The base foreach

The base form of foreach has the following form:

		 		 foreach($E_1$ in $D_1$, $\ldots$, $E_n$ in $D_n$, $LocalVars$,$Goal$) 

where $E_i$ is a pattern which is normally a variable but can be any term, and $D_i$ a collection, $LocalVars$, which is optional, is a list of variables in $Goal$ that are local to each iteration, and $Goal$ is a callable term. All variables in $E_i$'s are local variables. The foreach call means that for each combination of values $E_1 \in D_1$, $\ldots$, $E_n \in D_n$, the instance $Goal$ is executed after local variables are renamed. The call fails if any of the instances fails. Any variable, including the anonymous variable '_', that occurs in $Goal$ but is not in any $E_i$ or $LocalVars$ is shared by all iterations.

A collection takes one of the following forms:

• A list of terms.
• A list of numbers represented as an interval $Begin..Step..End$, which denotes the list of numbers [ $B_1,B_2,\ldots,B_k$] where $B_1=Begin$ and $B_i = B_{i-1}+Step$ for $i=2,...,k$. When $Step$ is positive, $B_k \le End$ and $B_k+Step>End$, and when $Step$ is negative, $B_k \ge End$ and $B_k+Step<End$. The notation can be abbreviated as $Begin..End$ when $Step=1$. For example, the interval 1..2..8 denotes the list [1,3,5,7].

• A term in the form ( $C_1,\ldots,C_m$) where each $C_i$ (i=1,...,m) is a collection of the same number of elements. Let $C_i$ be the list [ $e_{i1},...,e_{il}$] $(i=1,...,m)$. The term ( $C_1,\ldots,C_m$) denotes the list of tuples [ $(e_{11},...,e_{m1}),\ldots,(e_{1l},...,e_{ml})$]. For example, ([a,b,c],1..3) denotes the list of tuples [(a,1),(b,2),(c,3)].