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Hassan Abedi 2026-03-20 11:05:58 +01:00
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README2.md
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@ -210,27 +210,38 @@ cargo run -- --help
// Define a preorder theory // Define a preorder theory
theory Preorder { theory Preorder {
X : Sort; X : Sort;
leq : [a: X, b: X] -> Prop;
// Reflexivity // The ordering relation: x <= y
forall x : X. |- [a: x, b: x] leq; leq : [x: X, y: X] -> Prop;
// Transitivity // Reflexivity: x <= x
forall x : X, y : X, z : X. ax/refl : forall x : X.
[a: x, b: y] leq, [a: y, b: z] leq |- [a: x, b: z] leq; |- [x: x, y: x] leq;
// Transitivity: x <= y and y <= z implies x <= z
ax/trans : forall x : X, y : X, z : X.
[x: x, y: y] leq, [x: y, y: z] leq |- [x: x, y: z] leq;
} }
// Define an instance // Define an instance with automatic chase
instance Chain3 : Preorder = { // The 'chase' keyword applies axioms to compute the closure
instance Chain3 : Preorder = chase {
bot : X; bot : X;
mid : X; mid : X;
top : X; top : X;
[a: bot, b: mid] leq;
[a: mid, b: top] leq; // Assert the basic ordering; chase derives reflexive pairs
// and transitive closure (bot <= top)
[x: bot, y: mid] leq;
[x: mid, y: top] leq;
} }
``` ```
Then run `:chase Chain3` to compute the transitive closure. After loading this file, the chase algorithm automatically computes:
- Reflexive pairs: `bot <= bot`, `mid <= mid`, `top <= top`
- Transitive closure: `bot <= top`
You can also define an instance without `chase` and run `:chase Chain3` manually.
## Development ## Development