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Contrary to several other families of lambda terms, no closed formula orgenerating function is known and none of the sophisticated techniques devisedin analytic combinatorics can currently help with counting or generating theset of {\em simply-typed closed lambda terms} of a given size.  Moreover, their asymptotic scarcity among the set of closed lambda termsmakes counting them via brute force generation and type inference quicklyintractable, with previous published work showing counts for them only up tosize 10.  By taking advantage of the synergy between logic variables, unification withoccurs check and efficient backtracking in today's Prolog systems, we climb 4orders of magnitude above previously known counts by deriving progressivelyfaster Horn Clause programs that generate and/or count the set of closedsimply-typed lambda terms of sizes up to 14. A similar count for {\em closedsimply-typed normal forms} is also derived up to size 14.  {\em {\bf Keywords:} logic programming transformations, type inference,combinatorics of lambda terms, simply-typed lambda calculus, simply-typednormal forms. }

A Hiking Trip Through the Orders of Magnitude: Deriving Efficient Generators for Closed Simply-Typed Lambda Terms and Normal Forms