alt-ergo (1)

alt-ergo [ options ] file

Alt-Ergo is an automatic theorem prover. It takes as inputs an arbitrary polymorphic and multi-sorted first-order formula written is a why like syntax.

-h

Help. Will give you the full list of command line options.

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 *)

ERGOLIB

Alternative path for the Alt-Ergo library

Sylvain Conchon <[email protected]> and Evelyne Contejean <[email protected]>

Alt-Ergo web site: http://alt-ergo.lri.fr