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Is there a defined priority for pattern matching?

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6

$begingroup$

If you define a function g, like so:

g[x_?EvenQ] := "even"    

g[x_?NumberQ] := "number"

why will Mathematica always return g[2] == "Even", even though NumberQ[2] == True?

More specifically, is there a defined order in which Mathematica will try to match function cases? Does it evaluate the most specific match first?

pattern-matching expression-test

share|improve this question

edited 14 hours ago

wgoodall01

asked 14 hours ago

wgoodall01wgoodall01

1335

New contributor

wgoodall01 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  g[x_NumberQ] means to match arguments with the head NumberQ. What you want is to match arguments such that NumberQ[x] is True, which is g[x_?NumberQ]. Look up PatternTest[]. (Before you make this correction, make sure to run Clear[g] first.)
  $endgroup$
  – J. M. is computer-less♦
  14 hours ago
  
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  That's right---fixed.
  $endgroup$
  – wgoodall01
  14 hours ago
  

  
  
  
  


• 
  
  
  

  
  2
  

  
  
  
  
  
  

  
  $begingroup$
  Once you have made this fix, evaluate DownValues[g]; that should give a hint as to which case gets applied first. Generally, it tries to put special cases first before general ones.
  $endgroup$
  – J. M. is computer-less♦
  14 hours ago
  
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Or just execute ?g to see the order of the definitions.
  $endgroup$
  – Roman
  12 hours ago
  

  
  
  
  

add a comment | 

6

$begingroup$

If you define a function g, like so:

g[x_?EvenQ] := "even"    

g[x_?NumberQ] := "number"

why will Mathematica always return g[2] == "Even", even though NumberQ[2] == True?

More specifically, is there a defined order in which Mathematica will try to match function cases? Does it evaluate the most specific match first?

pattern-matching expression-test

share|improve this question

edited 14 hours ago

wgoodall01

asked 14 hours ago

wgoodall01wgoodall01

1335

New contributor

wgoodall01 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  g[x_NumberQ] means to match arguments with the head NumberQ. What you want is to match arguments such that NumberQ[x] is True, which is g[x_?NumberQ]. Look up PatternTest[]. (Before you make this correction, make sure to run Clear[g] first.)
  $endgroup$
  – J. M. is computer-less♦
  14 hours ago
  
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  That's right---fixed.
  $endgroup$
  – wgoodall01
  14 hours ago
  

  
  
  
  


• 
  
  
  

  
  2
  

  
  
  
  
  
  

  
  $begingroup$
  Once you have made this fix, evaluate DownValues[g]; that should give a hint as to which case gets applied first. Generally, it tries to put special cases first before general ones.
  $endgroup$
  – J. M. is computer-less♦
  14 hours ago
  
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Or just execute ?g to see the order of the definitions.
  $endgroup$
  – Roman
  12 hours ago
  

  
  
  
  

add a comment | 

$begingroup$

If you define a function g, like so:

g[x_?EvenQ] := "even"    

g[x_?NumberQ] := "number"

why will Mathematica always return g[2] == "Even", even though NumberQ[2] == True?

More specifically, is there a defined order in which Mathematica will try to match function cases? Does it evaluate the most specific match first?

pattern-matching expression-test

share|improve this question

edited 14 hours ago

wgoodall01

asked 14 hours ago

wgoodall01wgoodall01

1335

New contributor

wgoodall01 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

$endgroup$

g[x_?EvenQ] := "even"    

g[x_?NumberQ] := "number"

share|improve this question

edited 14 hours ago

wgoodall01

asked 14 hours ago

wgoodall01wgoodall01

1335

New contributor

wgoodall01 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

share|improve this question

edited 14 hours ago

wgoodall01

asked 14 hours ago

wgoodall01wgoodall01

1335

New contributor

wgoodall01 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

asked 14 hours ago

wgoodall01wgoodall01

1335

New contributor

wgoodall01 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

asked 14 hours ago

wgoodall01wgoodall01

1335

1 Answer
1

active

oldest

votes

11

$begingroup$

TheOrderingOfDefinitions

• ... The Wolfram System follows the principle of trying to put more general definitions after more specific ones. This means that special cases of rules are typically tried before more general cases.


• Although in many practical cases, the Wolfram System can recognize when one rule is more general than another, you should realize that this is not always possible. For example, if two rules both contain complicated /; conditions, it may not be possible to work out which is more general, and, in fact, there may not be a definite ordering. Whenever the appropriate ordering is not clear, the Wolfram System stores rules in the order you give them.

ClearAll[g]

g[x_?EvenQ] := "even"

g[x_?NumberQ] := "number"

g /@ {1, 2}

{"number", "even"}

ClearAll[h]

h[x_?NumberQ] := "number"

h[x_?EvenQ] := "even"

h /@ {1, 2}

{"number", "number"}

share|improve this answer

edited 14 hours ago

answered 14 hours ago

kglrkglr

186k10203422

$endgroup$

add a comment | 

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11

$begingroup$

TheOrderingOfDefinitions

• ... The Wolfram System follows the principle of trying to put more general definitions after more specific ones. This means that special cases of rules are typically tried before more general cases.


• Although in many practical cases, the Wolfram System can recognize when one rule is more general than another, you should realize that this is not always possible. For example, if two rules both contain complicated /; conditions, it may not be possible to work out which is more general, and, in fact, there may not be a definite ordering. Whenever the appropriate ordering is not clear, the Wolfram System stores rules in the order you give them.

ClearAll[g]

g[x_?EvenQ] := "even"

g[x_?NumberQ] := "number"

g /@ {1, 2}

{"number", "even"}

ClearAll[h]

h[x_?NumberQ] := "number"

h[x_?EvenQ] := "even"

h /@ {1, 2}

{"number", "number"}

share|improve this answer

edited 14 hours ago

answered 14 hours ago

kglrkglr

186k10203422

$endgroup$

add a comment | 

11

$begingroup$

TheOrderingOfDefinitions

• ... The Wolfram System follows the principle of trying to put more general definitions after more specific ones. This means that special cases of rules are typically tried before more general cases.


• Although in many practical cases, the Wolfram System can recognize when one rule is more general than another, you should realize that this is not always possible. For example, if two rules both contain complicated /; conditions, it may not be possible to work out which is more general, and, in fact, there may not be a definite ordering. Whenever the appropriate ordering is not clear, the Wolfram System stores rules in the order you give them.

ClearAll[g]

g[x_?EvenQ] := "even"

g[x_?NumberQ] := "number"

g /@ {1, 2}

{"number", "even"}

ClearAll[h]

h[x_?NumberQ] := "number"

h[x_?EvenQ] := "even"

h /@ {1, 2}

{"number", "number"}

share|improve this answer

edited 14 hours ago

answered 14 hours ago

kglrkglr

186k10203422

$endgroup$

add a comment | 

$begingroup$

TheOrderingOfDefinitions

• ... The Wolfram System follows the principle of trying to put more general definitions after more specific ones. This means that special cases of rules are typically tried before more general cases.


• Although in many practical cases, the Wolfram System can recognize when one rule is more general than another, you should realize that this is not always possible. For example, if two rules both contain complicated /; conditions, it may not be possible to work out which is more general, and, in fact, there may not be a definite ordering. Whenever the appropriate ordering is not clear, the Wolfram System stores rules in the order you give them.

ClearAll[g]

g[x_?EvenQ] := "even"

g[x_?NumberQ] := "number"

g /@ {1, 2}

{"number", "even"}

ClearAll[h]

h[x_?NumberQ] := "number"

h[x_?EvenQ] := "even"

h /@ {1, 2}

{"number", "number"}

share|improve this answer

edited 14 hours ago

answered 14 hours ago

kglrkglr

186k10203422

$endgroup$

ClearAll[g]

g[x_?EvenQ] := "even"

g[x_?NumberQ] := "number"

g /@ {1, 2}

ClearAll[h]

h[x_?NumberQ] := "number"

h[x_?EvenQ] := "even"

h /@ {1, 2}

share|improve this answer

edited 14 hours ago

answered 14 hours ago

kglrkglr

186k10203422

answered 14 hours ago

kglrkglr

186k10203422

answered 14 hours ago

kglrkglr

186k10203422