The base foreach

The base form of foreach has the following form:

aa aaa aaa aaa aaa aaa aaa 
		 		 foreach(E1 in D1, $\ldots$, En in Dn, LocalVars,Goal) 

E_i is a pattern that is normally a variable, but can also be any term. D_i a collection. LocalVars, which is optional, is a list of variables in Goal that are local to each iteration. Goal is a callable term. All of the variables in the 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 the local variables are renamed. The call fails if any of the instances fails. Any variable, including the anonymous variable '_', that occurs in Goal, is shared by all iterations, unless the variable is contained within an E_i or LocalVars.

A collection takes one of the following forms:

• A list of terms.
• A list of numbers that is represented as an interval Begin..Step..End, which denotes the list of numbers [ $B_1,B_2,\ldots,B_k$],where B₁=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. When Step is negative, $B_k \ge End$ and B_k+Step<End. When Step=1, the notation can be abbreviated as Begin..End. 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)].