# Inductive Validity Core¶

The inductive validity core generation is a post-analysis treatement that computes a minimal subset of the model elements (assumptions, guarantees, stateful equations, or node calls) that are sufficient to prove all properties.

To enable inductive validity core generation, run

kind2 <lustre_file> --ivc true


## Options¶

• --ivc_category {node_calls|contracts|equations|assertions|annotations} (default: all categories) – Minimize only a specific category of elements, repeat option to minimize multiple categories

• --ivc_only_main_node <bool> (default false) – Only elements of the main node are considered in the computation

• --ivc_all <bool> (default false) – Compute all the Minimal Inductive Validity Cores

• --ivc_approximate <bool> (default true) – Compute an approximation (superset) of a MIVC. Ignored if --ivc_all is true

• --ivc_smallest_first <bool> (default false) – Compute a smallest IVC first. If --ivc_all is false, the computed IVC will be a smallest one

• --ivc_must_set <bool> (default false) – Compute the MUST set in addition to the IVCs

• --print_ivc <bool> (default true) – Print the inductive validity core computed

• --print_ivc_complement <bool> (default false) – Print the complement of the inductive validity core computed (= the elements that were not necessary to prove the properties)

• --minimize_program {no|valid_lustre|concise} (default no) – Minimize the source Lustre program according to the inductive validity core(s) computed

• --ivc_output_dir <string> (default <INPUT_FILENAME>) – Output directory for the minimized programs

• --ivc_uc_timeout <int> (default 0) – Set a timeout for each unsat core check sent to the solver

• --ivc_precomputed_mcs <int> (default 0) – When computing all MIVCs, set a cardinality upper bound for the precomputed MCSs (helps prune space of candidates)

## Example¶

Let’s consider the following Lustre code:

contract fSpec(u,v: real) returns(r: real);
let
guarantee r >= 0.0;
guarantee true -> r >= pre(r);
guarantee r >= u;
guarantee r >= v;
tel;

node f(u, v : real) returns (r : real);
(*@contract import fSpec(u,v) returns (r) ; *)
var m1,m2: real;
let
m1 = if v > u then v else u;
m2 = if m1 > 0.0 then m1 else 0.0;
r = m2 -> if pre(r) > m1 then pre(r) else m1;
tel;

node main(x, y : real) returns (P : bool);
var a,b : real;
let
a = f(x,y);
b = f(y,x);
P = a >= x and a >= y and b >= x and b >= y;
--%PROPERTY P;
tel;


If we are interesting in determining which guarantees of the contract fSpec of f are needed to prove P, we should run this command:

kind2 <lustre_file> --ivc true --ivc_category contracts --ivc_only_main_node false --compositional true

• --ivc_category contracts: because we are only interested in minimizing the contract fSpec

• --ivc_only_main_node false: because fSpec is not the contract of the main node, so we need to consider all nodes

• --compositional true: as we want to minimize the contract of f and not its implementation, we need to enable compositional analysis

We obtain the following inductive validity core:

IVC (2 elements):
Node f
Guarantee fSpec[l11c12].guarantee[l6c4][3] at position [l6c4]
Guarantee fSpec[l11c12].guarantee[l7c4][4] at position [l7c4]


## Minimizing over a subset of the assumptions/guarantees¶

If you are interested in computing an IVC among a subset of the assumptions or guarantees, you can use the category annotations. The assumptions and guarantees that should be considered must be preceded by the keyword weakly. All the other assumptions and guarantees will be considered as always present when computing the IVCs.

For instance, we can modify the previous example as follows:

contract fSpec(u,v: real) returns(r: real);
let
weakly guarantee r >= 0.0;
guarantee true -> r >= pre(r);
weakly guarantee r >= u;
guarantee r >= v;
tel;

kind2 <lustre_file> --ivc true --ivc_category annotations --ivc_only_main_node false --compositional true


We obtain the following inductive validity core:

IVC (1 elements):
Node f
Guarantee fSpec[l11c12].weakly_guarantee[l6c4][3] at position [l6c4]


## Computing all Inductive Validity Cores¶

If we want to compute ALL the minimal inductive validity cores, we can use the following flags:

kind2 <lustre_file> --ivc true --ivc_all true

• --ivc_all true: specify that we want to compute all the IVCs