nx_world_demo_test.nx source
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1// nx_world_demo_test.nx -- 10 visual demos of registered primitives.
2// Run end-to-end via v2 kernel + visualisations + honest audit.
3
4import "nx_corpus_full.nx"
5import "nx_proof_emit.nx"
6import "nx_prove_propositional.nx"
7import "nx_proof_sqrt2_v3.nx"
8import "nx_arith.nx"
9import "nx_probability.nx"
10
11const SYM_A: nx_int = 1001
12const SYM_B: nx_int = 1002
13const SYM_P: nx_int = 1100
14
15func one_axiom(a: nx_int) -> *nx_int {
16 let arr: *nx_int = (sys_mmap(8)) as *nx_int
17 arr[0] = a
18 return arr
19}
20
21func empty_axioms() -> *nx_int {
22 return (sys_mmap(8)) as *nx_int
23}
24
25// ===== DEMO 1: deriv(x^3) ===========================================
26func demo1_deriv_x3() -> nx_int {
27 println("" as *u8)
28 println("===== DEMO 1: nx_calc_deriv applied to x^3 =====" as *u8)
29 let x: *Term = nx_calc_x()
30 let x3: *Term = nx_calc_pow(x, nx_calc_const_int(3))
31 let d: *Term = nx_calc_deriv(x3, NX_CALC_SYM_X)
32 print("input : x^3 = " as *u8); let _e1: nx_int = nx_emit_term(x3); println("" as *u8)
33 print("derivative: " as *u8); let _e2: nx_int = nx_emit_term(d); println("" as *u8)
34 print("(unsimplified output -- the chain rule expanded to (3 * (x ^ (3-1))) * 1)" as *u8)
35 println("" as *u8)
36 return 1
37}
38
39// ===== DEMO 2: matmul of 3x3 matrices ===============================
40func demo2_matmul() -> nx_int {
41 println("" as *u8)
42 println("===== DEMO 2: nx_mat_mul of two 3x3 matrices =====" as *u8)
43 let a: *Mat = nx_mat_new(3, 3)
44 let _a1: nx_int = nx_mat_set(a, 0, 0, 1)
45 let _a2: nx_int = nx_mat_set(a, 0, 1, 2)
46 let _a3: nx_int = nx_mat_set(a, 0, 2, 3)
47 let _a4: nx_int = nx_mat_set(a, 1, 0, 4)
48 let _a5: nx_int = nx_mat_set(a, 1, 1, 5)
49 let _a6: nx_int = nx_mat_set(a, 1, 2, 6)
50 let _a7: nx_int = nx_mat_set(a, 2, 0, 7)
51 let _a8: nx_int = nx_mat_set(a, 2, 1, 8)
52 let _a9: nx_int = nx_mat_set(a, 2, 2, 9)
53 let b: *Mat = nx_mat_new(3, 3)
54 let _b1: nx_int = nx_mat_set(b, 0, 0, 1)
55 let _b2: nx_int = nx_mat_set(b, 0, 1, 0)
56 let _b3: nx_int = nx_mat_set(b, 0, 2, 0)
57 let _b4: nx_int = nx_mat_set(b, 1, 0, 0)
58 let _b5: nx_int = nx_mat_set(b, 1, 1, 1)
59 let _b6: nx_int = nx_mat_set(b, 1, 2, 0)
60 let _b7: nx_int = nx_mat_set(b, 2, 0, 0)
61 let _b8: nx_int = nx_mat_set(b, 2, 1, 0)
62 let _b9: nx_int = nx_mat_set(b, 2, 2, 1)
63 let c: *Mat = nx_mat_mul(a, b)
64 println("A * I3 =" as *u8)
65 let _r: nx_int = nx_render_matrix(c.data, 3, 3)
66 if nx_mat_get(c, 0, 0) != 1 { return 0 }
67 if nx_mat_get(c, 2, 2) != 9 { return 0 }
68 return 1
69}
70
71// ===== DEMO 3: vec_dot with bar-chart of inputs =====================
72func demo3_dot() -> nx_int {
73 println("" as *u8)
74 println("===== DEMO 3: nx_vec_dot of two 5-vectors =====" as *u8)
75 let v1: *Vec = nx_vec_new(5)
76 let _s1: nx_int = nx_vec_set(v1, 0, 2)
77 let _s2: nx_int = nx_vec_set(v1, 1, 4)
78 let _s3: nx_int = nx_vec_set(v1, 2, 6)
79 let _s4: nx_int = nx_vec_set(v1, 3, 8)
80 let _s5: nx_int = nx_vec_set(v1, 4, 10)
81 let v2: *Vec = nx_vec_new(5)
82 let _t1: nx_int = nx_vec_set(v2, 0, 1)
83 let _t2: nx_int = nx_vec_set(v2, 1, 2)
84 let _t3: nx_int = nx_vec_set(v2, 2, 3)
85 let _t4: nx_int = nx_vec_set(v2, 3, 4)
86 let _t5: nx_int = nx_vec_set(v2, 4, 5)
87 println("v1 (visualised):" as *u8)
88 let _b1: nx_int = nx_render_bar(v1.data, 5)
89 println("v2 (visualised):" as *u8)
90 let _b2: nx_int = nx_render_bar(v2.data, 5)
91 let dot: nx_int = nx_vec_dot(v1, v2)
92 print("v1 . v2 = " as *u8); print_i64(dot); println(" (expected 110 = 2+8+18+32+50)" as *u8)
93 if dot != 110 { return 0 }
94 return 1
95}
96
97// ===== DEMO 4: finite induction emitting the chain ==================
98func demo4_induction() -> nx_int {
99 println("" as *u8)
100 println("===== DEMO 4: nx_arith_finite_induction P(0..3) -> P(3) =====" as *u8)
101 let ch: *K2Chain = nx_k2_chain_new(32)
102 let p_at_n: *Term = nx_term_app(SYM_P, 1, nx_arith_nat(0))
103 let p0: nx_int = nx_k2_axiom(ch, p_at_n)
104 let s0: nx_int = nx_k2_axiom(ch, nx_k2_imp(
105 nx_term_app(SYM_P, 1, nx_arith_nat(0)),
106 nx_term_app(SYM_P, 1, nx_arith_nat(1))))
107 let s1: nx_int = nx_k2_axiom(ch, nx_k2_imp(
108 nx_term_app(SYM_P, 1, nx_arith_nat(1)),
109 nx_term_app(SYM_P, 1, nx_arith_nat(2))))
110 let s2: nx_int = nx_k2_axiom(ch, nx_k2_imp(
111 nx_term_app(SYM_P, 1, nx_arith_nat(2)),
112 nx_term_app(SYM_P, 1, nx_arith_nat(3))))
113 let steps: *nx_int = (sys_mmap(24)) as *nx_int
114 steps[0] = s0; steps[1] = s1; steps[2] = s2
115 let p3: nx_int = nx_arith_finite_induction(ch, SYM_P, p0, steps, 3)
116 if p3 < 0 { return 0 }
117 let _e: nx_int = nx_emit_two_column(ch)
118 print("derived P(3) at chain index " as *u8); print_i64(p3); println("" as *u8)
119 return 1
120}
121
122// ===== DEMO 5: sqrt(2) irrational v3 chain emit =====================
123func demo5_sqrt2() -> nx_int {
124 println("" as *u8)
125 println("===== DEMO 5: nx_proof_sqrt2_v3 -- closed theorem |- NOT(sqrt(2)=p/q) =====" as *u8)
126 let v: nx_int = nx_proof_sqrt2_v3()
127 if v != NX_K2_OK { return 0 }
128 println(" v3 chain produced 16-node closed derivation; verify returned OK" as *u8)
129 println(" THEOREM (closed): sqrt(2) is irrational ∎" as *u8)
130 return 1
131}
132
133// ===== DEMO 6: auto-prover proves K combinator ====================
134func demo6_k_combinator() -> nx_int {
135 println("" as *u8)
136 println("===== DEMO 6: nx_prove auto-derives K combinator A => (B => A) =====" as *u8)
137 let ch: *K2Chain = nx_k2_chain_new(16)
138 let a: *Term = nx_term_const(SYM_A)
139 let b: *Term = nx_term_const(SYM_B)
140 let goal: *Term = nx_k2_imp(a, nx_k2_imp(b, a))
141 let ax: *nx_int = empty_axioms()
142 let proof_idx: nx_int = nx_prove(ch, ax, 0, goal)
143 if proof_idx < 0 { return 0 }
144 let _e: nx_int = nx_emit_two_column(ch)
145 print("auto-derived at chain index " as *u8); print_i64(proof_idx); println("" as *u8)
146 return 1
147}
148
149// ===== DEMO 7: chemistry molar mass H2O ============================
150func demo7_chem() -> nx_int {
151 println("" as *u8)
152 println("===== DEMO 7: nx_chem_molar_mass H2O via periodic table =====" as *u8)
153 let table: *Element = nx_chem_periodic_table()
154 let h: *Element = nx_chem_element_by_z(table, 1)
155 let o: *Element = nx_chem_element_by_z(table, 8)
156 print(" H atomic mass = " as *u8); print_i64(h.mass_q3); println(" milli-AMU" as *u8)
157 print(" O atomic mass = " as *u8); print_i64(o.mass_q3); println(" milli-AMU" as *u8)
158 let water: *Molecule = nx_chem_water()
159 let mw: nx_int = nx_chem_molar_mass_q3(water, table)
160 print(" H2O molar mass = " as *u8); print_i64(mw); println(" milli-AMU = 18.015 g/mol" as *u8)
161 if mw != 18015 { return 0 }
162 return 1
163}
164
165// ===== DEMO 8: dimensional analysis F = m * a =====================
166func demo8_dim_analysis() -> nx_int {
167 println("" as *u8)
168 println("===== DEMO 8: nx_dim_eq verifies F = m * a dimensionally =====" as *u8)
169 let lhs: *Dim = nx_dim_newton()
170 let rhs: *Dim = nx_dim_mul(nx_dim_kg(), nx_dim_acceleration())
171 print(" Newton dim : (m=" as *u8); print_i64(lhs.m)
172 print(", kg=" as *u8); print_i64(lhs.kg)
173 print(", s=" as *u8); print_i64(lhs.s); println(", ...)" as *u8)
174 print(" kg * accel : (m=" as *u8); print_i64(rhs.m)
175 print(", kg=" as *u8); print_i64(rhs.kg)
176 print(", s=" as *u8); print_i64(rhs.s); println(", ...)" as *u8)
177 let eq: nx_int = nx_dim_eq(lhs, rhs)
178 if eq != 1 { println(" FAIL: dims disagree" as *u8); return 0 }
179 println(" EQUAL -- F = m*a is dimensionally consistent" as *u8)
180 return 1
181}
182
183// ===== DEMO 9: probability inclusion-exclusion axiom =================
184func demo9_prob() -> nx_int {
185 println("" as *u8)
186 println("===== DEMO 9: nx_prob_axiom_inclusion_exclusion_2 emits IE axiom =====" as *u8)
187 let ch: *K2Chain = nx_k2_chain_new(8)
188 let a: *Term = nx_term_const(SYM_A)
189 let b: *Term = nx_term_const(SYM_B)
190 let ie: nx_int = nx_prob_axiom_inclusion_exclusion_2(ch, a, b)
191 if ie < 0 { return 0 }
192 let thm: *K2Thm = nx_k2_at(ch, ie)
193 print(" axiom Term: " as *u8); let _e: nx_int = nx_emit_term(thm.stmt); println("" as *u8)
194 println(" Pr(A union B) = Pr(A) + Pr(B) - Pr(A intersect B)" as *u8)
195 return 1
196}
197
198// ===== DEMO 10: fibonacci as line plot =============================
199func demo10_fibonacci() -> nx_int {
200 println("" as *u8)
201 println("===== DEMO 10: fibonacci sequence (1,1,2,3,5,8,13,21,34,55) line plot =====" as *u8)
202 let fibs: *nx_int = (sys_mmap(80)) as *nx_int
203 fibs[0] = 1; fibs[1] = 1; fibs[2] = 2; fibs[3] = 3; fibs[4] = 5
204 fibs[5] = 8; fibs[6] = 13; fibs[7] = 21; fibs[8] = 34; fibs[9] = 55
205 let _l: nx_int = nx_render_line(fibs, 10)
206 return 1
207}
208
209// ===== Audit table =================================================
210func print_audit() -> nx_int {
211 println("" as *u8)
212 println("=== HONEST corpus audit (cardinal: native-or-nothing) ===" as *u8)
213 println("" as *u8)
214 print(" This-session L3 (QED stack) : " as *u8); print_i64(NX_CORPUS_THIS_SESSION); println("" as *u8)
215 print(" Prior-session L3 (per MEMORY.md) : " as *u8); print_i64(NX_CORPUS_PRIOR_SESSIONS); println("" as *u8)
216 print(" Combined honest substrate count : " as *u8); print_i64(NX_CORPUS_HONEST_TOTAL); println("" as *u8)
217 println("" as *u8)
218 println(" Incumbent published counts (for HONEST comparison):" as *u8)
219 print(" Mathematica built-ins : " as *u8); print_i64(NX_INCUMBENT_MATHEMATICA); println("" as *u8)
220 print(" SciPy functions : " as *u8); print_i64(NX_INCUMBENT_SCIPY); println("" as *u8)
221 print(" NumPy array ops : " as *u8); print_i64(NX_INCUMBENT_NUMPY); println("" as *u8)
222 print(" HOL Light theorems : " as *u8); print_i64(NX_INCUMBENT_HOL_LIGHT); println("" as *u8)
223 print(" Lean Mathlib lemmas : " as *u8); print_i64(NX_INCUMBENT_LEAN_MATHLIB); println("" as *u8)
224 print(" Coq stdlib lemmas : " as *u8); print_i64(NX_INCUMBENT_COQ_STDLIB); println("" as *u8)
225 println("" as *u8)
226 println(" HONEST VERDICT (per cardinal feedback-honest-perf-verdict):" as *u8)
227 println(" + WIN callable-by-name registry scales fine to 100k+" as *u8)
228 println(" + WIN every entry is L3 (callable native impl), not L2.5 (name)" as *u8)
229 println(" + WIN kernel-checked proofs in LOGIC + PROOF + ARITH + PROB" as *u8)
230 println(" + WIN visual rendering CLI + browser SVG, both native, zero deps" as *u8)
231 println(" - LOSE_BIG raw count vs Lean Mathlib (200k); we are at ~2700" as *u8)
232 println(" - LOSE_BIG raw count vs Coq stdlib (50k); we are at ~2700" as *u8)
233 println(" - LOSE_BY_2x vs Mathematica (~5k); we have ~2700" as *u8)
234 println(" + WIN_BY_~5x vs NumPy (600); ~2700" as *u8)
235 println("" as *u8)
236 println(" named_improvement: ENGINE for OpenTheory replay -> ingest HOL Light" as *u8)
237 println(" named_improvement: parser for Lean Mathlib export -> arith re-derive" as *u8)
238 println(" named_improvement: scanner over runtime/*.nx for auto-bootstrap count" as *u8)
239 println(" refused: 'we have 100k+ ingested' -- third-party-trust cardinal forbids" as *u8)
240 return 0
241}
242
243func print_registry_summary(r: *PrimRegistry) -> nx_int {
244 println("" as *u8)
245 println("=== Per-domain registry breakdown (this session) ===" as *u8)
246 print(" total registered: " as *u8); print_i64(r.n); println("" as *u8)
247 print(" LOGIC : " as *u8); print_i64(nx_prim_count_by_domain(r, NX_DOMAIN_LOGIC)); println("" as *u8)
248 print(" ARITH : " as *u8); print_i64(nx_prim_count_by_domain(r, NX_DOMAIN_ARITH)); println("" as *u8)
249 print(" PROOF : " as *u8); print_i64(nx_prim_count_by_domain(r, NX_DOMAIN_PROOF)); println("" as *u8)
250 print(" CALC : " as *u8); print_i64(nx_prim_count_by_domain(r, NX_DOMAIN_CALC)); println("" as *u8)
251 print(" LINALG : " as *u8); print_i64(nx_prim_count_by_domain(r, NX_DOMAIN_LINALG)); println("" as *u8)
252 print(" PHYSICS : " as *u8); print_i64(nx_prim_count_by_domain(r, NX_DOMAIN_PHYSICS)); println("" as *u8)
253 print(" CHEM : " as *u8); print_i64(nx_prim_count_by_domain(r, NX_DOMAIN_CHEM)); println("" as *u8)
254 print(" PROB : " as *u8); print_i64(nx_prim_count_by_domain(r, NX_DOMAIN_PROB)); println("" as *u8)
255 print(" RENDER : " as *u8); print_i64(nx_prim_count_by_domain(r, NX_DOMAIN_RENDER)); println("" as *u8)
256 print(" DATA : " as *u8); print_i64(nx_prim_count_by_domain(r, NX_DOMAIN_DATA)); println("" as *u8)
257 return 0
258}
259
260func main() -> nx_exit {
261 println("=========================================================" as *u8)
262 println("nx_world_demo: 10 visual demos of registered primitives" as *u8)
263 println("=========================================================" as *u8)
264 let reg: *PrimRegistry = nx_corpus_full()
265 let _s: nx_int = print_registry_summary(reg)
266
267 var passed: nx_int = 0
268 passed = passed + demo1_deriv_x3()
269 passed = passed + demo2_matmul()
270 passed = passed + demo3_dot()
271 passed = passed + demo4_induction()
272 passed = passed + demo5_sqrt2()
273 passed = passed + demo6_k_combinator()
274 passed = passed + demo7_chem()
275 passed = passed + demo8_dim_analysis()
276 passed = passed + demo9_prob()
277 passed = passed + demo10_fibonacci()
278
279 println("" as *u8)
280 print("Demos passed: " as *u8); print_i64(passed); println(" / 10" as *u8)
281 let _a: nx_int = print_audit()
282 if passed == 10 { return 0 }
283 return 1
284}