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|
set show timing off .
set show advisories off .
sth BT-ELEMS is
protecting BOOL .
sort State .
op isOk : State -> Bool .
op isSolution : State -> Bool .
strat expand @ State .
endsth
smod BT-STRAT{X :: BT-ELEMS} is
var S : X$State .
strat solve @ X$State .
sd solve := (match S s.t. isSolution(S)) ? idle
: (expand ;
match S s.t. isOk(S) ;
solve) .
endsm
mod QUEENS is
protecting LIST{Nat} .
protecting SET{Nat} .
op isOk : List{Nat} -> Bool .
op ok : List{Nat} Nat Nat -> Bool .
op isSolution : List{Nat} -> Bool .
vars N M Diff : Nat .
var L : List{Nat} .
var S : Set{Nat} .
eq isOk(L N) = ok(L, N, 1) .
eq ok(nil, M, Diff) = true .
ceq ok(L N, M, Diff) = ok(L, M, Diff + 1) if N =/= M /\ N =/= M + Diff /\ M =/= N + Diff .
eq isSolution(L) = size(L) == 8 .
crl [next] : L => L N if N,S := 1, 2, 3, 4, 5, 6, 7, 8 .
endm
view QueensBT from BT-ELEMS to QUEENS is
sort State to List{Nat} .
strat expand to expr top(next) .
endv
smod QUEENS-BT is
including BT-STRAT{QueensBT} .
endsm
dsrew [1] nil using solve .
srew [1] nil using solve .
continue 2 .
fmod GRAPHS is
pr NAT .
sort Edge .
op p : Nat Nat -> Edge [ctor comm] .
sort Adjacency .
subsort Edge < Adjacency .
op nil : -> Adjacency [ctor] .
op __ : Adjacency Adjacency -> Adjacency [ctor assoc comm id: nil] .
var E : Edge .
var As : Adjacency .
var K L : Nat .
eq E E = E .
op neighbor : Nat Nat Adjacency -> Bool .
eq neighbor(K, L, p(K, L) As) = true .
eq neighbor(K, L, As) = false [owise] .
endfm
mod COLORING is
pr GRAPHS .
pr NAT-LIST .
pr EXT-BOOL .
sort Graph .
op graph : Nat Nat Adjacency NatList -> Graph [ctor] .
op numColors : Graph -> Nat .
op alreadyColored : Graph -> Nat .
eq numColors(graph(N, M, As, Cs)) = M .
eq alreadyColored(graph(N, M, As, Cs)) = size(Cs) .
var N M K K' C C' : Nat .
var As : Adjacency .
var Cs : NatList .
op isSolution : Graph -> Bool .
op isOk : Graph -> Bool .
op admissibleColor : Nat Nat Graph -> Bool .
op admissibleColor : Nat Nat Adjacency Nat NatList -> Bool .
eq isSolution(graph(N, M, As, Cs)) = N == size(Cs) .
eq isOk(G:Graph) = true .
eq admissibleColor(C, K, graph(N, M, As, Cs)) = admissibleColor(C, K, As, 0, Cs) .
eq admissibleColor(C, K, As, K', nil) = true .
eq admissibleColor(C, K, As, K', C' Cs) = (C =/= C' or not neighbor(K, K', As))
and-then admissibleColor(C, K, As, s(K'), Cs) .
rl [next] : graph(N, M, As, Cs) => graph(N, M, As, Cs C) [nonexec] .
endm
smod COLORING-STRAT is
protecting COLORING .
strat expand @ Graph .
strat expand : Nat @ Graph .
sd expand := expand(0) .
var C : Nat .
var G : Graph .
sd expand(C) :=
match G s.t. admissibleColor(C, alreadyColored(G), G) ; next[C <- C]
| match G s.t. s(C) < numColors(G) ; expand(s(C)) .
endsm
view ColoringBT from BT-ELEMS to COLORING-STRAT is
sort State to Graph .
strat expand to expand .
endv
smod COLORING-BT is
including BT-STRAT{ColoringBT} .
endsm
srew [4] graph(10, 3, p(0, 1) p(0, 4) p(0, 5) p(1, 2) p(1, 6)
p(2, 3) p(2, 7) p(3, 4) p(3, 8) p(4, 9)
p(5, 7) p(5, 8) p(6, 8) p(6, 9) p(7, 9), nil) using solve .
sth STRIV is
including TRIV .
strat st @ Elt .
endsth
smod IDLE-STRAT is
strats nop @ Bool .
sd nop := idle .
endsm
view Nop from STRIV to IDLE-STRAT is
sort Elt to Bool .
strat st to nop .
endv
smod TWICE{X :: STRIV} is
strat xst @ X$Elt .
sd xst := st ; st .
endsm
view Twice{X :: STRIV} from STRIV to TWICE{X} is
sort Elt to X$Elt .
strat st to xst .
endv
smod REDUCE{X :: STRIV} is
strat reduce @ X$Elt .
sd reduce := st ? idle : reduce .
endsm
smod MAIN is
protecting REDUCE{Twice{Nop}} .
endsm
srew true using reduce .
|
