Prooftrees

This package is for constructing proof trees in the style of natural deduction or the sequent calculus, for typst 0.7.0. Please do open issues for bugs etc :)

Features:

• Inferences can have arbitrarily many premises.
• Inference lines can have left and/or right labels¹
• Configurable² per tree and per line: premise spacing, the line stroke, etc... .
• They're proof trees.

¹ The placement of labels is currently very primitive, and requires much user intervention.

² Options are quite limited.

Usage

The user interface is inspired by bussproof's; a tree is constructed by a sequence of 'lines' that state their number of premises. src/prooftrees.typ contains the documentation and the main functions needed.

The code for some example trees can be seen in examples/prooftree_test.typ.

Examples

A single inference would be:

#import "@preview/prooftrees:0.1.0"

#prooftree.tree(
    prooftree.axi[$A => A$],
    prooftree.uni[$A => A, B$]
)

A more interesting example:

#import "@preview/prooftrees:0.1.0"

#prooftree.tree(
    prooftree.axi[$B => B$],
    prooftree.uni[$B => B, A$],
    prooftree.uni[$B => A, B$],
        prooftree.axi[$A => A$],
        prooftree.uni[$A => A, B$],
    prooftree.bin[$B => A, B$]
)

An n-ary inference can be made:

#import "@preview/prooftrees:0.1.0"

#prooftrees.tree(
    prooftrees.axi(pad(bottom: 2pt, [$P_1$])),
    prooftrees.axi(pad(bottom: 2pt, [$P_2$])),
    prooftrees.axi(pad(bottom: 2pt, [$P_3$])),
    prooftrees.axi(pad(bottom: 2pt, [$P_4$])),
    prooftrees.axi(pad(bottom: 2pt, [$P_5$])),
    prooftrees.axi(pad(bottom: 2pt, [$P_6$])),
    prooftrees.nary(6)[$C$],
)

Known Issues:

Superscripts and subscripts clip with the line

The boundaries of blocks containing math do not expand enough for sub/pscripts; I think this is a typst issue. Short-term fix: add manual vspace or padding in the cell.

Implementation

The placement of the line and conclusion is calculated using measure on the premises and labels, and doing geometric arithmetic with these values.