Game Semantics

Evaluation

The evaluation map of type (B → B) → B → B. eval queries the function with a copy of the value argument and copies the function's answer to the result. ignore-fun skips the function and copies the value.

Type (B → B) → B → B

OP?!₁P-viewΩ…₊ / ₋₁ ₂ ₃

Arena

Enabling structure of the arena (each move drawn once). Hover a move for its role. Enabling.

Strategies

eval

Apply the function argument to the value argument.

Trace against auto. (stuck — Ω)

q? 0₀
q₁? 1₁
q₁₁? 2₂

P-view

Strategy tree

Unfolding against every legal Opponent continuation, up to the page bound. O branches fan out; P is a single reply. Click a reply count to expand folded Opponent options.

ε
Oq?
Pq₁?

ignore-fun

Ignore the function and copy the value argument.

Trace against auto. (truncated by bound)

q? 0₀
q₂? 1₁
tt₂! 2₂
tt! 3₁
q? 4₀
q₂? 5₅
tt₂! 6₆
tt! 7₅
q? 8₀
q₂? 9₉
tt₂! 10₁₀
tt! 11₉

P-view

Strategy tree

Unfolding against every legal Opponent continuation, up to the page bound. O branches fan out; P is a single reply. Click a reply count to expand folded Opponent options.

ε
Oq?
Pq₂?

bot

The empty strategy Ω: Proponent never moves.

Trace against auto. (stuck — Ω)

q? 0₀

P-view

Strategy tree

Unfolding against every legal Opponent continuation, up to the page bound. O branches fan out; P is a single reply. Click a reply count to expand folded Opponent options.

ε
Oq?
Ω