# Derivations

The `ProofChecker`

class indicates that a code block will contain derivation
exercises. The `Playground`

class indicates that a code block will generate a
"playground" in which instead of checking whether the proof establishes
something set in advance, Carnap will figure out what the proof establishes and
display it at the top of the proof-box. The formal systems used can be
controlled using predefined classes, or by setting attributes on the code-block
(see below).

## Predefined classes

To get started, it's possible to create simple exercises in the propositional system of the Carnap book like this:

```
~~~{.ProofChecker .Prop}
1.1 P :|-: Q->P
~~~
```

Where the `:|-:`

again indicates a turnstile. The result is then:

Similarly,

```
~~~{.Playground .Prop}
~~~
```

generates

The class `Prop`

specifies that we wish to use the propositional formal system
of the Carnap book, and specifies a couple of UI-defaults for displaying proofs
in that system. The currently available predefined classes are:

Class Strings | Description |
---|---|

`.Prop` , `.FirstOrder` , `.SecondOrder` , `.PolySecondOrder` ,
`.MontagueSC` ,`.MontagueQC` , `ElementaryST` , `SeparativeST` |
Montague-Style systems, the first two of which are used in the Carnap book. |

`.LogicBookSD` , `LogicBookSDPlus` , `LogicBookPD` ,
`.LogicBookPDPlus` |
Fitch style systems based on Bergmann Moore and Nelson's Logic Book. |

`.ForallxSL` , `.ForallxSLPlus` , `.ForallxQL` |
Fitch-style systems based on Magnus's Forall x. |

`.ZachTFL` , `.ZachTFL2019` , `.ZachFOL` , `.ZachFOL2019` ,
`.ZachFOLPlus2019` |
Fitch-style systems based on the Calgary Remix of Forall x. |

`.IchikawaJenkinsSL` , `.IchikawaJenkinsQL` |
Fitch-style systems based on the Ichikawa-Jenkins Remix of Forall x. |

`HowardSnyderSL` ,`HowardSnyderPL` |
Systems based on Howard-Snyder's The Power of Logic. |

`HausmanSL` ,`HausmanPL` |
Systems based on Hausman's Logic and Philosophy. |

`.GoldfarbND` , `.GoldfarbAltND` , `.GoldfarbNDPlus` ,
`.GoldfarbAltNDPlus` |
Lemmon-style systems based on Goldfarb's Deductive Logic. |

`.TomassiPL` |
Lemmon-style system based on Tomassi's Logic |

`.HardegreeSL` , `.HardegreePL` , `.HardegreeWTL` ,
`.HardegreeL` , `.HardegreeK` , `.HardegreeT` , `.HardegreeB` ,
`.HardegreeD` , `.Hardegree4` , `.Hardegree5` , `.HardegreeMPL` |
Hardegree-style systems based on Hardegree's Modal Logic |

## Advanced Usage

#### Options

Like the other exercises, derivations allow for `points=VALUE`

and
`submission="none"`

.

Derivations, however, currently have a little more depth than the other types of exercises. There are, correspondingly, more options available:

Name | Effect |
---|---|

`guides` |
Includes vertical indentation-level indicators |

`fonts` |
Uses Fira Logic font, including ligatures for logical symbols |

`popout` |
Makes it possible to open the problem in a new window |

`render` |
Renders a picture of the proof as you type |

`indent` |
Automatically indents newlines to the level of the previous line |

`tabindent` |
Insert indent on tab press |

`resize` |
Automatically resizes proof area |

`exam` |
Allows for submission of work which is incomplete or incorrect |

These can all be included in the "options" string supplied to the options attribute of the code block, like this:

```
~~~{.ProofChecker .Prop options="indent fonts popout render autoIndent"}
1.8 P :|-: Q->P
|1.Show Q->P
|2. Q:AS
|3. P:PR
|4.:CD 3
~~~
```

The result of the above is:

An options string will override any options that are included by default in a
given predefined class. For example, `.Prop`

automatically turns on the
`resize`

option. However if we have just

```
~~~{.ProofChecker .Prop options="indent"}
1.9 P :|-: Q->P
~~~
```

We get a proofbox that resizes manually:

#### Partial Solutions

A partial solution to a problem can be included by following a problem with a
derivation that is line-by-line prefixed with the `|`

character, optionally
(for readability) followed by a line number followed by a period, like this:

```
~~~{.ProofChecker .Prop}
1.7 P :|-: Q->P
|1.Show Q->P
|2. Q:AS
|3. P:PR
|4.:CD 3
~~~
```

This gives us:

Everything after the line number (or the `|`

if you don't use numbers) is
included in the proof, so be careful about spaces!

You can also include a partial derivation without specific solution, by
replacing `.ProofChecker`

with `.Playground`

, writing for example:

```
~~~{.Playground .Prop}
|1.Show Q->P
|2. Q:AS
|3. P:PR
|4.:CD 3
~~~
```

which gives you a proof box that calculates what has been derived and displays it at the top, rather than calculating whether the derivation proves a given sequent, thus:

#### Feedback

The defaults for feedback (check the proof with every keypress) can also be overridden by setting the feedback attribute. The override options for feedback are

Name | Effect |
---|---|

`manual` |
require a button-press for feedback |

`syntaxonly` |
warn about syntax errors, but do not check proof for correctness |

`none` |
do not offer feedback |

So,

```
~~~{.ProofChecker .Prop submission="none" feedback="manual"}
1.10 P :|-: Q->P
~~~
```

produces

#### Systems

If you don't want to use a predefined class, you can set the system option manually.

The available propositional systems are: `prop`

`montagueSC`

`LogicBookSD`

`LogicBookSDPlus`

`hausmanSL`

`howardSnyderSL`

`ichikawaJenkinsSL`

`hausmanSL`

`magnusSL`

`magnusSLPlus`

`thomasBolducAndZachTFL`

`thomasBolducAndZachTFL2019`

`tomassiPL`

and `hardegreeSL`

. The available first-order systems are:
`firstOrder`

`montagueQC`

`magnusQL`

`thomasBolducAndZachFOL`

`thomasBolducAndZachFOL2019`

`thomasBolducAndZachFOLPlus2019`

`LogicBookPD`

`LogicBookPDPlus`

`hausmanPL`

`howardSnyderPL`

`ichikawaJenkinsQL`

`hardegreePL`

`goldfarbAltND`

`goldfarbNDPlus`

and `goldfarbAltNDPlus`

. The
available set theory systems are: `elementarySetTheory`

and
`separativeSetTheory`

. The available second-order systems are: `secondOrder`

and `PolySecondOrder`

. The available propositional modal logic systems are:
`hardegreeL`

`hardegreeK`

`hardegreeT`

`hardegreeB`

`hardegreeD`

`hardegree4`

and `hardegree5`

. The available predicate modal logic system is `hardegreeMPL`

,
and the available "world theory" system is `hardegreeWTL`

.

#### Initialization

The `init`

attribute may be set to "now" in order to check the proof as soon as
it is loaded, instead of waiting for a user interaction.

#### Indentation Guides

Besides just the indentation guide created by setting `guides`

in the options
string, there are several more refined overlays available for increasing the
readability of a typed proof. These are configured by setting the `guides`

attribute. The available options for guides are:

Name | Effect |
---|---|

`montague` |
Simple indentation gudie |

`fitch` |
A fitch style proof overlay |

`hausman` |
A Hausman style proof overlay |

`howard-snyder` |
A Howard-Snyder style proof overlay |

So,

```
~~~{.Playground .ForallxSL guides="fitch"}
P :AS
P/\P :&I 1 1
P :&E 2
P->P :->I 1-3
~~~
```

Produces: