# Functional Modelling System

IngmarDasseville

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## 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`

`_`

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