Pith Number

pith:47BAZ2UJ

pith:2026:47BAZ2UJCNHVBC2UC5FDFGVDLK

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A foundational characterization of Hoare Logic

Daniel Leivant

A partial-correctness assertion for an iterative program is provable in Hoare logic if and only if it is provable in second-order logic with first-order comprehension.

arxiv:2605.13944 v1 · 2026-05-13 · cs.LO · math.LO

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Claims

C1strongest claim

a partial-correctness assertion about an iterative program is provable in Hoare Logic iff it is provable in standard second-order logic with comprehension restricted to first-order predicates.

C2weakest assumption

The equivalence depends on the precise syntactic definitions of Hoare logic for iterative programs and on the exact restriction of comprehension to first-order predicates; any deviation in these definitions would invalidate the claimed if-and-only-if.

C3one line summary

Partial-correctness assertions for iterative programs are provable in Hoare logic if and only if they are provable in second-order logic with comprehension restricted to first-order predicates.

References

216 extracted · 216 resolved · 0 Pith anchors

[1] Stephen Simpson , title=

[2] Dynamic Logic

[3] Arithmetices principia, novo methodo exposita

[4] van Heijenoort 1931

[5] Ramified recurrence and computational complexity I : Word recurrence and poly-time

Formal links

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Receipt and verification

First computed	2026-05-17T23:39:13.821427Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e7c20cea89134f508b54174a329aa35a9c05ff05fb7632a430aceb11a2773e7e

Aliases

arxiv: 2605.13944 · arxiv_version: 2605.13944v1 · doi: 10.48550/arxiv.2605.13944 · pith_short_12: 47BAZ2UJCNHV · pith_short_16: 47BAZ2UJCNHVBC2U · pith_short_8: 47BAZ2UJ

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/47BAZ2UJCNHVBC2UC5FDFGVDLK \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: e7c20cea89134f508b54174a329aa35a9c05ff05fb7632a430aceb11a2773e7e

Canonical record JSON

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    "abstract_canon_sha256": "5f5f9129f7e6f98837f40572a283aecbf95bab1ba1c1654c33ff1488f90b3b6a",
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      "math.LO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.LO",
    "submitted_at": "2026-05-13T17:51:13Z",
    "title_canon_sha256": "4f040d277ff0466df169b64e0999ca093eae132788f3fb01990a048a68c7d613"
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  "source": {
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