solutions.

  • should only change schedule, but not remove goals.

propagator

[learn] about propagator and constraints

quotient

How to implement quotient in logic programming language?

https://en.wikipedia.org/wiki/Quotient_by_an_equivalence_relation

毕竟 equivalence relation 是 relation。

hypergraph based physics engine for game development

Physics has its beautiful application in physics engine of game development, is all about simulation.

Can we design a hypergraph based physics engine, where space itself is implemented by hypergraph, and dynamic is implemented by rewrite rules?

term rewriting

encode collatz rewrite in term rewrite

hypergraph rewriting

geometry of hypergraph.

from hypergraph to cell-complex via category theory.

encode collatz rewrite in hypergraph rewrite (to get a geometry)

use hypergraph rewriting to implement inet