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While formalisation guarantees correctness, the primary emphasis is on the computational content of proofs. Leveraging Minlog's built-in program extraction, we obtain executable terms and export them as Haskell code.
The efficiency of the extracted programs plays a central role. We show how performance considerations influence even the original formulation of theorems and proofs. In particular, we compare formalisations based on binary encodings of natural numbers with those using the traditional unary (successor-based) representation.
We present several core proofs in detail and reflect on the challenges that arise from formalisation in contrast to informal reasoning. The complete formalisation is available online and linked throughout. Minlog's tactic scripts are designed to follow the structure of natural-language proofs, allowing each derivation step to be traced precisely and thereby bridging the gap between formal and classical mathematical reasoning.
| Comments: | 56 pages, 6 figures |
| Subjects: | Logic (math.LO) |
| MSC classes: | 68V20 (Primary) 03F10, 03B35, 11Y05, 11Y16, 11A51 (Secondary) |
| ACM classes: | F.4.1 |
| Cite as: | arXiv:2504.03460 [math.LO] |
| (or arXiv:2504.03460v5 [math.LO] for this version) | |
| https://doi.org/10.48550/arXiv.2504.03460 arXiv-issued DOI via DataCite |
From: Franziskus Wiesnet [view email]
[v1]
Fri, 4 Apr 2025 14:10:00 UTC (41 KB)
[v2]
Fri, 11 Apr 2025 16:26:16 UTC (41 KB)
[v3]
Wed, 11 Feb 2026 19:28:19 UTC (94 KB)
[v4]
Tue, 17 Feb 2026 15:41:57 UTC (94 KB)
[v5]
Fri, 22 May 2026 14:42:06 UTC (93 KB)
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