The Proof Machine (2016)

Summary

× Welcome to The Incredible Proof Machine! What is this? This is a tool to perform proofs in various logics (e.g. propositional, predicate logic) visually: You simply add blocks that represent the various proofs steps, connect them properly, and if the conclusion turns green, then you have created a complete proof! Simply drag and drop to connect two dots; for some examples of completed proofs, see this paper. For a quick introduction to the UI, check out the introductory video on the Tea Leaves Programming channel (13min)! Why is this? The Incredible Proof Machine was created to convey the fun and joy of doing proofs, especially in a computer aided way, without first having to learn the syntax of a “real” thereom prover like Isabelle. Which keyboard shortcuts can I use? CTRL+Z: Undo change CTRL+Y: Redo change CTRL+A: Select all blocks BACKSPACE, DELETE: Delete selected blocks SHIFT+MOUSE1: Add block or region to selection Why is the conclusion not green? Because your proof is not a proof (yet). This can have these reasons: Some of your blocks have an input (an assumption) that is not connected to anything. These are red. Some of your connections connect propositions that are obviously different (marked red and marked with ☠), or they are underspecified and it is not clear whether they might be different or not (marked red and with ?). In the latter case, inserting an annotation block (✎P) can help. You have cycles in the proof. These are (you guessed it) marked red. You have wired up local hypotheses wrongly. Local hypotheses are those outputs that come out on the left of a dent in the block, and can only be used in the part of the proof that connects to the corresponding input on the right of the dent. Do I need to mention that these are marked red? How do I enter these funny characters? There are only a few places where you actually have to enter formulas, mostly if you want to use the ✎P-block or define your own tasks. There, you can use the following abbreviati...