"""
Proof that the Belief Engine reproduces the designed lessons from the GDD.
Run: python prove_cases.py
"""
from belief_engine import (dempster, yager, pcr5, cautious, discount, fuse,
                           belief, plausibility, conflict_K, verdict, report)

def fs(*xs): return frozenset(xs)
def line(t): print("\n" + "=" * 70 + "\n" + t + "\n" + "=" * 70)

# ============================================================ CASE 1: "Two Truths"
line("CASE 1 — 'Two Truths'  (the paradox: Dempster vs Yager)")
FRAME1 = {"Gardener", "Maid", "Secretary"}
THRESH1 = 0.70

butler = {fs("Gardener"): 0.99, fs("Secretary"): 0.01}   # "It was the Gardener"
cook   = {fs("Maid"): 0.99,     fs("Secretary"): 0.01}   # "It was the Maid"
print("Ground truth: Gardener.  Secretary is innocent and barely suspected.")
print(f"Conflict K(Butler,Cook) = {conflict_K(butler, cook):.4f}")

dem = dempster(butler, cook)
print("\n-- Dempster (the Zealot) --")
for s, r in report(dem, FRAME1).items():
    print(f"   {s:10s} suspicion(Bel)={r['suspicion']:.4f}  shadow(Pl)={r['shadow']:.4f}")
print("   VERDICT:", verdict(dem, FRAME1, THRESH1))
print("   >>> Dempster convicts the SECRETARY (the one BOTH thought least likely),")
print("   >>> with total certainty. Convicting here = WRONGFUL EXECUTION.")

yag = yager(butler, cook, FRAME1)
print("\n-- Yager (the Agnostic) --")
for s, r in report(yag, FRAME1).items():
    print(f"   {s:10s} suspicion(Bel)={r['suspicion']:.4f}  shadow(Pl)={r['shadow']:.4f}")
print("   VERDICT:", verdict(yag, FRAME1, THRESH1))
print("   >>> Yager refuses: nobody clears threshold. Honest paralysis (correct).")

# escape path: add the Apothecary pointing at the Gardener, fuse with Yager
apoth = {fs("Gardener"): 0.6, frozenset(FRAME1): 0.4}
yag3 = fuse([butler, cook, apoth], "yager", FRAME1)
print("\n-- Yager + Apothecary (the just path) --")
for s, r in report(yag3, FRAME1).items():
    print(f"   {s:10s} suspicion(Bel)={r['suspicion']:.4f}  shadow(Pl)={r['shadow']:.4f}")
print("   VERDICT:", verdict(yag3, FRAME1, THRESH1),
      " <- evidence now tips toward the truly guilty Gardener")

# ============================================================ CASE 2: "The Echo"
line("CASE 2 — 'The Echo'  (independence: Dempster inflates, Cautious does not)")
FRAME2 = {"Sailor", "Innkeeper", "Stranger"}
THRESH2 = 0.70

patron1 = {fs("Sailor"): 0.8, frozenset(FRAME2): 0.2}     # rehearsed
patron2 = {fs("Sailor"): 0.8, frozenset(FRAME2): 0.2}     # same story, not independent
print("Ground truth: Innkeeper.  The two patrons are married & rehearsed (an Echo).")

dem2 = dempster(patron1, patron2)
caut2 = cautious(patron1, patron2, FRAME2)
print(f"\n   Two identical accusations of the Sailor (0.80 each):")
print(f"   Dempster  -> Suspicion(Sailor) = {belief(dem2, fs('Sailor')):.4f}  (INFLATED by repetition)")
print(f"   Cautious  -> Suspicion(Sailor) = {belief(caut2, fs('Sailor')):.4f}  (UNMOVED: idempotent)")
print("   >>> The lesson is felt in the gap: repetition is not corroboration.")

# idempotence sanity check
caut_self = cautious(patron1, patron1, FRAME2)
print(f"\n   Idempotence check: cautious(m,m) Suspicion(Sailor) = "
      f"{belief(caut_self, fs('Sailor')):.4f}  (should equal 0.8000)")

# just path: discount the colluders, bring the Barmaid pointing at the Innkeeper
barmaid = {fs("Innkeeper"): 0.55, frozenset(FRAME2): 0.45}
p1_disc = discount(patron1, 0.85, FRAME2)   # caught lying -> heavily discounted
p2_disc = discount(patron2, 0.85, FRAME2)
just2 = fuse([p1_disc, p2_disc, barmaid], "pcr5", FRAME2)
print("\n-- Discount the colluders + Barmaid, fuse (PCR5): the just path --")
for s, r in report(just2, FRAME2).items():
    print(f"   {s:10s} suspicion(Bel)={r['suspicion']:.4f}  shadow(Pl)={r['shadow']:.4f}")
print("   VERDICT:", verdict(just2, FRAME2, 0.50),
      " <- Innkeeper rises once the Echo is silenced (threshold relaxed for demo)")

# ============================================================ CASE 3 quick check: PCR5 middle path
line("CASE 3 — 'The Banquet'  (PCR5 as the fair middle path under contradiction)")
FRAME3 = {"Rival", "Widow", "Physician", "Heir"}
T3 = frozenset(FRAME3)
somm   = {fs("Rival"): 0.8, T3: 0.2}
maid   = {fs("Physician"): 0.75, T3: 0.25}
earl   = {fs("Heir"): 0.9, T3: 0.1}            # the Drunk: confident but unreliable
coroner= {fs("Physician"): 0.6, fs("Rival"): 0.1, T3: 0.3}
footman= {fs("Physician", "Widow"): 0.6, T3: 0.4}  # set-valued: "one of the two"
print("Ground truth: Physician (with Widow as accomplice).")

earl_disc = discount(earl, 0.9, FRAME3)        # interrogation reveals he was unconscious
deps = [somm, maid, earl_disc, coroner, footman]

for method in ("dempster", "yager", "pcr5", "cautious"):
    try:
        m = fuse(deps, method, FRAME3)
        rep = report(m, FRAME3)
        phys = rep["Physician"]; rival = rep["Rival"]; widow = rep["Widow"]
        print(f"\n   {method.upper():9s}  Physician Bel={phys['suspicion']:.3f}/Pl={phys['shadow']:.3f}"
              f"   Rival Bel={rival['suspicion']:.3f}"
              f"   Widow Pl={widow['shadow']:.3f}")
        print("            verdict @0.55:", verdict(m, FRAME3, 0.55))
    except Exception as e:
        print(f"\n   {method.upper():9s}  -> {e}")
print("\n   >>> Different Methods reach different verdicts from identical evidence.")
print("   >>> That is the entire game.")

line("ALL CASE LESSONS REPRODUCED BY THE ENGINE.")