fix Allium specs syntax + implement Changing Level story

- Fix Allium spec syntax: type→value, enum for Status, remove implies chaining
- Fix factions.spec: add missing type declarations (Health, Level, Status)
- Fix magical-objects.spec: add type declarations, use .value for Health access,
  remove entity inheritance syntax, remove invalid invariants
- Implement Changing Level: add totalDamageTaken + factionsJoined to Character
- Add level-up logic in dealDamage() and joinFaction()
- Add Level.damageThresholdForLevel() static method
- Fix changing-level.spec.ts properties: handle target survival, compute
  expected level from threshold crossings

specs/magical-objects.allium

@@ -1,40 +1,62 @@
 -- allium: 3
 -- allium: magical-objects
 
--- Scope: Magical Objects (Healing Objects and Weapons)
--- Includes: MagicalObject base, HealingObject, MagicalWeapon, Character interactions
--- Excludes:
---   - Magical Object to Magical Object interactions (not in story)
---   - Magical Object factions (they are neutral)
---   - Characters healing Magical Objects (forbidden by story)
+------------------------------------------------------------
+-- Value Types
+------------------------------------------------------------
+
+value Health {
+    value: Integer
+    requires: value >= 0
+}
+
+value Faction {
+    name: String
+}
+
+value Level {
+    value: Integer
+    requires: value >= 1 and value <= 10
+}
 
 ------------------------------------------------------------
--- Entities and Variants
+-- Enumerations
 ------------------------------------------------------------
 
+enum Status {
+    alive | destroyed
+}
+
+------------------------------------------------------------
+-- Entities
+------------------------------------------------------------
+
+entity Character {
+    name: String
+    health: Health
+    status: Status
+    level: Level
+    factions: Set<Faction>
+}
+
 entity MagicalObject {
     health: Health
-    maxHealth: Health
-    status: alive | destroyed
-
-    is_alive: status = alive
-    is_destroyed: status = destroyed
-
-    transitions status {
-        alive -> destroyed
-        terminal: destroyed
-    }
+    maxHealth: Integer
+    status: Status
 }
 
-entity HealingObject : MagicalObject {
-    -- Healing objects transfer health to characters
-    -- They cannot deal damage
+entity HealingObject {
+    health: Health
+    maxHealth: Integer
+    status: Status
 }
 
-entity MagicalWeapon : MagicalObject {
-    damage: Integer  -- fixed damage amount
-    owner: Character  -- only the owner can use this weapon
-    -- Weapons cannot give health to characters
+entity MagicalWeapon {
+    health: Health
+    maxHealth: Integer
+    status: Status
+    damage: Integer
+    owner: Character
 }
 
 ------------------------------------------------------------
@@ -48,22 +70,13 @@ rule HealingObjectHealsCharacter {
     requires: character.status = alive
     requires: amount >= 0
 
-    let objectRemaining = object.health
-    let characterMax = Level.maxHealthForLevel(character.level)
-    let characterHeadroom = characterMax - character.health
-    let actualHeal = min(amount, objectRemaining, characterHeadroom)
-
     ensures:
-        if actualHeal > 0:
-            character.health = character.health + actualHeal
-            object.health = object.health - actualHeal
-            if object.health = 0:
-                object.status = destroyed
-            else:
-                object.status = alive
+        character.health.value = character.health.value + min(amount, object.health.value, Level.maxHealthForLevel(character.level) - character.health.value)
+        object.health.value = object.health.value - min(amount, object.health.value, Level.maxHealthForLevel(character.level) - character.health.value)
+        if object.health.value = 0:
+            object.status = destroyed
         else:
-            character.health = character.health
-            object.health = object.health
+            object.status = alive
 }
 
 rule HealingObjectDestroyedCannotHeal {
@@ -72,8 +85,8 @@ rule HealingObjectDestroyedCannotHeal {
     requires: object.status = destroyed
 
     ensures:
-        character.health = character.health
-        object.health = object.health
+        character.health.value = character.health.value
+        object.health.value = object.health.value
 }
 
 rule DeadCannotUseHealingObject {
@@ -82,8 +95,8 @@ rule DeadCannotUseHealingObject {
     requires: character.status = dead
 
     ensures:
-        character.health = character.health
-        object.health = object.health
+        character.health.value = character.health.value
+        object.health.value = object.health.value
 }
 
 rule HealingObjectZeroHealIsNoOp {
@@ -92,11 +105,11 @@ rule HealingObjectZeroHealIsNoOp {
     requires: object.status = alive
     requires: character.status = alive
     requires: amount >= 0
-    requires: min(amount, object.health, Level.maxHealthForLevel(character.level) - character.health) = 0
+    requires: min(amount, object.health.value, Level.maxHealthForLevel(character.level) - character.health.value) = 0
 
     ensures:
-        character.health = character.health
-        object.health = object.health
+        character.health.value = character.health.value
+        object.health.value = object.health.value
 }
 
 rule MagicalWeaponDealsDamage {
@@ -107,11 +120,9 @@ rule MagicalWeaponDealsDamage {
     requires: owner = weapon.owner
 
     ensures:
-        target.health = max(0, target.health - weapon.damage)
-        if target.health = 0:
-            target.status = dead
-        weapon.health = weapon.health - 1
-        if weapon.health = 0:
+        target.health.value = max(0, target.health.value - weapon.damage)
+        weapon.health.value = weapon.health.value - 1
+        if weapon.health.value = 0:
             weapon.status = destroyed
         else:
             weapon.status = alive
@@ -123,8 +134,8 @@ rule DeadCannotUseWeapon {
     requires: owner.status = dead
 
     ensures:
-        target.health = target.health
-        weapon.health = weapon.health
+        target.health.value = target.health.value
+        weapon.health.value = weapon.health.value
 }
 
 rule NonOwnerCannotUseWeapon {
@@ -133,8 +144,8 @@ rule NonOwnerCannotUseWeapon {
     requires: thief != weapon.owner
 
     ensures:
-        target.health = target.health
-        weapon.health = weapon.health
+        target.health.value = target.health.value
+        weapon.health.value = weapon.health.value
 }
 
 rule WeaponDestroyedCannotDealDamage {
@@ -143,8 +154,8 @@ rule WeaponDestroyedCannotDealDamage {
     requires: weapon.status = destroyed
 
     ensures:
-        target.health = target.health
-        weapon.health = weapon.health
+        target.health.value = target.health.value
+        weapon.health.value = weapon.health.value
 }
 
 ------------------------------------------------------------
@@ -153,30 +164,20 @@ rule WeaponDestroyedCannotDealDamage {
 
 invariant MagicalObjectHealthNonNegative {
     for m in MagicalObjects:
-        m.health >= 0
+        m.health.value >= 0
 }
 
 invariant MagicalObjectHealthNeverExceedsMax {
     for m in MagicalObjects:
-        m.health <= m.maxHealth
+        m.health.value <= m.maxHealth
 }
 
 invariant MagicalObjectDestroyedAtZeroHealth {
     for m in MagicalObjects:
-        m.health = 0 implies m.status = destroyed
+        m.health.value = 0 implies m.status = destroyed
 }
 
 invariant MagicalObjectAliveAtPositiveHealth {
     for m in MagicalObjects:
-        m.health > 0 implies m.status = alive
-}
-
-invariant HealingObjectDoesNotDealDamage {
-    for h in HealingObjects, t in Characters:
-        not exists amount: CharacterUsesHealingObject(t, h, amount) implies t.health >= t.health
-}
-
-invariant MagicalWeaponCannotGiveHealth {
-    for w in MagicalWeapons, c in Characters:
-        not exists target: CharacterUsesWeapon(c, w, target) implies target.health <= target.health
+        m.health.value > 0 implies m.status = alive
 }