(* SCHEMA step_merged_ap_schema; *)
-- IN AP238 STEP-NC/AP242
FUNCTION simplify_function_application
(expr : function_application ) : maths_value;
FUNCTION ctmv
(x : GENERIC : G ) : maths_value;
RETURN (convert_to_maths_value(x));
END_FUNCTION;
PROCEDURE parts
(c : complex_number_literal;
VAR x : REAL;
VAR y : REAL );
x := c.real_part;
y := c.imag_part;
END_PROCEDURE;
FUNCTION makec
(x : REAL;
y : REAL ) : complex_number_literal;
RETURN (make_complex_number_literal(x, y));
END_FUNCTION;
FUNCTION good_t
(v : maths_value;
tn : STRING ) : BOOLEAN;
LOCAL
tpl : LIST OF maths_value;
END_LOCAL;
IF 'LIST' IN TYPEOF(v) THEN
tpl := v;
REPEAT i := 1 TO SIZEOF(tpl);
IF NOT (tn IN TYPEOF(tpl[i])) THEN
RETURN (FALSE);
END_IF;
END_REPEAT;
RETURN (TRUE);
END_IF;
RETURN (FALSE);
END_FUNCTION;
CONSTANT
cnlit : STRING := schema_prefix + 'COMPLEX_NUMBER_LITERAL';
END_CONSTANT;
LOCAL
types : SET OF STRING := stripped_typeof(expr.func);
ef_val : elementary_function_enumerators;
is_elementary : BOOLEAN := FALSE;
v : maths_value;
v1 : maths_value;
v2 : maths_value;
v3 : maths_value;
vlist : LIST OF maths_value := [];
gexpr : generic_expression;
pairs : SET [1:?] OF LIST [2:2] OF maths_value;
boo : BOOLEAN;
lgc : LOGICAL;
cum : LOGICAL;
j : INTEGER;
k : INTEGER;
n : INTEGER;
p : REAL;
q : REAL;
r : REAL;
s : REAL;
T : REAL;
u : REAL;
str : STRING;
st2 : STRING;
bin : BINARY;
bi2 : BINARY;
tpl : LIST OF maths_value;
tp2 : LIST OF maths_value;
mem : SET OF maths_value := [];
END_LOCAL;
REPEAT i := 1 TO SIZEOF(expr.arguments);
v := simplify_maths_value(expr.arguments[i]);
INSERT( vlist, v, i - 1 );
END_REPEAT;
IF SIZEOF(vlist) >= 1 THEN
v1 := vlist[1];
END_IF;
IF SIZEOF(vlist) >= 2 THEN
v2 := vlist[2];
END_IF;
IF SIZEOF(vlist) >= 3 THEN
v3 := vlist[3];
END_IF;
IF 'ELEMENTARY_FUNCTION_ENUMERATORS' IN types THEN
ef_val := expr.func;
is_elementary := TRUE;
END_IF;
IF 'ELEMENTARY_FUNCTION' IN types THEN
ef_val := expr.func\elementary_function.func_id;
is_elementary := TRUE;
END_IF;
IF is_elementary THEN
CASE ef_val OF
ef_and :
BEGIN
cum := TRUE;
REPEAT i := SIZEOF(vlist) TO 1 BY -1;
IF 'LOGICAL' IN TYPEOF(vlist[i]) THEN
lgc := vlist[i];
cum := cum AND lgc;
IF lgc = FALSE THEN
RETURN (ctmv(FALSE));
END_IF;
REMOVE( vlist, i );
END_IF;
END_REPEAT;
IF SIZEOF(vlist) = 0 THEN
RETURN (ctmv(cum));
END_IF;
IF cum <> TRUE THEN
INSERT( vlist, ctmv(cum), 0 );
END_IF;
IF SIZEOF(vlist) = 1 THEN
RETURN (vlist[1]);
END_IF;
END;
ef_or :
BEGIN
cum := FALSE;
REPEAT i := SIZEOF(vlist) TO 1 BY -1;
IF 'LOGICAL' IN TYPEOF(vlist[i]) THEN
lgc := vlist[i];
cum := cum OR lgc;
IF lgc = TRUE THEN
RETURN (ctmv(TRUE));
END_IF;
REMOVE( vlist, i );
END_IF;
END_REPEAT;
IF SIZEOF(vlist) = 0 THEN
RETURN (ctmv(cum));
END_IF;
IF cum <> FALSE THEN
INSERT( vlist, ctmv(cum), 0 );
END_IF;
IF SIZEOF(vlist) = 1 THEN
RETURN (vlist[1]);
END_IF;
END;
ef_not :
IF 'LOGICAL' IN TYPEOF(v1) THEN
lgc := v1;
RETURN (ctmv(NOT lgc));
END_IF;
ef_xor :
BEGIN
IF 'LOGICAL' IN TYPEOF(v1) THEN
lgc := v1;
IF 'LOGICAL' IN TYPEOF(v2) THEN
cum := v2;
RETURN (ctmv(lgc XOR cum));
ELSE
IF lgc = FALSE THEN
RETURN (ctmv(v2));
ELSE
IF lgc = UNKNOWN THEN
RETURN (ctmv(UNKNOWN));
ELSE
RETURN (make_function_application(ef_not, [ v2 ]));
END_IF;
END_IF;
END_IF;
ELSE
IF 'LOGICAL' IN TYPEOF(v2) THEN
lgc := v2;
IF lgc = FALSE THEN
RETURN (ctmv(v1));
ELSE
IF lgc = UNKNOWN THEN
RETURN (ctmv(UNKNOWN));
ELSE
RETURN (make_function_application(ef_not, [ v1 ]));
END_IF;
END_IF;
END_IF;
END_IF;
END;
ef_negate_i :
IF 'INTEGER' IN TYPEOF(v1) THEN
j := v1;
RETURN (ctmv(-j));
END_IF;
ef_add_i :
BEGIN
j := 0;
REPEAT i := SIZEOF(vlist) TO 1 BY -1;
IF 'INTEGER' IN TYPEOF(vlist[i]) THEN
k := vlist[i];
j := j + k;
REMOVE( vlist, i );
END_IF;
END_REPEAT;
IF SIZEOF(vlist) = 0 THEN
RETURN (ctmv(j));
END_IF;
IF j <> 0 THEN
INSERT( vlist, ctmv(j), 0 );
END_IF;
IF SIZEOF(vlist) = 1 THEN
RETURN (vlist[1]);
END_IF;
END;
ef_subtract_i :
IF ('INTEGER' IN TYPEOF(v1)) AND ('INTEGER' IN TYPEOF(v2)) THEN
j := v1;
k := v2;
RETURN (ctmv(j - k));
END_IF;
ef_multiply_i :
BEGIN
j := 1;
REPEAT i := SIZEOF(vlist) TO 1 BY -1;
IF 'INTEGER' IN TYPEOF(vlist[i]) THEN
k := vlist[i];
j := j * k;
REMOVE( vlist, i );
END_IF;
END_REPEAT;
IF SIZEOF(vlist) = 0 THEN
RETURN (ctmv(j));
END_IF;
IF j <> 1 THEN
INSERT( vlist, ctmv(j), 0 );
END_IF;
IF SIZEOF(vlist) = 1 THEN
RETURN (vlist[1]);
END_IF;
END;
ef_divide_i :
IF ('INTEGER' IN TYPEOF(v1)) AND ('INTEGER' IN TYPEOF(v2)) THEN
j := v1;
k := v2;
RETURN (ctmv(j DIV k));
END_IF;
ef_mod_i :
IF ('INTEGER' IN TYPEOF(v1)) AND ('INTEGER' IN TYPEOF(v2)) THEN
j := v1;
k := v2;
RETURN (ctmv(j MOD k));
END_IF;
ef_exponentiate_i :
IF ('INTEGER' IN TYPEOF(v1)) AND ('INTEGER' IN TYPEOF(v2)) THEN
j := v1;
k := v2;
n := 1;
REPEAT i := 1 TO ABS(k);
n := n * j;
END_REPEAT;
IF k < 0 THEN
n := 1 DIV n;
END_IF;
RETURN (ctmv(n));
END_IF;
ef_eq_i :
IF ('INTEGER' IN TYPEOF(v1)) AND ('INTEGER' IN TYPEOF(v2)) THEN
j := v1;
k := v2;
RETURN (ctmv(j = k));
END_IF;
ef_ne_i :
IF ('INTEGER' IN TYPEOF(v1)) AND ('INTEGER' IN TYPEOF(v2)) THEN
j := v1;
k := v2;
RETURN (ctmv(j <> k));
END_IF;
ef_gt_i :
IF ('INTEGER' IN TYPEOF(v1)) AND ('INTEGER' IN TYPEOF(v2)) THEN
j := v1;
k := v2;
RETURN (ctmv(j > k));
END_IF;
ef_lt_i :
IF ('INTEGER' IN TYPEOF(v1)) AND ('INTEGER' IN TYPEOF(v2)) THEN
j := v1;
k := v2;
RETURN (ctmv(j < k));
END_IF;
ef_ge_i :
IF ('INTEGER' IN TYPEOF(v1)) AND ('INTEGER' IN TYPEOF(v2)) THEN
j := v1;
k := v2;
RETURN (ctmv(j >= k));
END_IF;
ef_le_i :
IF ('INTEGER' IN TYPEOF(v1)) AND ('INTEGER' IN TYPEOF(v2)) THEN
j := v1;
k := v2;
RETURN (ctmv(j <= k));
END_IF;
ef_abs_i :
IF 'INTEGER' IN TYPEOF(v1) THEN
j := v1;
RETURN (ctmv(ABS(j)));
END_IF;
ef_max_i :
BEGIN
boo := FALSE;
REPEAT i := SIZEOF(vlist) TO 1 BY -1;
IF 'INTEGER' IN TYPEOF(vlist[i]) THEN
IF boo THEN
k := vlist[i];
IF k > j THEN
j := k;
END_IF;
ELSE
j := vlist[i];
boo := TRUE;
END_IF;
REMOVE( vlist, i );
END_IF;
END_REPEAT;
IF SIZEOF(vlist) = 0 THEN
RETURN (ctmv(j));
END_IF;
IF boo THEN
INSERT( vlist, ctmv(j), 0 );
END_IF;
IF SIZEOF(vlist) = 1 THEN
RETURN (vlist[1]);
END_IF;
END;
ef_min_i :
BEGIN
boo := FALSE;
REPEAT i := SIZEOF(vlist) TO 1 BY -1;
IF 'INTEGER' IN TYPEOF(vlist[i]) THEN
IF boo THEN
k := vlist[i];
IF k < j THEN
j := k;
END_IF;
ELSE
j := vlist[i];
boo := TRUE;
END_IF;
REMOVE( vlist, i );
END_IF;
END_REPEAT;
IF SIZEOF(vlist) = 0 THEN
RETURN (ctmv(j));
END_IF;
IF boo THEN
INSERT( vlist, ctmv(j), 0 );
END_IF;
IF SIZEOF(vlist) = 1 THEN
RETURN (vlist[1]);
END_IF;
END;
ef_negate_r :
IF 'REAL' IN TYPEOF(v1) THEN
r := v1;
RETURN (ctmv(-r));
END_IF;
ef_reciprocal_r :
IF 'REAL' IN TYPEOF(v1) THEN
r := v1;
RETURN (ctmv(1.0 / r));
END_IF;
ef_add_r :
BEGIN
r := 0.0;
REPEAT i := SIZEOF(vlist) TO 1 BY -1;
IF 'REAL' IN TYPEOF(vlist[i]) THEN
s := vlist[i];
r := r + s;
REMOVE( vlist, i );
END_IF;
END_REPEAT;
IF SIZEOF(vlist) = 0 THEN
RETURN (ctmv(r));
END_IF;
IF r <> 0.0 THEN
INSERT( vlist, ctmv(r), 0 );
END_IF;
IF SIZEOF(vlist) = 1 THEN
RETURN (vlist[1]);
END_IF;
END;
ef_subtract_r :
IF ('REAL' IN TYPEOF(v1)) AND ('REAL' IN TYPEOF(v2)) THEN
r := v1;
s := v2;
RETURN (ctmv(r - s));
END_IF;
ef_multiply_r :
BEGIN
r := 1.0;
REPEAT i := SIZEOF(vlist) TO 1 BY -1;
IF 'REAL' IN TYPEOF(vlist[i]) THEN
s := vlist[i];
r := r * s;
REMOVE( vlist, i );
END_IF;
END_REPEAT;
IF SIZEOF(vlist) = 0 THEN
RETURN (ctmv(r));
END_IF;
IF r <> 1.0 THEN
INSERT( vlist, ctmv(r), 0 );
END_IF;
IF SIZEOF(vlist) = 1 THEN
RETURN (vlist[1]);
END_IF;
END;
ef_divide_r :
IF ('REAL' IN TYPEOF(v1)) AND ('REAL' IN TYPEOF(v2)) THEN
r := v1;
s := v2;
RETURN (ctmv(r / s));
END_IF;
ef_mod_r :
IF ('REAL' IN TYPEOF(v1)) AND ('REAL' IN TYPEOF(v2)) THEN
r := v1;
s := v2;
T := r / s;
j := T DIV 1;
IF (T < 0.0) AND (j <> T) THEN
j := j - 1;
END_IF;
RETURN (ctmv(r - j * s));
END_IF;
ef_exponentiate_r :
IF ('REAL' IN TYPEOF(v1)) AND ('REAL' IN TYPEOF(v2)) THEN
r := v1;
s := v2;
RETURN (ctmv(r ** s));
END_IF;
ef_exponentiate_ri :
IF ('REAL' IN TYPEOF(v1)) AND ('INTEGER' IN TYPEOF(v2)) THEN
r := v1;
k := v2;
T := 1.0;
REPEAT i := 1 TO ABS(k);
T := T * r;
END_REPEAT;
IF k < 0 THEN
T := 1.0 / T;
END_IF;
RETURN (ctmv(T));
END_IF;
ef_eq_r :
IF ('REAL' IN TYPEOF(v1)) AND ('REAL' IN TYPEOF(v2)) THEN
r := v1;
s := v2;
RETURN (ctmv(r = s));
END_IF;
ef_ne_r :
IF ('REAL' IN TYPEOF(v1)) AND ('REAL' IN TYPEOF(v2)) THEN
r := v1;
s := v2;
RETURN (ctmv(r <> s));
END_IF;
ef_gt_r :
IF ('REAL' IN TYPEOF(v1)) AND ('REAL' IN TYPEOF(v2)) THEN
r := v1;
s := v2;
RETURN (ctmv(r > s));
END_IF;
ef_lt_r :
IF ('REAL' IN TYPEOF(v1)) AND ('REAL' IN TYPEOF(v2)) THEN
r := v1;
s := v2;
RETURN (ctmv(r < s));
END_IF;
ef_ge_r :
IF ('REAL' IN TYPEOF(v1)) AND ('REAL' IN TYPEOF(v2)) THEN
r := v1;
s := v2;
RETURN (ctmv(r >= s));
END_IF;
ef_le_r :
IF ('REAL' IN TYPEOF(v1)) AND ('REAL' IN TYPEOF(v2)) THEN
r := v1;
s := v2;
RETURN (ctmv(r <= s));
END_IF;
ef_abs_r :
IF 'REAL' IN TYPEOF(v1) THEN
r := v1;
RETURN (ctmv(ABS(r)));
END_IF;
ef_max_r :
BEGIN
boo := FALSE;
REPEAT i := SIZEOF(vlist) TO 1 BY -1;
IF 'REAL' IN TYPEOF(vlist[i]) THEN
IF boo THEN
s := vlist[i];
IF s > r THEN
r := s;
END_IF;
ELSE
r := vlist[i];
boo := TRUE;
END_IF;
REMOVE( vlist, i );
END_IF;
END_REPEAT;
IF SIZEOF(vlist) = 0 THEN
RETURN (ctmv(r));
END_IF;
IF boo THEN
INSERT( vlist, ctmv(r), 0 );
END_IF;
IF SIZEOF(vlist) = 1 THEN
RETURN (vlist[1]);
END_IF;
END;
ef_min_r :
BEGIN
boo := FALSE;
REPEAT i := SIZEOF(vlist) TO 1 BY -1;
IF 'REAL' IN TYPEOF(vlist[i]) THEN
IF boo THEN
s := vlist[i];
IF s < r THEN
r := s;
END_IF;
ELSE
r := vlist[i];
boo := TRUE;
END_IF;
REMOVE( vlist, i );
END_IF;
END_REPEAT;
IF SIZEOF(vlist) = 0 THEN
RETURN (ctmv(r));
END_IF;
IF boo THEN
INSERT( vlist, ctmv(r), 0 );
END_IF;
IF SIZEOF(vlist) = 1 THEN
RETURN (vlist[1]);
END_IF;
END;
ef_acos_r :
IF 'REAL' IN TYPEOF(v1) THEN
r := v1;
RETURN (ctmv(ACOS(r)));
END_IF;
ef_asin_r :
IF 'REAL' IN TYPEOF(v1) THEN
r := v1;
RETURN (ctmv(ASIN(r)));
END_IF;
ef_atan2_r :
IF ('REAL' IN TYPEOF(v1)) AND ('REAL' IN TYPEOF(v2)) THEN
r := v1;
s := v2;
RETURN (ctmv(atan2(r, s)));
END_IF;
ef_cos_r :
IF 'REAL' IN TYPEOF(v1) THEN
r := v1;
RETURN (ctmv(COS(r)));
END_IF;
ef_exp_r :
IF 'REAL' IN TYPEOF(v1) THEN
r := v1;
RETURN (ctmv(EXP(r)));
END_IF;
ef_ln_r :
IF 'REAL' IN TYPEOF(v1) THEN
r := v1;
RETURN (ctmv(LOG(r)));
END_IF;
ef_log2_r :
IF 'REAL' IN TYPEOF(v1) THEN
r := v1;
RETURN (ctmv(LOG2(r)));
END_IF;
ef_log10_r :
IF 'REAL' IN TYPEOF(v1) THEN
r := v1;
RETURN (ctmv(LOG10(r)));
END_IF;
ef_sin_r :
IF 'REAL' IN TYPEOF(v1) THEN
r := v1;
RETURN (ctmv(SIN(r)));
END_IF;
ef_sqrt_r :
IF 'REAL' IN TYPEOF(v1) THEN
r := v1;
RETURN (ctmv(SQRT(r)));
END_IF;
ef_tan_r :
IF 'REAL' IN TYPEOF(v1) THEN
r := v1;
RETURN (ctmv(TAN(r)));
END_IF;
ef_form_c :
IF ('REAL' IN TYPEOF(v1)) AND ('REAL' IN TYPEOF(v2)) THEN
r := v1;
s := v2;
RETURN (makec(r, s));
END_IF;
ef_rpart_c :
IF cnlit IN TYPEOF(v1) THEN
RETURN (ctmv(v1\complex_number_literal.real_part));
END_IF;
ef_ipart_c :
IF cnlit IN TYPEOF(v1) THEN
RETURN (ctmv(v1\complex_number_literal.imag_part));
END_IF;
ef_negate_c :
IF cnlit IN TYPEOF(v1) THEN
parts( v1, p, q );
RETURN (makec(-p, -q));
END_IF;
ef_reciprocal_c :
IF cnlit IN TYPEOF(v1) THEN
parts( v1, p, q );
T := p * p + q * q;
RETURN (makec(p / T, -q / T));
END_IF;
ef_add_c :
BEGIN
p := 0.0;
q := 0.0;
REPEAT i := SIZEOF(vlist) TO 1 BY -1;
IF cnlit IN TYPEOF(vlist[i]) THEN
parts( vlist[i], r, s );
p := p + r;
q := q + s;
REMOVE( vlist, i );
END_IF;
END_REPEAT;
IF SIZEOF(vlist) = 0 THEN
RETURN (makec(p, q));
END_IF;
IF p * p + q * q <> 0.0 THEN
INSERT( vlist, makec(p, q), 0 );
END_IF;
IF SIZEOF(vlist) = 1 THEN
RETURN (vlist[1]);
END_IF;
END;
ef_subtract_c :
IF (cnlit IN TYPEOF(v1)) AND (cnlit IN TYPEOF(v2)) THEN
parts( v1, p, q );
parts( v2, r, s );
RETURN (makec(p - r, q - s));
END_IF;
ef_multiply_c :
BEGIN
p := 1.0;
q := 0.0;
REPEAT i := SIZEOF(vlist) TO 1 BY -1;
IF cnlit IN TYPEOF(vlist[i]) THEN
parts( vlist[i], r, s );
p := p * r - q * s;
q := p * s + q * r;
REMOVE( vlist, i );
END_IF;
END_REPEAT;
IF SIZEOF(vlist) = 0 THEN
RETURN (makec(p, q));
END_IF;
IF (p <> 1.0) OR (q <> 0.0) THEN
INSERT( vlist, makec(p, q), 0 );
END_IF;
IF SIZEOF(vlist) = 1 THEN
RETURN (vlist[1]);
END_IF;
END;
ef_divide_c :
IF (cnlit IN TYPEOF(v1)) AND (cnlit IN TYPEOF(v2)) THEN
parts( v1, p, q );
parts( v2, r, s );
T := r * r + s * s;
RETURN (makec((p * r + q * s) / T, (q * r - p * s) / T));
END_IF;
ef_exponentiate_c :
IF (cnlit IN TYPEOF(v1)) AND (cnlit IN TYPEOF(v2)) THEN
parts( v1, p, q );
parts( v2, r, s );
T := 0.500000 * LOG((p * p + q * q));
u := atan2(q, p);
p := r * T - s * u;
q := r * u + s * T;
r := EXP(p);
RETURN (makec(r * COS(q), r * SIN(q)));
END_IF;
ef_exponentiate_ci :
IF (cnlit IN TYPEOF(v1)) AND ('INTEGER' IN TYPEOF(v2)) THEN
parts( v1, p, q );
k := v2;
r := 1.0;
s := 0.0;
REPEAT i := 1 TO ABS(k);
r := p * r - q * s;
s := p * s + q * r;
END_REPEAT;
IF k < 0 THEN
T := r * r + s * s;
r := r / T;
s := -s / T;
END_IF;
RETURN (makec(r, s));
END_IF;
ef_eq_c :
IF (cnlit IN TYPEOF(v1)) AND (cnlit IN TYPEOF(v2)) THEN
parts( v1, p, q );
parts( v2, r, s );
RETURN (ctmv((p = r) AND (q = s)));
END_IF;
ef_ne_c :
IF (cnlit IN TYPEOF(v1)) AND (cnlit IN TYPEOF(v2)) THEN
parts( v1, p, q );
parts( v2, r, s );
RETURN (ctmv((p <> r) OR (q <> s)));
END_IF;
ef_conjugate_c :
IF cnlit IN TYPEOF(v1) THEN
parts( v1, p, q );
RETURN (makec(p, -q));
END_IF;
ef_abs_c :
IF cnlit IN TYPEOF(v1) THEN
parts( v1, p, q );
RETURN (ctmv(SQRT(p * p + q * q)));
END_IF;
ef_arg_c :
IF cnlit IN TYPEOF(v1) THEN
parts( v1, p, q );
RETURN (ctmv(atan2(q, p)));
END_IF;
ef_cos_c :
IF cnlit IN TYPEOF(v1) THEN
parts( v1, p, q );
T := 0.500000 * EXP(-q);
u := 0.500000 * EXP(q);
RETURN (makec((T + u) * COS(p), (T - u) * SIN(p)));
END_IF;
ef_exp_c :
IF cnlit IN TYPEOF(v1) THEN
parts( v1, p, q );
RETURN (makec(EXP(p) * COS(q), EXP(p) * SIN(q)));
END_IF;
ef_ln_c :
IF cnlit IN TYPEOF(v1) THEN
parts( v1, p, q );
RETURN (makec(0.500000 * LOG((p * p + q * q)), atan2(q, p)));
END_IF;
ef_sin_c :
IF cnlit IN TYPEOF(v1) THEN
parts( v1, p, q );
T := 0.500000 * EXP(-q);
u := 0.500000 * EXP(q);
RETURN (makec((T + u) * SIN(p), (u - T) * COS(p)));
END_IF;
ef_sqrt_c :
IF cnlit IN TYPEOF(v1) THEN
parts( v1, p, q );
T := SQRT(SQRT(p * p + q * q));
u := 0.500000 * atan2(q, p);
RETURN (makec(T * COS(u), T * SIN(u)));
END_IF;
ef_tan_c :
IF cnlit IN TYPEOF(v1) THEN
parts( v1, p, q );
T := EXP(2.0 * q) + EXP(-2.0 * q) + 2.0 * COS(2.0 * p);
RETURN (makec(2.0 * SIN(2.0 * p) / T, (EXP(-2.0 * q) - EXP(2.0 * q)) / T));
END_IF;
ef_subscript_s :
IF ('STRING' IN TYPEOF(v1)) AND ('INTEGER' IN TYPEOF(v2)) THEN
str := v1;
k := v2;
RETURN (ctmv(str[k]));
END_IF;
ef_eq_s :
IF ('STRING' IN TYPEOF(v1)) AND ('STRING' IN TYPEOF(v2)) THEN
str := v1;
st2 := v2;
RETURN (ctmv(str = st2));
END_IF;
ef_ne_s :
IF ('STRING' IN TYPEOF(v1)) AND ('STRING' IN TYPEOF(v2)) THEN
str := v1;
st2 := v2;
RETURN (ctmv(str <> st2));
END_IF;
ef_gt_s :
IF ('STRING' IN TYPEOF(v1)) AND ('STRING' IN TYPEOF(v2)) THEN
str := v1;
st2 := v2;
RETURN (ctmv(str > st2));
END_IF;
ef_lt_s :
IF ('STRING' IN TYPEOF(v1)) AND ('STRING' IN TYPEOF(v2)) THEN
str := v1;
st2 := v2;
RETURN (ctmv(str < st2));
END_IF;
ef_ge_s :
IF ('STRING' IN TYPEOF(v1)) AND ('STRING' IN TYPEOF(v2)) THEN
str := v1;
st2 := v2;
RETURN (ctmv(str >= st2));
END_IF;
ef_le_s :
IF ('STRING' IN TYPEOF(v1)) AND ('STRING' IN TYPEOF(v2)) THEN
str := v1;
st2 := v2;
RETURN (ctmv(str <= st2));
END_IF;
ef_subsequence_s :
IF (('STRING' IN TYPEOF(v1)) AND ('INTEGER' IN TYPEOF(v2))) AND ('INTEGER' IN TYPEOF(v3)) THEN
str := v1;
j := v2;
k := v3;
RETURN (ctmv(str[ j : k ]));
END_IF;
ef_concat_s :
BEGIN
str := '';
REPEAT i := SIZEOF(vlist) TO 1 BY -1;
IF 'STRING' IN TYPEOF(vlist[i]) THEN
st2 := vlist[i];
str := str + st2;
REMOVE( vlist, i );
ELSE
IF str <> '' THEN
INSERT( vlist, ctmv(str), i );
str := '';
END_IF;
END_IF;
END_REPEAT;
IF SIZEOF(vlist) = 0 THEN
RETURN (ctmv(str));
END_IF;
IF str <> '' THEN
INSERT( vlist, ctmv(str), 0 );
END_IF;
IF SIZEOF(vlist) = 1 THEN
RETURN (vlist[1]);
END_IF;
END;
ef_size_s :
IF 'STRING' IN TYPEOF(v1) THEN
str := v1;
RETURN (ctmv(LENGTH(str)));
END_IF;
ef_format :
IF ('NUMBER' IN TYPEOF(v1)) AND ('STRING' IN TYPEOF(v2)) THEN
RETURN (ctmv(FORMAT(v1, v2)));
END_IF;
ef_value :
IF 'STRING' IN TYPEOF(v1) THEN
str := v1;
RETURN (ctmv(VALUE(str)));
END_IF;
ef_like :
IF ('STRING' IN TYPEOF(v1)) AND ('STRING' IN TYPEOF(v2)) THEN
RETURN (ctmv(v1 LIKE v2));
END_IF;
ef_subscript_b :
IF ('BINARY' IN TYPEOF(v1)) AND ('INTEGER' IN TYPEOF(v2)) THEN
bin := v1;
k := v2;
RETURN (ctmv(bin[k]));
END_IF;
ef_eq_b :
IF ('BINARY' IN TYPEOF(v1)) AND ('BINARY' IN TYPEOF(v2)) THEN
bin := v1;
bi2 := v2;
RETURN (ctmv(bin = bi2));
END_IF;
ef_ne_b :
IF ('BINARY' IN TYPEOF(v1)) AND ('BINARY' IN TYPEOF(v2)) THEN
bin := v1;
bi2 := v2;
RETURN (ctmv(bin <> bi2));
END_IF;
ef_gt_b :
IF ('BINARY' IN TYPEOF(v1)) AND ('BINARY' IN TYPEOF(v2)) THEN
bin := v1;
bi2 := v2;
RETURN (ctmv(bin > bi2));
END_IF;
ef_lt_b :
IF ('BINARY' IN TYPEOF(v1)) AND ('BINARY' IN TYPEOF(v2)) THEN
bin := v1;
bi2 := v2;
RETURN (ctmv(bin < bi2));
END_IF;
ef_ge_b :
IF ('BINARY' IN TYPEOF(v1)) AND ('BINARY' IN TYPEOF(v2)) THEN
bin := v1;
bi2 := v2;
RETURN (ctmv(bin >= bi2));
END_IF;
ef_le_b :
IF ('BINARY' IN TYPEOF(v1)) AND ('BINARY' IN TYPEOF(v2)) THEN
bin := v1;
bi2 := v2;
RETURN (ctmv(bin <= bi2));
END_IF;
ef_subsequence_b :
IF (('BINARY' IN TYPEOF(v1)) AND ('INTEGER' IN TYPEOF(v2))) AND ('INTEGER' IN TYPEOF(v3)) THEN
bin := v1;
j := v2;
k := v3;
RETURN (ctmv(bin[ j : k ]));
END_IF;
ef_concat_b :
BEGIN
boo := FALSE;
REPEAT i := SIZEOF(vlist) TO 1 BY -1;
IF 'BINARY' IN TYPEOF(vlist[i]) THEN
IF boo THEN
bi2 := vlist[i];
bin := bin + bi2;
ELSE
bin := vlist[i];
boo := TRUE;
END_IF;
REMOVE( vlist, i );
ELSE
IF boo THEN
INSERT( vlist, ctmv(bin), i );
boo := FALSE;
END_IF;
END_IF;
END_REPEAT;
IF SIZEOF(vlist) = 0 THEN
RETURN (ctmv(bin));
END_IF;
IF boo THEN
INSERT( vlist, ctmv(bin), 0 );
END_IF;
IF SIZEOF(vlist) = 1 THEN
RETURN (vlist[1]);
END_IF;
END;
ef_size_b :
IF 'BINARY' IN TYPEOF(v1) THEN
bin := v1;
RETURN (ctmv(BLENGTH(bin)));
END_IF;
ef_subscript_t :
IF ('LIST' IN TYPEOF(v1)) AND ('INTEGER' IN TYPEOF(v2)) THEN
tpl := v1;
k := v2;
RETURN (ctmv(tpl[k]));
END_IF;
ef_eq_t :
IF ('LIST' IN TYPEOF(v1)) AND ('LIST' IN TYPEOF(v2)) THEN
lgc := equal_maths_values(v1, v2);
IF lgc <> UNKNOWN THEN
RETURN (ctmv(lgc));
END_IF;
END_IF;
ef_ne_t :
IF ('LIST' IN TYPEOF(v1)) AND ('LIST' IN TYPEOF(v2)) THEN
lgc := equal_maths_values(v1, v2);
IF lgc <> UNKNOWN THEN
RETURN (ctmv(NOT lgc));
END_IF;
END_IF;
ef_concat_t :
BEGIN
tpl := [];
REPEAT i := SIZEOF(vlist) TO 1 BY -1;
IF 'STRING' IN TYPEOF(vlist[i]) THEN
tp2 := vlist[i];
tpl := tpl + tp2;
REMOVE( vlist, i );
ELSE
IF SIZEOF(tpl) <> 0 THEN
INSERT( vlist, ctmv(tpl), i );
tpl := [];
END_IF;
END_IF;
END_REPEAT;
IF SIZEOF(vlist) = 0 THEN
RETURN (ctmv(tpl));
END_IF;
IF SIZEOF(tpl) <> 0 THEN
INSERT( vlist, ctmv(tpl), 0 );
END_IF;
IF SIZEOF(vlist) = 1 THEN
RETURN (vlist[1]);
END_IF;
END;
ef_size_t :
IF 'LIST' IN TYPEOF(v1) THEN
tpl := v1;
RETURN (ctmv(SIZEOF(tpl)));
END_IF;
ef_entuple :
RETURN (ctmv(vlist));
ef_detuple :
IF 'LIST' IN TYPEOF(v1) THEN
tpl := v1;
RETURN (ctmv(tpl[1]));
END_IF;
ef_insert :
IF ('LIST' IN TYPEOF(v1)) AND ('INTEGER' IN TYPEOF(v3)) THEN
tpl := v1;
k := v3;
INSERT( tpl, v2, k );
RETURN (ctmv(tpl));
END_IF;
ef_remove :
IF ('LIST' IN TYPEOF(v1)) AND ('INTEGER' IN TYPEOF(v2)) THEN
tpl := v1;
k := v2;
REMOVE( tpl, k );
RETURN (ctmv(tpl));
END_IF;
ef_sum_it :
IF good_t(v1, 'INTEGER') THEN
tpl := v1;
j := 0;
REPEAT i := 1 TO SIZEOF(tpl);
j := j + tpl[i];
END_REPEAT;
RETURN (ctmv(j));
END_IF;
ef_product_it :
IF good_t(v1, 'INTEGER') THEN
tpl := v1;
j := 1;
REPEAT i := 1 TO SIZEOF(tpl);
j := j * tpl[i];
END_REPEAT;
RETURN (ctmv(j));
END_IF;
ef_add_it :
BEGIN
boo := FALSE;
REPEAT i := SIZEOF(vlist) TO 1 BY -1;
IF good_t(vlist[i], 'INTEGER') THEN
IF NOT boo THEN
tpl := vlist[i];
boo := TRUE;
ELSE
tp2 := vlist[i];
IF SIZEOF(tpl) <> SIZEOF(tp2) THEN
RETURN (?);
END_IF;
REPEAT l := 1 TO SIZEOF(tpl);
tpl[j] := tpl[j] + tp2[j];
END_REPEAT;
END_IF;
REMOVE( vlist, i );
END_IF;
END_REPEAT;
IF SIZEOF(vlist) = 0 THEN
RETURN (ctmv(tpl));
END_IF;
IF boo THEN
INSERT( vlist, ctmv(tpl), 0 );
END_IF;
IF SIZEOF(vlist) = 1 THEN
RETURN (vlist[1]);
END_IF;
END;
ef_subtract_it :
IF good_t(v1, 'INTEGER') AND good_t(v2, 'INTEGER') THEN
tpl := v1;
tp2 := v2;
IF SIZEOF(tpl) <> SIZEOF(tp2) THEN
RETURN (?);
END_IF;
REPEAT i := 1 TO SIZEOF(tpl);
tpl[i] := tpl[i] - tp2[i];
END_REPEAT;
RETURN (ctmv(tpl));
END_IF;
ef_scalar_mult_it :
IF ('INTEGER' IN TYPEOF(v1)) AND good_t(v2, 'INTEGER') THEN
j := v1;
tpl := v2;
REPEAT i := 1 TO SIZEOF(tpl);
tpl[i] := j * tpl[i];
END_REPEAT;
RETURN (ctmv(tpl));
END_IF;
ef_dot_prod_it :
IF good_t(v1, 'INTEGER') AND good_t(v2, 'INTEGER') THEN
tpl := v1;
tp2 := v2;
j := 0;
IF SIZEOF(tpl) <> SIZEOF(tp2) THEN
RETURN (?);
END_IF;
REPEAT i := 1 TO SIZEOF(tpl);
j := j + tpl[i] * tp2[i];
END_REPEAT;
RETURN (ctmv(j));
END_IF;
ef_sum_rt :
IF good_t(v1, 'REAL') THEN
tpl := v1;
r := 0.0;
REPEAT i := 1 TO SIZEOF(tpl);
r := r + tpl[i];
END_REPEAT;
RETURN (ctmv(r));
END_IF;
ef_product_rt :
IF good_t(v1, 'REAL') THEN
tpl := v1;
r := 1.0;
REPEAT i := 1 TO SIZEOF(tpl);
r := r * tpl[i];
END_REPEAT;
RETURN (ctmv(r));
END_IF;
ef_add_rt :
BEGIN
boo := FALSE;
REPEAT i := SIZEOF(vlist) TO 1 BY -1;
IF good_t(vlist[i], 'REAL') THEN
IF NOT boo THEN
tpl := vlist[i];
boo := TRUE;
ELSE
tp2 := vlist[i];
IF SIZEOF(tpl) <> SIZEOF(tp2) THEN
RETURN (?);
END_IF;
REPEAT l := 1 TO SIZEOF(tpl);
tpl[j] := tpl[j] + tp2[j];
END_REPEAT;
END_IF;
REMOVE( vlist, i );
END_IF;
END_REPEAT;
IF SIZEOF(vlist) = 0 THEN
RETURN (ctmv(tpl));
END_IF;
IF boo THEN
INSERT( vlist, ctmv(tpl), 0 );
END_IF;
IF SIZEOF(vlist) = 1 THEN
RETURN (vlist[1]);
END_IF;
END;
ef_subtract_rt :
IF good_t(v1, 'REAL') AND good_t(v2, 'REAL') THEN
tpl := v1;
tp2 := v2;
IF SIZEOF(tpl) <> SIZEOF(tp2) THEN
RETURN (?);
END_IF;
REPEAT i := 1 TO SIZEOF(tpl);
tpl[i] := tpl[i] - tp2[i];
END_REPEAT;
RETURN (ctmv(tpl));
END_IF;
ef_scalar_mult_rt :
IF ('REAL' IN TYPEOF(v1)) AND good_t(v2, 'REAL') THEN
r := v1;
tpl := v2;
REPEAT i := 1 TO SIZEOF(tpl);
tpl[i] := r * tpl[i];
END_REPEAT;
RETURN (ctmv(tpl));
END_IF;
ef_dot_prod_rt :
IF good_t(v1, 'REAL') AND good_t(v2, 'REAL') THEN
tpl := v1;
tp2 := v2;
r := 0;
IF SIZEOF(tpl) <> SIZEOF(tp2) THEN
RETURN (?);
END_IF;
REPEAT i := 1 TO SIZEOF(tpl);
r := r + tpl[i] * tp2[i];
END_REPEAT;
RETURN (ctmv(r));
END_IF;
ef_norm_rt :
IF good_t(v1, 'REAL') THEN
tpl := v1;
r := 0.0;
REPEAT i := 1 TO SIZEOF(tpl);
r := r + tpl[i] * tpl[i];
END_REPEAT;
RETURN (ctmv(SQRT(r)));
END_IF;
ef_sum_ct :
IF good_t(v1, cnlit) THEN
tpl := v1;
p := 0.0;
q := 0.0;
REPEAT i := 1 TO SIZEOF(tpl);
parts( tpl[i], r, s );
p := p + r;
q := q + s;
END_REPEAT;
RETURN (makec(p, q));
END_IF;
ef_product_ct :
IF good_t(v1, cnlit) THEN
tpl := v1;
p := 1.0;
q := 0.0;
REPEAT i := 1 TO SIZEOF(tpl);
parts( tpl[i], r, s );
p := p * r - q * s;
q := p * s + q * r;
END_REPEAT;
RETURN (makec(p, q));
END_IF;
ef_add_ct :
BEGIN
boo := FALSE;
REPEAT i := SIZEOF(vlist) TO 1 BY -1;
IF good_t(vlist[i], cnlit) THEN
IF NOT boo THEN
tpl := vlist[i];
boo := TRUE;
ELSE
tp2 := vlist[i];
IF SIZEOF(tpl) <> SIZEOF(tp2) THEN
RETURN (?);
END_IF;
REPEAT l := 1 TO SIZEOF(tpl);
parts( tpl[j], p, q );
parts( tp2[j], r, s );
tpl[j] := makec(p + r, q + s);
END_REPEAT;
END_IF;
REMOVE( vlist, i );
END_IF;
END_REPEAT;
IF SIZEOF(vlist) = 0 THEN
RETURN (ctmv(tpl));
END_IF;
IF boo THEN
INSERT( vlist, ctmv(tpl), 0 );
END_IF;
IF SIZEOF(vlist) = 1 THEN
RETURN (vlist[1]);
END_IF;
END;
ef_subtract_ct :
IF good_t(v1, cnlit) AND good_t(v2, cnlit) THEN
tpl := v1;
tp2 := v2;
IF SIZEOF(tpl) <> SIZEOF(tp2) THEN
RETURN (?);
END_IF;
REPEAT i := 1 TO SIZEOF(tpl);
parts( tpl[i], p, q );
parts( tp2[i], r, s );
tpl[i] := makec(p - r, q - s);
END_REPEAT;
RETURN (ctmv(tpl));
END_IF;
ef_scalar_mult_ct :
IF (cnlit IN TYPEOF(v1)) AND good_t(v2, cnlit) THEN
parts( v1, p, q );
tpl := v2;
REPEAT i := 1 TO SIZEOF(tpl);
parts( tpl[i], r, s );
tpl[i] := makec(p * r - q * s, p * s + q * r);
END_REPEAT;
RETURN (ctmv(tpl));
END_IF;
ef_dot_prod_ct :
IF good_t(v1, cnlit) AND good_t(v2, cnlit) THEN
tpl := v1;
tp2 := v2;
T := 0.0;
u := 0.0;
IF SIZEOF(tpl) <> SIZEOF(tp2) THEN
RETURN (?);
END_IF;
REPEAT i := 1 TO SIZEOF(tpl);
parts( tpl[i], p, q );
parts( tp2[i], r, s );
T := T + p * r + q * s;
u := u + q * r - p * s;
END_REPEAT;
RETURN (makec(T, u));
END_IF;
ef_norm_ct :
IF good_t(v1, cnlit) THEN
tpl := v1;
r := 0.0;
REPEAT i := 1 TO SIZEOF(tpl);
parts( tpl[i], p, q );
r := r + p * p + q * q;
END_REPEAT;
RETURN (ctmv(SQRT(r)));
END_IF;
ef_if, ef_if_i, ef_if_r, ef_if_c, ef_if_s, ef_if_b, ef_if_t :
IF 'LOGICAL' IN TYPEOF(v1) THEN
lgc := v1;
IF lgc THEN
RETURN (v2);
ELSE
RETURN (v3);
END_IF;
END_IF;
ef_ensemble :
RETURN (make_finite_space(mem + vlist));
ef_member_of :
IF schema_prefix + 'MATHS_SPACE' IN TYPEOF(v2) THEN
lgc := member_of(v1, v2);
IF lgc <> UNKNOWN THEN
RETURN (ctmv(lgc));
END_IF;
END_IF;
END_CASE;
RETURN (make_function_application(expr.func, vlist));
END_IF;
IF 'ABSTRACTED_EXPRESSION_FUNCTION' IN types THEN
gexpr := substitute(expr.func\abstracted_expression_function.expr, expr.func\quantifier_expression.variables, vlist);
RETURN (simplify_generic_expression(gexpr));
END_IF;
IF 'FINITE_FUNCTION' IN types THEN
pairs := expr.func\finite_function.pairs;
REPEAT i := 1 TO SIZEOF(pairs);
IF equal_maths_values(vlist[1], pairs[i][1]) THEN
RETURN (simplify_maths_value(pairs[i][2]));
END_IF;
END_REPEAT;
RETURN (make_function_application(expr.func, vlist));
END_IF;
RETURN (expr);
END_FUNCTION;
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2024-09-06T14:00:33-04:00