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# Finite Set API Examples
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This document provides usage examples for the finite set API in Java and C#.
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## Java Example
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```java
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import com.microsoft.z3.*;
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public class FiniteSetExample {
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public static void main(String[] args) {
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try (Context ctx = new Context()) {
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// Create finite set sort over integers
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Sort intSort = ctx.getIntSort();
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FiniteSetSort intSetSort = ctx.mkFiniteSetSort(intSort);
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// Check if it's a finite set sort
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boolean isFiniteSet = ctx.isFiniteSetSort(intSetSort);
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System.out.println("Is finite set sort: " + isFiniteSet);
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// Get the element sort (basis)
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Sort basis = ctx.getFiniteSetSortBasis(intSetSort);
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System.out.println("Element sort: " + basis);
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// Create sets
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Expr emptySet = ctx.mkFiniteSetEmpty(intSetSort);
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IntExpr one = ctx.mkInt(1);
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IntExpr two = ctx.mkInt(2);
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Expr singleton1 = ctx.mkFiniteSetSingleton(one);
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Expr singleton2 = ctx.mkFiniteSetSingleton(two);
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// Set operations
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Expr union = ctx.mkFiniteSetUnion(singleton1, singleton2);
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Expr intersect = ctx.mkFiniteSetIntersect(union, singleton1);
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Expr difference = ctx.mkFiniteSetDifference(union, singleton1);
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// Set queries
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BoolExpr member = ctx.mkFiniteSetMember(one, union);
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Expr size = ctx.mkFiniteSetSize(union);
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BoolExpr subset = ctx.mkFiniteSetSubset(singleton1, union);
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// Create integer range [1..10]
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Expr range = ctx.mkFiniteSetRange(ctx.mkInt(1), ctx.mkInt(10));
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// Solve with finite sets
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Solver solver = ctx.mkSolver();
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solver.add(ctx.mkFiniteSetMember(one, union));
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solver.add(ctx.mkEq(ctx.mkFiniteSetSize(union), ctx.mkInt(2)));
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Status status = solver.check();
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System.out.println("Solver result: " + status);
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}
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}
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}
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```
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## C# Example
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```csharp
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using System;
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using Microsoft.Z3;
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class FiniteSetExample
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{
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static void Main(string[] args)
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{
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using (Context ctx = new Context())
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{
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// Create finite set sort over integers
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Sort intSort = ctx.IntSort;
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FiniteSetSort intSetSort = ctx.MkFiniteSetSort(intSort);
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// Check if it's a finite set sort
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bool isFiniteSet = ctx.IsFiniteSetSort(intSetSort);
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Console.WriteLine($"Is finite set sort: {isFiniteSet}");
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// Get the element sort (basis)
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Sort basis = ctx.GetFiniteSetSortBasis(intSetSort);
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// Or use the property:
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Sort basis2 = intSetSort.Basis;
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Console.WriteLine($"Element sort: {basis}");
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// Create sets
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Expr emptySet = ctx.MkFiniteSetEmpty(intSetSort);
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IntExpr one = ctx.MkInt(1);
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IntExpr two = ctx.MkInt(2);
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Expr singleton1 = ctx.MkFiniteSetSingleton(one);
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Expr singleton2 = ctx.MkFiniteSetSingleton(two);
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// Set operations
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Expr union = ctx.MkFiniteSetUnion(singleton1, singleton2);
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Expr intersect = ctx.MkFiniteSetIntersect(union, singleton1);
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Expr difference = ctx.MkFiniteSetDifference(union, singleton1);
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// Set queries
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BoolExpr member = ctx.MkFiniteSetMember(one, union);
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Expr size = ctx.MkFiniteSetSize(union);
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BoolExpr subset = ctx.MkFiniteSetSubset(singleton1, union);
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// Create integer range [1..10]
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Expr range = ctx.MkFiniteSetRange(ctx.MkInt(1), ctx.MkInt(10));
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// Solve with finite sets
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Solver solver = ctx.MkSolver();
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solver.Add(ctx.MkFiniteSetMember(one, union));
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solver.Add(ctx.MkEq(ctx.MkFiniteSetSize(union), ctx.MkInt(2)));
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Status status = solver.Check();
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Console.WriteLine($"Solver result: {status}");
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}
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}
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}
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```
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## API Methods
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### Sort Operations
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- **Java**: `mkFiniteSetSort(Sort elemSort)`, `isFiniteSetSort(Sort s)`, `getFiniteSetSortBasis(Sort s)`
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- **C#**: `MkFiniteSetSort(Sort elemSort)`, `IsFiniteSetSort(Sort s)`, `GetFiniteSetSortBasis(Sort s)`
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### Set Constructors
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- **Java**: `mkFiniteSetEmpty(Sort setSort)`, `mkFiniteSetSingleton(Expr elem)`, `mkFiniteSetRange(Expr low, Expr high)`
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- **C#**: `MkFiniteSetEmpty(Sort setSort)`, `MkFiniteSetSingleton(Expr elem)`, `MkFiniteSetRange(Expr low, Expr high)`
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### Set Operations
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- **Java**: `mkFiniteSetUnion(Expr s1, Expr s2)`, `mkFiniteSetIntersect(Expr s1, Expr s2)`, `mkFiniteSetDifference(Expr s1, Expr s2)`
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- **C#**: `MkFiniteSetUnion(Expr s1, Expr s2)`, `MkFiniteSetIntersect(Expr s1, Expr s2)`, `MkFiniteSetDifference(Expr s1, Expr s2)`
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### Set Queries
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- **Java**: `mkFiniteSetMember(Expr elem, Expr set)`, `mkFiniteSetSize(Expr set)`, `mkFiniteSetSubset(Expr s1, Expr s2)`
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- **C#**: `MkFiniteSetMember(Expr elem, Expr set)`, `MkFiniteSetSize(Expr set)`, `MkFiniteSetSubset(Expr s1, Expr s2)`
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### Set Transformations
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- **Java**: `mkFiniteSetMap(Expr f, Expr set)`, `mkFiniteSetFilter(Expr f, Expr set)`
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- **C#**: `MkFiniteSetMap(Expr f, Expr set)`, `MkFiniteSetFilter(Expr f, Expr set)`
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## Notes
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- Finite sets are distinct from array-based sets and provide a more direct representation
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- The finite set sort extends `Sort` directly (not `ArraySort`)
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- All operations follow the SMT-LIB2 finite set theory syntax
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- Native bindings are auto-generated from the C API during build
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