/* 

  Regex in reverse - decompose regular expressions in Picat v3.

  From codegolf: 
  Regex in reverse - decompose regular expressions
  https://codegolf.stackexchange.com/questions/25378/regex-in-reverse-decompose-regular-expressions
  """
  The Problem

  I have a bunch of regular expressions that I need to use in some code, but I'm 
  using a programming language that doesn't support regex! Luckily, I know that the 
  test string will have a maximum length and will be composed of printable ASCII only.

  The Challenge

  You must input a regex and a number n, and output every string composed of printable 
  ASCII (ASCII codes 32 to 126 inclusive, to ~, no tabs or newlines) of length less than or 
  equal to n that matches that regex. You may not use built-in regular expressions or 
  regex matching functions in your code at all. Regular expressions will be limited to 
  the following:

  *  Literal characters (and escapes, which force a character to be literal, so \. 
     is a literal ., \n is a literal n (equivalent to just n), and \w is equivalent 
     to w. You do not need to support escape sequences.)

  *  . - wildcard (any character)

  *  Character classes, [abc] means "a or b or c" and [d-f] means anything from d to f 
     (so, d or e or f). The only characters that have special meaning in a character 
     class are [ and ] (which will always be escaped, so don't worry about those), 
     \ (the escape character, of course), ^ at the beginning of the character class 
     (which is a negation), and - (which is a range).
  * | - the OR operator, alternation. foo|bar means either foo or bar, and (ab|cd)e 
    matches either abe or cde.
  *  * - match the previous token repeated zero or more times, greedy (it tries to 
     repeat as many times as possible)
  *  + - repeated one or more times, greedy
  *  ? - zero or one times
  * Grouping with parentheses, to group tokens for |, *. +, or ?

  The input regex will always be valid (i.e., you do not have to handle input like 
  ?abc or (foo or any invalid input). You may output the strings in any order 
  you would like, but each string must appear only once (don't output any 
  duplicates).

  The Test Cases

  Input: .*, 1
  Output: (empty string), , !, ", ..., }, ~

  Input: w\w+, 3
  Output: ww, www

  Input: [abx-z][^ -}][\\], 3
  Output: a~\, b~\, x~\, y~\, z~\

  Input: ab*a|c[de]*, 3
  Output: c, cd, ce, aa, cde, ced, cdd, cee, aba

  Input: (foo)+(bar)?!?, 6
  Output: foo, foo!, foofoo, foobar

  Input: (a+|b*c)d, 4
  Output: ad, cd, aad, bcd, aaad, bbcd

  Input: p+cg, 4
  Output: pcg, ppcg

  Input: a{3}, 4
  Output: a{3}

  The Winner

  This is code-golf, so the shortest code in bytes will win!
  """

  This Picat model was created by Hakan Kjellerstrand, hakank@gmail.com
  See also my Picat page: http://www.hakank.org/picat/

*/


import util.


main => go.


go ?=>
  % generate_string("w\\w+", 3,S),
  % generate_string("[abx-z][^ -}][\\\\]", 3, S),
  % generate_string("[^ ]+", 3, S), % 839514 strings
  generate_string("[abc]+[xyz]+", 3, S), % 63 strings
  println(s=S),
  fail,
  nl.

go => true.

% See mankell.pi and mankell_v3.pi
% (Same result, but in different order)
go2 ?=>
  % Kjellerstrand (48)
  println("kjellerstrand:"),
  K = findall(S,generate_string("k(je|ä)ll(er|ar)?(st|b)r?an?d",15,S)),
  println(K),
  println(len=K.len),
  nl,
  % Henning Mankell (1296)
  println("henning mankell"),
  M = findall(S,generate_string("[hm][ea](nk|n|nn)(ing|ell|all) [hm][ea](nk|n|nn)(ing|ell|all)",15,S)),
  % println(M),
  println(len=M.len),

  nl.
go2 => true.

% The tests.
% Correct words but not always in correct order (fixing this by split.sort.join).
go3 ?=>
  Tests = [
     [".*", 1, "(empty string), , !, \", ..., }, ~"], 
     ["w\\w+", 3, "ww, www"],
     ["[abx-z][^ -}][\\\\]", 3,"a~\\, b~\\, x~\\, y~\\, z~\\"],
     % ["ab*a|c[de]*", 3, "c, cd, ce, aa, cde, ced, cdd, cee, aba"], % not correct order
     ["ab*a|c[de]*", 3, "c, cd, ce, aa, cde, ced, cdd, cee, aba".split(", ").sort.join(", ")],
     ["(foo)+(bar)?!?", 6,"foo, foo!, foofoo, foobar".split(", ").sort.join(", ")],
     ["(a+|b*c)d", 4, "ad, cd, aad, bcd, aaad, bbcd".split(", ").sort.join(", ")],
     ["p+cg", 4, "pcg, ppcg"],
     ["a{3}", 4, "a{3}"],

     ["price[1234]",10,"price1, price2, price3, price4"],
     ["[a-c][a-c][a-c]",6,"aaa, aab, aac, aba, abb, abc, aca, acb, acc, baa, bab, bac, bba, bbb, bbc, bca, bcb, bcc, caa, cab, cac, cba, cbb, cbc, cca, ccb, ccc"], % hakank
     ["a(l(la?)?|n(anas|n(as?)?)?)?",20,"a, al, all, alla, an, ananas, ann, anna, annas"],
     ["(a|[bpk]a)lla",10,"alla, balla, kalla, palla"],
     ["(a(nd|t)|do|end|for|i[ns]|not|o[fr]|use)",10,"and, at, do, end, for, in, is, not, of, or, use"],
     % Generating all combinations of a, b, and c of length N.
     ["(a|b|c)+",3,"a, b, c, aa, ab, ac, ba, bb, bc, ca, cb, cc, aaa, aab, aac, aba, abb, abc, aca, acb, acc, baa, bab, bac, bba, bbb, bbc, bca, bcb, bcc, caa, cab, cac, cba, cbb, cbc, cca, ccb, ccc".split(", ").sort.join(", ")],
     
     % See regex_match_number.pi
     ["(eight|f(ive|our)|nine|one|s(even|ix)|t(hree|wo))",5,"one,two,three,four,five,six,seven,eight,nine".split(",").sort.join(", ")],
     ["(e(ight(een)?|leven)|f(i(fteen|ve)|our(teen)?)|nine(teen)?|one|s(even(teen)?|ix(teen)?)|t(en|h(irteen|ree)|w(elve|o)))",10,["one","two","three","four","five","six","seven","eight","nine","ten","eleven","twelve","thirteen","fourteen","fifteen","sixteen","seventeen","eighteen","nineteen"].sort.join(", ")]
  ],
  foreach([Regex,N,Check] in Tests)
    println([regex=Regex,n=N,check=Check]),
    All=findall(S,generate_string(Regex, N, S)).sort().join(", "),
    println(All),
    if All == Check then
      println(ok)
    else
      println(not_ok)
    end,
    nl
  end,

  nl.

go3 => true.


go4 ?=>
  wordle_regexp(Regex),
  N = 5,
  All=findall(S,generate_string(Regex, N, S)),
  println(all=All),
  println(All.len),
  nl.
go4 => true.

%
% Prolog solution by ankh-morpork (adjusted to Picat by hakank)
% From
% https://codegolf.stackexchange.com/questions/25378/regex-in-reverse-decompose-regular-expressions
%
% Prolog, ungolfed
%
generate_string(R, L, S) :-
    % parse regex
    % string_codes(R, RC),
    RC = to_codes(R), % hakank
    regex_union(RE, RC, []),

    % bound string length
    between(0, L, M),
    bp.length(SC, M), % hakank

    % find string
    match(SC, RE, []),

    % string_codes(S, SC).
    S = [chr(C) : C in SC]. % hakank

% Parsers
%%%%%%%%%  

regex_union(R) -->regex_concat(S), regex_union1(S, R).

regex_union1(R,T) --> [124], regex_concat(S), regex_union1($regex_union(R,S), T).
regex_union1(R, R) --> [].

regex_concat(R) --> regex_op(S), regex_concat1(S, R).

regex_concat1(R, T) --> regex_op(S), regex_concat1($regex_concat(R,S), T).
regex_concat1(R, R) --> [].

regex_op(regex_kleene(R)) --> regex_lit(R), [42].
regex_op(regex_concat(R,regex_kleene(R))) --> regex_lit(R), [43].
regex_op(regex_union(regex_empty,R)) --> regex_lit(R), [63].
regex_op(R) --> regex_lit(R).

regex_lit(regex_char([C])) --> [C], {\+ regex_ctrl(C)}.
regex_lit(regex_char([C])) --> [92], [C].

regex_lit(regex_char(CS)) --> [46],
          % {findall(C, between(32,126, C), CS)}.
          {CS = findall(C, between(32,126, C))}. % hakank        

regex_lit(regex_char(DS)) --> 
    [91], [94], !, class_body(CS), [93],
    % {findall(C, (between(32, 126, C), \+ member(C, CS)), DS)}.
    {DS = findall(C, (between(32, 126, C), \+ member(C, CS)))}. % hakank
regex_lit(regex_char(CS)) --> [91], class_body(CS), [93].

regex_lit(R) --> [40], regex_union(R), [41].

class_body([C|T]) --> class_lit(C),class_body(T).
class_body(CS) -->
    class_lit(C0), [45], class_lit(C1), class_body(T),
    % {findall(C, between(C0, C1, C), H), append(H,T,CS)}.
    {H = findall(C, between(C0, C1, C)), append(H,T,CS)}. % hakank
class_body([]) --> [].

class_lit(C) --> [C], {\+ class_ctrl(C)}.
class_lit(C) --> [92], [C].

class_ctrl(C) :- CS=to_codes("\\[]-"), member(C, CS). % hakank
regex_ctrl(C) :- CS=to_codes("\\.[]|+?*()"), member(C, CS). % hakank

% Regex Engine
%%%%%%%%%%%%%% 

% The regex empty matches any string without consuming any characters.
match(S, regex_empty, S).

% A regex consisting of a single character matches any string starting with
% that character. The chanter is consumed.
match([C|S], regex_char(CS), S) :- member(C, CS).

% A union of two regex only needs to satisify one of the branches.
match(S, regex_union(L,R), T) :- match(S, L, T); match(S, R, T).     

% A concat of two regex must satisfy the left and then the right.
match(S, regex_concat(L, R), U) :- match(S, L, T), match(T, R, U).

% The kleene closure of a regex can match the regex 0 times or it can the regex
% once before matching the kleene closure again.
match(S, regex_kleene(_), S).
match(S, regex_kleene(K), U) :- match(S, K, T), S != T, match(T, $regex_kleene(K), U).


% See wordle_dcg.pi for comparison (using DCG)
wordle_regexp(Wordle) :-
  % This (prefix) regex was generated by make_regex.pi (go3/0).
  Wordle = "(a(b(a(ck|se|te)|b(ey|ot)|hor|ide|led|o(de|rt|ut|ve)|use|yss)|c(orn|rid|tor|ute)|d(a(ge|pt)|ept|mi[nt]|o(be|pt|r[en])|ult)|f(fix|ire|o(ot|ul)|ter)|g(a(in|pe|te)|ent|i(le|ng)|low|o(ny|ra)|ree)|head|i(der|sle)|l(arm|bum|ert|gae|i(bi|en|gn|ke|ve)|l(ay|ey|o[twy])|o(ft|n[eg]|of|ud)|pha|t(ar|er))|m(a(ss|ze)|b(er|le)|end|i(ss|ty)|ong|pl[ey]|use)|n(g(e[lr]|le|ry|st)|ime|kle|n(ex|oy|ul)|ode|tic|vil)|orta|p(art|hid|ing|nea|pl[ey]|ron|tly)|r(bor|dor|ena|gue|ise|mor|o(ma|se)|r(ay|ow)|son|tsy)|s(cot|hen|ide|kew|s(ay|et))|t(o(ll|ne)|tic)|u(di[ot]|gur|nty)|v(ail|ert|ian|oid)|w(a(it|ke|r[de]|sh)|ful|oke)|xi(al|o[mn])|zure)|b(a(con|d(ge|ly)|g(el|gy)|ker|l(er|my)|n(al|jo)|r(ge|on)|s(al|i[clns]|te)|t(ch|he|on|ty)|wdy|you)|e(a(ch|dy|rd|st)|e(ch|fy)|fit|g(a[nt]|et|in|un)|ing|l(ch|ie|l[ey]|ow)|nch|r(et|ry|th)|set|tel|vel|zel)|i(ble|cep|ddy|got|l(ge|ly)|ng[eo]|ome|r(ch|th)|son|tty)|l(a(ck|de|me|n[dk]|re|st|ze)|e(a[kt]|e[dp]|nd|ss)|i(mp|n[dk]|ss|tz)|o(at|ck|ke|nd|o[dm]|wn)|u(er|ff|nt|r[bt]|sh))|o(a(rd|st)|bby|n(ey|go|us)|o(by|st|t[hy]|z[ey])|r(ax|ne)|s(om|sy)|tch|u(gh|le|nd)|wel|xer)|r(a(ce|i[dn]|ke|nd|s[hs]|v[eo]|w[ln])|e(a[dk]|ed)|i(ar|be|ck|de|ef|n[egky]|sk)|o(ad|il|ke|o[dkm]|th|wn)|u(nt|sh|te))|u(d(dy|ge)|g(gy|le)|il[dt]|l(ge|ky|ly)|n(ch|ny)|r(ly|nt|st)|s(ed|hy)|t(ch|te)|xom|yer)|ylaw)|c(a(b(al|by|in|le)|c(ao|he|ti)|d(dy|et)|gey|irn|me[lo]|n(al|dy|ny|o[en])|p(er|ut)|r(at|go|ol|ry|ve)|ste|t(ch|er|ty)|u(lk|se)|vil)|e(ase|dar|llo)|h(a(f[ef]|i[nr]|lk|mp|nt|os|r[dmt]|s[em])|e(a[pt]|ck|e[kr]|s[st])|i(ck|de|ef|l[dil]|me|na|rp)|o(ck|ir|ke|r[de]|se)|u(ck|mp|nk|rn|te))|i(der|gar|nch|rca|vi[cl])|l(a(ck|im|mp|n[gk]|s[hps])|e(a[nrt]|ft|rk)|i(ck|ff|mb|n[gk])|o(ak|ck|ne|se|th|u[dt]|ve|wn)|u(ck|ed|mp|ng))|o(a(ch|st)|bra|coa|lo[nr]|m(et|fy|ic|ma)|n(ch|do|ic)|pse|r(al|er|ny)|u(ch|gh|ld|nt|pe|rt)|ve[nrty]|wer|yly)|r(a(ck|ft|mp|n[ek]|s[hs]|te|ve|wl|z[ey])|e(a[km]|do|e[dkp]|me|p[et]|s[st])|i(ck|e[dr]|m[ep]|sp)|o(ak|ck|n[ey]|ok|ss|up|w[dn])|u(de|el|m[bp]|s[ht])|ypt)|u(bic|min|r(io|ly|ry|se|v[ey])|tie)|y(ber|cle|nic))|d(a(ddy|i(ly|ry|sy)|lly|n(ce|dy)|tum|unt)|e(a(lt|th)|b(ar|it|u[gt])|c(a[ly]|o[ry]|ry)|fer|i(gn|ty)|l(ay|ta|ve)|m(on|ur)|n(im|se)|p(ot|th)|rby|t(er|ox)|uce|vil)|i(ary|cey|git|lly|mly|n(er|g[oy])|ode|r(ge|ty)|sco|t(ch|t[oy])|ver|zzy)|o(dg[ey]|gma|ing|lly|n(or|ut)|pey|u(bt|gh)|w(dy|el|ny|ry)|zen)|r(a(ft|in|ke|ma|nk|pe|w[ln])|e(a[dm]|ss)|i(e[dr]|ft|ll|nk|ve)|o(it|ll|ne|o[lp]|ss|ve|wn)|u(id|nk)|y(er|ly))|u(chy|lly|m(my|py)|nce|s(ky|ty)|tch|vet)|w(arf|el[lt])|ying)|e(a(g(er|le)|r(ly|th)|sel|te[nr])|bony|clat|di(ct|fy)|erie|gret|ight|ject|king|l(ate|bow|der|e(ct|gy)|fin|i(de|te)|ope|ude)|m(ail|be[dr]|cee|pty)|n(act|dow|em[ay]|joy|nui|sue|t(er|ry)|voy)|po(ch|xy)|qu(al|ip)|r(ase|ect|ode|ror|upt)|s(say|ter)|t(h(er|ic|os)|ude)|v(ade|e(nt|ry)|ict|oke)|x(a(ct|lt)|cel|ert|i(le|st)|pel|t(ol|ra)|ult)|ying)|f(a(ble|cet|i(nt|ry|th)|lse|n(cy|ny)|rce|t(al|ty)|u(lt|na)|vor)|e(ast|cal|ign|l(la|on)|m(me|ur)|nce|r(al|ry)|t(al|ch|id|us)|ver|wer)|i(b(er|re)|cus|e(ld|nd|ry)|ft[hy]|ght|l(e[rt]|ly|my|th)|n(al|ch|er)|rst|shy|xer|zzy)|jord|l(a(ck|i[lr]|k[ey]|me|nk|re|s[hk])|e(ck|et|sh)|i(ck|er|n[gt]|rt)|o(at|ck|o[dr]|ra|ss|u[rt]|wn)|u(ff|id|ke|me|n[gk]|sh|te)|yer)|o(amy|c(al|us)|ggy|ist|l(io|ly)|r(ay|ce|g[eo]|t[ehy]|um)|und|yer)|r(a(il|me|nk|ud)|e(ak|e[dr]|sh)|i(ar|ed|ll|sk|tz)|o(ck|n[dt]|st|th|wn|ze)|uit)|u(dge|gue|lly|n(gi|ky|ny)|r(or|ry)|ssy|zzy))|g(a(ffe|ily|m(er|ma|ut)|ssy|u(dy|ge|nt|ze)|vel|wky|y(er|ly)|zer)|e(cko|e(ky|se)|n(ie|re))|ho(st|ul)|i(ant|ddy|psy|r(ly|th)|ve[nr])|l(a(de|nd|re|ss|ze)|ea[mn]|i(de|nt)|o(at|be|om|ry|ss|ve)|yph)|n(ash|ome)|o(dly|ing|l(em|ly)|n(ad|er)|o(dy|ey|fy|se)|rge|u(ge|rd))|r(a(ce|de|ft|i[ln]|n[dt]|p[eh]|s[ps]|te|v[ey]|ze)|e(at|e[dnt])|i(ef|ll|m[ey]|nd|pe)|o(an|in|om|pe|ss|u[pt]|ve|w[ln])|u(el|ff|nt))|u(a(rd|va)|es[st]|i(de|l[det]|se)|l(ch|ly)|m(bo|my)|ppy|st[oy])|ypsy)|h(a(bit|iry|lve|ndy|ppy|r(dy|em|py|ry|sh)|st[ey]|t(ch|er)|u(nt|te)|v(en|oc)|zel)|e(a(dy|r[dt]|th|v[ey])|dge|fty|ist|l(ix|lo)|nce|ron)|i(lly|nge|pp[oy]|tch)|o(ard|bby|ist|lly|mer|n(ey|or)|r(de|ny|se)|t(el|ly)|u(nd|se)|ve[lr]|wdy)|u(m(an|id|or|ph|us)|n(ch|ky)|rry|s(ky|sy)|tch)|y(dro|ena|men|per))|i(ci(ly|ng)|d(eal|io[mt]|ler|yll)|gloo|liac|m(age|bue|p(el|ly))|n(ane|box|cur|dex|e(pt|rt)|fer|got|l(ay|et)|ner|put|t(er|ro))|onic|r(ate|ony)|s(let|sue)|tchy|vory)|j(a(unt|zzy)|e(lly|rky|tty|wel)|iffy|o(i(nt|st)|ker|lly|ust)|u(dge|ic[ey]|m(bo|py)|nt[ao]|ror))|k(a(ppa|rma|yak)|ebab|haki|i(nky|osk|tty)|n(a(ck|ve)|e(ad|e[dl]|lt)|ife|o(ck|ll|wn))|oala|rill)|l(a(b(el|or)|d(en|le)|ger|n(ce|ky)|p(el|se)|r(ge|va)|sso|t(ch|er|he|te)|ugh|yer)|e(a(ch|fy|ky|nt|pt|rn|s[eht]|ve)|dge|e(ch|ry)|fty|g(al|gy)|m(on|ur)|per|ve[lr])|i(bel|ege|ght|ken|lac|m(bo|it)|n(e[nr]|go)|pid|the|v(er|id))|lama|o(a(my|th)|bby|c(al|us)|dge|fty|gi[cn]|o(py|se)|rry|ser|us[ey]|ver|w(er|ly)|yal)|u(c(id|ky)|m(en|py)|n(ar|ch|ge)|pus|r(ch|id)|sty)|y(ing|mph|nch|ric))|m(a(c(aw|ho|ro)|d(am|ly)|fia|g(ic|ma)|ize|jor|ker|m(bo|m[ay])|n(g[aeoy]|i[ac]|ly|or)|ple|r(ch|ry|sh)|s(on|se)|t(ch|ey)|uve|xim|y(be|or))|e(a(ly|nt|ty)|cca|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