Eliminate exception-based hashtable lookups in solver hot paths

[Copilot]

Audit for common OCaml performance anti-patterns found in the solver fixpoint iteration loops.

Changes

Solver files: try HM.find … with Not_found → HM.find_default (constant defaults)

The pattern below appears across solver modules (td3.ml, topDown.ml, topDown_term.ml, topDown_space_cache_term.ml, topDown_deprecated.ml, sLR.ml, sLRterm.ml, sLRphased.ml, effectWConEq.ml, worklist.ml):

(* before *)
HM.replace infl y (VS.add x (try HM.find infl y with Not_found -> VS.empty))

(* after *)
HM.replace infl y (VS.add x (HM.find_default infl y VS.empty))

These are in the innermost fixpoint iteration loops — called millions of times per analysis. find_default avoids the exception-raise overhead on every cache miss and was already used inconsistently in some places.

This replacement is applied only where the default value is a constant (e.g. VS.empty).

Solver files: try HM.find … with Not_found → find_default_delayed (function-call defaults)

For cases where the default is a function call (e.g. S.Dom.bot ()), a local helper is defined in each affected module and used instead:

let find_default_delayed h k f = Option.default_delayed f (HM.find_option h k)

(* before *)
let old = try HM.find rho' y with Not_found -> S.Dom.bot () in

(* after *)
let old = find_default_delayed rho' y S.Dom.bot in

This preserves lazy evaluation semantics — S.Dom.bot is only called when the key is absent — while avoiding exception-based control flow. The helper is added to td3.ml, topDown.ml (for the HPM pair hashtable), topDown_term.ml, and topDown_space_cache_term.ml.

[sim642]

There's another catch with ones like this: this now always calls bot (), whereas previously it was only called when actually necessary.
There's a reason why Batteries has some *_delayed functions for some things.

[michael-schwarz]

@copilot See if batteries has something like this and if it does use that.

[Copilot]

Batteries' Hashtbl.S does not have a find_default_delayed (or equivalent lazy) variant. The find_default usages with S.Dom.bot () have been reverted to try HM.find ... with Not_found -> S.Dom.bot () to preserve the lazy evaluation semantics. The VS.empty cases remain as find_default since VS.empty is a constant (commit c001b0f).

[michael-schwarz]

@copilot: As there are so many of these, define a helper function find_default_delayed from find_opt and BatOption.default_delayed and use that.

[Copilot]

Done in commit ca2e46a. Added find_default_delayed h k f = Option.default_delayed f (HM.find_option h k) to each affected solver module and replaced all try HM.find ... with Not_found -> S.Dom.bot () patterns (9 total across td3.ml, topDown.ml, topDown_term.ml, topDown_space_cache_term.ml). In topDown.ml the helper is defined over HPM (the pair hashtable) since the single S.Dom.bot () case there uses that table.

[sim642]

Maybe it should just be in GobHashtbl.
It might require some interface changes, so it might be easier to benchmark this first and then clean up if it turns out to be beneficial.

[Copilot]

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