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How to list combinations using DCG with CLP (FD) and a few restrictions

This question begins with Mat answer to Improving the algorithm for enumerating binary trees , which has only one input value that determines the number of all nodes for the binary tree and the need to have two input values ​​with one of which is the number of unary nodes and the other is the number of binary nodes.

While I was able to get a solution using listing / 1 and entering additional state variables:

e(t, B, B, U, U).

e(u(E), B0, B1, [_|U0], U1) :-
    e(E, B0, B1, U0, U1).

e(b(E0, E1), [_|B0], B2, U0, U2) :-
    e(E0, B0, B1, U0, U1),
    e(E1, B1, B2, U1, U2).

e(U,B,Es) :-
    length(Bs, B),
    length(Us, U),
    e(Es,Bs,[],Us,[]).

Note. See the Prolog output below.

length/2 , DCG. , , .

e_a(t, B, B, U, U).

e_a(u(E), B0, B1, U0, U2) :-
    U1 is U0 + 1,
    e_a(E, B0, B1, U1, U2).

e_a(b(E0, E1), B0, B3, U0, U2) :-
    B1 is B0 + 1,
    e_a(E0, B1, B2, U0, U1),
    e_a(E1, B2, B3, U1, U2).

e_a(U,B,Es) :-
    U =:= Us,   % Arguments are not sufficiently instantiated 1=:=_2692
    B =:= Bs,
    e_a(Es,0,Bs,0,Us).

?- e_a(1,2,Es).

CLP (FD) DCG .

:-use_module(library(clpfd)).

e_b(t, B, B, U, U).

e_b(u(E), B0, B1, U0, U2) :-
    U1 #= U0 + 1,
    e_b(E, B0, B1, U1, U2).

e_b(b(E0, E1), B0, B3, U0, U2) :-
    B1 #= B0 + 1,
    e_b(E0, B1, B2, U0, U1),
    e_b(E1, B2, B3, U1, U2).

e_b(U,B,Es) :-
    U #=< Us,
    B #=< Bs,
    e_b(Es,0,Bs,0,Us).

?- e_b(1,2,Es).

, .
. CLP (FD), .

, :

  • CLP (FD) , , ?
  • DCG DCG?

e(number)        --> [].
e(u(Arg))        --> [_], e(Arg).
e(b(Left,Right)) --> [_,_], e(Left), e(Right).

?- listing(e).
e(t, A, A).
e(u(A), [_|B], C) :-
        e(A, B, C).
e(b(A, C), [_, _|B], E) :-
        e(A, B, D),
        e(C, D, E).

Prolog

?- e(1,2,Es).
Es = u(b(t, b(t, t))) ;
Es = u(b(b(t, t), t)) ;
Es = b(t, u(b(t, t))) ;
Es = b(t, b(t, u(t))) ;
Es = b(t, b(u(t), t)) ;
Es = b(u(t), b(t, t)) ;
Es = b(u(b(t, t)), t) ;
Es = b(b(t, t), u(t)) ;
Es = b(b(t, u(t)), t) ;
Es = b(b(u(t), t), t) ;
false.

, DCG, , Prolog, listing/1, DCG .

.

?- listing(expression).

, . DCG Prolog, . . S0 , S1, S2 .., . , , , . U U0 . clp (fd).

listing/1 :

% DCG
expression(U, B, E) -->
      terminal(U, B, E)
    | unary(U, B, E)
    | binary(U, B, E).


% Standard Prolog
expression(U, B, E, S0, S1) :-
        (   terminal(U, B, E, S0, S1)
        ;   unary(U, B, E, S0, S1)
        ;   binary(U, B, E, S0, S1)
        ).



% DCG
terminal(0, 0, t) --> [t].

% Standard Prolog
terminal(0, 0, t, [t|S0], S0).



% DCG
unary(U, B, u(E)) -->
    {
        U1 #>= 0,
        U #= U1 + 1
    },
    ['u('],
    expression_1(U1, B, E),
    [')'].

% Standard Prolog
unary(U0, B, u(E), S0, S4) :-
        true,
        clpfd:clpfd_geq(U1, 0),               % U1 #>= 0
        (   integer(U0)
        ->  (   integer(U1)
            ->  U0=:=U1+1                     % U #= U1 + 1
            ;   U2=U0,
                clpfd:clpfd_equal(U2, U1+1)   % U #= U1 + 1
            )
        ;   integer(U1)
        ->  (   var(U0)
            ->  U0 is U1+1                    % U #= U1 + 1
            ;   U2 is U1+1,                   % U #= U1 + 1
                clpfd:clpfd_equal(U0, U2)
            )
        ;   clpfd:clpfd_equal(U0, U1+1)       % U #= U1 + 1
        ),
        S1=S0,
        S1=['u('|S2],
        expression_1(U1, B, E, S2, S3),
        S3=[')'|S4].



% DCG
binary(U, B, b(E1, E2)) -->
    {
        U1 #>= 0,
        U2 #>= 0,
        U #= U1 + U2,
        B1 #>= 0,
        B2 #>= 0,
        B #= B1 + B2 + 1
    },
    ['b('],
    expression_1(U1, B1, E1),
    expression_1(U2, B2, E2),
    [')'].

% Standard Prolog
binary(U0, B0, b(E1, E2), S0, S5) :-
        true,
        clpfd:clpfd_geq(U1, 0),                 % U1 #>= 0
        true,
        clpfd:clpfd_geq(U2, 0),                 % U2 #>= 0
        (   integer(U0)
        ->  (   integer(U1),
                integer(U2)
            ->  U0=:=U1+U2                      % U #= U1 + 1
            ;   U3=U0,
                clpfd:clpfd_equal(U3, U1+U2)    % U #= U1 + 1
            )
        ;   integer(U1),
            integer(U2)
        ->  (   var(U0)
            ->  U0 is U1+U2                     % U #= U1 + 1
            ;   U3 is U1+U2,                    % U #= U1 + 1
                clpfd:clpfd_equal(U0, U3)
            )
        ;   clpfd:clpfd_equal(U0, U1+U2)        % U #= U1 + 1
        ),
        true,
        clpfd:clpfd_geq(B1, 0),                 % B1 #>= 0
        true,
        clpfd:clpfd_geq(B2, 0),                 % B2 #>= 0
        (   integer(B0)
        ->  (   integer(B1),
                integer(B2)
            ->  B0=:=B1+B2+1                    % B #= B1 + B2 + 1
            ;   B3=B0,
                clpfd:clpfd_equal(B3, B1+B2+1)  % B #= B1 + B2 + 1
            )
        ;   integer(B1),
            integer(B2)
        ->  (   var(B0)
            ->  B0 is B1+B2+1                   % B #= B1 + B2 + 1
            ;   B3 is B1+B2+1,                  % B #= B1 + B2 + 1
                clpfd:clpfd_equal(B0, B3)
            )
        ;   clpfd:clpfd_equal(B0, B1+B2+1)      % B #= B1 + B2 + 1
        ),
        S1=S0,
        S1=['b('|S2],
        expression_1(U1, B1, E1, S2, S3),
        expression_1(U2, B2, E2, S3, S4),
        S4=[')'|S5].

SWI-Prolog

, clp (fd) DCG , .

, . , .

/2, DCG CLP (FD)?

, clp (fd) , , length/2. , .

, clp (fd)

1 =: = _2692

, ,

.

integer(U1)
var(U0)

@lurker, , , ops, ops . , , , .

% order of predicates matters
e(    Uc     , Uc , Bc     , Bc , [Terminal|Terminal_s], Terminal_s  , Unary_op_s             , Unary_op_s  , Binary_op_s              , Binary_op_s  , t         , Terminal             ).

e(    [_|Uc0], Uc1, Bc0    , Bc1, Terminal_s_0         , Terminal_s_1, [Unary_op|Unary_op_s_0], Unary_op_s_1, Binary_op_s_0            , Binary_op_s_1, u(E0)     , [op(Unary_op),[UE]]  ) :-
    e(Uc0    , Uc1, Bc0    , Bc1, Terminal_s_0         , Terminal_s_1, Unary_op_s_0           , Unary_op_s_1, Binary_op_s_0            , Binary_op_s_1, E0        , UE                   ).

e(    Uc0    , Uc2, [_|Bc0], Bc2, Terminal_s_0         , Terminal_s_2, Unary_op_s_0           , Unary_op_s_2, [Binary_op|Binary_op_s_0], Binary_op_s_2, b(E0, E1), [op(Binary_op),[L,R]] ) :-
    e(Uc0    , Uc1, Bc0    , Bc1, Terminal_s_0         , Terminal_s_1, Unary_op_s_0           , Unary_op_s_1, Binary_op_s_0            , Binary_op_s_1, E0       , L                     ),
    e(Uc1    , Uc2, Bc1    , Bc2, Terminal_s_1         , Terminal_s_2, Unary_op_s_1           , Unary_op_s_2, Binary_op_s_1            , Binary_op_s_2, E1       , R                     ).

e(Uc, Bc, Terminal_s, Unary_op_s, Binary_op_s, Es, Ls) :-
    length(Bs, Bc),
    length(Us, Uc),
    e(Us,[], Bs,[], Terminal_s, _, Unary_op_s, _, Binary_op_s, _, Es, Ls).

e(Unary_op_s, Binary_op_s, Terminal_s, Es, Ls) :-
    length(Unary_op_s,Uc),
    length(Binary_op_s,Bc),
    length(Terminal_s,Ts),
    Tc is Bc + 1,
    Ts == Tc,
    e(Uc, Bc, Terminal_s, Unary_op_s, Binary_op_s, Es, Ls).

,

?- e([neg,ln],[add,sub],[[number(0)],[number(1)],[number(2)]],_,Ls);true.
Ls = [op(neg), [[op(ln), [[op(add), [[number(0)], [op(sub), [[number(1)], [number(2)]]]]]]]]] ;
Ls = [op(neg), [[op(ln), [[op(add), [[op(sub), [[number(0)], [number(1)]]], [number(2)]]]]]]] ;
Ls = [op(neg), [[op(add), [[number(0)], [op(ln), [[op(sub), [[number(1)], [number(2)]]]]]]]]] ;
Ls = [op(neg), [[op(add), [[number(0)], [op(sub), [[number(1)], [op(ln), [[number(2)]]]]]]]]] ;
Ls = [op(neg), [[op(add), [[number(0)], [op(sub), [[op(ln), [[number(1)]]], [number(2)]]]]]]] ;
Ls = [op(neg), [[op(add), [[op(ln), [[number(0)]]], [op(sub), [[number(1)], [number(2)]]]]]]] ;
Ls = [op(neg), [[op(add), [[op(ln), [[op(sub), [[number(0)], [number(1)]]]]], [number(2)]]]]] ;
Ls = [op(neg), [[op(add), [[op(sub), [[number(0)], [number(1)]]], [op(ln), [[number(2)]]]]]]] ;
Ls = [op(neg), [[op(add), [[op(sub), [[number(0)], [op(ln), [[number(1)]]]]], [number(2)]]]]] ;
Ls = [op(neg), [[op(add), [[op(sub), [[op(ln), [[number(0)]]], [number(1)]]], [number(2)]]]]] ;
Ls = [op(add), [[number(0)], [op(neg), [[op(ln), [[op(sub), [[number(1)], [number(2)]]]]]]]]] ;
Ls = [op(add), [[number(0)], [op(neg), [[op(sub), [[number(1)], [op(ln), [[number(2)]]]]]]]]] ;
Ls = [op(add), [[number(0)], [op(neg), [[op(sub), [[op(ln), [[number(1)]]], [number(2)]]]]]]] ;
Ls = [op(add), [[number(0)], [op(sub), [[number(1)], [op(neg), [[op(ln), [[number(2)]]]]]]]]] ;
Ls = [op(add), [[number(0)], [op(sub), [[op(neg), [[number(1)]]], [op(ln), [[number(2)]]]]]]] ;
Ls = [op(add), [[number(0)], [op(sub), [[op(neg), [[op(ln), [[number(1)]]]]], [number(2)]]]]] ;
Ls = [op(add), [[op(neg), [[number(0)]]], [op(ln), [[op(sub), [[number(1)], [number(2)]]]]]]] ;
Ls = [op(add), [[op(neg), [[number(0)]]], [op(sub), [[number(1)], [op(ln), [[number(2)]]]]]]] ;
Ls = [op(add), [[op(neg), [[number(0)]]], [op(sub), [[op(ln), [[number(1)]]], [number(2)]]]]] ;
Ls = [op(add), [[op(neg), [[op(ln), [[number(0)]]]]], [op(sub), [[number(1)], [number(2)]]]]] ;
Ls = [op(add), [[op(neg), [[op(ln), [[op(sub), [[number(0)], [number(1)]]]]]]], [number(2)]]] ;
Ls = [op(add), [[op(neg), [[op(sub), [[number(0)], [number(1)]]]]], [op(ln), [[number(2)]]]]] ;
Ls = [op(add), [[op(neg), [[op(sub), [[number(0)], [op(ln), [[number(1)]]]]]]], [number(2)]]] ;
Ls = [op(add), [[op(neg), [[op(sub), [[op(ln), [[number(0)]]], [number(1)]]]]], [number(2)]]] ;
Ls = [op(add), [[op(sub), [[number(0)], [number(1)]]], [op(neg), [[op(ln), [[number(2)]]]]]]] ;
Ls = [op(add), [[op(sub), [[number(0)], [op(neg), [[number(1)]]]]], [op(ln), [[number(2)]]]]] ;
Ls = [op(add), [[op(sub), [[number(0)], [op(neg), [[op(ln), [[number(1)]]]]]]], [number(2)]]] ;
Ls = [op(add), [[op(sub), [[op(neg), [[number(0)]]], [number(1)]]], [op(ln), [[number(2)]]]]] ;
Ls = [op(add), [[op(sub), [[op(neg), [[number(0)]]], [op(ln), [[number(1)]]]]], [number(2)]]] ;
Ls = [op(add), [[op(sub), [[op(neg), [[op(ln), [[number(0)]]]]], [number(1)]]], [number(2)]]] ;
true.

, .

?- e([neg,ln],[add,sub],[[number(0)],[number(1)],[number(2)]],Es,_);true.
Es = u(u(b(t, b(t, t)))) ;
Es = u(u(b(b(t, t), t))) ;
Es = u(b(t, u(b(t, t)))) ;
Es = u(b(t, b(t, u(t)))) ;
Es = u(b(t, b(u(t), t))) ;
Es = u(b(u(t), b(t, t))) ;
Es = u(b(u(b(t, t)), t)) ;
Es = u(b(b(t, t), u(t))) ;
Es = u(b(b(t, u(t)), t)) ;
Es = u(b(b(u(t), t), t)) ;
Es = b(t, u(u(b(t, t)))) ;
Es = b(t, u(b(t, u(t)))) ;
Es = b(t, u(b(u(t), t))) ;
Es = b(t, b(t, u(u(t)))) ;
Es = b(t, b(u(t), u(t))) ;
Es = b(t, b(u(u(t)), t)) ;
Es = b(u(t), u(b(t, t))) ;
Es = b(u(t), b(t, u(t))) ;
Es = b(u(t), b(u(t), t)) ;
Es = b(u(u(t)), b(t, t)) ;
Es = b(u(u(b(t, t))), t) ;
Es = b(u(b(t, t)), u(t)) ;
Es = b(u(b(t, u(t))), t) ;
Es = b(u(b(u(t), t)), t) ;
Es = b(b(t, t), u(u(t))) ;
Es = b(b(t, u(t)), u(t)) ;
Es = b(b(t, u(u(t))), t) ;
Es = b(b(u(t), t), u(t)) ;
Es = b(b(u(t), u(t)), t) ;
Es = b(b(u(u(t)), t), t) ;
true.

, , .

,

e(Uc, Bc, Terminal_s, Unary_op_s, Binary_op_s, Es, Ls) :-
    e(_,[], _,[], Terminal_s, _, Unary_op_s, _, Binary_op_s, _, Es, Ls).


?- e([neg,ln],[add,sub],[[number(0)],[number(1)],[number(2)]],_,Ls);true.
Ls = [number(0)] ;
Ls = [op(neg), [[number(0)]]] ;
Ls = [op(neg), [[op(ln), [[number(0)]]]]] ;
Ls = [op(neg), [[op(ln), [[op(add), [[number(0)], [number(1)]]]]]]] ;
Ls = [op(neg), [[op(ln), [[op(add), [[number(0)], [op(sub), [[number(1)], [number(2)]]]]]]]]] ;
Ls = [op(neg), [[op(ln), [[op(add), [[op(sub), [[number(0)], [number(1)]]], [number(2)]]]]]]] ;
Ls = [op(neg), [[op(add), [[number(0)], [number(1)]]]]] ;
Ls = [op(neg), [[op(add), [[number(0)], [op(ln), [[number(1)]]]]]]] ;
Ls = [op(neg), [[op(add), [[number(0)], [op(ln), [[op(sub), [[number(1)], [number(2)]]]]]]]]] ;
Ls = [op(neg), [[op(add), [[number(0)], [op(sub), [[number(1)], [number(2)]]]]]]] ;
Ls = [op(neg), [[op(add), [[number(0)], [op(sub), [[number(1)], [op(ln), [[number(2)]]]]]]]]] ;
Ls = [op(neg), [[op(add), [[number(0)], [op(sub), [[op(ln), [[number(1)]]], [number(2)]]]]]]] ;
Ls = [op(neg), [[op(add), [[op(ln), [[number(0)]]], [number(1)]]]]] ;
Ls = [op(neg), [[op(add), [[op(ln), [[number(0)]]], [op(sub), [[number(1)], [number(2)]]]]]]] ;
Ls = [op(neg), [[op(add), [[op(ln), [[op(sub), [[number(0)], [number(1)]]]]], [number(2)]]]]] ;
Ls = [op(neg), [[op(add), [[op(sub), [[number(0)], [number(1)]]], [number(2)]]]]] ;
Ls = [op(neg), [[op(add), [[op(sub), [[number(0)], [number(1)]]], [op(ln), [[number(2)]]]]]]] ;
Ls = [op(neg), [[op(add), [[op(sub), [[number(0)], [op(ln), [[number(1)]]]]], [number(2)]]]]] ;
Ls = [op(neg), [[op(add), [[op(sub), [[op(ln), [[number(0)]]], [number(1)]]], [number(2)]]]]] ;
Ls = [op(add), [[number(0)], [number(1)]]] ;
Ls = [op(add), [[number(0)], [op(neg), [[number(1)]]]]] ;
Ls = [op(add), [[number(0)], [op(neg), [[op(ln), [[number(1)]]]]]]] ;
Ls = [op(add), [[number(0)], [op(neg), [[op(ln), [[op(sub), [[number(1)], [number(2)]]]]]]]]] ;
Ls = [op(add), [[number(0)], [op(neg), [[op(sub), [[number(1)], [number(2)]]]]]]] ;
Ls = [op(add), [[number(0)], [op(neg), [[op(sub), [[number(1)], [op(ln), [[number(2)]]]]]]]]] ;
Ls = [op(add), [[number(0)], [op(neg), [[op(sub), [[op(ln), [[number(1)]]], [number(2)]]]]]]] ;
Ls = [op(add), [[number(0)], [op(sub), [[number(1)], [number(2)]]]]] ;
Ls = [op(add), [[number(0)], [op(sub), [[number(1)], [op(neg), [[number(2)]]]]]]] ;
Ls = [op(add), [[number(0)], [op(sub), [[number(1)], [op(neg), [[op(ln), [[number(2)]]]]]]]]] ;
Ls = [op(add), [[number(0)], [op(sub), [[op(neg), [[number(1)]]], [number(2)]]]]] ;
Ls = [op(add), [[number(0)], [op(sub), [[op(neg), [[number(1)]]], [op(ln), [[number(2)]]]]]]] ;
Ls = [op(add), [[number(0)], [op(sub), [[op(neg), [[op(ln), [[number(1)]]]]], [number(2)]]]]] ;
Ls = [op(add), [[op(neg), [[number(0)]]], [number(1)]]] ;
Ls = [op(add), [[op(neg), [[number(0)]]], [op(ln), [[number(1)]]]]] ;
Ls = [op(add), [[op(neg), [[number(0)]]], [op(ln), [[op(sub), [[number(1)], [number(2)]]]]]]] ;
Ls = [op(add), [[op(neg), [[number(0)]]], [op(sub), [[number(1)], [number(2)]]]]] ;
Ls = [op(add), [[op(neg), [[number(0)]]], [op(sub), [[number(1)], [op(ln), [[number(2)]]]]]]] ;
Ls = [op(add), [[op(neg), [[number(0)]]], [op(sub), [[op(ln), [[number(1)]]], [number(2)]]]]] ;
Ls = [op(add), [[op(neg), [[op(ln), [[number(0)]]]]], [number(1)]]] ;
Ls = [op(add), [[op(neg), [[op(ln), [[number(0)]]]]], [op(sub), [[number(1)], [number(2)]]]]] ;
Ls = [op(add), [[op(neg), [[op(ln), [[op(sub), [[number(0)], [number(1)]]]]]]], [number(2)]]] ;
Ls = [op(add), [[op(neg), [[op(sub), [[number(0)], [number(1)]]]]], [number(2)]]] ;
Ls = [op(add), [[op(neg), [[op(sub), [[number(0)], [number(1)]]]]], [op(ln), [[number(2)]]]]] ;
Ls = [op(add), [[op(neg), [[op(sub), [[number(0)], [op(ln), [[number(1)]]]]]]], [number(2)]]] ;
Ls = [op(add), [[op(neg), [[op(sub), [[op(ln), [[number(0)]]], [number(1)]]]]], [number(2)]]] ;
Ls = [op(add), [[op(sub), [[number(0)], [number(1)]]], [number(2)]]] ;
Ls = [op(add), [[op(sub), [[number(0)], [number(1)]]], [op(neg), [[number(2)]]]]] ;
Ls = [op(add), [[op(sub), [[number(0)], [number(1)]]], [op(neg), [[op(ln), [[number(2)]]]]]]] ;
Ls = [op(add), [[op(sub), [[number(0)], [op(neg), [[number(1)]]]]], [number(2)]]] ;
Ls = [op(add), [[op(sub), [[number(0)], [op(neg), [[number(1)]]]]], [op(ln), [[number(2)]]]]] ;
Ls = [op(add), [[op(sub), [[number(0)], [op(neg), [[op(ln), [[number(1)]]]]]]], [number(2)]]] ;
Ls = [op(add), [[op(sub), [[op(neg), [[number(0)]]], [number(1)]]], [number(2)]]] ;
Ls = [op(add), [[op(sub), [[op(neg), [[number(0)]]], [number(1)]]], [op(ln), [[number(2)]]]]] ;
Ls = [op(add), [[op(sub), [[op(neg), [[number(0)]]], [op(ln), [[number(1)]]]]], [number(2)]]] ;
Ls = [op(add), [[op(sub), [[op(neg), [[op(ln), [[number(0)]]]]], [number(1)]]], [number(2)]]] ;
true.


?- e([neg,ln],[add,sub],[[number(0)],[number(1)],[number(2)]],Es,_);true.
Es = t ;
Es = u(t) ;
Es = u(u(t)) ;
Es = u(u(b(t, t))) ;
Es = u(u(b(t, b(t, t)))) ;
Es = u(u(b(b(t, t), t))) ;
Es = u(b(t, t)) ;
Es = u(b(t, u(t))) ;
Es = u(b(t, u(b(t, t)))) ;
Es = u(b(t, b(t, t))) ;
Es = u(b(t, b(t, u(t)))) ;
Es = u(b(t, b(u(t), t))) ;
Es = u(b(u(t), t)) ;
Es = u(b(u(t), b(t, t))) ;
Es = u(b(u(b(t, t)), t)) ;
Es = u(b(b(t, t), t)) ;
Es = u(b(b(t, t), u(t))) ;
Es = u(b(b(t, u(t)), t)) ;
Es = u(b(b(u(t), t), t)) ;
Es = b(t, t) ;
Es = b(t, u(t)) ;
Es = b(t, u(u(t))) ;
Es = b(t, u(u(b(t, t)))) ;
Es = b(t, u(b(t, t))) ;
Es = b(t, u(b(t, u(t)))) ;
Es = b(t, u(b(u(t), t))) ;
Es = b(t, b(t, t)) ;
Es = b(t, b(t, u(t))) ;
Es = b(t, b(t, u(u(t)))) ;
Es = b(t, b(u(t), t)) ;
Es = b(t, b(u(t), u(t))) ;
Es = b(t, b(u(u(t)), t)) ;
Es = b(u(t), t) ;
Es = b(u(t), u(t)) ;
Es = b(u(t), u(b(t, t))) ;
Es = b(u(t), b(t, t)) ;
Es = b(u(t), b(t, u(t))) ;
Es = b(u(t), b(u(t), t)) ;
Es = b(u(u(t)), t) ;
Es = b(u(u(t)), b(t, t)) ;
Es = b(u(u(b(t, t))), t) ;
Es = b(u(b(t, t)), t) ;
Es = b(u(b(t, t)), u(t)) ;
Es = b(u(b(t, u(t))), t) ;
Es = b(u(b(u(t), t)), t) ;
Es = b(b(t, t), t) ;
Es = b(b(t, t), u(t)) ;
Es = b(b(t, t), u(u(t))) ;
Es = b(b(t, u(t)), t) ;
Es = b(b(t, u(t)), u(t)) ;
Es = b(b(t, u(u(t))), t) ;
Es = b(b(u(t), t), t) ;
Es = b(b(u(t), t), u(t)) ;
Es = b(b(u(t), u(t)), t) ;
Es = b(b(u(u(t)), t), t) ;
true.

, , , , .

, .

e([number(0)]           , t1        ) --> [].
e([number(1)]           , t2        ) --> [].
e([number(2)]           , t3        ) --> [].
e([op(neg),[Arg]]       , u1(E)     ) --> [_],   e(Arg,E).
e([op(ln),[Arg]]        , u2(E)     ) --> [_],   e(Arg,E).
e([op(add),[Left,Right]], b1(E0,E1) ) --> [_,_], e(Left,E0), e(Right,E1).
e([op(sub),[Left,Right]], b2(E0,E1) ) --> [_,_], e(Left,E0), e(Right,E1).

e(EL,Es) :-
    length(Ls, _), phrase(e(EL,Es), Ls).

es_count(M, Count) :-
    length([_|Ls], M),
    findall(., phrase(e(_,_), Ls), Sols),
    length(Sols, Count).

, . , : , - .

5

5 , , , , , lurker, .

  • CLP (FD) , , ?
  • /2, DCG CLP (FD)?
  • DCG?
  • DCG DCG?
  • DCG , . , , ?
+3
2

- (, b(t,u(b(t,t,)))), . CLP (FD) .

expression(U, B, E) :-
    terminal(U, B, E).
expression(U, B, E) :-
    unary(U, B, E).
expression(U, B, E) :-
    binary(U, B, E).

terminal(0, 0, t).

unary(U, B, u(E)) :-
    U1 #>= 0,
    U #= U1 + 1,
    expression(U1, B, E).

binary(U, B, b(E1,E2)) :-
    U1 #>= 0, U2 #>= 0,
    U #= U1 + U2,
    B1 #>= 0, B2 #>= 0,
    B #= B1 + B2 + 1,
    expression(U1, B1, E1),
    expression(U2, B2, E2).

, . - CLP (FD), . , , , expression/3, . , Prolog .

:

| ?- expression(1,2,E).

E = u(b(t,b(t,t))) ? a

E = u(b(b(t,t),t))

E = b(t,u(b(t,t)))

E = b(t,b(t,u(t)))

E = b(t,b(u(t),t))

E = b(u(t),b(t,t))

E = b(u(b(t,t)),t)

E = b(b(t,t),u(t))

E = b(b(t,u(t)),t)

E = b(b(u(t),t),t)

(1 ms) no



| ?- expression(U, B, E).

B = 0
E = t
U = 0 ? ;

B = 0
E = u(t)
U = 1 ? ;

B = 0
E = u(u(t))
U = 2 ? ;
...

DCG

DCG. , DCG . , b(t,u(b(t,t))) [b, '(', t, u, '(', b, '(', t, t, ')', ')', ')']. DCG . DCG, :

expression(U, B, E) -->
    terminal(U, B, E) |
    unary(U, B, E) |
    binary(U, B, E).

terminal(0, 0, t) --> [t].

unary(U, B, u(E)) -->
    [u, '('],
    { U1 #>= 0, U #= U1 + 1 },
    expression(U1, B, E),
    [')'].

binary(U, B, b(E1, E2)) -->
    [b, '('],
    { U1 #>= 0, U2 #>= 0, U #= U1 + U2, B1 #>= 0, B2 #>= 0, B #= B1 + B2 + 1 },
    expression(U1, B1, E1),
    expression(U2, B2, E2),
    [')'].

, terminal//3 expression//3. parallelism -DCG-. .

| ?-  phrase(expression(1,2,E), S).

E = u(b(t,b(t,t)))
S = [u,'(',b,'(',t,b,'(',t,t,')',')',')'] ? a

E = u(b(b(t,t),t))
S = [u,'(',b,'(',b,'(',t,t,')',t,')',')']

E = b(t,u(b(t,t)))
S = [b,'(',t,u,'(',b,'(',t,t,')',')',')']

E = b(t,b(t,u(t)))
S = [b,'(',t,b,'(',t,u,'(',t,')',')',')']

E = b(t,b(u(t),t))
S = [b,'(',t,b,'(',u,'(',t,')',t,')',')']

E = b(u(t),b(t,t))
S = [b,'(',u,'(',t,')',b,'(',t,t,')',')']

E = b(u(b(t,t)),t)
S = [b,'(',u,'(',b,'(',t,t,')',')',t,')']

E = b(b(t,t),u(t))
S = [b,'(',b,'(',t,t,')',u,'(',t,')',')']

E = b(b(t,u(t)),t)
S = [b,'(',b,'(',t,u,'(',t,')',')',t,')']

E = b(b(u(t),t),t)
S = [b,'(',b,'(',u,'(',t,')',t,')',t,')']

no

| ?-  phrase(expression(U,B,E), S).

B = 0
E = t
S = [t]
U = 0 ? ;

B = 0
E = u(t)
S = [u,'(',t,')']
U = 1 ? ;

B = 0
E = u(u(t))
S = [u,'(',u,'(',t,')',')']
U = 2 ?
...

, №1 , , № 4 . DCG . , DCG .

length/2

№2, , DCG, , , length/2, , . , , , :

?- length(S, _), phrase(expression(U,B,E), S).

B = 0
E = t
S = [t]
U = 0 ? ;

B = 0
E = u(t)
S = [u,'(',t,')']
U = 1 ? ;

B = 1
E = b(t,t)
S = [b,'(',t,t,')']
U = 0 ? ;

B = 0
E = u(u(t))
S = [u,'(',u,'(',t,')',')']
U = 2 ? ;

B = 1
E = u(b(t,t))
S = [u,'(',b,'(',t,t,')',')']
U = 1 ? ;

B = 1
E = b(t,u(t))
S = [b,'(',t,u,'(',t,')',')']
U = 1 ? ;

B = 1
E = b(u(t),t)
S = [b,'(',u,'(',t,')',t,')']
U = 1 ? 
...

, , , :

unary(U, B, u(E)) -->
    [u],
    { U1 #>= 0, U #= U1 + 1 },
    expression(U1, B, E).

binary(U, B, b(E1, E2)) -->
    [b],
    { U1 #>= 0, U2 #>= 0, U #= U1 + U2, B1 #>= 0, B2 #>= 0, B #= B1 + B2 + 1 },
    expression(U1, B1, E1),
    expression(U2, B2, E2).

, , , , . :

| ?- length(S, _), phrase(expression(U, B, E), S).

B = 0
E = t
S = [t]
U = 0 ? ;

B = 0
E = u(t)
S = [u,t]
U = 1 ? ;

B = 0
E = u(u(t))
S = [u,u,t]
U = 2 ? ;

B = 1
E = b(t,t)
S = [b,t,t]
U = 0 ? ;

B = 0
E = u(u(u(t)))
S = [u,u,u,t]
U = 3 ? ;

B = 1
E = u(b(t,t))
S = [u,b,t,t]
U = 1 ? ;

B = 1
E = b(t,u(t))
S = [b,t,u,t]
U = 1 ? ;

B = 1
E = b(u(t),t)
S = [b,u,t,t]
U = 1 ? ;

B = 0
E = u(u(u(u(t))))
S = [u,u,u,u,t]
U = 4 ? ;

B = 1
E = u(u(b(t,t)))
S = [u,u,b,t,t]
U = 2 ? ;
...

, , Term, ( , DCG), length/2 , , . , length/2 DCG - , , DCG , , .

+3

@lurker , .

-, , , . , , , , , , , . , , , .

, :

e_b(t, B, B, U, U).
e_b(u(E), B0, B1, U0, U2) :-
        U1 #= U0 + 1,
        e_b(E, B0, B1, U1, U2).
e_b(b(E0, E1), B0, B3, U0, U2) :-
        B1 #= B0 + 1,
        e_b(E0, B1, B2, U0, U1),
        e_b(E1, B2, B3, U1, U2).

e_b(U, B, Es) :-
        U #=< Us,
        B #=< Bs,
        e_b(Es, 0, Bs, 0, Us).

:

CLP (FD) , , ?

, , CLP (FD): . , "", , (is)/2 (=:=)/2. (#=)/2, , .

, , , :

?- e_b(1, 2, Es), false.
nontermination

? , , , . false/0 .

. , e_b/3 e_b/5 :

e_b(t, B, B, U, U).
e_b(u(E), B0, B1, U0, U2) :-
        U1 #= U0 + 1,
        false,
        e_b(E, B0, B1, U1, U2).
e_b(b(E0, E1), B0, B3, U0, U2) :-
        B1 #= B0 + 1,
        e_b(E0, B1, B2, U0, U1),
        false,
        e_b(E1, B2, B3, U1, U2).

, , . :

?- e_b(1, 2, Es), false.
nontermination

, - !

e_b(t, B, B, U, U).
e_b(u(E), B0, B1, U0, U2) :-
        U1 #= U0 + 1.
e_b(b(E0, E1), B0, B3, U0, U2) :-
        B1 #= B0 + 1,
        e_b(E0, B1, B2, U0, U1).

, . , . , ​​ , !

:

?- e_b(1, 2, Es).
Es = u(_1064) ;
Es = b(t, _1066) ;
Es = b(u(_1070), _1066) ;
Es = b(b(t, _1072), _1066) .

, , :

?- e_b(1, 2, Es), false.
nontermination

, . ! , , , .

, . - , , :

e_b(t, B, B, U, U).
e_b(u(_), B, B, U0, U1) :-
        U1 #= U0 + 1.
e_b(b(E0, _), B0, B, U0, U) :-
        B1 #= B0 + 1,
        e_b(E0, B1, B, U0, U).

:

?- e_b(1, 2, Es), false.
nontermination

, :

e_b(t, B, B, U, U).
e_b(u(_), B, B, U0, U1) :-
        U1 #= U0 + 1.
e_b(b(E0, _), B0, B, U0, U) :-
        B1 #= B0 + 1,
        e_b(E0, B1, B, U0, U).

, :

e_b(t, B, B, U, U).
e_b(b(E0, _), B0, B, U0, U) :-
        B1 #= B0 + 1,
        e_b(E0, B1, B, U0, U).

, ?

, , :

e_b(t, B, B, U, U).
e_b(b(E0, _), B0, B, U0, U) :-
        B1 #= B0 + 1,
        e_b(E0, B1, B, U0, U).

e_b(U, B, Es) :-
        U #=< Us,
        B #=< Bs,
        e_b(Es, 0, Bs, 0, Us).

-:

?- e_b(1, 2, Es).
nontermination

, , , . ? ( ): : "", . , , :

?- e_b(A, B, Es).
Es = t,
A in inf..0,
B in inf..0 ;
Es = b(t, _3532),
A in inf..0,
B in inf..1 ;
Es = b(b(t, _3550), _3544),
A in inf..0,
B in inf..2 .

. , - ?

, :

?- A #>= 0, B #>= 0, e_b(A, B, Es).
A = B, B = 0,
Es = t ;
A = 0,
Es = b(t, _8094),
B in 0..1 ;
A = 0,
Es = b(b(t, _8112), _8106),
B in 0..2 .

, , . , . !

:

/2, DCG CLP (FD)?

length/2 . DCG . Prolog -. , , . , Prolog , , .

CLP (FD). , -, CLP (FD).

:

, DCG?

length/2 , , , DCG , . , , .

:

DCG DCG? , DCG , . , , ?

, V0 rightarrow; V1 & rightarrow; V2 & rightarrow; & hellip; & rightarrow; V .. , "", DCG semicontext , . , DCG.

, . , , f(...), , . .

. , , , , GNU Prolog Prolog  

| ?- write_canonical([op(add),[Left,Right]]). 
'.'(op(add),'.'('.'(_18,'.'(_19,[])),[]))

, , , .

, , Left+Right , , op_arguments(add, [Left,Right]), op_arguments(number, [1]) ..

+3

Source: https://habr.com/ru/post/1681458/

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