19.13 Boolean expressions $\,\langle$ exp ${}_{1}$ $\rangle\,$ andalso $\,\langle$ exp ${}_{2}$ $\rangle\,$ and $\,\langle$ exp ${}_{1}$ $\rangle\,$ orelse $\,\langle$ exp ${}_{2}$ $\rangle\,$

The boolean type is predefined as follows:

datatype bool = false | true

The name of data constructors usually begins with an capital letter, these two constructors are exceptions of such a convention.

For any two expressions $\,\langle$ exp ${}_{1}$ $\rangle\,$ and $\,\langle$ exp ${}_{2}$ $\rangle\,$ of bool type, the following constructs are provided.

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Logical conjunction： $\,\langle$ exp ${}_{1}$ $\rangle\,$ andalso $\,\langle$ exp ${}_{2}$ $\rangle\,$

It evaluates $\,\langle$ exp ${}_{1}$ $\rangle\,$ at first. If the value of $\,\langle$ exp ${}_{1}$ $\rangle\,$ is true, then it evaluates $\,\langle$ exp ${}_{2}$ $\rangle\,$ and returns its value as the result of the entire expression. Otherwise, the value of this expression is false. In this case, $\,\langle$ exp ${}_{2}$ $\rangle\,$ is not evaluated.
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Logical disjunction： $\,\langle$ exp ${}_{1}$ $\rangle\,$ orelse $\,\langle$ exp ${}_{2}$ $\rangle\,$

It evaluates $\,\langle$ exp ${}_{1}$ $\rangle\,$ at first. If the value of $\,\langle$ exp ${}_{1}$ $\rangle\,$ is false, then it evaluates $\,\langle$ exp ${}_{2}$ $\rangle\,$ and returns its value as the result of the entire expression. Otherwise, the value of this expression is true. In this case, $\,\langle$ exp ${}_{2}$ $\rangle\,$ is not evaluated.

Since it may ignore the second expressions, these operations are provided as language constructs, not functions.

These syntaxes are left-associative and in the same precedence. Therefore,

false andalso true orelse false

is interpreted as (false andalso true) orelse false and hence is evaluated to false.

Other operations on bool type are provided as functions. For example,

not : bool -> bool