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| 1 | +/- Copyright 2026 The Fuchsia Authors |
| 2 | +
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| 3 | +Licensed under a BSD-style license <LICENSE-BSD>, Apache License, Version 2.0 |
| 4 | +<LICENSE-APACHE or https://www.apache.org/licenses/LICENSE-2.0>, or the MIT |
| 5 | +license <LICENSE-MIT or https://opensource.org/licenses/MIT>, at your option. |
| 6 | +This file may not be copied, modified, or distributed except according to |
| 7 | +those terms. -/ |
| 8 | + |
| 9 | +module |
| 10 | +public import ModelPrelude |
| 11 | +@[expose] public section |
| 12 | + |
| 13 | +/-! |
| 14 | +These kernel-checked examples explain Aeneas's native total and partial |
| 15 | +contracts independently of our spec macro. They pin successful results, tuple |
| 16 | +postconditions, panic rejection, and divergence behavior. The independently |
| 17 | +written theorem types prevent a change in syntax from silently changing the |
| 18 | +claim. Total contracts require successful execution even for a True |
| 19 | +postcondition. Partial contracts may diverge, but still reject panic. |
| 20 | +-/ |
| 21 | +open Aeneas Aeneas.Std AeneasSpecs |
| 22 | +namespace ContractTests |
| 23 | + |
| 24 | +-- Omitted requirements mean True; a successful result is still required. |
| 25 | +theorem identity_spec (x : Nat) : |
| 26 | + Result.ok x |
| 27 | + ⦃ ret => ret = x ⦄ := by |
| 28 | + exact WP.spec.ret rfl |
| 29 | + |
| 30 | +-- Named requirements are available without introductions in the proof body. |
| 31 | +theorem transitive_spec (x y z : Nat) |
| 32 | + (hxy : x = y) |
| 33 | + (hyz : y = z) : |
| 34 | + Result.ok x |
| 35 | + ⦃ ret => ret = z ⦄ := by |
| 36 | + exact WP.spec.ret (hxy.trans hyz) |
| 37 | + |
| 38 | +-- Reuse Aeneas's tuple-aware binders for returns and mutable post-states. |
| 39 | +theorem tuple_spec (x : Nat) : |
| 40 | + Result.ok (x, x + 1) |
| 41 | + ⦃ ret x' => ret = x ∧ x' = x + 1 ⦄ := by |
| 42 | + simp |
| 43 | + |
| 44 | +theorem diverging_spec : |
| 45 | + (Result.div : Result Nat) |
| 46 | + ⦃ _ => False ⦄div := by |
| 47 | + exact WP.dspec.div _ |
| 48 | + |
| 49 | +theorem partial_identity_spec (x : Nat) : |
| 50 | + Result.ok x |
| 51 | + ⦃ ret => ret = x ⦄div := by |
| 52 | + exact WP.dspec.ret rfl |
| 53 | + |
| 54 | +-- These independently written types pin the exported theorem types and outcomes. |
| 55 | +example : ∀ x : Nat, WP.spec (Result.ok x) (fun ret => ret = x) := identity_spec |
| 56 | +example : ∀ x y z : Nat, x = y → y = z → |
| 57 | + WP.spec (Result.ok x) (fun ret => ret = z) := transitive_spec |
| 58 | +example : ∀ x : Nat, WP.spec (Result.ok (x, x + 1)) |
| 59 | + (fun (ret, x') => ret = x ∧ x' = x + 1) := tuple_spec |
| 60 | +example : WP.dspec (Result.div : Result Nat) (fun _ => False) := diverging_spec |
| 61 | +example : ∀ x : Nat, WP.dspec (Result.ok x) (fun ret => ret = x) := partial_identity_spec |
| 62 | + |
| 63 | +theorem panic_rejected : |
| 64 | + ¬ WP.spec (Result.fail Error.panic : Result Nat) (fun _ => True) := by simp |
| 65 | + |
| 66 | +theorem divergence_rejected : |
| 67 | + ¬ WP.spec (Result.div : Result Nat) (fun _ => True) := by simp |
| 68 | + |
| 69 | +-- Partial correctness must reject panic and incorrect successful returns too. |
| 70 | +theorem partial_panic_rejected : |
| 71 | + ¬ WP.dspec (Result.fail Error.panic : Result Nat) (fun _ => True) := by simp |
| 72 | + |
| 73 | +theorem partial_wrong_return_rejected : |
| 74 | + ¬ WP.dspec (Result.ok 0) (fun ret : Nat => ret = 1) := by simp |
| 75 | + |
| 76 | +-- A generic identity shares one explicit dictionary and the same witness on |
| 77 | +-- input and output, even when the dictionary rejects some representations. |
| 78 | +theorem modeled_identity {Raw : Type} (provider : RustModel Raw) (raw : Raw) |
| 79 | + (value : provider.Model) (h : provider.decode raw = some value) : |
| 80 | + WP.spec (Result.ok raw) (fun out => |
| 81 | + ∃ decoded, provider.decode out = some decoded ∧ decoded = value) := |
| 82 | + WP.spec.ret ⟨value, h, rfl⟩ |
| 83 | + |
| 84 | +-- A dependent ghost retains its exact domain in mathematical input scope. |
| 85 | +theorem modeled_position {Raw : Type} (provider : RustModel Raw) |
| 86 | + (length : provider.Model → Nat) (raw : Raw) (value : provider.Model) |
| 87 | + (h : provider.decode raw = some value) (position : Fin (length value)) : |
| 88 | + WP.spec (Result.ok raw) (fun out => |
| 89 | + ∃ decoded, provider.decode out = some decoded ∧ position.val < length decoded) := |
| 90 | + WP.spec.ret ⟨value, h, position.isLt⟩ |
| 91 | + |
| 92 | +-- An accepted execution cannot return a decoder-rejected representation, even |
| 93 | +-- when its authored postcondition contributes no information. |
| 94 | +theorem rejected_output_rejected {Raw : Type} (provider : RustModel Raw) |
| 95 | + (raw : Raw) (h : provider.decode raw = none) : |
| 96 | + ¬ WP.spec (Result.ok raw) (fun out => |
| 97 | + ∃ decoded, provider.decode out = some decoded ∧ True) := by |
| 98 | + simp [WP.spec_ok, h] |
| 99 | + |
| 100 | +theorem partial_rejected_output_rejected {Raw : Type} (provider : RustModel Raw) |
| 101 | + (raw : Raw) (h : provider.decode raw = none) : |
| 102 | + ¬ WP.dspec (Result.ok raw) (fun out => |
| 103 | + ∃ decoded, provider.decode out = some decoded ∧ True) := by |
| 104 | + simp [h] |
| 105 | + |
| 106 | +-- Rust absence and Rust errors remain successful decoded constructor cases. |
| 107 | +example : (@modelOption Usize (modelUScalar .Usize)).decode none = some none := rfl |
| 108 | +example : (@modelRustResult Usize Unit (modelUScalar .Usize) modelUnit).decode |
| 109 | + (.Err ()) = some (.Err ()) := rfl |
| 110 | + |
| 111 | +end ContractTests |
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