# Output Format

`plasp` 3 translates SAS and PDDL files into a uniform ASP fact format.

## Overview

Essentially, `plasp`’s output format consists of [state variables](#variables) that are modified by [actions](#actions) if their preconditions are fulfilled.
Variables reference [entities](#constants-objects) that are affected by the actions.
As with PDDL, the objective is to achieve a specific [goal](#goal) starting from an [initial state](#initial-state) by executing a sequence of actions.

`plasp`’s variables correspond to the multivalued variables in SAS.
PDDL predicates are turned into Boolean variables to make the output format consistent.

Actions are modeled exactly as PDDL actions and SAS operators.

## In a Nutshell

Consider the following, simplistic PDDL problem of turning a switch on:

```lisp
; simplistic example of turning a switch on
(define (domain switch)
	(:requirements :typing)
	(:types switch)
	(:predicates
		(on ?x - switch))
	(:action turn-on
		:parameters
			(?x - switch)
		:precondition
			(not (on ?x))
		:effect
			(on ?x)))

; example problem with one switch
(define (problem switch-problem)
	(:domain switch)
	(:objects a - switch)
	(:init
		(not (on a)))
	(:goal
		(on a)))
```

This is translated by `plasp translate` into the following output format (slightly restructured for clarity):

```prolog
% declares the type “type("switch")”
type(type("switch")).

% introduces a switch “constant("a")”
constant(constant("a")).
has(constant("a"), type("switch")).

% declares a variable “variable(on(X))” for switches X
variable(variable(("on", X))) :- has(X, type("switch")).

% variables may have the values true and false
boolean(true).
boolean(false).
contains(X, value(X, B)) :- variable(X), boolean(B).

% declares the action “action(turnOn(X))”, which requires switch X to be off and then turns it on
action(action(("turn-on", X))) :- has(X, type("switch")).
precondition(action(("turn-on", X)), variable(("on", X)), value(variable(("on", X)), false))
    :- action(action(("turn-on", X))).
postcondition(action(("turn-on", X)), effect(unconditional), variable(("on", X)), value(variable(("on", X)), true))
    :- action(action(("turn-on", X))).

% initially, the switch is off
initialState(variable(("on", constant("a"))), value(variable(("on", constant("a"))), false)).

% in the end, the switch should be on
goal(variable(("on", constant("a"))), value(variable(("on", constant("a"))), true)).
```

## Syntax and Semantics

`plasp` structures the translated ASP facts into multiple sections, which are explained in the following.

### Feature Requirements

```prolog
% declares a required feature
requires(feature(<name>)).
```

`plasp` recognizes and declares advanced features used by the input problem, such as [conditional effects](#actions), [mutex groups](#mutex-groups) and [axiom rules](#axiom-rules) (currently only SAS).
See the [full list of supported features](feature-requirements.md) for more information.

The feature requirement predicates may be used in meta encodings to warn about unsupported features.

### Types

```prolog
% declares a <type>
type(type(<name>)).

% specifies that <type 1> inherits <type 2>
inherits(<type 1>, <type 2>).

% specifies <constant> to have type <type>
has(<constant>, <type>).
```

[Variables](#variables), [constants](#constants-objects), and [objects](#constants-objects) may be typed. Types are only available with PDDL and if typing is enabled.

`plasp` automatically generates all matching `has` predicates for objects with types that inherit other types.

### Variables

```prolog
% declares a <variable>
variable(variable(<name>)).

% adds a <value> to the domain of a <variable>
contains(<variable>, <value>).
```

`plasp`’s variables represent the current state of the planning problem.
Variables are linked to the problem's [objects](#constants-objects) and [constants](#constants-objects).

`plasp`’s variables are multivalued, and each variable has exactly one value at each point in time.

With SAS, variable names are numbers starting at 0, `variable(<number>)`.
SAS variables are inherently multivalued, which results in two or more values of the form `value(<SAS predicate>, <SAS value>)` for each variable.

With PDDL, Boolean variables are created from the PDDL predicates.
Variables are named after the PDDL predicate signatures, `variable(<PDDL predicate>).`
Each variable contains exactly two values (one `true`, one `false`) of the form `value(<variable>, <bool>)`.
Note that with PDDL, values contain the corresponding variables as the first argument to make the format consistent with the multi-valued variables obtained with SAS input.

### Derived Variables

```prolog
% declares a <derived variable>
derivedVariable(derivedVariable(<name>)).

% adds a <value> to the domain of a <derived variable>
contains(<derived variable>, <value>).
```

Derived variables are introduced whenever the translator needs to use [derived predicates](#derived-predicates).
When the preconditions of a [derived predicate](#derived-predicates) are met, the corresponding derived variable (named after the derived predicate) is set as an effect.

Derived variables are analogously defined to common variables and may also be referenced in preconditions, conditions of conditional effects, and goal descriptions, just as variables.

In contrast to common variables, derived variables *are not subject to inertia rules.*
In other words, derived variables are computed for each time step separately, and reset when going to the next time step (their values don’t automatically carry over to the next time step).

### Actions

```prolog
% declares an <action>
action(action(<name>)).

% defines that as a precondition to <action>, <variable> and <derived variable> must have value <value>
precondition(<action>, <variable>, <value>).
precondition(<action>, <derived variable>, <value>).

% defines that after applying <action>, <variable> is assigned <value>
postcondition(<action>, effect(<number>), <variable>, <value>).

% defines the condition of a conditional effect
precondition(effect(<number>), <variable>, <value>).
precondition(effect(<number>), <derived variable>, <value>).

% specifies the costs of applying <action>
costs(<action>, <number>).
```

Actions may require certain [variables](#variables) (or [derived variables](#derived-variables)) to have specific values in order to be executed.
After applying an action, variables get new values according to the action's postconditions.

Actions may have *conditional effects*, that is, certain postconditions are only applied if additional conditions are satisfied.
For this reason, each conditional effect is uniquely identified with a predicate `effect(<number>)` as the second argument of the `postcondition` facts.
The conditions of conditional effects are given by additional `precondition` facts that take the respective `effect(<number>)` predicates as the first argument.

Unconditional effects are identified with `effect(unconditional)`.

Conditional effects are currently only supported with SAS input problems.

Actions may also have *action costs* required to apply them. Action costs are currently supported for SAS only.

### Derived Predicates

```prolog
% declares a <derived predicate> of with conjunctive (type(and)) or disjunctive (type(or)) preconditions
derivedPredicate(derivedPredicate(<name>), type(<and/or>)).

% defines that as a precondition to <derived predicate>, <variable> and <derived variable> must have value <value>
precondition(<derived predicate>, type(<and/or>), <variable>, <value>).
precondition(<derived predicate>, type(<and/or>), <derived variable>, <value>).

% defines that after applying <action>, <derived variable> is assigned <value>
postcondition(<derived predicate>, type(<and/or>), effect(<number>), <derived variable>, <value>).

% defines the condition of a conditional effect
precondition(effect(<number>), <variable>, <value>).
precondition(effect(<number>), <derived variable>, <value>).

% specifies the costs of applying <action>
costs(<action>, <number>).
```

Derived predicates are introduced by the translator when there are nested expressions or disjunctions in action preconditions, conditions of conditional effects, or goal descriptions.
Derived predicates operate on [derived variables](#derived-variables) of the same name.

Like actions, derived predicates must satisfy preconditions in order for their effect to be applicable.
The effect of all derived predicates is to set the corresponding [derived variables](#derived-variables) to `true` or `false`.

In contrast to actions, however, derived predicates specify whether their preconditions are to be interpreted as a *conjunction* (`type(and)`) or as a *disjunction* (`type(or)`).
Encoding authors need to ensure that derived predicate preconditions are interpreted in the correct way.

### Constants/Objects

```prolog
% declares a <constant> or object
constant(constant(<name>)).

% specifies <constant> to have type type(<name>)
has(<constant>, <type>).
```

Constants and objects are the entities that are affected by [actions](#actions), for instance, the blocks in a Blocks World problem.
Constants are global for a domain, while objects are problem-specific.

`plasp` does not distinguish between the two (modeling both as constants), as both are identically used static identifiers.

### Initial State

```prolog
% initializes <variable> with a specific <value>
initialState(<variable>, <value>).
```

The initial state contains all [variable](#variables) assignments that hold before executing any [actions](#actions).

Note that with PDDL, `plasp` sets all unspecified initial state variables to `false` in order to make the initial state total.

### Goal

```prolog
% specifies that <variable> and <derived variable> shall obtain a respective <value> in the end
goal(<variable>, <value>).
goal(<derived variable>, <value>).
```

The goal specifies all assignments of [variables](#variables) and [derived variables](#derived-variables) that have to be fulfilled after executing the action sequence.

### Mutex Groups

```prolog
% declares a <mutex group>
mutexGroup(mutexGroup(<number>)).

% adds the assignment of <variable> to <value> to a <mutex group>
contains(<mutex group>, <variable>, <value>).
```

SAS contains information about mutually exclusive [variable](#variables) assignments.
That is, *at most one* variable assignment of each mutex group must be satisfied at all times.

Mutex group facts are only present with SAS input programs and not PDDL.

Mutex groups contain essential information in order to find plans correctly.
That is, if mutex groups are present in `plasp`’s output, they have to be accounted for appropriately.

### Axiom Rules

```prolog
% declares an <axiom rule>
axiomRule(axiomRule(<number>)).

% defines that as a precondition to <axiom rule>, <variable> must have value <value>
precondition(<axiom rule>, <variable>, <value>).

% defines that after applying <axiom rule>, <variable> is assigned <value>
postcondition(<axiom rule>, effect(unconditional), <variable>, <value>).
```

Axiom rules are similar to [actions](#actions) in that they modify [variables](#variables) if certain preconditions are satisfied.
However, axiom rules must be applied *immediately* as soon as their preconditions are satisfied.

The second argument of `postcondition`, `effect(unconditional)`, is not used and exists only for consistency with [actions](#actions).

Axiom rule facts are only present with SAS input programs and not PDDL.

Axiom rules contain essential information in order to find plans correctly.
That is, if axiom rules are present in `plasp`’s output, they have to be accounted for appropriately.