https://github.com/endjin/z3.linq
LINQ bindings for the Z3 theorem prover from Microsoft Research.
https://github.com/endjin/z3.linq
dotnet linq z3
Last synced: 9 months ago
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LINQ bindings for the Z3 theorem prover from Microsoft Research.
- Host: GitHub
- URL: https://github.com/endjin/z3.linq
- Owner: endjin
- License: mit
- Created: 2021-11-23T11:49:44.000Z (over 4 years ago)
- Default Branch: main
- Last Pushed: 2025-07-23T02:51:08.000Z (11 months ago)
- Last Synced: 2025-10-02T04:54:55.815Z (9 months ago)
- Topics: dotnet, linq, z3
- Language: C#
- Homepage:
- Size: 479 KB
- Stars: 39
- Watchers: 11
- Forks: 3
- Open Issues: 9
-
Metadata Files:
- Readme: README.md
- License: LICENSE
Awesome Lists containing this project
README
# Z3.Linq
.NET 8.0 LINQ bindings for the [Z3 theorem prover](https://github.com/Z3Prover/z3) from [Microsoft Research](https://www.microsoft.com/en-us/research/).
Based on the proof of concept by [Bart De Smet](https://github.com/bartdesmet) which was curated into [Z3.LinqBinding](https://github.com/RicardoNiepel/Z3.LinqBinding) by [Ricardo Niepel](https://github.com/RicardoNiepel).
## Examples
A number of examples are included in this solution, which you can run [from .NET Interactive](examples/z3-problems.dib) (requires [Visual Studio Code](https://code.visualstudio.com/)) or [from Visual Studio](solutions/Z3.Linq.Demo/Program.cs).
### Problem - 1st Order Propositional Logic
Provide a solution where either X is true or Y is true, but not both (using a [ValueTuple](https://docs.microsoft.com/en-us/dotnet/api/system.valuetuple?view=net-6.0)).
```csharp
using (var ctx = new Z3Context())
{
var theorem = from t in ctx.NewTheorem<(bool x, bool y)>()
where t.x ^ t.y
select t;
var result = theorem.Solve();
Console.WriteLine(result);
}
```
### Problem - Linear Algebra
Solve the following system with 3 variables, with linear equalities and inequalities:
$$
x_1 - x_2 \ge 1
\\
x_1 - x_2 \le 3
\\
x_1 = 2x_3 + x_2
$$
```csharp
using (var ctx = new Z3Context())
{
var theorem = from t in ctx.NewTheorem>()
where t.X1 - t.X2 >= 1
where t.X1 - t.X2 <= 3
where t.X1 == (2 * t.X3) + t.X2
select t;
var result = theorem.Solve();
Console.WriteLine(result);
}
```
### Problem - Price Optimised Oil Purchasing
In this example, we have two countries that produce crude oil which we refine into three end-products: gasoline, jet fuel, and lubricant. The crude oil from each country yields different quantities of end-products once the oil is refined:
| | Saudi Arabia | Venezuela |
|--- | --- | --- |
| Cost | $20 / barrel | $15 / barrel |
| Max Order | 9000 barrels | 6000 barrels |
| Refining % | 30% gasolene | 40% gasolene |
| | 40% jet fuel | 20% jet fuel |
| | 20% lubricant | 30% lubricant |
| | 10% waste | 10% waste |
Given we need to produce the following volume of refined end-product:
| Product | Amount (barrels) |
| --- | --- |
| Gasolene | 1900 |
| Jet Fuel | 1500 |
| Lubricant | 500 |
What is the most cost efficient purchase strategy of crude oil from Saudi Arabia and Venezuela?
```csharp
using (var ctx = new Z3Context())
{
var theorem = from t in ctx.NewTheorem<(double sa, double vz)>()
where 0.3 * t.sa + 0.4 * t.vz >= 1900 // Gasolene
where 0.4 * t.sa + 0.2 * t.vz >= 1500 // Jet fuel
where 0.2 * t.sa + 0.3 * t.vz >= 500 // Lubricant
where 0 <= t.sa && t.sa <= 9000 // Max # barrels we can purchase
where 0 <= t.vz && t.vz <= 6000 // Max # barrels we can purchase
orderby (20.0 * t.sa) + (15.0 * t.vz) // Optimize for cost
select t;
var result = theorem.Solve();
Console.WriteLine($"SA: {result.sa} barrels (${result.sa * 20}), VZ: {result.vz} barrels (${result.vz * 15})");
}
```
### Problem - Minimizing Shipping Costs
In this example, you want to minimize the cost of shipping goods from 2 different warehouses to 4 different customers. Each warehouse has a limited supply and each customer has a certain demand.
Cost of shipping ($ per product):
| | Customer 1 | Customer 2 | Customer 3 | Customer 4 |
|-------------|------------|------------|------------|------------|
| Warehouse 1 | $1.00 | $3.00 | $0.50 | $4.00 |
| Warehouse 2 | $2.50 | $5.00 | $1.50 | $2.50 |
Number of products shipped:
| | Customer 1 | Customer 2 | Customer 3 | Customer 4 | Total shipped | | Available |
|---------------------|------------|-------------|------------|------------|---------------|----|-----------|
| Warehouse 1 | 0 | 13,000 | 15,000 | 32,000 | 60,000 | <= | 60,000 |
| Warehouse 2 | 30,000 | 10,000 | 0 | 0 | 40,000 | <= | 80,000 |
| Total received | 30,000 | 23,000 | 15,000 | 32,000 | | | |
| Ordered | 35,000 | 22,000 | 18,000 | 30,000 | | | |
| Total Shipping Cost | | $299,500.00 | | | | | |
1. The objective is to minimize the cost (Total Shipping Cost).
2. The variables are the number of products to ship from each warehouse to each customer.
3. The constraints are the number of products ordered and the number of products available in each warehouse.
```csharp
using (var ctx = new Z3Context())
{
var theorem =
from t in ctx.NewTheorem<(double w1c1, double w1c2, double w1c3, double w1c4, double w2c1, double w2c2, double w2c3, double w2c4)>()
where t.w1c1 + t.w1c2 + t.w1c3 + t.w1c4 <= 60_000 // Warehouse 1 Product Availability
where t.w2c1 + t.w2c2 + t.w2c3 + t.w2c4 <= 80_000 // Warehouse 2 Product Availability
where t.w1c1 + t.w2c1 == 35_000 && (t.w1c1 >= 0 && t.w2c1 >= 0) // Customer 1 Orders
where t.w1c2 + t.w2c2 == 22_000 && (t.w1c2 >= 0 && t.w2c2 >= 0) // Customer 2 Orders
where t.w1c3 + t.w2c3 == 18_000 && (t.w1c3 >= 0 && t.w2c3 >= 0) // Customer 3 Orders
where t.w1c4 + t.w2c4 == 30_000 && (t.w1c4 >= 0 && t.w2c4 >= 0) // Customer 4 Orders
orderby (1.00 * t.w1c1) + (3.00 * t.w1c2) + (0.50 * t.w1c3) + (4.00 * t.w1c4) +
(2.50 * t.w2c1) + (5.00 * t.w2c2) + (1.50 * t.w2c3) + (2.50 * t.w2c4) // Optimize for Total Shipping Cost
select t;
var result = theorem.Solve();
Console.WriteLine($"| | Customer 1 | Customer 2 | Customer 3 | Customer 4 |");
Console.WriteLine($"|---------------------|------------|-------------|------------|------------|");
Console.WriteLine($"| Warehouse 1 | {result.w1c1} | {result.w1c2} | {result.w1c3} | {result.w1c4} |");
Console.WriteLine($"| Warehouse 2 | {result.w2c1} | {result.w2c2} | {result.w2c3} | {result.w2c4} |");
Console.WriteLine();
Console.WriteLine(string.Create(CultureInfo.CreateSpecificCulture("en-US"), $"Total Cost: {1.00 * result.w1c1 + 3.00 * result.w1c2 + 0.50 * result.w1c3 + 4.00 * result.w1c4 + 2.50 * result.w2c1 + 5.00 * result.w2c2 + 1.50 * result.w2c3 + 2.50 * result.w2c4:C}"));
}
```
## Getting Started
You can install the [Z3.Linq NuGet Package](https://www.nuget.org/packages/Z3.Linq/).
### For Polyglot Notebooks
Add the package:
```
#r "nuget:Z3.Linq"
```
Then add the following using statements:
```csharp
using System;
using Z3.Linq;
```
Then you can copy any of the above samples.
### For Visual Studio
Add the `Z3.Linq` package.
Configure your application to [target x64 platform](https://docs.microsoft.com/en-us/visualstudio/ide/how-to-configure-projects-to-target-platforms?view=vs-2022). This is a requirement as `Z3.Linq` uses the [Microsoft.Z3](https://www.nuget.org/packages/Microsoft.Z3/) package.
## Contributing
There are a number of ways in which you could contribute to this project:
- Create new examples!
- Improve the documentation.
- Report / fix bugs.
- Suggest any implementation improvements or optimizations.
- Blog about the project!
All PRs are welcome.
## History
2009: [Bart De Smet](https://github.com/bartdesmet) describes a prototype LINQ to Z3 binding in three blog posts:
* [LINQ to Z3 - Part 1 – Exploring The Z3 Theorem Prover](docs/blogs/part-01-exploring-the-z3-theorem-prover.md)
* [LINQ to Z3 - Part 2 – LINQ to the Unexpected](docs/blogs/part-02-linq-to-the-unexpected.md)
* [LINQ to Z3 - Part 3 – Theorem Solving On Steroids](docs/blogs/part-03-theorem-solving-on-steroids.md)
2010: Bart was [interviewed on Channel 9](https://vimeo.com/648767290) about the LINQ to Z3 concept:
[](https://vimeo.com/648767290)
2012: Bart presented [LINQ to Everything](https://vimeo.com/648776168) at TechEd Europe 2012:
[](https://vimeo.com/648776168)
2015: Z3 was open sourced under the MIT license and the [source code was moved to GitHub](https://github.com/Z3Prover/z3), where it is actively maintained.
2015: [Ricardo Niepel](https://github.com/RicardoNiepel) (Microsoft) publishes the sample as [Z3.LinqBinding](https://github.com/RicardoNiepel/Z3.LinqBinding) using `.NET 4.5` and Z3 binaries `4.4.0`
2018: [Jean-Sylvain Boige](https://github.com/jsboige) ([My Intelligence Agency](https://github.com/MyIntelligenceAgency)) adds [Missionaries And Cannibals sample](https://github.com/MyIntelligenceAgency/Z3.LinqBinding).
2020: [Karel Frajtak](https://github.com/kfrajtak) adds [support for fractions](https://github.com/kfrajtak/Z3.LinqBinding).
2021: [Howard van Rooijen](https://github.com/HowardvanRooijen) and [Ian Griffiths](https://github.com/idg10) ([endjin](https://github.com/endjin)) upgrade the project to `.NET 6.0`, added `Optimize` support via LINQ's `OrderBy`, [ValueTuple](https://docs.microsoft.com/en-us/dotnet/api/system.valuetuple?view=net-6.0) support, demonstrate using `record` types, and fix nullability issues. They upgraded the solution to use [Z3 NuGet package](https://www.nuget.org/packages/Microsoft.Z3.x64/), merged in features from [Jean-Sylvain Boige](https://github.com/jsboige) and [Karel Frajtak](https://github.com/kfrajtak) forks, created archives of Bart's original blog posts and talks. They republished the project as [Z3.Linq](https://github.com/endjin/Z3.Linq), created a new [Polyglot Notebook](https://github.com/dotnet/interactive) of [samples](examples/z3-problems.dib), and published a NuGet package [Z3.Linq](https://www.nuget.org/packages/Z3.Linq/).
2023: [Whit Waldo](https://github.com/WhitWaldo) upgrades the project to `.NET 8.0`
## Project Sponsor
This project is sponsored by [endjin](https://endjin.com), a UK based Technology Consultancy which specializes in Data, AI, DevOps & Cloud, and is a [.NET Foundation Corporate Sponsor](https://dotnetfoundation.org/membership/corporate-sponsorship).
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## Code of conduct
This project has adopted a code of conduct adapted from the [Contributor Covenant](http://contributor-covenant.org/) to clarify expected behavior in our community. This code of conduct has been [adopted by many other projects](http://contributor-covenant.org/adopters/). For more information see the [Code of Conduct FAQ](https://opensource.microsoft.com/codeofconduct/faq/) or contact [hello@endjin.com](mailto:hello@endjin.com) with any additional questions or comments.
## IP Maturity Model (IMM)
The [IP Maturity Model](https://github.com/endjin/Endjin.Ip.Maturity.Matrix) is endjin's IP quality assessment framework, which we've developed over a number of years when doing due diligence assessments of 3rd party systems. We've codified the approach into a [configurable set of rules](https://github.com/endjin/Endjin.Ip.Maturity.Matrix.RuleDefinitions), which are committed into the [root of a repo](imm.yaml), and a [Azure Function HttpTrigger](https://github.com/endjin/Endjin.Ip.Maturity.Matrix/tree/main/Solutions/Endjin.Ip.Maturity.Matrix.Host) HTTP endpoint which can evaluate the ruleset, and render an svg badge for display in repo's `readme.md`.
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