Mathematica Asked on November 28, 2020
I want a rule that would transform, for example, And[i,F[j,k],l,G[m,F[j,k],n],p]
into And[i,F[j,k],l,G[m,T,n],p]
, where F
, G
and T
are either just symbols or, say, defined by F[u_,v_]:=Or[F1[Or[Not[u],v],F2[v]]
or G[x_,y_,z_]:=Or[G1[x,y],G2[z,x]]
or T=H[False,True]
or something even more complicated.
I have defined the following rule:
And[u___, x_, v___, y_, w___] :> And[u, x, v, y //. x -> T, w]
It never changes any expression. How should I do it properly?
Try this:
expr = And[i, F[j, k], l, G[m, F[j, k], n], p];
MapAt[ReplaceAll[#, F[j, k] -> T] &, expr, {4, 2}]
(* i && F[j, k] && l && G[m, T, n] && p *)
Have fun!
Answered by Alexei Boulbitch on November 28, 2020
ClearAll[F]
in = And[i, F[j, k], l, G[m, F[j, k], n], p]
i && F[j, k] && l && G[m, F[j, k], n] && p
in2 = And[i, F[j, k], l, G[m, F[j, k], n], Nest[H, F[1], 5] + p]
i && F[j, k] && l && G[m, F[j, k], n] && p + H[H[H[H[H[F[1]]]]]]
1. You can use Replace
with level specification {2, ∞}
:
Replace[in, F[__] -> T, {2, ∞}]
i && F[j, k] && l && G[m, T, n] && p
Replace[in2, F[__] -> T, {2, ∞}]
i && F[j, k] && l && G[m, T, n] && p + H[H[H[H[H[T]]]]]
2. Alternatively, use TagSetDelayed
to define behavior of F
inside expressions with designated heads:
ClearAll[F];
F /: (head : G | H)[a___, F[__], b___] := head[a, T, b];
in
i && F[j, k] && l && G[m, T, n] && p
in2
i && F[j, k] && l && G[m, T, n] && p + H[H[H[H[H[T]]]]]
Answered by kglr on November 28, 2020
Myself I tried something as general as possible. It would be great if somebody could optimize this, I feel it is far from perfect.
step[list_] := Module[{ul = Union[list], l, newl = {}, k, res},
l = Length[ul];
For[k = 1, k <= l, k++,
AppendTo[newl,
ul[[k]] /. Table[ul[[j]] -> T, {j, Complement[Range[l], {k}]}]
]
];
res = And @@ newl;
Return[If[Head[res] === And,
Table[res[[k]], {k, Length[res]}], {res}]]
]
stab[list_] := FixedPoint[step, list]
myAnd[u___] := And @@ stab[{u}]
Answered by მამუკა ჯიბლაძე on November 28, 2020
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