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normalize_constraints.pl
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:- module(normalize_constraints, [normalizeConstraints/3], [assertions, isomodes, doccomments]).
%! \title Constraint normalization for interpolant
%
% \module
% Converts const into `AX<=b` (for interpolant generation)
:- use_module(library(write)).
:- use_module(library(lists)).
go :-
numbervars(A,0,_),
normalizeConstraints([1*A < 90], [A], C),
write(C).
normalizeConstraints([], _,[]).
normalizeConstraints([C|Cs], VarList, Cs2):-
normalizeConstraint(C, VarList,C1),
!,
normalizeConstraints(Cs, VarList,Cs1),
append(C1,Cs1,Cs2).
normalizeConstraint(T1=<T2, VarList, C):-
normalizeLC(T1, VarList, L1, R1),
normalizeRC(T2, VarList, L2, R2),
append(L1,L2, Left),
append(R1,R2, Right),
list2NonList(Left,LeftNL),
list2NonList(Right,RightNL),
C= [LeftNL =< RightNL].
normalizeConstraint(T1<T2, VarList, C):-
normalizeLC(T1, VarList, L1, R1),
normalizeRC(T2, VarList, L2, R2),
append(L1,L2, Left),
append(R1,R2, Right),
list2NonList(Left,LeftNL),
list2NonList(Right,RightNL),
C = [LeftNL < RightNL].
%this is valid over integer
%RightNL1 is RightNL - 1,
%C= [LeftNL =< RightNL1].
normalizeConstraint(T1>T2, VarList, C):-
normalizeConstraint(T2<T1, VarList, C).
normalizeConstraint(T1>=T2, VarList, C):-
normalizeConstraint(T2=<T1, VarList, C).
normalizeConstraint(T1=T2, VarList, C):-
normalizeConstraints([T2=<T1,T1=<T2 ], VarList, C).
normalizeConstraint1(-(0), _, 0):-
!.
normalizeConstraint1(T1, _, N1):-
formatNumber(T1,N1),
number(N1),
!.
normalizeConstraint1(-(T1), VarList, -1* C1):-
normalizeConstraint1(T1, VarList, C1),
!.
normalizeConstraint1(- (-A * T1), VarList, A* C1):-
normalizeConstraint1(T1, VarList, C1),
!.
normalizeConstraint1(- (A * T1), VarList, -A* C1):-
normalizeConstraint1(T1, VarList, C1),
!.
normalizeConstraint1( -(T1 + T2) , VarList, C1 + C2):-
normalizeConstraint1(- T1, VarList, C1),
normalizeConstraint1(- T2, VarList, C2).
normalizeConstraint1( -(T1 - T2) , VarList, C1 + C2):-
normalizeConstraint1(- T1, VarList, C1),
normalizeConstraint1(T2, VarList, C2).
normalizeConstraint1(T1, _, T1).
normalizeLC(T1 + T2, VarList, Left, Right):-
!,
normalizeLC(T1, VarList, L1, R1),
normalizeLC(T2, VarList, L2, R2),
addLeft(L1,L2, Left),
addRight(R1,R2,Right).
normalizeLC(T1 - T2, VarList,Left, Right):-
!,
normalizeConstraint1(-T2, VarList,T2N),
normalizeLC(T1 + T2N, VarList, Left, Right).
%normalizeLC(T1, VarList, L1, R1),
%normalizeLC(T2, VarList, L2, R2),
%subLeft(L1,L2, Left),
%subRight(R1,R2,Right).
normalizeLC(- T1, _, [], [N]):-
formatNumber(T1, N),
number(N),
!.
normalizeLC(T1, _, [], [N]):-
number(T1),
formatNumber(-T1, N),
!.
normalizeLC(T1, VarList, [T1], []):-
member2(T1, VarList),
!.
normalizeLC(A*T1, VarList, [N*T1], []):-
member2(T1, VarList),
formatNumber(A, N),
!.
normalizeRC(T1 + T2, VarList, Left, Right):-
normalizeRC(T1, VarList, L1, R1),
normalizeRC(T2, VarList, L2, R2),
addLeft(L1,L2, Left),
addRight(R1,R2,Right).
normalizeRC(T1 - T2, VarList, Left, Right):-
normalizeConstraint1(-T2, VarList,T2N),
normalizeRC(T1 + T2N, VarList, Left, Right).
%normalizeRC(T1, VarList, L1, R1),
%normalizeRC(T2, VarList, L2, R2),
%subLeft(L1,L2, Left),
%subRight(R1,R2,Right).
normalizeRC(-T2, VarList, [T2], []):-
member2(T2, VarList),
!.
normalizeRC(T2, _, [], [N]):-
formatNumber(T2, N),
number(N),
!.
normalizeRC(T2, VarList, [-1*T2], []):-
member2(T2, VarList),
!.
normalizeRC(-A*T2, VarList, [N*T2], []):-
member2(T2, VarList),
formatNumber(A, N),
!.
normalizeRC(A*T2, VarList, [N*T2], []):-
member2(T2, VarList),
formatNumber(-A, N),
!.
addLeft(L1,[], L1):-!.
addLeft([],L2, L2):-!.
addLeft(L1,L2, [L]):-
list2NonList(L1, L1N),
list2NonList(L2, L2N),
L= L1N + L2N.
addRight(L1,[], L1):-!.
addRight([],L2, L2):-!.
addRight(L1,L2, [L]):-
list2NonList(L1, L1N),
list2NonList(L2, L2N),
L is L1N + L2N.
subLeft(L1,[], L1):- !.
subLeft([],L2, [L3]):-
list2NonList(L2, L2NL),
L3 is 0 - L2NL,
!.
subLeft(L1,L2, [L]):-
list2NonList(L1, L1N),
list2NonList(L2, L2N),
L= L1N - L2N.
subRight(L1,[], L1):-!.
subRight([],L2, [L3]):-
list2NonList(L2, L2NL),
L3 is 0 - L2NL,
!.
subRight(L1,L2, [L]):-
list2NonList(L1, L1N),
list2NonList(L2, L2N),
L is L1N - L2N.
list2NonList([],0) :-
!.
list2NonList([A],A) :-
!.
list2NonList([A|As],L) :-
list2NonList(As,As1),
L= A + As1.
list2conj([],0) :-
!.
list2conj([A],A) :-
!.
list2conj([A|As],L) :-
list2conj(As,As1),
L= (A,As1).
formatNumber(+(N), N):-number(N),!.
formatNumber(-(N), K):-number(N), K is 0-N,!.
formatNumber(N,N):-number(N),!.
member2(X, [X|_]) :- !.
member2(X, [_|Tail]) :-
member2(X, Tail).