prolog-tablinglisted

# Prolog Tabling & SLG Resolution Guidelines Use this skill when implementing recursive graph algorithms, transitive closures, Datalog queries, or dynamic programming in Prolog engines that support tabling (SLG resolution). ## 1. When to Use Tabling Tabling (memoization of subgoals and answers) guarantees termination for left-recursive and cyclic graph queries: - **Graph Reachability & Transitive Closures** (avoiding infinite loops in cyclic graphs) - **Grammar Parsing with Left Recursion** - **Datalog-style Deductive Database Queries** - **Dynamic Programming** (e.g. shortest path, Fibonacci, editing distances) --- ## 2. Declaration Syntax Declare tabling directives before predicate definitions: ```prolog % SWI-Prolog / Scryer / Trealla (where supported) :- table reach/2. % Cyclic graph reachability reach(X, Y) :- edge(X, Y). reach(X, Y) :- reach(X, Z), edge(Z, Y). ``` --- ## 3. Answer Subsumption & Mode Directed Tabling When computing min/max/sum costs over graphs, use mode-directed tabling or answer subsumption: ```prolog % SWI-Prolog mode-directed tabling for shortest path: :- table shortest_path(?, ?, min). shortest_path(X, Y, Dist) :- edge(X, Y, Dist). shortest_path(X, Y, Dist) :- shortest_path(X, Z, D1), edge(Z, Y, D2), Dist is D1 + D2. ``` --- ## 4. Portability & Fallbacks For Prolog engines without tabling support (or when writing portable ISO code), fall back to an explicit **visited list accumulator**: ```prolog % Portable fallback for