# prooftree - Man Page

proof-tree display for Proof General

## Synopsis

**prooftree** [*Options...*]

## Description

**Prooftree** visualizes proof trees during proof development with **Proof General**. Currently it only works for **Coq**, though adding support for other proof assistants should be relatively easy.

To start a proof-tree display, hit the **Prooftree** icon in the **Proof General** tool-bar or select the menu entry *Proof-General* -> *Start/Stop Prooftree* or type *C-c C-d* (which runs *proof-tree-external-display-toggle*). Inside a proof, this will immediately start a proof-tree display for the current proof. Outside a proof, **Proof General** remembers to start the proof-tree display for the next proof.

Under normal circumstances **Prooftree** is started by **Proof General** as an **Emacs** subprocess. The user interacts with **Prooftree** only through the graphical user interface. A substantial part of the proof-tree visualization task is done by **Proof General**. Therefore not only the **Prooftree** command line arguments but also other aspects can only be configured inside **Proof General**, see **Proof General Customization** below.

## Options

- -help
Print synopsis and exit.

- -config
Open the configuration dialog on startup (if you want to change the configuration without starting

**Proof General**).- -geometry
*spec* Sets the X geometry of the main window.

*spec*is a standard X geometry string in the form Ā*xpos*x*ypos*[+*xoff*[+*yoff*]].- -tee
*file* Write all input to

*file*(usually for debugging purposes).- -debug
Provide more details on errors.

- -help-dialog
Open the help dialog on startup. Mainly useful for proofreading the help text.

- -test-coq-evar-parser
*data* Call the

**Coq**evar parser on*data*, pretty print the result and exit. Useful for debugging the evar parser only.

## Main Proof Display

**Prooftree** opens one window for each proof that it is requested to display. This window contains the proof-tree graph and a small display for sequents and proof commands.

### Colors

The branches in the proof-tree graph are colored according to their state. **Prooftree** distinguishes between the following states.

- current (blue by default)
The current branch is the branch from the root of the proof tree to the current goal.

- unproven (default foreground color)
A branch is unproven if it contains open proof goals.

- proved incomplete (cyan by default)
An incompletely proved branch has its proof finished, but some of the existential variables that have been introduced in this branch are not (yet) instantiated.

- proved partially (dark green by default)
In a partially proved branch all existential variables of the branch itself are instantiated, but some of those instantiations contain existential variables from other branches that are not (yet) instantiated.

- proved complete (green by default)
A branch is proved complete if all its existential variables are instantiated with terms that themselves do not contain any existential variables.

- cheated (red by default)
A cheated branch contains a cheating proof command, such as

*admit*

The colors as well as many other **Prooftree** parameters can be changed in the **Prooftree Configuration Dialog** (see below).

### Sequent Display

The sequent display below the proof tree normally shows the ancestor sequent of the current goal. With a single left mouse click one can display any goal or proof command in the sequent display. A single click outside the proof tree will switch back to default behavior. The initial size of the sequent display can be set in the **Prooftree Configuration Dialog**. A value of 0 hides the sequent display.

### Tool Tips

Abbreviated proof commands and sequents are shown in full as tool tips when the mouse pointer rests over them. Both, the tool tips for abbreviated proof commands and for sequents can be independently switched off in the **Prooftree Configuration Dialog**. The length at which proof commands are abbreviated can be configured as well.

### Additional Displays

A double click or a shift-click displays any goal or proof command in an additional window. These additional windows are automatically updated, for instance, if an existential variable is instantiated. For additional sequent displays one can browse the instantiation history of the sequent using the forward and backward buttons. These additional windows can be *detached* from the proof tree. A detached display is neither automatically updated nor automatically deleted.

### Existential Variables

**Prooftree** keeps track of existential variables, whether they have been instantiated and whether they depend on some other, not (yet) instantiated existential. It uses different colors for proved branches that created currently not instantiated existential variables and branches that only depend on some not instantiated existential created in different branches. The list of currently not (yet) instantiated existential variables is appended to proof commands and sequents in tool-tips and the other displays.

The **Existential Variable Dialog** displays a table with all existential variables of the current proof and their dependencies. Each line of the table contains a button that marks the proof command that introduced this variable (with yellow background, by default) and, if present, the proof command that instantiated this variable (with orange background, by default).

### Main Menu

The *Menu* button displays the main menu. The *Clone* item clones the current proof tree in an additional window. This additional window continues to display a snapshot of the cloned proof tree, no matter what happens with the original proof.

The *Show current* and *Show selected* items move the viewport of the proof tree such that the current proof goal, or, respectively, the selected node will be visible (if they exist).

The *Exit* item terminates **Prooftree** and closes all proof-tree displays.

The remaining four items display, respectively, the **Existential Variable Dialog**, the **Prooftree Configuration Dialog**, and the **Help** and **About** windows.

### Context Menu

A right click displays the *Context Menu*, which contains additional items.

The item *Undo to point* is active over sequent nodes in the proof tree. There, it sends an retract or undo request to Proof General that retracts the scripting buffer up to that sequent.

The items *Insert command* and *Insert subproof* are active over proof commands. They sent, respectively, the selected proof command or all proof commands in the selected subtree, to Proof General, which inserts them at point.

## Configuration

### Prooftree Configuration Dialog

The configuration dialog permits to change fonts, colors, layout parameters for proof tree drawing, to configure tool tips, initial window sizes and some other points. Changes in the configuration dialog take immediate effect. The *Save* button stores the current configuration (as marshaled **OCaml** record) in *~/.prooftree*, which will overwrite the built-in default configuration for the following **Prooftree** runs. The *Revert* button loads and applies the saved configuration. The *Cancel* and *OK* buttons close the dialog, but *Cancel* additionally resets the configuration to the state before the start of the dialog. To avoid opening partial file names, the *Log Proof General input* check box is deactivated when typing the log file name.

### Proof General Customization

The location of the **Prooftree** executable and the command line arguments are in the customization group *proof-tree*. Prover specific points, such as the regular expressions for navigation and cheating commands are in the customization group *proof-tree-internals*. To visit a customization group, type *M-x customize-group* followed by the name of the customization group inside **Proof General**.

## Limitations

In additional sequent displays, the information about existential variables is only shown for the latest version of the sequent and not for older versions in the instantiation history.

The synchronization between Proof General and Prooftree is not perfect. There are a few race conditions which are unlikely to occur during interactive proof development but can be triggered by asserting larger parts of a proof or by very quick user actions.

- In a situation, where a goal contains an existential variable, this variable is instantiated (in different branch of the proof), and the goal is shelved and quickly unshelved, it might happen that the updated sequent text (containing the instantiating of the existential variable) is associated with the unshelved version of the goal.
- Spawned subgoals and the instantiating of existential variables cause asynchronous update-sequent messages sent to
**Prooftree**. When quickly retracting portions of the proof, the corresponding undo message might overtake same update-sequent messages and thereby confuse**Prooftree**.

## Prerequisites

This version of **Prooftree** requires **Coq** 8.11 or better and **Proof General** from March 2021 or later.

## Files

- ~/.prooftree
Saved

**Prooftree**configuration. Is loaded at application start-up for overwriting the built-in default configuration. Must contain a marshaled**OCaml**configuration record.

## See Also

- The
**Prooftree**web page, http://askra.de/software/prooftree/ - The
**Proof General Adapting Manual** contains now partially outdated information about adapting

**Prooftree**for a new proof assistant (see https://proofgeneral.github.io/doc/master/adaptingman/).

## History

**Prooftree** was developed in 2011 to help to keep orientation in larger **Coq** proofs. The first versions required patches for **Coq**. After a meeting with the **Coq** development team at the third **Coq** workshop in Nijmegen, the Netherlands, in 2011, Arnaud Spiwack added the necessary support for **Prooftree** to **Coq** and **Prooftree** version 0.8 was the first version that worked with **Coq** 8.4beta and the **Proof General** development version.

The user friendly names for existential variables, introduced in **Coq** 8.6 broke many **Prooftree** features for existential variables and the removal of the *Show Goal id* command in **Coq** 8.7 broke **Prooftree** completely. In 2019, Jim Fehrle added the necessary support for **Prooftree** again to **Coq** 8.11. The existential variable printout and the *Show Goal* command were slightly generalized, making it possible to simplify the proof tree code in **Proof General** quite a bit.

## Credits

**Prooftree** has been inspired by the proof tree display of **PVS**.

## Author

Hendrik Tews <prooftree at askra.de>