# Functional Modelling System

## Syntax Overview

This document should serve as a quick overview of the statements which are possible in IDP4.

### Directives

Directives are always of the form # directiveName number.

Supported directives are:

• nbModels, determines the number of models which need to be printed
• printFullStructure, determines whether the full ASP structure needs to be outputted to the model or not
• printASP, determines whether the full ASP source needs to be printed or not
• constrain, determines whether you want to see all the structures given the definitions or only the models
• inline, determines whether the inliner does its work
• pushNegs, determines whether negations are pushed

#### Scripts

It is possible to directly write external functions scripts for use in clingo. These are not conform the other directives. (See the example for more info about these)

### Imports

Import statements are of the form: import "filename.fml".

A file containing only definitions is considered a library file and can be imported. Some useful symbols are predefined in the stdlib which is implicitly imported.

### Declarations

It is possible to introduce a new symbol in a few ways:

• a := expression., which defines the new symbol a to have the interpretation of the expressions.
• a :: subset of expression., which introduces a to be a subset of the set determined by the expression.
• a :: element of expression., same as the previous one but a will be a single element instead of the full set
• a :: function to expression., which introduces a to be a unary function with codomain the set determined by the expression
• a :: predicate., which introduces a to be a predicate (a unary function to booleans).
• a :: proposition., introduces a to be a proposition
• a\2 :: constructor., introduces the binary constructor function a
• a\2 :: external function., introduces the binary external function a, this should only be used in conjunction with a script directive

### Expressions

Expressions are based on the lambda calculus:

• ! set predicate is used to say that the function predicate should hold for every member of set set.
• ? set predicate same as ! but existential.
• Arithmetic operators over integers + - / * are supported.
• Comparison operators over integers < =< >= > = ~= are supported
• Boolean operators & | ~ <=> => <= are supported
• Integers and strings can be used 1 "Hello World"
• let a := 1 ; b := 2 in a+b. is used to locally define a and b so this expressions evaluates to 3
• {x,y || a <- {{1,2},{3,4}}, x <- a, x != 1, y := x + 1} the set consisting of the x and y's, such that a is an element of the set {{1,2},{3,4}}, x is an element of a, x is not equal to 1, and y is one larger than x.
• if p then a else b represents is equal to a if boolean p is true, and b otherwise.

#### Patterns

• variableName
• constructor [arg1 arg2 ...]
• 5, "a"
• <5
• >5
• _