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Functional Modelling System
IngmarDasseville
24.2K views
01
Tutorial
Introduction
FMS as a calculator
(Anonymous) Functions
Tuples and Constructors
Sets
The End
02
Advanced Topics
Recursion
Translation
Translation (cont.)
03
Appendix
Syntax
Code Examples
11/11
Code Examples
Previous:
Syntax
Code Examples
Simple Equation
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a :: element of {1,2,3}.
b :: element of {1,2,3}.
a + b = 5.
Run
Propositions
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p :: proposition.
q :: proposition.
p | q.
Run
Graph Coloring
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#printDetail 0.
//Declaration of given sets
borders := {("a","b"), ("b","c"), ("c","a")}.
colours := {1..3}.
//Declaration of the interpretation we are looking
for
colorof/1 :: function to colours.
! borders (\(x,y) -> colorof x ~= colorof y).
Run
NQueens
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dom := {1..8}.
column/1 :: function to dom.
alldiff f := ! dom (\x -> ! dom (\y -> x ~= y => f
x ~= f y)).
! {
column,
\x -> x - column x,
\x -> x + column x
} alldiff.
Run
Peano
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//declare s and nil as constructors
s/1 :: constructor.
nil/0 :: constructor.
//converts explains how to build a peano number fr
om an integer
conv x := case x of 0 -> nil; > 0 -> s (conv (x-1)
);.
//c is a number which should have a certain peano
representation
c :: element of {1..10}.
conv c = s ( s( s( s (nil)))).
//d is the peano representation of 3
d := conv 3.
relevant d.
Run
Transitive Closure
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closure s := union s { (a,d) ||
(a,b) <- (closure s),
(c,d) <- (closure s),
b = c
}.
s := {(1,2) , (2,3) , (3,4)}.
sClosed := closure s.
relevant sClosed.
Run
External Functions
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#script(lua)
clingo = require("clingo")
N = clingo.Number
function gcd(a, b)
if a.number == 0 then
return b
else
na = a.number
nb = b.number
nc = nb % na
return gcd(N(nc), a)
end
end
#end.
gcd :: external Int -> Int -> Int.
gcd 15 20 = 5.
Run
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