Tarski Games with retractable moves

A Game Semantic for Mathematical Proofs

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1. Introduction to Tarski Game Semantic
2. Adding Irreversible Backtracking
3. Adding Reversible Backtracking
4. A Semantic of Constructive Implication
5. A Semantic of Cut
6. A Program implementing Tarski Games with backtracking

6. A Program implementing Tarski Games with backtracking


In the previous sections, we produced all examples through a program, BCK, assisting two player taking the role of Eloise and Abelard in the play. The programs allows the two players to fix the rule of the play: no backtracking, irreversible backtracking, reversible backtracking, backtracking on hypotheses only, backtracking only by Eloise or by both players. The programs decides who moves next, giving him or her a list of moves, and check the correctness of the play. The program also produce a tree-like picture of the state of the play, helping each player to decide the next move. You need a Mathematica intepreter to run the program, and even just to look at its code. Otherwise you can only look to the examples of the site. In the subsite:

A Program implementing Tarski Games with backtracking



we copied the entire code of the program, together with some comments.



Above: Mathematica is a powerful and flexible tool for designing prototypes (drawing by Giovanni Bertoglio).
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