WolframLang: Change Expression by Pattern

By Xah Lee. Date: . Last updated: .

Intro to Expression Transformation by Rules

The following functions transform expression by a rule or list of rules.

Pattern Matching and Expression Tree Depth Level Spec

One important aspect is what level of tree depth to match a pattern.

It has effect on the match when the pattern itself is a nested expression.

Replace First Occurrence or All Occurrences

Both Replace and ReplaceAll replace all occurrences. (the “All” in “ReplaceAll” refers to levels.)

Some functions have a optional parameter that specify doing just the first n occurrences. e.g. Cases. 〔see WolframLang: Filter List〕

Function that Transform Expression by Pattern

ReplaceAll[expr, rules]
ReplaceRepeated[expr, rules]

🔸 SHORT SYNTAX: expr //. rules

repeatedly performs ReplaceAll until expr no longer changes.

ReplaceRepeated 

ReplaceRepeated [
 { 2, 3, 4, {99, 6}},
 x_Integer?(Function[ UnsameQ[ Mod[ #, 5 ], 0 ] ]) :> x + 1
]
(* {5, 5, 5, {100, 10}} *)

Replace with Depth Level Restriction

Replace[expr, rules, levelSpec]

transform expression but matching only at levelSpec.

By default, it is level {0}, meaning whole expression. 〔see WolframLang: Pattern Matching and Level Spec〕

Replace 

(* importance of level spec for non-flat patterns *)

(* match at level 1 to 99 *)
Replace[ {1, {2, {3, {4}}}}, {_Integer, {_Integer}} -> x, {1,99}]
(* {1, {2, x}} *)

(* match at level 1 only *)
Replace[ {1, {2, {3, {4}}}}, {_Integer, {_Integer}} -> x, {1}]
(* {1, {2, {3, {4}}}} *)
(* no match found *)
ReplaceList[expr, rules]
  • Transform entire expression and return a list of steps of each rule applied.
  • 🛑 WARNING: match against entire expression, not parts of it.

ReplaceList

Replace at Specific Position

ReplaceAt[expr, rules, n]

transforms expr by replacing nth element using rules

ReplaceAt

ReplaceAt[expr, rules, positionSpec]

transforms expr by replacing the particular positions using rules

Pattern Matching