Add reduce_to_prover

[mrmr1993]

This PR adds reduce_to_prover, which

• takes a Checked.t
• precomputes everything inside the Checked.t except for As_prover blocks
• stores the As_prover blocks as maps over the Run_state.t
• bundles them together into 1 function, wraps it in a Checked.Direct

Effectively, this caches everything that can be known ahead of time in closures around the As_prover blocks, so that creating a proof from reduce_to_prover Data_spec.[...] main only runs the As_prover blocks from main.

Combined with #145, this gives:

$ `which time` dune exec coda tra -- -witness-reduced -repeat 4
[1] Base constraint system satisfied
[2] Base constraint system satisfied
[3] Base constraint system satisfied
[4] Base constraint system satisfied
24.81user 0.99system 0:25.91elapsed 99%CPU (0avgtext+0avgdata 955468maxresident)k
0inputs+3432outputs (0major+371949minor)pagefaults 0swaps
$ `which time` dune exec coda tra -- -witness-reduced -repeat 10
[1] Base constraint system satisfied
[2] Base constraint system satisfied
[3] Base constraint system satisfied
[4] Base constraint system satisfied
[5] Base constraint system satisfied
[6] Base constraint system satisfied
[7] Base constraint system satisfied
[8] Base constraint system satisfied
[9] Base constraint system satisfied
[10] Base constraint system satisfied
55.83user 1.18system 0:56.95elapsed 100%CPU (0avgtext+0avgdata 987632maxresident)k
0inputs+3440outputs (0major+547695minor)pagefaults 0swaps

vs. without calling reduce_to_prover:

$ `which time` dune exec coda tra -- -witness-only -repeat 4
[1] Base constraint system satisfied
[2] Base constraint system satisfied
[3] Base constraint system satisfied
[4] Base constraint system satisfied
49.79user 1.07system 0:51.56elapsed 98%CPU (0avgtext+0avgdata 125312maxresident)k
23544inputs+3432outputs (8major+322816minor)pagefaults 0swaps

That is, reduce_to_prover runs in 45% of the time for 10 runs, or 50% for 4 runs.

(I overwrote my benchmarks file by mistake, so I haven't included a comparison with current master..)

[mrmr1993]

Without #145:

$ `which time` dune exec coda tra -- -witness-reduced -repeat 4
[1] Base constraint system satisfied
[2] Base constraint system satisfied
[3] Base constraint system satisfied
[4] Base constraint system satisfied
28.32user 1.08system 0:29.89elapsed 98%CPU (0avgtext+0avgdata 983228maxresident)k
20408inputs+3456outputs (6major+437105minor)pagefaults 0swaps
$ `which time` dune exec coda tra -- -witness-reduced -repeat 10
[1] Base constraint system satisfied
[2] Base constraint system satisfied
[3] Base constraint system satisfied
[4] Base constraint system satisfied
[5] Base constraint system satisfied
[6] Base constraint system satisfied
[7] Base constraint system satisfied
[8] Base constraint system satisfied
[9] Base constraint system satisfied
[10] Base constraint system satisfied
67.37user 1.53system 1:08.83elapsed 100%CPU (0avgtext+0avgdata 1096508maxresident)k
0inputs+3456outputs (0major+714216minor)pagefaults 0swaps

$ `which time` dune exec coda tra -- -witness-only -repeat 4
[1] Base constraint system satisfied
[2] Base constraint system satisfied
[3] Base constraint system satisfied
[4] Base constraint system satisfied
58.82user 1.12system 0:59.87elapsed 100%CPU (0avgtext+0avgdata 133016maxresident)k
0inputs+3456outputs (0major+459649minor)pagefaults 0swaps

• 4 runs takes 49% of the time of master
• 10 runs takes 45% of the time of master
• 4 runs (with Use mutable add for Cvar.eval #145) takes 43% of the time of master
• 10 runs (with Use mutable add for Cvar.eval #145) takes 38% of the time of master

[imeckler]

Not sure if this allocates but you could also do Fn.id