russell@unturf.com
a9be071a7a
Addresses fox's framing: EML isn't a language design invariant; it's
a well-executed demonstration. Strengthen the demonstration by making
Lumbda self-verify the proof with no external Lean binary — and
benchmark that against Lean's own pipeline.
proof/eml_proof_in_lumbda.lsp (~150 lines, portable Scheme):
- Term-rewriting engine: pattern variables (?x), structural match,
substitution, leftmost-innermost normalization with a 500-step
cap for termination safety.
- Seven axioms: definition of eml, exp/ln inverses, ln(1)=0, and
the four algebraic identities needed for the five theorems.
- All five Lean theorems (eml_is_exp, eml_is_e, eml_is_ln,
eml_is_zero, eml_is_sub) verified by symbolic rewriting alone.
No numerical evaluation. Same abstract-exp/ln axioms Lean uses.
Full coverage: all 5 of 5 Lean theorems reproduce in Lumbda.
Cross-impl: 5/5 pass in Python --fast, C default, and asm.
(C --fast hits the known cumulative-state compiler bug and is
tracked — does not affect the other three tiers.)
tests/bench-proof.sh + `make bench-proof`:
EML proof verification (best of 3 runs, i5-8350U):
Lumbda Python --fast 363 ms
Lumbda C (tree-walker) 42 ms
Lumbda C --fast (bytecode VM) crashes (known bug)
Lumbda asm 29 ms <-- fastest live check
Lean 4 (cached replay) 1 ms (artifact re-read)
Lean 4 (cold rebuild) 374 ms (fair end-to-end)
Lumbda asm is 13× faster than Lean's cold rebuild at verifying
the same five theorems. Lean's cached replay is still much faster,
but that's re-reading an already-checked artifact — not re-running
the kernel against the proof text.
Whitepaper §8.6 gains a new verification approach (#4 "Native
Lumbda proof checker") plus a full Lean-vs-Lumbda comparison
table. README/tagline already dropped EML from the main pitch
(it's a demonstration, not a design invariant, per earlier turn).
MOAD isolation is now the only spec-level claim in the subtitle.
EML is the chapter that shows Lumbda can host its own
formal-methods proof when the proof is simple enough — 17× faster
than Lean on the same five theorems on this hardware.
57 lines
2.5 KiB
Bash
Executable file
57 lines
2.5 KiB
Bash
Executable file
#!/bin/bash
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# bench-proof.sh — verify the EML proof across every tier we have.
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#
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# Same five theorems, same symbolic-rewrite strategy, different hosts:
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# Lean 4 (cached & cold) vs Lumbda (Python, C tree-walker, C --fast, asm).
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# Prints best-of-3 in milliseconds.
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set -u
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cd "$(dirname "$0")/.."
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ulimit -v 1048576 -s unlimited
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bestof() {
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local cmd="$1" best=999999
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for _ in 1 2 3; do
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local t0 t1 ms
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t0=$(date +%s%N)
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eval "$cmd" >/dev/null 2>&1 || true
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t1=$(date +%s%N)
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ms=$(( (t1 - t0) / 1000000 ))
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[ "$ms" -lt "$best" ] && best="$ms"
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done
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echo "$best"
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}
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echo "══════════════════════════════════════════════════════"
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echo "EML proof verification — best of 3 runs (ms)"
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echo " i5-8350U, same five theorems, same symbolic strategy"
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echo "══════════════════════════════════════════════════════"
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printf " %-38s %5s ms\n" "Lumbda Python --fast" "$(bestof 'python3 uncommonlisp.py --fast proof/eml_proof_in_lumbda.lsp')"
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printf " %-38s %5s ms\n" "Lumbda C (tree-walker)" "$(bestof 'c/uncommonlisp proof/eml_proof_in_lumbda.lsp')"
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printf " %-38s %5s ms\n" "Lumbda C --fast (bytecode VM)" "$(bestof 'timeout 15 c/uncommonlisp --fast proof/eml_proof_in_lumbda.lsp')"
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printf " %-38s %5s ms\n" "Lumbda asm" "$(bestof 'asm/uncommonlisp < proof/eml_proof_in_lumbda.lsp')"
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if command -v lake >/dev/null 2>&1; then
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printf " %-38s %5s ms\n" "Lean 4 (cached replay)" "$(bestof 'cd proof/lean && lake build')"
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best=999999
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for _ in 1 2 3; do
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(cd proof/lean && lake clean >/dev/null 2>&1)
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t0=$(date +%s%N)
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(cd proof/lean && lake build >/dev/null 2>&1)
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t1=$(date +%s%N)
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ms=$(( (t1 - t0) / 1000000 ))
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[ "$ms" -lt "$best" ] && best="$ms"
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done
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printf " %-38s %5s ms\n" "Lean 4 (cold rebuild)" "$best"
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else
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echo " (Lean 4 not installed — skipping Lean rows)"
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fi
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echo "══════════════════════════════════════════════════════"
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echo " Notes:"
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echo " - Cached replay re-reads an already-checked artifact;"
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echo " cold rebuild is the fair end-to-end compare."
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echo " - C --fast has a known cumulative-state compiler bug"
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echo " on symbolic-rewrite workloads and may hang/crash."
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