# Conditionals

The Wolfram Language provides various ways to set up *conditionals*, which specify that particular expressions should be evaluated only if certain conditions hold.

lhs:=rhs/;test | use the definition only if test evaluates to True |

If[test,then,else] | evaluate then if test is True, and else if it is False |

Which[test_{1},value_{1},test_{2},…] | evaluate the test_{i} in turn, giving the value associated with the first one that is True |

Switch[expr,form_{1},value_{1},form_{2},…] | compare expr with each of the form_{i}, giving the value associated with the first form it matches |

Switch[expr,form_{1},value_{1},form_{2},…,_,def] | use def as a default value |

Piecewise[{{value_{1},test_{1}},…},def] | give the value corresponding to the first test_{i} which yields True |

When you write programs in the Wolfram Language, you will often have a choice between making a single definition whose right‐hand side involves several branches controlled by If functions, or making several definitions, each controlled by an appropriate /; condition. By using several definitions, you can often produce programs that are both clearer, and easier to modify.

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The function If provides a way to choose between two alternatives. Often, however, there will be more than two alternatives. One way to handle this is to use a nested set of If functions. Usually, however, it is instead better to use functions like Which and Switch.

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An important point about symbolic systems such as the Wolfram Language is that the conditions you give may yield neither True nor False. Thus, for example, the condition x==y does not yield True or False unless x and y have specific values, such as numerical ones.

If[test,then,else,unknown] | a form of If which includes the expression to use if test is neither True nor False |

TrueQ[expr] | give True if expr is True, and False otherwise |

lhs===rhsorSameQ[lhs,rhs] | give True if lhs and rhs are identical, and False otherwise |

lhs=!=rhsorUnsameQ[lhs,rhs] | give True if lhs and rhs are not identical, and False otherwise |

MatchQ[expr,form] | give True if the pattern form matches expr, and give False otherwise |

Functions for dealing with symbolic conditions.

The main difference between lhs===rhs and lhs==rhs is that === always returns True or False, whereas == can leave its input in symbolic form, representing a symbolic equation, as discussed in "Equations". You should typically use === when you want to test the *structure* of an expression, and == if you want to test mathematical equality. The Wolfram Language pattern matcher effectively uses === to determine when one literal expression matches another.

In setting up conditionals, you will often need to use combinations of tests, such as test_{1}&&test_{2}&&…. An important point is that the result from this combination of tests will be False if *any* of the test_{i} yield False. The Wolfram Language always evaluates the test_{i} in turn, stopping if any of the test_{i} yield False.

expr_{1}&&expr_{2}&&expr_{3} | evaluate until one of the expr_{i} is found to be False |

expr_{1}expr_{2}expr_{3} | evaluate until one of the expr_{i} is found to be True |

Evaluation of logical expressions.

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The way that the Wolfram Language evaluates logical expressions allows you to combine sequences of tests where later tests may make sense only if the earlier ones are satisfied. The behavior, which is analogous to that found in languages such as C, is convenient in constructing many kinds of Wolfram Language programs.