A theory of functional arrays with integer indexes . This theory provides a built-in type ('a,'b) farray
and a built-in syntax for manipulating arrays.
For instance, given an abstract datatype tau and a functional array t of type (int, tau) farray
declared as follows:
type tau
logic t : (int, tau) farray
The expressions:
t[i] denotes the value stored in t at index i
t[i1<-v1,...,in<-vn] denotes an array which stores the same values as t for every index except
possibly i1,...,in, where it stores value v1,...,vn. This expression is equivalent to
((t[i1<-v1])[i2<-v2])...[in<-vn].
Examples.
t[0<-v][1<-w]
t[0<-v, 1<-w]
t[0<-v, 1<-w][1]
A theory of enumeration types.
For instance an enumeration type t with constructors A, B, C is defined as follows :
type t = A | B | C
Which means that all values of type t are equal to either A, B or C. And that all these
constructors are distinct.
A theory of polymorphic records.
For instance a polymorphic record type 'a t with two labels a and b of type 'a and int
respectively is defined as follows:
type 'a t = { a : 'a; b : int }
The expressions { a = 4; b = 5 } and { r with b = 3} denote records, while the dot notation r.a is
used to access to labels.
Alt-Ergo (v. >= 0.95) allows the user to force the type of terms using the syntax <term> : <type>. The
example below illustrates the use of this new feature.
type 'a list
logic nil : 'b list
logic f : 'c list -> int
goal g1 : f(nil) = f(nil) (* not valid because the two instances of nil may have different types
*)
goal g2 : f(nil:'d list) = f(nil:'d list) (* valid *)
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