Add lcp (longest common prefix of list) with cv_trans support #1765
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Define lcp as a list-based wrapper around longest_prefix:
lcp ls = longest_prefix (set ls)
Add supporting definitions and theorems in rich_listScript.sml:
- lcp_def, lcp_nil, lcp_sing, lcp_cons2: definition and recursion equations
- lcp_thm: lcp is a prefix of all elements and is maximal
- longest_prefix_PAIR_prefix, longest_prefix_PAIR_maximal: helper lemmas
- common_prefixes_INSERT2, longest_prefix_INSERT2: key lemmas for recursion
- longest_prefix_assoc: associativity of longest_prefix on pairs
- lcp2_def: binary version lcp2 x y = longest_prefix {x;y}
- lcp2_thm, lcp_oneline: case-based equations for cv_trans
Add cv_trans support in cv_stdScript.sml:
- cv_trans_pre for lcp2 and lcp with precondition proofs
This enables efficient computation of longest common prefixes using
cv_compute. This is used in Verifereum for Merkle Patricia trees.
Co-Authored-By: Claude Opus 4.5 <[email protected]>
Co-Authored-By: Claude Opus 4.5 <[email protected]>
Co-Authored-By: Claude Opus 4.5 <[email protected]>
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Define lcp as a list-based wrapper around longest_prefix:
lcp ls = longest_prefix (set ls)
Add supporting definitions and theorems in rich_listScript.sml:
Add cv_trans support in cv_stdScript.sml:
This enables efficient computation of longest common prefixes using cv_compute. This is used in Verifereum for Merkle Patricia trees.