adelhult / fitch

Fitch-style natural deduction proof-editor

Fitch

Fitch is a small command-line editor for writing natural deduction (propositional logic) proofs. However, the program hasn't been extensively tested and was just written to get a chance to play around with propositional logic and the wonderful chumsky parser combinator library. But it can be rather helpful for generating LaTeX and avoid having to manually typeset proofs.

See the video for a short demo:

demo.webm

Usage

Assuming you have Rust installed. Clone the repo and run:

cd fitch_cli
cargo run

You can then start using fitch by typing a command followed by a series of arguments:

• premise <formula> - Add a new premise
• copy <step index> - Copy a previously proven formula
• assume <formula> - Create a new proof box (sub-proof) with some assumption
• discharge - Close a proof box
• rule <rule name> <rule arguments...> - Apply a rule given some step indices. See a list of rules below.
• undo - Undo the latest step
• quit - Quit the program
• help - Print a help message
• latex - Generate LaTeX code to typeset your proof

Rules

The rules are the same as those presented in Huth and Ryan Logic in Computer Science. (With the expection that $\neg \varphi$ is encoded as $\varphi \to \bot$).

Name	Arguments	Explanation
and_i	StepIndex StepIndex	phi psi ----------- phi ^ psi
and_e_lhs	StepIndex	phi ^ psi ----------- phi
and_e_rhs	StepIndex	phi ^ psi ----------- psi
or_i_lhs	StepIndex Prop	phi ------------ phi \/ psi
or_i_rhs	Prop StepIndex	psi ------------ phi \/ psi
or_e	StepIndex StepIndex StepIndex	phi \/ psi [phi]...chi [psi]...chi ------------------------------------- chi
neg_i	StepIndex	[phi]...bottom ---------------- neg phi
neg_e	StepIndex StepIndex	phi neg phi ---------------- bottom
imply_i	StepIndex	[phi]...psi ------------- psi
imply_e	StepIndex StepIndex	phi phi -> psi --------------------- psi
bottom-e	StepIndex Prop	bottom ------------ phi
neg_neg_e	StepIndex	neg (neg phi) --------------- phi
mt	StepIndex StepIndex	phi -> psi neg psi ------------------------ neg phi
neg_neg_i	StepIndex	phi --------------- neg (neg phi)
PBC	StepIndex	[not phi]...bottom -------------------- phi
LEM	Prop	---------------- phi \/ neg phi