Wolfram: Pattern Matching and Level Spec

Specify Depth Level of Expression for Pattern Matching

A important aspect of pattern matching is at what depth levels of an expression to match.

For example, if the pattern is

{x_, y_}

and the expression is

{1,{2,{3,4}}}

, it can match any of

• {3,4} → x match 3, y match 4
• {2,{3,4}} → x match 2, y match {3,4}
• {1,{2,{3,4}}} → x match 1, y match {2,{3,4}}

depending on the Level Spec (Tree Depth) used.

(* importance of level spec for patterns *)

(* s------------------------------ *)

(* match at level 0 only *)
Replace[ {1,{2,{3,4}}}, {x_, y_} -> g[x,y], {0}]
(* g[1, {2, {3, 4}}] *)

(* s------------------------------ *)

(* match at level 1 only *)
Replace[ {1,{2,{3,4}}}, {x_, y_} -> g[x,y], {1}]
(* {1, g[2, {3, 4}]} *)

(* s------------------------------ *)

(* match at level 2 only *)
Replace[ {1,{2,{3,4}}}, {x_, y_} -> g[x,y], {2}]
(* {1, {2, g[3, 4]}} *)

(* s------------------------------ *)

(* match at level 1 to Infinity *)
Replace[ {1,{2,{3,4}}}, {x_, y_} -> g[x,y], {1,Infinity}]
(* {1, g[2, g[3, 4]]} *)

(* match at level 0 to Infinity *)
Replace[ {1,{2,{3,4}}}, {x_, y_} -> g[x,y], {0,Infinity}]
(* g[1, g[2, g[3, 4]]] *)