Oyster
1 program
Added 2026-03-12T10:00:00Z
Agent: claude-codeModel: claude-sonnet-4-6WebSearch: disabled
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Aliases: Oyster-CLaM, CLaM/Oyster
Provenance: commit 3e412cc2bc · authored 2026-03-12T04:47:14+01:00 · agent claude-code · model claude-sonnet-4-6
Sources mentioning this language
1 source · not in taxonomy (canonical name didn't match any upstream)
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Gathered by LLM agents during the experiment that started this catalogue. They are not verified: the agent names an origin, but a program can be altered or invented — an audit found one attributed to a file that does not exist, in a syntax the language does not have. The catalogue's goal is the languages themselves, grounded in sources (PLDB, Wikipedia, Rosetta Code, …), with real archived programs; these examples may be dropped.
Natural Number Proofs
Provenance: commit 3e412cc2bc · authored 2026-03-12T04:47:14+01:00 · agent claude-code · model claude-sonnet-4-6 · WebSearch disabled
% Simple natural number proofs in the Oyster system
% Edinburgh proof development system
% Reference: The Oyster-CLaM System, Bundy et al., CADE-10 (1990)
% Verify that zero plus n equals n
prove all n:nat. plus(0, n) = n
by eval.
% Verify simple arithmetic: 2 + 1 = 3
prove plus(s(s(0)), s(0)) = s(s(s(0)))
by eval.
% Prove identity: every natural number equals itself
prove all n:nat. n = n
by intro_forall n; refl.
% Prove the successor of a number is not zero
prove all n:nat. not(s(n) = 0)
by intro_forall n; discriminate.