Tweak render rules to handle precedence

Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>

renderrules.bergamot

@@ -1,3 +1,23 @@
+PrecApp @ prec(app(?l, ?r), 100, left) <-;
+PrecPlus @ prec(plus(?l, ?r), 80, either) <-;
+PrecAbs @ prec(abs(?x, ?t, ?e), 0, right) <-;
+PrecArr @ prec(tarr(?l, ?r), 0, right) <-;
+
+SelectHead @ select(cons([?t, ?v], ?rest), ?default, ?v) <- ?t;
+SelectTail @ select(cons([?t, ?v], ?rest), ?default, ?found) <- not(?t), select(?rest, ?default, ?found);
+SelectEmpty @ select(nil, ?default, ?default) <-;
+
+ParenthAssocLeft @ parenthassoc(?a_i, left, right) <-;
+ParenthAssocRight @ parenthassoc(?a_i, right, left) <-;
+ParenthAssocNone @ parenthassoc(?a_i, none, ?pos) <-;
+ParenthAssocNeq @ parenthassoc(?a_i, ?a_o, ?pos) <- not(symeq(?a_i, ?a_o));
+
+Parenth @ parenth(?inner, ?outer, ?pos, ?strin, ?strout) <-
+    prec(?inner, ?p_i, ?a_i), prec(?outer, ?p_o, ?a_o),
+    join(["(", ?strin, ")"], ?strinparen),
+    select([ [less(?p_i, ?p_o), strinparen], [less(?p_o, ?p_i), ?strin], [ parenthassoc(?a_i, ?a_o, ?pos), ?strinparen ] ], ?strin, ?strout);
+ParenthFallback @ parenth(?inner, ?outer, ?pos, ?strin, ?strin) <-;
+
 LatexListNil @ latexlist(nil, nil) <-;
 LatexListCons @ latexlist(cons(?x, ?xs), cons(?l_x, ?l_s)) <- latex(?x, ?l_x), latexlist(?xs, ?l_s);
 
@@ -10,19 +30,30 @@ NonEmpty @ nonempty(cons(?x, ?xs)) <-;
 LatexInt @ latex(?i, ?l) <- int(?i), tostring(?i, ?l);
 LatexStr @ latex(?s, ?l) <- str(?s), escapestring(?s, ?l_1), latexifystring(?s, ?l_2), join(["\\texttt{\"", ?l_2, "\"}"], ?l);
 LatexMeta @ latex(metavariable(?l), ?l) <-;
-LatexSym @ latex(?s, ?l) <- sym(?s), tostring(?s, ?l_1), join(["\\text{", ?l_1,"}"], ?l);
-LatexCall @ latex(?c, ?l) <- call(?c, ?n, ?ts), nonempty(?ts), latexlist(?ts, ?lts_1), intercalate(", ", ?lts_1, ?lts_2), join(?lts_2, ?lts_3), join(["\\text{", ?n, "}", "(", ?lts_3, ")"], ?l);
 LatexIntLit @ latex(intlit(?i), ?l) <- latex(?i, ?l);
 LatexStrLit @ latex(strlit(?s), ?l) <- latex(?s, ?l);
-LatexPlus @ latex(plus(?e_1, ?e_2), ?l) <- latex(?e_1, ?l_1), latex(?e_2, ?l_2), join([?l_1, " + ", ?l_2], ?l);
+LatexVar @ latex(var(?s), ?l) <- latex(?s, ?l);
+LatexPlus @ latex(plus(?e_1, ?e_2), ?l) <-
+    latex(?e_1, ?l_1), latex(?e_2, ?l_2),
+    parenth(?e_1, plus(?e_1, ?e_2), left, ?l_1, ?lp_1),
+    parenth(?e_2, plus(?e_1, ?e_2), right, ?l_2, ?lp_2),
+    join([?lp_1, " + ", ?lp_2], ?l);
 LatexPair @ latex(pair(?e_1, ?e_2), ?l) <- latex(?e_1, ?l_1), latex(?e_2, ?l_2), join(["(", ?l_1, ",  ", ?l_2, ")"], ?l);
 LatexAbs @ latex(abs(?x, ?t, ?e), ?l) <- latex(?e, ?l_e), latex(?t, ?l_t), latex(?x, ?l_x), join(["\\lambda ", ?l_x, " : ", ?l_t, " . ", ?l_e], ?l);
-LatexApp @ latex(app(?e_1, ?e_2), ?l) <- latex(?e_1, ?l_1), latex(?e_2, ?l_2), join([?l_1, " \\enspace ", ?l_2], ?l);
+LatexApp @ latex(app(?e_1, ?e_2), ?l) <-
+    latex(?e_1, ?l_1), latex(?e_2, ?l_2),
+    parenth(?e_1, app(?e_1, ?e_2), left, ?l_1, ?lp_1),
+    parenth(?e_2, app(?e_1, ?e_2), right, ?l_2, ?lp_2),
+    join([?lp_1, " \\enspace ", ?lp_2], ?l);
 
 LatexTInt @ latex(tint, "\\text{tint}") <-;
 LatexTStr @ latex(tstr, "\\text{tstr}") <-;
-LatexTArr @ latex(tarr(?t_1, ?t_2), ?l) <- latex(?t_1, ?l_1), latex(?t_2, ?l_2), join([?l_1, " \\to ", ?l_2], ?l);
-LatexTPair @ latex(tpair(?t_1, ?t_2), ?l) <- latex(?t_1, ?l_1), latex(?t_2, ?l_2), join([?l_1, " \\times ", ?l_2], ?l);
+LatexTArr @ latex(tarr(?t_1, ?t_2), ?l) <-
+    latex(?t_1, ?l_1), latex(?t_2, ?l_2),
+    parenth(?t_1, tarr(?t_1, ?t_2), left, ?l_1, ?lp_1),
+    parenth(?t_2, tarr(?t_1, ?t_2), right, ?l_2, ?lp_2),
+    join([?lp_1, " \\to ", ?lp_2], ?l);
+LatexTPair @ latex(tpair(?t_1, ?t_2), ?l) <- latex(?t_1, ?l_1), latex(?t_2, ?l_2), join(["(", ?l_1, ", ", ?l_2, ")"], ?l);
 
 LatexTypeEmpty @ latex(empty, "\\varnothing") <-;
 LatexTypeExtend @ latex(extend(?a, ?b, ?c), ?l) <- latex(?a, ?l_a), latex(?b, ?l_b), latex(?c, ?l_c), join([?l_a, " , ", ?l_b, " : ", ?l_c], ?l);
@@ -30,3 +61,8 @@ LatexTypeInenv @ latex(inenv(?x, ?t, ?G), ?l) <-latex(?x, ?l_x), latex(?t, ?l_t)
 
 LatexTypeBin @ latex(type(?e, ?t), ?l) <- latex(?e, ?l_e), latex(?t, ?l_t), join([?l_e, " : ", ?l_t], ?l);
 LatexTypeTer @ latex(type(?G, ?e, ?t), ?l) <- latex(?G, ?l_G), latex(?e, ?l_e), latex(?t, ?l_t), join([?l_G, " \\vdash ", ?l_e, " : ", ?l_t], ?l);
+
+LatexIsInt @ latex(int(?e), ?l) <- latex(?e, ?l_e), join([?l_e, " \\in \\mathbb{Z}"], ?l);
+LatexIsStr @ latex(str(?e), ?l) <- latex(?e, ?l_e), join([?l_e, " \\in \\mathbb{S}"], ?l);
+LatexSym @ latex(?s, ?l) <- sym(?s), tostring(?s, ?l_1), join(["\\text{", ?l_1,"}"], ?l);
+LatexCall @ latex(?c, ?l) <- call(?c, ?n, ?ts), nonempty(?ts), latexlist(?ts, ?lts_1), intercalate(", ", ?lts_1, ?lts_2), join(?lts_2, ?lts_3), join(["\\text{", ?n, "}", "(", ?lts_3, ")"], ?l);