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polimani.pl
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@ -1,15 +1,81 @@
%% -*- mode: prolog-*- %% -*- mode: prolog-*-
%% vim: set softtabstop=4 shiftwidth=4 tabstop=4 expandtab: %% vim: set softtabstop=4 shiftwidth=4 tabstop=4 expandtab:
%% Follows 'Coding guidelines for Prolog' - Theory and Practice of Logic Programming
%% https://doi.org/10.1017/S1471068411000391
%% Import the Constraint Logic Programming over Finite Domains lybrary /**
%% Essentially, this library improves the way Prolog deals with integers, *
%% allowing more predicates to be reversible. * polimani.pl
%% For instance, number(N) is always false, which prevents the *
%% reversing of a predicate. * Assignment 1 - Polynomial Manipulator
* Programming in Logic - DCC-FCUP
*
* Diogo Peralta Cordeiro
* up201705417@fc.up.pt
*
* Hugo David Cordeiro Sales
* up201704178@fc.up.pt
*
*********************************************
* Follows 'Coding guidelines for Prolog' *
* https://doi.org/10.1017/S1471068411000391 *
*********************************************
*/
/* Import the Constraint Logic Programming over Finite Domains lybrary
* Essentially, this library improves the way Prolog deals with integers,
* allowing more predicates to be reversible.
* For instance, number(N) is always false, which prevents the
* reversing of a predicate.
*/
:- use_module(library(clpfd)). :- use_module(library(clpfd)).
/*******************************
* USER INTERFACE *
*******************************/
/*
poly2list/2 transforms a list representing a polynomial (second
argument) into a polynomial represented as an expression (first argu-
ment) and vice-versa.
*/
poly2list(P, L) :-
polynomial_to_list(P, L).
/*
simpolylist/2 simplifies a polynomial represented as a list into
another polynomial as a list.
*/
simpoly_list(L, S) :-
simplify_polynomial_list(L, S).
/*
simpoly/2 simplifies a polynomial represented as an expression
as another polynomial as an expression.
*/
simpoly(P, S) :-
simplify_polynomial(P, S).
/*
scalepoly/3 multiplies a polynomial represented as an expression by a scalar
resulting in a second polynomial. The two first arguments are assumed to
be ground. The polynomial resulting from the sum is in simplified form.
*/
scalepoly(P1, P2, S) :-
scale_polynomial(P1, P2, S).
/*
addpoly/3 adds two polynomials as expressions resulting in a
third one. The two first arguments are assumed to be ground.
The polynomial resulting from the sum is in simplified form.
*/
addpoly(P1, P2, S) :-
add_polynomial(P1, P2, S).
/*******************************
* BACKEND *
*******************************/
%% polynomial_variable_list(-List) is det %% polynomial_variable_list(-List) is det
% %
% List of possible polynomial variables % List of possible polynomial variables
@ -84,6 +150,8 @@ term(L * R) :-
%@ false. %@ false.
%% ?- term(a). %% ?- term(a).
%@ false. %@ false.
%% ?- term(-1*x).
%@ true .
%% ?- term((-3)*x^2). %% ?- term((-3)*x^2).
%@ true . %@ true .
%% ?- term(3.2*x). %% ?- term(3.2*x).
@ -178,8 +246,17 @@ term_to_list(P, [P2]) :-
%% Tests: %% Tests:
%% ?- term_to_list(1, X). %% ?- term_to_list(1, X).
%@ X = [1] . %@ X = [1] .
%% ?- term_to_list(-1, X).
%@ X = [-1] .
%% ?- term_to_list(1*2*y*z*23*x*y*x^3*x, X). %% ?- term_to_list(1*2*y*z*23*x*y*x^3*x, X).
%@ X = [x^1, x^3, y^1, x^1, 23, z^1, y^1, 2, 1] . %@ X = [x^1, x^3, y^1, x^1, 23, z^1, y^1, 2, 1] .
%% ?- term_to_list(X, [-1]).
%@ X = -1 .
%% ?- term_to_list(X, [x^1, -1]).
%@ X = -1*x .
%% ?- term_to_list(X, [- 1, x^1]).
%@ false.
%@ X = x* -1 .
%% ?- term_to_list(X, [y^1, x^1]). %% ?- term_to_list(X, [y^1, x^1]).
%@ X = x*y . %@ X = x*y .
%% ?- term_to_list(X, [x^4]). %% ?- term_to_list(X, [x^4]).
@ -203,7 +280,7 @@ simplify_term(Term_In, Term_Out) :-
Term_Out = Term_In Term_Out = Term_In
); );
exclude(==(1), L2, L3), exclude(==(1), L2, L3),
join_like_terms(L3, L4), join_similar_parts_of_term(L3, L4),
sort(0, @>=, L4, L5), sort(0, @>=, L4, L5),
term_to_list(Term_Out, L5) term_to_list(Term_Out, L5)
), ),
@ -227,112 +304,218 @@ simplify_term(Term_In, Term_Out) :-
%% ?- simplify_term(x^(-3), X). %% ?- simplify_term(x^(-3), X).
%@ false. %@ false.
%% join_like_terms(+List, -List) %% join_similar_parts_of_term(+List, -List)
% %
% Combine powers of the same variable in the given list % Combine powers of the same variable in the given list
% %
join_like_terms([P1, P2 | L], [B^N | L2]) :- join_similar_parts_of_term([P1, P2 | L], L2) :-
power(P1), power(P1),
power(P2), power(P2),
B^N1 = P1, B^N1 = P1,
B^N2 = P2, B^N2 = P2,
N is N1 + N2, N is N1 + N2,
join_like_terms(L, L2). join_similar_parts_of_term([B^N | L], L2).
join_like_terms([N1, N2 | L], [N | L2]) :- join_similar_parts_of_term([N1, N2 | L], L2) :-
number(N1), number(N1),
number(N2), number(N2),
N is N1 * N2, N is N1 * N2,
join_like_terms(L, L2). join_similar_parts_of_term([N | L], L2).
join_like_terms([X | L], [X | L2]) :- join_similar_parts_of_term([X | L], [X | L2]) :-
join_like_terms(L, L2). join_similar_parts_of_term(L, L2).
join_like_terms([], []). join_similar_parts_of_term([], []).
%% Tests: %% Tests:
%% ?- join_like_terms([2, 3, x^1, x^2], T). %% ?- join_similar_parts_of_term([3], T).
%@ T = [3].
%% ?- join_similar_parts_of_term([x^2], T).
%@ T = [x^2].
%% ?- join_similar_parts_of_term([x^1, x^1, x^1, x^1], T).
%@ T = [x^4] .
%% ?- join_similar_parts_of_term([2, 3, x^1, x^2], T).
%@ T = [6, x^3] . %@ T = [6, x^3] .
%% ?- join_like_terms([2, 3, x^1, x^2, y^1, y^6], T). %% ?- join_similar_parts_of_term([2, 3, x^1, x^2, y^1, y^6], T).
%@ T = [6, x^3, y^7] . %@ T = [6, x^3, y^7] .
%% simplify_polynomial(+P:atom, -P2:atom) is det %% simplify_polynomial(+P:atom, -P2:atom) is det
% %
% Simplifies a polynomial. % Simplifies a polynomial.
% TODO: not everything is a +, there are -
% %
simplify_polynomial(M, M2) :- simplify_polynomial(0, 0) :-
%% Are we dealing with a valid term?
%is_term_valid_in_predicate(M, "simplify_polynomial(M, M2)"),
%% term(M),
%% If so, simplify it.
simplify_term(M, M2),
!. !.
simplify_polynomial(P + 0, P) :- simplify_polynomial(P, P2) :-
%% Ensure valid term polynomial_to_list(P, L),
%is_term_valid_in_predicate(P, "simplify_polynomial(P + 0, P)"), maplist(term_to_list, L, L2),
term(P), maplist(sort(0, @>=), L2, L3),
sort(0, @>=, L3, L4),
maplist(join_similar_parts_of_term, L4, L5),
maplist(sort(0, @=<), L5, L6),
join_similar_terms(L6, L7),
maplist(reverse, L7, L8),
maplist(term_to_list, L9, L8),
delete(L9, 0, L10),
sort(0, @=<, L10, L11),
list_to_polynomial(L11, P2),
!. !.
simplify_polynomial(0 + P, P) :-
%% Ensure valid term
%is_term_valid_in_predicate(P, "simplify_polynomial(0 + P, P)"),
term(P),
!.
simplify_polynomial(P + M, P2 + M2) :-
simplify_polynomial(P, P2),
simplify_term(M, M2).
simplify_polynomial(P + M, P2 + M3) :-
monomial_parts(M, _, XExp),
delete_monomial(P, XExp, M2, P2),
!,
add_monomial(M, M2, M3).
simplify_polynomial(P + M, P2 + M2) :-
simplify_polynomial(P, P2),
simplify_term(M, M2).
%% Tests: %% Tests:
%% ?- simplify_polynomial(1, X). %% ?- simplify_polynomial(1, X).
%@ false. %@ X = 1.
%@ false. %% ?- simplify_polynomial(0, X).
%@ Invalid term in simplify_polynomial(M, M2): 1 %@ X = 0.
%@ false. %% ?- simplify_polynomial(x, X).
%@ X = x.
%% ?- simplify_polynomial(x*x, X).
%@ X = x^2.
%% ?- simplify_polynomial(2 + 2, X).
%@ X = 2*2.
%% ?- simplify_polynomial(x + x, X).
%@ X = 2*x.
%% ?- simplify_polynomial(0 + x*x, X).
%@ X = x^2.
%% ?- simplify_polynomial(x^2*x + 3*x^3, X).
%@ X = 4*x^3.
%% ?- simplify_polynomial(x^2*x + 3*x^3 + x^3 + x*x*x, X).
%@ X = 6*x^3.
%% ?- simplify_polynomial(x^2*x + 3*x^3 + x^3 + x*x*4 + z, X).
%@ X = 5*x^3+4*x^2+z.
%% ?- simplify_polynomial(x + 1 + x, X).
%@ X = 2*x+1.
%% ?- simplify_polynomial(x + 1 + x + 1 + x + 1 + x, X).
%@ X = 4*x+3*1.
%% join_similar_terms(+P:ListList, -P2:ListList) is det
%% simplify_polynomial_list(+L1,-L3) is det
% %
% Simplifies a list of polynomials % Joins similar sublists representing terms by using
% `add_terms` to check if they can be merged and perform
% the addition. Requires the list of list be sorted with
% `maplist(sort(0, @>=), L, L2),
% sort(0, @>=, L2, L3)`
% and that the sublists to be sorted with
% `sort(0, @=<)` since that is inherited from `add_terms`
% %
simplify_polynomial_list([L1], L3) :- join_similar_terms([TL, TR | L], L2) :-
simplify_polynomial(L1, L2), %% Check if terms can be added and add them
L3 = [L2]. add_terms(TL, TR, T2),
simplify_polynomial_list([L1|L2],L3) :- %% Recurse, accumulation on the first element
simplify_polynomial(L1, P1), join_similar_terms([T2 | L], L2),
simplify_polynomial_list(L2, P2), %% Give only first result. Red cut
L3 = [P1|P2],
% There is nothing further to compute at this point
!. !.
join_similar_terms([X | L], [X | L2]) :-
%% If a pair of elements can't be added, skip one
%% and recurse
join_similar_terms(L, L2),
%% Give only first result. Red cut
!.
join_similar_terms([], []).
%% Tests:
%% ?- join_similar_terms([[2, x^3], [3, x^3], [x^3]], L).
%@ L = [[6, x^3]].
%% term_to_canon(+T:List, -T2:List) is det
%
% Adds a 1 if there's no number in the list
% Requires the list to be sorted such that the
% numbers come first. For instance with
% `sort(0, @=<)`
%
term_to_canon([T | TS], [1, T | TS]) :-
%% Since the list is sorted, if the first element
%% is not a number, then we need to add the 1
not(number(T)),
%% Give only first result. Red cut
!.
term_to_canon(L, L).
%% Tests:
%% ?- term_to_canon([2], T).
%@ T = [2].
%% ?- term_to_canon([x^3], T).
%@ T = [1, x^3].
%% ?- term_to_canon([x^3, z], T).
%@ T = [1, x^3, z].
%% ?- term_to_canon([2, x^3], T).
%@ T = [2, x^3].
%% add_terms(+L:List, +R:List, -Result:List) is det
%
% Adds two terms represented as list by adding
% the coeficients if the power is the same.
% Requires the list of terms to be simplified.
%
add_terms([NL | TL], [NR | TR], [N2 | TL2]) :-
term_to_canon([NL | TL], [NL2 | TL2]),
term_to_canon([NR | TR], [NR2 | TR2]),
TL2 == TR2,
N2 is NL2 + NR2.
%% Tests
%% ?- add_terms([1], [1], R).
%@ R = [2].
%% ?- add_terms([x], [x], R).
%@ R = [2, x].
%% ?- add_terms([2, x^3], [x^3], R).
%@ R = [3, x^3].
%% ?- add_terms([2, x^3], [3, x^3], R).
%@ R = [5, x^3].
%% simplify_polynomial_list(+L:list, -S:list) is det
%
% Simplifies a polynomial represented as a list
%
simplify_polynomial_list(L, S) :-
polynomial_to_list(P1, L),
simplify_polynomial(P1, P2),
polynomial_to_list(P2, S).
%% polynomial_to_list(+P:polynomial, -L:List) %% polynomial_to_list(+P:polynomial, -L:List)
% %
% Converts a polynomial in a list. % Converts a polynomial in a list.
% TODO: not everything is a +, there are -
% %
polynomial_to_list(T1 + T2, L) :- polynomial_to_list(L - T, [T2 | LS]) :-
polynomial_to_list(T1, L1), term(T),
L = [T2|L1], negate_term(T, T2),
% The others computations are semantically meaningless polynomial_to_list(L, LS).
!. polynomial_to_list(L + T, [T | LS]) :-
polynomial_to_list(P, L) :- term(T),
L = [P]. polynomial_to_list(L, LS).
polynomial_to_list(T, [T]) :-
term(T).
%% Tests: %% Tests:
%%?- polynomial_to_list(2*x^2+5+y*2, S). %% ?- polynomial_to_list(2, S).
%@S = [y*2, 5, 2*x^2]. %@ S = [2] .
%% ?- polynomial_to_list(x^2, S).
%@ S = [x^2] .
%% ?- polynomial_to_list(x^2 + x^2, S).
%@ S = [x^2, x^2] .
%% ?- polynomial_to_list(2*x^2+5+y*2, S).
%@ S = [y*2, 5, 2*x^2] .
%% ?- polynomial_to_list(2*x^2+5-y*2, S).
%@ S = [-2*y, 5, 2*x^2] .
%% ?- polynomial_to_list(2*x^2-5-y*2, S).
%@ S = [-2*y, -5, 2*x^2] .
%% ?- polynomial_to_list(P, [2]).
%@ P = 2 .
%% ?- polynomial_to_list(P, [x]).
%@ P = x .
%% ?- polynomial_to_list(P, [x^2, x, 2.3]).
%@ Action (h for help) ? abort
%@ % Execution Aborted
%@ P = -2.3+x+x^2 .
%% list_to_polynomial(+P:polynomial, -L:List) %% list_to_polynomial(+P:polynomial, -L:List)
% %
% Converts a list in a polynomial. % Converts a list in a polynomial.
% TODO: not everything is a +, there are -
% %
list_to_polynomial([T1|T2], P) :- list_to_polynomial([T1|T2], P) :-
list_to_polynomial(T2, L1), list_to_polynomial(T2, L1),
( (
not(L1 = []), not(L1 = []),
P = L1+T1 (
term_string(T1, S1),
string_chars(S1, [First|_]),
First = -,
term_string(L1, S2),
string_concat(S2,S1,S3),
term_string(P, S3)
;
P = L1+T1
)
; ;
P = T1 P = T1
), ),
@ -343,6 +526,31 @@ list_to_polynomial(T, P) :-
%% Tests: %% Tests:
%% TODO %% TODO
%% negate_term(T, T2) is det
%
% Negate the coeficient of a term and return the negated term
%
negate_term(T, T2) :-
term_to_list(T, L),
sort(0, @=<, L, L2),
term_to_canon(L2, L3),
[N | R] = L3,
%% (-)/1 is an operator, needs to be evaluated, otherwise
%% it gives a symbolic result, which messes with further processing
N2 is -N,
reverse([N2 | R], L4),
term_to_list(T2, L4),
!.
%% Tests:
%% ?- negate_term(1, R).
%@ R = -1.
%% ?- negate_term(x, R).
%@ R = -1*x.
%% ?- negate_term(x^2, R).
%@ R = -1*x^2.
%% ?- negate_term(3*x*y^2, R).
%@ R = -3*x*y^2.
%% append_two_atoms_with_star(+V1, +V2, -R) is det %% append_two_atoms_with_star(+V1, +V2, -R) is det
% %
% Returns R = V1 * V2 % Returns R = V1 * V2
@ -370,11 +578,9 @@ scale_polynomial(P, C, S) :-
polynomial_to_list(P, L), polynomial_to_list(P, L),
maplist(append_two_atoms_with_star(C), L, L2), maplist(append_two_atoms_with_star(C), L, L2),
list_to_polynomial(L2, S). list_to_polynomial(L2, S).
%simplify_polynomial(S1, S).
%% Tests: %% Tests:
%% ?- scale_polynomial(3*x^2, 2, S). %% ?- scale_polynomial(3*x^2, 2, S).
%@ S = 2*3*x^2. %@ S = 2*3*x^2.
%@ S = 2*(3*x^2).
%% add_polynomial(+P1:polynomial,+P2:polynomial,-S:polynomial) is det %% add_polynomial(+P1:polynomial,+P2:polynomial,-S:polynomial) is det
% %
@ -389,70 +595,3 @@ add_polynomial(P1, P2, S) :-
simplify_polynomial(P, S). simplify_polynomial(P, S).
%% Tests: %% Tests:
% %
%% monomial_parts(X, Y, Z)
%
% TODO Maybe remove
% Separate monomial into it's parts. Given K*X^N, gives K and N
%
monomial_parts(X, 1, X) :-
power(X),
!.
monomial_parts(X^N, 1, X^N) :-
power(X^N),
!.
monomial_parts(K * M, K, M) :-
number(K),
!.
monomial_parts(K, K, indep) :-
number(K),
!.
delete_monomial(M, X, M, 0) :-
term(M),
monomial_parts(M, _, X),
!.
delete_monomial(M + M2, X, M, M2) :-
term(M2),
term(M),
monomial_parts(M, _, X),
!.
delete_monomial(P + M, X, M, P) :-
term(M),
monomial_parts(M, _, X),
!.
delete_monomial(P + M2, X, M, P2 + M2) :-
delete_monomial(P, X, M, P2).
add_monomial(K1, K2, K3) :-
number(K1),
number(K2), !,
K3 is K1 + K2.
add_monomial(M1, M2, M3) :-
monomial_parts(M1, K1, XExp),
monomial_parts(M2, K2, XExp),
K3 is K1 + K2,
p_aux_add_monomial(K3, XExp, M3).
p_aux_add_monomial(K, indep, K) :-
!.
p_aux_add_monomial(0, _, 0) :-
!.
p_aux_add_monomial(1, XExp, XExp) :-
!.
p_aux_add_monomial(K, XExp, K * XExp).
closure_simplify_polynomial(P, P) :-
simplify_polynomial(P, P2),
P==P2,
!.
closure_simplify_polynomial(P, P3) :-
simplify_polynomial(P, P2),
closure_simplify_polynomial(P2, P3),
!.
list_to_term([N | NS], N * L) :-
number(N),
term_to_list(L, NS).