philzook58

(*
ocamlfind ocamlc -package bap -package core_kernel -linkpkg -linkall baptest.ml 
js_of_ocaml +dynlink.js +toplevel.js +zarith_stubs_js/runtime.js +zarith_stubs_js/biginteger.js \
  +base/base_internalhash_types/runtime.js +base/runtime.js +time_now/runtime.js +bin_prot/runtime.js \
  +ppx_expect/collector/runtime.js +base_bigstring/runtime.js +core_kernel/strftime.js +core_kernel/runtime.js \
  +bigstringaf/runtime.js --linkall --extern-fs --toplevel a.out
*)

open Core_kernel
open Bap.Std

philzook58

#include <stdlib.h>
#include <stdio.h>
#include <string.h>
#include <time.h>

#define FLAG_BUFFER 128
#define MAX_SYM_LEN 4

typedef struct Stonks {
	int shares;

philzook58

import operator
from z3 import *

def lift(z3assert):
    def res(s):
        s.push()
        s.add(z3assert)
        if s.is_good():
            yield
        s.pop()

philzook58

(*|
A data structure that I've been more and more interested in recently is the disjoint set datastructure or union-find.
https://en.wikipedia.org/wiki/Disjoint-set_data_structure It's used in egraphs, unification, prolog, and graph connectivity.

I realized a cute representation that is easy to use and prover stuff about, although very inefficient compared to the usual version of disjoint set. It uses a simple functional representation based off the observation that the preimages of a function form disjoint sets. This representation is somewhat analogous to using functions to represent Maps in Coq like in Software Foundations. https://softwarefoundations.cis.upenn.edu/lf-current/Maps.html

The nice thing about this is that it really avoids any termination stickiness. Termination of the `find_root` operation of a union find in an explicit array or tree is not at all obvious and requires side proof or a refined type.
The termination ultimately comes from the fact that you used a finite number of unions to cons

philzook58

struct IntDisjointMap
    parents::Vector{Int64}
    values::Vector{Any}
    merge_fun
end

IntDisjointMap(merge_fun) = IntDisjointMap(Vector{Int64}[], [], merge_fun)

Base.length(x::IntDisjointMap) = length(x.parents)

philzook58

use egg::{*, rewrite as rw};
use wasm_bindgen::prelude::*;
use std::time::Duration;

define_language! {
    enum CatLanguage {
        // string variant with no children
        "id" = IdMorph(Id),
        "om" = OTimesM([Id; 2]),
        "oo" = OTimesO([Id; 2]),

philzook58

This is a simple script to convert Metatheory.jl https://github.com/0x0f0f0f/Metatheory.jl theories into an Egg https://egraphs-good.github.io/ query for comparison.

Get a rust toolchain https://rustup.rs/

Make a new project

cargo new my_project
cd my_project

philzook58

using Pkg
Pkg.activate("metatheory")
Pkg.add(url="https://github.com/0x0f0f0f/Metatheory.jl.git")
using Metatheory
using Metatheory.EGraphs

cat_theory = @theory begin
	hom(hom(f, ob(a), ob(b)) ⋅ hom(id(ob(b)), ob(b), ob(b)), ob(a), ob(b)) == hom(f, ob(a), ob(b))
	hom(hom(id(ob(a)), ob(a), ob(a)) ⋅ hom(f, ob(a), ob(b)), ob(a), ob(b)) == hom(f, ob(a), ob(b))
	hom(hom(f, ob(a), ob(b)) ⋅ hom(hom(g, ob(b), ob(c)) ⋅ hom(h, ob(c), ob(d)), ob(b), ob(d)), ob(a), ob(d)) == hom(hom(hom(f, ob(a), ob(b)) ⋅ hom(g, ob(b), ob(c)), ob(a), ob(c)) ⋅ hom(h, ob(c), ob(d)), ob(a), ob(d))

philzook58

(*|

I had a fun time giving a Z3 tutorial at Formal Methods for the Informal Engineer (FMIE) https://fmie2021.github.io/ (videos coming soon hopefully!). I got to be kind of the "fun dad" with the Z3 tutorial https://github.com/philzook58/z3_tutorial , while at times it felt a bit like Cody's Coq tutorial https://github.com/codyroux/broad-coq-tutorial was trying to feed the kids their vegetables. He knew it was going to be like this from the outset and had a fun little analogy of me downhill skiing while he was about to go on a cross country slog.

There are a number of factors to this. 
* I could use Z3's python bindings giving an air of familiarity, whereas everything was incredibly foreign in Coq.
* Z3 can actually be used to declaratively state problems and automatically calculate solutions to them with very little user help, which gives it a lot more "Wow" factor.
* Coq is a tool that requires significantly more background to even comprehend what the hell it is. I still think many aspects of it are tota

philzook58

% Follow paper exactly.  https://arxiv.org/abs/1804.02452 See Appendix A
% Difference from unison model.mzn: Try not using integers. Try to use better minizinc syntax. Much simplified

include "globals.mzn";

%% ---------------------------------------
%% PARAMETERS
%% ---------------------------------------

% Type definitions