# 1. Getting Started with CCalc

## 1.1. CCalc Input: Transition Systems

Transition system TS1 from Section 0.1 can be described in the input language of CCalc as follows:

```:- constants
p :: inertialFluent;
a :: exogenousAction.

a causes p.
```
This description consists of the declarations of the constants p and a (the first 3 lines) and a proposition (the last line). The declaration part begins with the heading :- constants and ends with a period. The proposition is followed by a period also. A semicolon separates the two declarations from each other. Within each declaration, the symbol :: separates the constant that is being declared from the symbol that indicates what kind of constant it is.

Note that p is declared here as an inertialFluent, rather than simply a fluent, and a is declared as an exogenousAction, rather than simply an action. See Section 0.2 above for a brief, informal discussion of these ideas.

Transition system TS2 is actually a family of transition systems, one for each value of N. The following piece of code defines the system corresponding to N=3:

```:- constants
c :: inertialFluent(0..3);
a :: exogenousAction.

a causes c=1 if c=0.
a causes c=2 if c=1.
a causes c=3 if c=2.

nonexecutable a if c=3.
```
In the declaration of c, the symbol inertialFluent is followed by (0..3) to indicate that the possible values of this fluent are integers between 0 and 3, rather than f and t. Each of the causes propositions is conditional -- it includes if. For instance, the first of them describes the effect of action a when it is executed in a state satisfying c=0. The nonexecutable proposition in the last line tells us that the transition system does not have an edge that begins at the vertex c=3 and is labeled a=t. (Without this proposition, such an edge would be included in the transition system, according to the semantics of C+. Since the causes propositions in this action description do not postulate any effect of a on c when c=3, this edge, by inertia, would be a loop.)

The causes propositions in this example follow a simple pattern, and the input language of CCalc allows us to use this fact to make the action description more compact:

```:- constants
c :: inertialFluent(0..3);
a :: exogenousAction.

:- variables
I :: 0..2.

a causes c=I+1 if c=I.

nonexecutable a if c=3.
```
The letter I is declared here to be a variable ranging over 0,1,2, and we use it in a "schematic proposition" that represents a set of 3 instances. In CCalc code, capital letters and identifiers beginning with a capital letter are customarily used as variables, but not as constants (or as anything else, for that matter). This convention is related to the fact that CCalc is written in Prolog. Violating this convention is considered, in some cases, a syntax error.

The last piece of code can be further improved by treating the value of N as a macro:

```:- macros
n -> 3.

:- constants
c :: inertialFluent(0..n);
a :: exogenousAction.

:- variables
I :: 0..n-1.

a causes c=I+1 if c=I.

nonexecutable a if c=n.
```
The macro definition instructs CCalc to replace every occurrence of n in the rest of the file by 3, as a preprocessing step.

Forward to Section 1.2: CCalc Input: Queries
Back to Section 0.3: Queries