CSE505/C/nqueens.idp

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2024-02-21 23:53:58 -05:00
vocabulary V {
type index isa int
queen(index, index)
n : index
type diag isa int
diag1(index, index) : diag
diag2(index, index) : diag
type dist isa int
k: dist
}
structure S : V {
index = {1..4}
diag = {1..7}
n = 4
k = 2
}
theory T : V {
{ diag1(x, y) = x - y + n. }
{ diag2(x, y) = x + y - 1. }
!x : ?=1y : queen(x, y). //(1)
!y : ?=1x : queen(x, y). //(2)
!d : #{x y : queen(x, y) & diag1(x, y) = d} < 2. //(3)
!d : #{x y : queen(x, y) & diag2(x, y) = d} < 2. //(4)
~? x1 y1 x2 y2: queen(x1, y1) & queen(x2, y2) & ~x1 = x2 & abs(x1-x2) + abs(y1-y2) =< k.
//~? x1 y1 x2 y2: queen(x1, y1) & queen(x2, y2) & abs(x1-y1) = 3.
}
procedure main() {
/* Important: the option xsb is not present in every installation, in order to obtain
* efficient definition evaluation with XSB, you should compile IDP yourself
* (as XSB cannot be distributed with dynamically linked binaries
*/
stdoptions.xsb=true // use XSB to calculate definitions that can be
// calculated in advance
diags = calculatedefinitions(T,S) // calculate the definitions for symbols diag1 and diag2
// The resulting variable (diags) contains a single structure
// in which the defined symbols are two-valued
print("Definitions calculated:\n"..tostring(diags))
stdoptions.nbmodels=0 // search for all models
solutions = modelexpand(T,diags) // solutions is now a (Lua) table with all models
// Note that instead of diags, we could also do modelexpand on S,
// since the standard modelexpand workflow contains a call to
// calculatedefinitions
print(#solutions.." models found") // "#" retrieves table size, .. is the lua concatenation
for i,sol in ipairs(solutions) do // A for-loop to iterate over all solutions.
print("model "..i..":") // ipairs is a builtin Lua procedure which allows you
// to loop over the index and table elements of a table
print(sol)
end
}