add isl_basic_set_*_lp_val
[platform/upstream/isl.git] / isl_input.c
index fc27090..164a269 100644 (file)
@@ -1,26 +1,32 @@
 /*
  * Copyright 2008-2009 Katholieke Universiteit Leuven
  * Copyright 2010      INRIA Saclay
+ * Copyright 2012      Ecole Normale Superieure
  *
- * Use of this software is governed by the GNU LGPLv2.1 license
+ * Use of this software is governed by the MIT license
  *
  * Written by Sven Verdoolaege, K.U.Leuven, Departement
  * Computerwetenschappen, Celestijnenlaan 200A, B-3001 Leuven, Belgium
  * and INRIA Saclay - Ile-de-France, Parc Club Orsay Universite,
  * ZAC des vignes, 4 rue Jacques Monod, 91893 Orsay, France 
+ * and Ecole Normale Superieure, 45 rue d’Ulm, 75230 Paris, France
  */
 
 #include <ctype.h>
 #include <stdio.h>
 #include <string.h>
-#include <strings.h>
-#include <isl_set.h>
-#include <isl_seq.h>
-#include <isl_div.h>
-#include "isl_stream.h"
-#include "isl_map_private.h"
-#include "isl_obj.h"
+#include <isl_ctx_private.h>
+#include <isl_map_private.h>
+#include <isl/set.h>
+#include <isl/seq.h>
+#include <isl_stream_private.h>
+#include <isl/obj.h>
 #include "isl_polynomial_private.h"
+#include <isl/union_map.h>
+#include <isl_mat_private.h>
+#include <isl_aff_private.h>
+#include <isl/list.h>
+#include <isl_val_private.h>
 
 struct variable {
        char                    *name;
@@ -68,7 +74,7 @@ static void vars_drop(struct vars *v, int n)
 {
        struct variable *var;
 
-       if (!v)
+       if (!v || !v->v)
                return;
 
        v->n -= n;
@@ -87,7 +93,7 @@ static struct variable *variable_new(struct vars *v, const char *name, int len,
                                int pos)
 {
        struct variable *var;
-       var = isl_alloc_type(v->ctx, struct variable);
+       var = isl_calloc_type(v->ctx, struct variable);
        if (!var)
                goto error;
        var->name = strdup(name);
@@ -123,37 +129,131 @@ static int vars_pos(struct vars *v, const char *s, int len)
        return pos;
 }
 
-static __isl_give isl_basic_map *set_name(__isl_take isl_basic_map *bmap,
-       enum isl_dim_type type, unsigned pos, char *name)
+static int vars_add_anon(struct vars *v)
 {
-       char *prime;
+       v->v = variable_new(v, "", 0, v->n);
 
-       if (!bmap)
-               return NULL;
-       if (!name)
-               return bmap;
+       if (!v->v)
+               return -1;
+       v->n++;
 
-       prime = strchr(name, '\'');
-       if (prime)
-               *prime = '\0';
-       bmap->dim = isl_dim_set_name(bmap->dim, type, pos, name);
-       if (prime)
-               *prime = '\'';
+       return 0;
+}
 
-       if (!bmap->dim)
+/* Obtain next token, with some preprocessing.
+ * In particular, evaluate expressions of the form x^y,
+ * with x and y values.
+ */
+static struct isl_token *next_token(struct isl_stream *s)
+{
+       struct isl_token *tok, *tok2;
+
+       tok = isl_stream_next_token(s);
+       if (!tok || tok->type != ISL_TOKEN_VALUE)
+               return tok;
+       if (!isl_stream_eat_if_available(s, '^'))
+               return tok;
+       tok2 = isl_stream_next_token(s);
+       if (!tok2 || tok2->type != ISL_TOKEN_VALUE) {
+               isl_stream_error(s, tok2, "expecting constant value");
                goto error;
+       }
 
-       return bmap;
+       isl_int_pow_ui(tok->u.v, tok->u.v, isl_int_get_ui(tok2->u.v));
+
+       isl_token_free(tok2);
+       return tok;
 error:
-       isl_basic_map_free(bmap);
+       isl_token_free(tok);
+       isl_token_free(tok2);
+       return NULL;
+}
+
+/* Read an isl_val from "s".
+ *
+ * The following token sequences are recognized
+ *
+ *     "infty"         ->      infty
+ *     "-" "infty"     ->      -infty
+ *     "NaN"           ->      NaN
+ *     n "/" d         ->      n/d
+ *     v               ->      v
+ *
+ * where n, d and v are integer constants.
+ */
+__isl_give isl_val *isl_stream_read_val(struct isl_stream *s)
+{
+       struct isl_token *tok = NULL;
+       struct isl_token *tok2 = NULL;
+       isl_val *val;
+
+       tok = next_token(s);
+       if (!tok) {
+               isl_stream_error(s, NULL, "unexpected EOF");
+               goto error;
+       }
+       if (tok->type == ISL_TOKEN_INFTY) {
+               isl_token_free(tok);
+               return isl_val_infty(s->ctx);
+       }
+       if (tok->type == '-' &&
+           isl_stream_eat_if_available(s, ISL_TOKEN_INFTY)) {
+               isl_token_free(tok);
+               return isl_val_neginfty(s->ctx);
+       }
+       if (tok->type == ISL_TOKEN_NAN) {
+               isl_token_free(tok);
+               return isl_val_nan(s->ctx);
+       }
+       if (tok->type != ISL_TOKEN_VALUE) {
+               isl_stream_error(s, tok, "expecting value");
+               goto error;
+       }
+
+       if (isl_stream_eat_if_available(s, '/')) {
+               tok2 = next_token(s);
+               if (!tok2) {
+                       isl_stream_error(s, NULL, "unexpected EOF");
+                       goto error;
+               }
+               if (tok2->type != ISL_TOKEN_VALUE) {
+                       isl_stream_error(s, tok2, "expecting value");
+                       goto error;
+               }
+               val = isl_val_rat_from_isl_int(s->ctx, tok->u.v, tok2->u.v);
+               val = isl_val_normalize(val);
+       } else {
+               val = isl_val_int_from_isl_int(s->ctx, tok->u.v);
+       }
+
+       isl_token_free(tok);
+       isl_token_free(tok2);
+       return val;
+error:
+       isl_token_free(tok);
+       isl_token_free(tok2);
        return NULL;
 }
 
+/* Read an isl_val from "str".
+ */
+struct isl_val *isl_val_read_from_str(struct isl_ctx *ctx,
+       const char *str)
+{
+       isl_val *val;
+       struct isl_stream *s = isl_stream_new_str(ctx, str);
+       if (!s)
+               return NULL;
+       val = isl_stream_read_val(s);
+       isl_stream_free(s);
+       return val;
+}
+
 static int accept_cst_factor(struct isl_stream *s, isl_int *f)
 {
        struct isl_token *tok;
 
-       tok = isl_stream_next_token(s);
+       tok = next_token(s);
        if (!tok || tok->type != ISL_TOKEN_VALUE) {
                isl_stream_error(s, tok, "expecting constant value");
                goto error;
@@ -172,91 +272,269 @@ error:
        return -1;
 }
 
-static struct isl_vec *accept_affine(struct isl_stream *s, struct vars *v);
+/* Given an affine expression aff, return an affine expression
+ * for aff % d, with d the next token on the stream, which is
+ * assumed to be a constant.
+ *
+ * We introduce an integer division q = [aff/d] and the result
+ * is set to aff - d q.
+ */
+static __isl_give isl_pw_aff *affine_mod(struct isl_stream *s,
+       struct vars *v, __isl_take isl_pw_aff *aff)
+{
+       struct isl_token *tok;
+       isl_pw_aff *q;
+
+       tok = next_token(s);
+       if (!tok || tok->type != ISL_TOKEN_VALUE) {
+               isl_stream_error(s, tok, "expecting constant value");
+               goto error;
+       }
+
+       q = isl_pw_aff_copy(aff);
+       q = isl_pw_aff_scale_down(q, tok->u.v);
+       q = isl_pw_aff_floor(q);
+       q = isl_pw_aff_scale(q, tok->u.v);
+
+       aff = isl_pw_aff_sub(aff, q);
+
+       isl_token_free(tok);
+       return aff;
+error:
+       isl_pw_aff_free(aff);
+       isl_token_free(tok);
+       return NULL;
+}
+
+static __isl_give isl_pw_aff *accept_affine(struct isl_stream *s,
+       __isl_take isl_space *dim, struct vars *v);
+static __isl_give isl_pw_aff_list *accept_affine_list(struct isl_stream *s,
+       __isl_take isl_space *dim, struct vars *v);
 
-static __isl_give isl_vec *accept_affine_factor(struct isl_stream *s,
-       struct vars *v)
+static __isl_give isl_pw_aff *accept_minmax(struct isl_stream *s,
+       __isl_take isl_space *dim, struct vars *v)
 {
-       struct isl_token *tok = NULL;
-       isl_vec *aff = NULL;
+       struct isl_token *tok;
+       isl_pw_aff_list *list = NULL;
+       int min;
 
        tok = isl_stream_next_token(s);
+       if (!tok)
+               goto error;
+       min = tok->type == ISL_TOKEN_MIN;
+       isl_token_free(tok);
+
+       if (isl_stream_eat(s, '('))
+               goto error;
+
+       list = accept_affine_list(s, isl_space_copy(dim), v);
+       if (!list)
+               goto error;
+
+       if (isl_stream_eat(s, ')'))
+               goto error;
+
+       isl_space_free(dim);
+       return min ? isl_pw_aff_list_min(list) : isl_pw_aff_list_max(list);
+error:
+       isl_space_free(dim);
+       isl_pw_aff_list_free(list);
+       return NULL;
+}
+
+static __isl_give isl_pw_aff *accept_div(struct isl_stream *s,
+       __isl_take isl_space *dim, struct vars *v)
+{
+       struct isl_token *tok;
+       int f = 0;
+       int c = 0;
+       isl_pw_aff *pwaff = NULL;
+
+       if (isl_stream_eat_if_available(s, ISL_TOKEN_FLOORD))
+               f = 1;
+       else if (isl_stream_eat_if_available(s, ISL_TOKEN_CEILD))
+               c = 1;
+       if (f || c) {
+               if (isl_stream_eat(s, '('))
+                       goto error;
+       } else {
+               if (isl_stream_eat(s, '['))
+                       goto error;
+       }
+
+       pwaff = accept_affine(s, isl_space_copy(dim), v);
+
+       if (f || c) {
+               if (isl_stream_eat(s, ','))
+                       goto error;
+
+               tok = next_token(s);
+               if (!tok)
+                       goto error;
+               if (tok->type != ISL_TOKEN_VALUE) {
+                       isl_stream_error(s, tok, "expected denominator");
+                       isl_stream_push_token(s, tok);
+                       goto error;
+               }
+               isl_pw_aff_scale_down(pwaff,  tok->u.v);
+               isl_token_free(tok);
+       }
+
+       if (c)
+               pwaff = isl_pw_aff_ceil(pwaff);
+       else
+               pwaff = isl_pw_aff_floor(pwaff);
+
+       if (f || c) {
+               if (isl_stream_eat(s, ')'))
+                       goto error;
+       } else {
+               if (isl_stream_eat(s, ']'))
+                       goto error;
+       }
+
+       isl_space_free(dim);
+       return pwaff;
+error:
+       isl_space_free(dim);
+       isl_pw_aff_free(pwaff);
+       return NULL;
+}
+
+static __isl_give isl_pw_aff *accept_affine_factor(struct isl_stream *s,
+       __isl_take isl_space *dim, struct vars *v)
+{
+       struct isl_token *tok = NULL;
+       isl_pw_aff *res = NULL;
+
+       tok = next_token(s);
        if (!tok) {
                isl_stream_error(s, NULL, "unexpected EOF");
                goto error;
        }
-       if (tok->type == ISL_TOKEN_IDENT) {
+
+       if (tok->type == ISL_TOKEN_AFF) {
+               res = isl_pw_aff_copy(tok->u.pwaff);
+               isl_token_free(tok);
+       } else if (tok->type == ISL_TOKEN_IDENT) {
                int n = v->n;
                int pos = vars_pos(v, tok->u.s, -1);
+               isl_aff *aff;
+
                if (pos < 0)
                        goto error;
                if (pos >= n) {
+                       vars_drop(v, v->n - n);
                        isl_stream_error(s, tok, "unknown identifier");
                        goto error;
                }
 
-               aff = isl_vec_alloc(v->ctx, 1 + v->n);
+               aff = isl_aff_zero_on_domain(isl_local_space_from_space(isl_space_copy(dim)));
                if (!aff)
                        goto error;
-               isl_seq_clr(aff->el, aff->size);
-               isl_int_set_si(aff->el[1 + pos], 1);
+               isl_int_set_si(aff->v->el[2 + pos], 1);
+               res = isl_pw_aff_from_aff(aff);
                isl_token_free(tok);
        } else if (tok->type == ISL_TOKEN_VALUE) {
                if (isl_stream_eat_if_available(s, '*')) {
-                       aff = accept_affine_factor(s, v);
-                       aff = isl_vec_scale(aff, tok->u.v);
+                       res = accept_affine_factor(s, isl_space_copy(dim), v);
+                       res = isl_pw_aff_scale(res, tok->u.v);
                } else {
-                       aff = isl_vec_alloc(v->ctx, 1 + v->n);
-                       if (!aff)
-                               goto error;
-                       isl_seq_clr(aff->el, aff->size);
-                       isl_int_set(aff->el[0], tok->u.v);
+                       isl_local_space *ls;
+                       isl_aff *aff;
+                       ls = isl_local_space_from_space(isl_space_copy(dim));
+                       aff = isl_aff_zero_on_domain(ls);
+                       aff = isl_aff_add_constant(aff, tok->u.v);
+                       res = isl_pw_aff_from_aff(aff);
                }
                isl_token_free(tok);
        } else if (tok->type == '(') {
                isl_token_free(tok);
                tok = NULL;
-               aff = accept_affine(s, v);
-               if (!aff)
+               res = accept_affine(s, isl_space_copy(dim), v);
+               if (!res)
                        goto error;
                if (isl_stream_eat(s, ')'))
                        goto error;
+       } else if (tok->type == '[' ||
+                   tok->type == ISL_TOKEN_FLOORD ||
+                   tok->type == ISL_TOKEN_CEILD) {
+               isl_stream_push_token(s, tok);
+               tok = NULL;
+               res = accept_div(s, isl_space_copy(dim), v);
+       } else if (tok->type == ISL_TOKEN_MIN || tok->type == ISL_TOKEN_MAX) {
+               isl_stream_push_token(s, tok);
+               tok = NULL;
+               res = accept_minmax(s, isl_space_copy(dim), v);
        } else {
                isl_stream_error(s, tok, "expecting factor");
                goto error;
        }
+       if (isl_stream_eat_if_available(s, '%') ||
+           isl_stream_eat_if_available(s, ISL_TOKEN_MOD)) {
+               isl_space_free(dim);
+               return affine_mod(s, v, res);
+       }
        if (isl_stream_eat_if_available(s, '*')) {
                isl_int f;
                isl_int_init(f);
                isl_int_set_si(f, 1);
                if (accept_cst_factor(s, &f) < 0) {
                        isl_int_clear(f);
-                       goto error;
+                       goto error2;
+               }
+               res = isl_pw_aff_scale(res, f);
+               isl_int_clear(f);
+       }
+       if (isl_stream_eat_if_available(s, '/')) {
+               isl_int f;
+               isl_int_init(f);
+               isl_int_set_si(f, 1);
+               if (accept_cst_factor(s, &f) < 0) {
+                       isl_int_clear(f);
+                       goto error2;
                }
-               aff = isl_vec_scale(aff, f);
+               res = isl_pw_aff_scale_down(res, f);
                isl_int_clear(f);
        }
 
-       return aff;
+       isl_space_free(dim);
+       return res;
 error:
        isl_token_free(tok);
-       isl_vec_free(aff);
+error2:
+       isl_pw_aff_free(res);
+       isl_space_free(dim);
        return NULL;
 }
 
-static struct isl_vec *accept_affine(struct isl_stream *s, struct vars *v)
+static __isl_give isl_pw_aff *add_cst(__isl_take isl_pw_aff *pwaff, isl_int v)
+{
+       isl_aff *aff;
+       isl_space *space;
+
+       space = isl_pw_aff_get_domain_space(pwaff);
+       aff = isl_aff_zero_on_domain(isl_local_space_from_space(space));
+       aff = isl_aff_add_constant(aff, v);
+
+       return isl_pw_aff_add(pwaff, isl_pw_aff_from_aff(aff));
+}
+
+static __isl_give isl_pw_aff *accept_affine(struct isl_stream *s,
+       __isl_take isl_space *dim, struct vars *v)
 {
        struct isl_token *tok = NULL;
-       struct isl_vec *aff;
+       isl_local_space *ls;
+       isl_pw_aff *res;
        int sign = 1;
 
-       aff = isl_vec_alloc(v->ctx, 1 + v->n);
-       if (!aff)
-               return NULL;
-       isl_seq_clr(aff->el, aff->size);
+       ls = isl_local_space_from_space(isl_space_copy(dim));
+       res = isl_pw_aff_from_aff(isl_aff_zero_on_domain(ls));
+       if (!res)
+               goto error;
 
        for (;;) {
-               tok = isl_stream_next_token(s);
+               tok = next_token(s);
                if (!tok) {
                        isl_stream_error(s, NULL, "unexpected EOF");
                        goto error;
@@ -266,15 +544,21 @@ static struct isl_vec *accept_affine(struct isl_stream *s, struct vars *v)
                        isl_token_free(tok);
                        continue;
                }
-               if (tok->type == '(' || tok->type == ISL_TOKEN_IDENT) {
-                       isl_vec *aff2;
+               if (tok->type == '(' || tok->type == '[' ||
+                   tok->type == ISL_TOKEN_MIN || tok->type == ISL_TOKEN_MAX ||
+                   tok->type == ISL_TOKEN_FLOORD ||
+                   tok->type == ISL_TOKEN_CEILD ||
+                   tok->type == ISL_TOKEN_IDENT ||
+                   tok->type == ISL_TOKEN_AFF) {
+                       isl_pw_aff *term;
                        isl_stream_push_token(s, tok);
                        tok = NULL;
-                       aff2 = accept_affine_factor(s, v);
+                       term = accept_affine_factor(s, isl_space_copy(dim), v);
                        if (sign < 0)
-                               aff2 = isl_vec_scale(aff2, s->ctx->negone);
-                       aff = isl_vec_add(aff, aff2);
-                       if (!aff)
+                               res = isl_pw_aff_sub(res, term);
+                       else
+                               res = isl_pw_aff_add(res, term);
+                       if (!res)
                                goto error;
                        sign = 1;
                } else if (tok->type == ISL_TOKEN_VALUE) {
@@ -282,20 +566,27 @@ static struct isl_vec *accept_affine(struct isl_stream *s, struct vars *v)
                                isl_int_neg(tok->u.v, tok->u.v);
                        if (isl_stream_eat_if_available(s, '*') ||
                            isl_stream_next_token_is(s, ISL_TOKEN_IDENT)) {
-                               isl_vec *aff2;
-                               aff2 = accept_affine_factor(s, v);
-                               aff2 = isl_vec_scale(aff2, tok->u.v);
-                               aff = isl_vec_add(aff, aff2);
-                               if (!aff)
+                               isl_pw_aff *term;
+                               term = accept_affine_factor(s,
+                                                       isl_space_copy(dim), v);
+                               term = isl_pw_aff_scale(term, tok->u.v);
+                               res = isl_pw_aff_add(res, term);
+                               if (!res)
                                        goto error;
                        } else {
-                               isl_int_add(aff->el[0], aff->el[0], tok->u.v);
+                               res = add_cst(res, tok->u.v);
                        }
                        sign = 1;
+               } else {
+                       isl_stream_error(s, tok, "unexpected isl_token");
+                       isl_stream_push_token(s, tok);
+                       isl_pw_aff_free(res);
+                       isl_space_free(dim);
+                       return NULL;
                }
                isl_token_free(tok);
 
-               tok = isl_stream_next_token(s);
+               tok = next_token(s);
                if (tok && tok->type == '-') {
                        sign = -sign;
                        isl_token_free(tok);
@@ -312,183 +603,204 @@ static struct isl_vec *accept_affine(struct isl_stream *s, struct vars *v)
                }
        }
 
-       return aff;
+       isl_space_free(dim);
+       return res;
 error:
+       isl_space_free(dim);
        isl_token_free(tok);
-       isl_vec_free(aff);
+       isl_pw_aff_free(res);
        return NULL;
 }
 
-static __isl_give isl_basic_map *read_var_list(struct isl_stream *s,
-       __isl_take isl_basic_map *bmap, enum isl_dim_type type, struct vars *v)
+static int is_comparator(struct isl_token *tok)
 {
-       int i = 0;
-       struct isl_token *tok;
-
-       while ((tok = isl_stream_next_token(s)) != NULL) {
-               int new_name = 0;
-
-               if (tok->type == ISL_TOKEN_IDENT) {
-                       int n = v->n;
-                       int p = vars_pos(v, tok->u.s, -1);
-                       if (p < 0)
-                               goto error;
-                       new_name = p >= n;
-               }
-
-               if (new_name) {
-                       bmap = isl_basic_map_add(bmap, type, 1);
-                       bmap = set_name(bmap, type, i, v->v->name);
-                       isl_token_free(tok);
-               } else if (tok->type == ISL_TOKEN_IDENT ||
-                          tok->type == ISL_TOKEN_VALUE) {
-                       struct isl_vec *vec;
-                       int k;
-                       if (type == isl_dim_param) {
-                               isl_stream_error(s, tok,
-                                               "expecting unique identifier");
-                               goto error;
-                       }
-                       isl_stream_push_token(s, tok);
-                       tok = NULL;
-                       vec = accept_affine(s, v);
-                       if (!vec)
-                               goto error;
-                       v->v = variable_new(v, "", 0, v->n);
-                       if (!v->v)
-                               goto error;
-                       v->n++;
-                       bmap = isl_basic_map_add(bmap, type, 1);
-                       bmap = isl_basic_map_extend_constraints(bmap, 1, 0);
-                       k = isl_basic_map_alloc_equality(bmap);
-                       if (k >= 0) {
-                               isl_seq_cpy(bmap->eq[k], vec->el, vec->size);
-                               isl_int_set_si(bmap->eq[k][vec->size], -1);
-                       }
-                       isl_vec_free(vec);
-                       if (k < 0)
-                               goto error;
-               } else
-                       break;
-
-               tok = isl_stream_next_token(s);
-               if (!tok || tok->type != ',')
-                       break;
+       if (!tok)
+               return 0;
 
-               isl_token_free(tok);
-               i++;
+       switch (tok->type) {
+       case ISL_TOKEN_LT:
+       case ISL_TOKEN_GT:
+       case ISL_TOKEN_LE:
+       case ISL_TOKEN_GE:
+       case ISL_TOKEN_NE:
+       case '=':
+               return 1;
+       default:
+               return 0;
        }
-       if (tok)
-               isl_stream_push_token(s, tok);
-
-       return bmap;
-error:
-       isl_token_free(tok);
-       isl_basic_map_free(bmap);
-       return NULL;
 }
 
-static __isl_give isl_mat *accept_affine_list(struct isl_stream *s,
-       struct vars *v)
+static struct isl_map *read_disjuncts(struct isl_stream *s,
+       struct vars *v, __isl_take isl_map *map, int rational);
+static __isl_give isl_pw_aff *accept_extended_affine(struct isl_stream *s,
+       __isl_take isl_space *dim, struct vars *v, int rational);
+
+/* Accept a ternary operator, given the first argument.
+ */
+static __isl_give isl_pw_aff *accept_ternary(struct isl_stream *s,
+       __isl_take isl_map *cond, struct vars *v, int rational)
 {
-       struct isl_vec *vec;
-       struct isl_mat *mat;
-       struct isl_token *tok = NULL;
+       isl_space *dim;
+       isl_pw_aff *pwaff1 = NULL, *pwaff2 = NULL, *pa_cond;
 
-       vec = accept_affine(s, v);
-       mat = isl_mat_from_row_vec(vec);
-       if (!mat)
+       if (!cond)
                return NULL;
 
-       for (;;) {
-               tok = isl_stream_next_token(s);
-               if (!tok) {
-                       isl_stream_error(s, NULL, "unexpected EOF");
-                       goto error;
-               }
-               if (tok->type != ',') {
-                       isl_stream_push_token(s, tok);
-                       break;
-               }
-               isl_token_free(tok);
+       if (isl_stream_eat(s, '?'))
+               goto error;
 
-               vec = accept_affine(s, v);
-               mat = isl_mat_vec_concat(mat, vec);
-               if (!mat)
-                       return NULL;
-       }
+       dim = isl_space_wrap(isl_map_get_space(cond));
+       pwaff1 = accept_extended_affine(s, dim, v, rational);
+       if (!pwaff1)
+               goto error;
+
+       if (isl_stream_eat(s, ':'))
+               goto error;
+
+       dim = isl_pw_aff_get_domain_space(pwaff1);
+       pwaff2 = accept_extended_affine(s, dim, v, rational);
+       if (!pwaff1)
+               goto error;
 
-       return mat;
+       pa_cond = isl_set_indicator_function(isl_map_wrap(cond));
+       return isl_pw_aff_cond(pa_cond, pwaff1, pwaff2);
 error:
-       isl_mat_free(mat);
+       isl_map_free(cond);
+       isl_pw_aff_free(pwaff1);
+       isl_pw_aff_free(pwaff2);
        return NULL;
 }
 
-static struct isl_basic_map *add_div_definition(struct isl_stream *s,
-       struct vars *v, struct isl_basic_map *bmap, int k)
+/* Accept an affine expression that may involve ternary operators.
+ * We first read an affine expression.
+ * If it is not followed by a comparison operator, we simply return it.
+ * Otherwise, we assume the affine epxression is part of the first
+ * argument of a ternary operator and try to parse that.
+ */
+static __isl_give isl_pw_aff *accept_extended_affine(struct isl_stream *s,
+       __isl_take isl_space *dim, struct vars *v, int rational)
 {
+       isl_space *space;
+       isl_map *cond;
+       isl_pw_aff *pwaff;
        struct isl_token *tok;
-       int seen_paren = 0;
-       struct isl_vec *aff;
+       int line = -1, col = -1;
+       int is_comp;
 
-       if (isl_stream_eat(s, '['))
-               goto error;
+       tok = isl_stream_next_token(s);
+       if (tok) {
+               line = tok->line;
+               col = tok->col;
+               isl_stream_push_token(s, tok);
+       }
+
+       pwaff = accept_affine(s, dim, v);
+       if (rational)
+               pwaff = isl_pw_aff_set_rational(pwaff);
+       if (!pwaff)
+               return NULL;
 
        tok = isl_stream_next_token(s);
        if (!tok)
-               goto error;
-       if (tok->type == '(') {
-               seen_paren = 1;
-               isl_token_free(tok);
-       } else
-               isl_stream_push_token(s, tok);
+               return isl_pw_aff_free(pwaff);
 
-       aff = accept_affine(s, v);
-       if (!aff)
-               goto error;
+       is_comp = is_comparator(tok);
+       isl_stream_push_token(s, tok);
+       if (!is_comp)
+               return pwaff;
 
-       isl_seq_cpy(bmap->div[k] + 1, aff->el, aff->size);
+       tok = isl_token_new(s->ctx, line, col, 0);
+       if (!tok)
+               return isl_pw_aff_free(pwaff);
+       tok->type = ISL_TOKEN_AFF;
+       tok->u.pwaff = pwaff;
 
-       isl_vec_free(aff);
+       space = isl_pw_aff_get_domain_space(pwaff);
+       cond = isl_map_universe(isl_space_unwrap(space));
 
-       if (seen_paren && isl_stream_eat(s, ')'))
-               goto error;
-       if (isl_stream_eat(s, '/'))
-               goto error;
+       isl_stream_push_token(s, tok);
 
-       tok = isl_stream_next_token(s);
-       if (!tok)
-               goto error;
-       if (tok->type != ISL_TOKEN_VALUE) {
-               isl_stream_error(s, tok, "expected denominator");
-               isl_stream_push_token(s, tok);
-               goto error;
+       cond = read_disjuncts(s, v, cond, rational);
+
+       return accept_ternary(s, cond, v, rational);
+}
+
+static __isl_give isl_map *read_var_def(struct isl_stream *s,
+       __isl_take isl_map *map, enum isl_dim_type type, struct vars *v,
+       int rational)
+{
+       isl_pw_aff *def;
+       int pos;
+       isl_map *def_map;
+
+       if (type == isl_dim_param)
+               pos = isl_map_dim(map, isl_dim_param);
+       else {
+               pos = isl_map_dim(map, isl_dim_in);
+               if (type == isl_dim_out)
+                       pos += isl_map_dim(map, isl_dim_out);
+               type = isl_dim_in;
        }
-       isl_int_set(bmap->div[k][0], tok->u.v);
-       isl_token_free(tok);
+       --pos;
 
-       if (isl_stream_eat(s, ']'))
-               goto error;
+       def = accept_extended_affine(s, isl_space_wrap(isl_map_get_space(map)),
+                                       v, rational);
+       def_map = isl_map_from_pw_aff(def);
+       def_map = isl_map_equate(def_map, type, pos, isl_dim_out, 0);
+       def_map = isl_set_unwrap(isl_map_domain(def_map));
+
+       map = isl_map_intersect(map, def_map);
+
+       return map;
+}
 
-       if (isl_basic_map_add_div_constraints(bmap, k) < 0)
+static __isl_give isl_pw_aff_list *accept_affine_list(struct isl_stream *s,
+       __isl_take isl_space *dim, struct vars *v)
+{
+       isl_pw_aff *pwaff;
+       isl_pw_aff_list *list;
+       struct isl_token *tok = NULL;
+
+       pwaff = accept_affine(s, isl_space_copy(dim), v);
+       list = isl_pw_aff_list_from_pw_aff(pwaff);
+       if (!list)
                goto error;
 
-       return bmap;
+       for (;;) {
+               tok = isl_stream_next_token(s);
+               if (!tok) {
+                       isl_stream_error(s, NULL, "unexpected EOF");
+                       goto error;
+               }
+               if (tok->type != ',') {
+                       isl_stream_push_token(s, tok);
+                       break;
+               }
+               isl_token_free(tok);
+
+               pwaff = accept_affine(s, isl_space_copy(dim), v);
+               list = isl_pw_aff_list_concat(list,
+                               isl_pw_aff_list_from_pw_aff(pwaff));
+               if (!list)
+                       goto error;
+       }
+
+       isl_space_free(dim);
+       return list;
 error:
-       isl_basic_map_free(bmap);
+       isl_space_free(dim);
+       isl_pw_aff_list_free(list);
        return NULL;
 }
 
-static struct isl_basic_map *read_defined_var_list(struct isl_stream *s,
-       struct vars *v, struct isl_basic_map *bmap)
+static __isl_give isl_map *read_defined_var_list(struct isl_stream *s,
+       struct vars *v, __isl_take isl_map *map, int rational)
 {
        struct isl_token *tok;
 
        while ((tok = isl_stream_next_token(s)) != NULL) {
-               int k;
                int p;
                int n = v->n;
-               unsigned total = isl_basic_map_total_dim(bmap);
 
                if (tok->type != ISL_TOKEN_IDENT)
                        break;
@@ -500,20 +812,14 @@ static struct isl_basic_map *read_defined_var_list(struct isl_stream *s,
                        isl_stream_error(s, tok, "expecting unique identifier");
                        goto error;
                }
-               isl_token_free(tok);
-
-               bmap = isl_basic_map_cow(bmap);
-               bmap = isl_basic_map_extend_dim(bmap, isl_dim_copy(bmap->dim),
-                                               1, 0, 2);
 
-               if ((k = isl_basic_map_alloc_div(bmap)) < 0)
-                       goto error;
-               isl_seq_clr(bmap->div[k], 1 + 1 + total);
+               map = isl_map_add_dims(map, isl_dim_out, 1);
 
+               isl_token_free(tok);
                tok = isl_stream_next_token(s);
                if (tok && tok->type == '=') {
                        isl_token_free(tok);
-                       bmap = add_div_definition(s, v, bmap, k);
+                       map = read_var_def(s, map, isl_dim_out, v, rational);
                        tok = isl_stream_next_token(s);
                }
 
@@ -525,163 +831,411 @@ static struct isl_basic_map *read_defined_var_list(struct isl_stream *s,
        if (tok)
                isl_stream_push_token(s, tok);
 
-       return bmap;
+       return map;
 error:
        isl_token_free(tok);
-       isl_basic_map_free(bmap);
+       isl_map_free(map);
        return NULL;
 }
 
-static __isl_give isl_basic_map *read_tuple(struct isl_stream *s,
-       __isl_take isl_basic_map *bmap, enum isl_dim_type type, struct vars *v)
+static int next_is_tuple(struct isl_stream *s)
 {
        struct isl_token *tok;
+       int is_tuple;
 
        tok = isl_stream_next_token(s);
-       if (!tok || tok->type != '[') {
-               isl_stream_error(s, tok, "expecting '['");
-               goto error;
+       if (!tok)
+               return 0;
+       if (tok->type == '[') {
+               isl_stream_push_token(s, tok);
+               return 1;
        }
-       isl_token_free(tok);
-       bmap = read_var_list(s, bmap, type, v);
-       tok = isl_stream_next_token(s);
-       if (!tok || tok->type != ']') {
-               isl_stream_error(s, tok, "expecting ']'");
-               goto error;
+       if (tok->type != ISL_TOKEN_IDENT && !tok->is_keyword) {
+               isl_stream_push_token(s, tok);
+               return 0;
        }
-       isl_token_free(tok);
 
-       return bmap;
-error:
-       if (tok)
-               isl_token_free(tok);
-       isl_basic_map_free(bmap);
-       return NULL;
+       is_tuple = isl_stream_next_token_is(s, '[');
+
+       isl_stream_push_token(s, tok);
+
+       return is_tuple;
+}
+
+/* Allocate an initial tuple with zero dimensions and an anonymous,
+ * unstructured space.
+ * A tuple is represented as an isl_multi_pw_aff.
+ * The range space is the space of the tuple.
+ * The domain space is an anonymous space
+ * with a dimension for each variable in the set of variables in "v".
+ * If a given dimension is not defined in terms of earlier dimensions in
+ * the input, then the corresponding isl_pw_aff is set equal to one time
+ * the variable corresponding to the dimension being defined.
+ */
+static __isl_give isl_multi_pw_aff *tuple_alloc(struct vars *v)
+{
+       return isl_multi_pw_aff_alloc(isl_space_alloc(v->ctx, 0, v->n, 0));
+}
+
+/* Is "pa" an expression in term of earlier dimensions?
+ * The alternative is that the dimension is defined to be equal to itself,
+ * meaning that it has a universe domain and an expression that depends
+ * on itself.  "i" is the position of the expression in a sequence
+ * of "n" expressions.  The final dimensions of "pa" correspond to
+ * these "n" expressions.
+ */
+static int pw_aff_is_expr(__isl_keep isl_pw_aff *pa, int i, int n)
+{
+       isl_aff *aff;
+
+       if (!pa)
+               return -1;
+       if (pa->n != 1)
+               return 1;
+       if (!isl_set_plain_is_universe(pa->p[0].set))
+               return 1;
+
+       aff = pa->p[0].aff;
+       if (isl_int_is_zero(aff->v->el[aff->v->size - n + i]))
+               return 1;
+       return 0;
+}
+
+/* Does the tuple contain any dimensions that are defined
+ * in terms of earlier dimensions?
+ */
+static int tuple_has_expr(__isl_keep isl_multi_pw_aff *tuple)
+{
+       int i, n;
+       int has_expr = 0;
+       isl_pw_aff *pa;
+
+       if (!tuple)
+               return -1;
+       n = isl_multi_pw_aff_dim(tuple, isl_dim_out);
+       for (i = 0; i < n; ++i) {
+               pa = isl_multi_pw_aff_get_pw_aff(tuple, i);
+               has_expr = pw_aff_is_expr(pa, i, n);
+               isl_pw_aff_free(pa);
+               if (has_expr < 0 || has_expr)
+                       break;
+       }
+
+       return has_expr;
+}
+
+/* Add a dimension to the given tuple.
+ * The dimension is initially undefined, so it is encoded
+ * as one times itself.
+ */
+static __isl_give isl_multi_pw_aff *tuple_add_dim(
+       __isl_take isl_multi_pw_aff *tuple, struct vars *v)
+{
+       isl_space *space;
+       isl_aff *aff;
+       isl_pw_aff *pa;
+
+       tuple = isl_multi_pw_aff_add_dims(tuple, isl_dim_in, 1);
+       space = isl_multi_pw_aff_get_domain_space(tuple);
+       aff = isl_aff_zero_on_domain(isl_local_space_from_space(space));
+       aff = isl_aff_add_coefficient_si(aff, isl_dim_in, v->n, 1);
+       pa = isl_pw_aff_from_aff(aff);
+       tuple = isl_multi_pw_aff_flat_range_product(tuple,
+                                           isl_multi_pw_aff_from_pw_aff(pa));
+
+       return tuple;
+}
+
+/* Set the name of dimension "pos" in "tuple" to "name".
+ * During printing, we add primes if the same name appears more than once
+ * to distinguish the occurrences.  Here, we remove those primes from "name"
+ * before setting the name of the dimension.
+ */
+static __isl_give isl_multi_pw_aff *tuple_set_dim_name(
+       __isl_take isl_multi_pw_aff *tuple, int pos, char *name)
+{
+       char *prime;
+
+       if (!name)
+               return tuple;
+
+       prime = strchr(name, '\'');
+       if (prime)
+               *prime = '\0';
+       tuple = isl_multi_pw_aff_set_dim_name(tuple, isl_dim_set, pos, name);
+       if (prime)
+               *prime = '\'';
+
+       return tuple;
+}
+
+/* Read an affine expression from "s" and replace the definition
+ * of dimension "pos" in "tuple" by this expression.
+ *
+ * accept_extended_affine requires a wrapped space as input.
+ * The domain space of "tuple", on the other hand is an anonymous space,
+ * so we have to adjust the space of the isl_pw_aff before adding it
+ * to "tuple".
+ */
+static __isl_give isl_multi_pw_aff *read_tuple_var_def(struct isl_stream *s,
+       __isl_take isl_multi_pw_aff *tuple, int pos, struct vars *v,
+       int rational)
+{
+       isl_space *space;
+       isl_pw_aff *def;
+
+       space = isl_space_wrap(isl_space_alloc(s->ctx, 0, v->n, 0));
+       def = accept_extended_affine(s, space, v, rational);
+       space = isl_space_set_alloc(s->ctx, 0, v->n);
+       def = isl_pw_aff_reset_domain_space(def, space);
+       tuple = isl_multi_pw_aff_set_pw_aff(tuple, pos, def);
+
+       return tuple;
 }
 
-static struct isl_basic_map *add_constraints(struct isl_stream *s,
-       struct vars *v, struct isl_basic_map *bmap);
+/* Read a list of variables and/or affine expressions and return the list
+ * as an isl_multi_pw_aff.
+ * The elements in the list are separated by either "," or "][".
+ * If "comma" is set then only "," is allowed.
+ */
+static __isl_give isl_multi_pw_aff *read_tuple_var_list(struct isl_stream *s,
+       struct vars *v, int rational, int comma)
+{
+       int i = 0;
+       struct isl_token *tok;
+       isl_multi_pw_aff *res;
+
+       res = tuple_alloc(v);
+
+       if (isl_stream_next_token_is(s, ']'))
+               return res;
+
+       while ((tok = next_token(s)) != NULL) {
+               int new_name = 0;
+
+               res = tuple_add_dim(res, v);
+
+               if (tok->type == ISL_TOKEN_IDENT) {
+                       int n = v->n;
+                       int p = vars_pos(v, tok->u.s, -1);
+                       if (p < 0)
+                               goto error;
+                       new_name = p >= n;
+               }
+
+               if (tok->type == '*') {
+                       if (vars_add_anon(v) < 0)
+                               goto error;
+                       isl_token_free(tok);
+               } else if (new_name) {
+                       res = tuple_set_dim_name(res, i, v->v->name);
+                       isl_token_free(tok);
+                       if (isl_stream_eat_if_available(s, '='))
+                               res = read_tuple_var_def(s, res, i, v,
+                                                       rational);
+               } else {
+                       isl_stream_push_token(s, tok);
+                       tok = NULL;
+                       if (vars_add_anon(v) < 0)
+                               goto error;
+                       res = read_tuple_var_def(s, res, i, v, rational);
+               }
+
+               tok = isl_stream_next_token(s);
+               if (!comma && tok && tok->type == ']' &&
+                   isl_stream_next_token_is(s, '[')) {
+                       isl_token_free(tok);
+                       tok = isl_stream_next_token(s);
+               } else if (!tok || tok->type != ',')
+                       break;
+
+               isl_token_free(tok);
+               i++;
+       }
+       if (tok)
+               isl_stream_push_token(s, tok);
+
+       return res;
+error:
+       isl_token_free(tok);
+       return isl_multi_pw_aff_free(res);
+}
 
-static struct isl_basic_map *add_exists(struct isl_stream *s,
-       struct vars *v, struct isl_basic_map *bmap)
+/* Read a tuple and represent it as an isl_multi_pw_aff.  See tuple_alloc.
+ */
+static __isl_give isl_multi_pw_aff *read_tuple(struct isl_stream *s,
+       struct vars *v, int rational, int comma)
 {
        struct isl_token *tok;
-       int n = v->n;
-       int extra;
-       int seen_paren = 0;
-       int i;
-       unsigned total;
+       char *name = NULL;
+       isl_multi_pw_aff *res = NULL;
 
        tok = isl_stream_next_token(s);
        if (!tok)
                goto error;
-       if (tok->type == '(') {
-               seen_paren = 1;
+       if (tok->type == ISL_TOKEN_IDENT || tok->is_keyword) {
+               name = strdup(tok->u.s);
                isl_token_free(tok);
+               if (!name)
+                       goto error;
        } else
                isl_stream_push_token(s, tok);
-
-       bmap = read_defined_var_list(s, v, bmap);
-       if (!bmap)
-               goto error;
-
-       if (isl_stream_eat(s, ':'))
+       if (isl_stream_eat(s, '['))
                goto error;
-       bmap = add_constraints(s, v, bmap);
-       if (seen_paren && isl_stream_eat(s, ')'))
+       if (next_is_tuple(s)) {
+               isl_multi_pw_aff *out;
+               int n;
+               res = read_tuple(s, v, rational, comma);
+               if (isl_stream_eat(s, ISL_TOKEN_TO))
+                       goto error;
+               out = read_tuple(s, v, rational, comma);
+               n = isl_multi_pw_aff_dim(out, isl_dim_out);
+               res = isl_multi_pw_aff_add_dims(res, isl_dim_in, n);
+               res = isl_multi_pw_aff_range_product(res, out);
+       } else
+               res = read_tuple_var_list(s, v, rational, comma);
+       if (isl_stream_eat(s, ']'))
                goto error;
-       return bmap;
+
+       if (name) {
+               res = isl_multi_pw_aff_set_tuple_name(res, isl_dim_out, name);
+               free(name);
+       }
+
+       return res;
 error:
-       isl_basic_map_free(bmap);
-       return NULL;
+       free(name);
+       return isl_multi_pw_aff_free(res);
 }
 
-static __isl_give isl_basic_map *construct_constraint(
-       __isl_take isl_basic_map *bmap, enum isl_token_type type,
-       isl_int *left, isl_int *right)
+/* Read a tuple from "s" and add it to "map".
+ * The tuple is initially represented as an isl_multi_pw_aff.
+ * We first create the appropriate space in "map" based on the range
+ * space of this isl_multi_pw_aff.  Then, we add equalities based
+ * on the affine expressions.  These live in an anonymous space,
+ * however, so we first need to reset the space to that of "map".
+ */
+static __isl_give isl_map *read_map_tuple(struct isl_stream *s,
+       __isl_take isl_map *map, enum isl_dim_type type, struct vars *v,
+       int rational, int comma)
 {
-       int k;
-       unsigned len;
-       struct isl_ctx *ctx;
+       int i, n;
+       isl_multi_pw_aff *tuple;
+       isl_space *space = NULL;
 
-       if (!bmap)
-               return NULL;
-       len = 1 + isl_basic_map_total_dim(bmap);
-       ctx = bmap->ctx;
+       tuple = read_tuple(s, v, rational, comma);
+       if (!tuple)
+               goto error;
 
-       k = isl_basic_map_alloc_inequality(bmap);
-       if (k < 0)
+       n = isl_multi_pw_aff_dim(tuple, isl_dim_out);
+       space = isl_space_range(isl_multi_pw_aff_get_space(tuple));
+       if (!space)
                goto error;
-       if (type == ISL_TOKEN_LE)
-               isl_seq_combine(bmap->ineq[k], ctx->negone, left,
-                                              ctx->one, right,
-                                              len);
-       else if (type == ISL_TOKEN_GE)
-               isl_seq_combine(bmap->ineq[k], ctx->one, left,
-                                              ctx->negone, right,
-                                              len);
-       else if (type == ISL_TOKEN_LT) {
-               isl_seq_combine(bmap->ineq[k], ctx->negone, left,
-                                              ctx->one, right,
-                                              len);
-               isl_int_sub_ui(bmap->ineq[k][0], bmap->ineq[k][0], 1);
-       } else if (type == ISL_TOKEN_GT) {
-               isl_seq_combine(bmap->ineq[k], ctx->one, left,
-                                              ctx->negone, right,
-                                              len);
-               isl_int_sub_ui(bmap->ineq[k][0], bmap->ineq[k][0], 1);
+
+       if (type == isl_dim_param) {
+               if (isl_space_has_tuple_name(space, isl_dim_set) ||
+                   isl_space_is_wrapping(space)) {
+                       isl_die(s->ctx, isl_error_invalid,
+                               "parameter tuples cannot be named or nested",
+                               goto error);
+               }
+               map = isl_map_add_dims(map, type, n);
+               for (i = 0; i < n; ++i) {
+                       isl_id *id;
+                       if (!isl_space_has_dim_name(space, isl_dim_set, i))
+                               isl_die(s->ctx, isl_error_invalid,
+                                       "parameters must be named",
+                                       goto error);
+                       id = isl_space_get_dim_id(space, isl_dim_set, i);
+                       map = isl_map_set_dim_id(map, isl_dim_param, i, id);
+               }
+       } else if (type == isl_dim_in) {
+               isl_set *set;
+
+               set = isl_set_universe(isl_space_copy(space));
+               if (rational)
+                       set = isl_set_set_rational(set);
+               set = isl_set_intersect_params(set, isl_map_params(map));
+               map = isl_map_from_domain(set);
        } else {
-               isl_seq_combine(bmap->ineq[k], ctx->one, left,
-                                              ctx->negone, right,
-                                              len);
-               isl_basic_map_inequality_to_equality(bmap, k);
+               isl_set *set;
+
+               set = isl_set_universe(isl_space_copy(space));
+               if (rational)
+                       set = isl_set_set_rational(set);
+               map = isl_map_from_domain_and_range(isl_map_domain(map), set);
        }
 
-       return bmap;
+       for (i = 0; i < n; ++i) {
+               isl_pw_aff *pa;
+               isl_space *space;
+               isl_aff *aff;
+               isl_set *set;
+               isl_map *map_i;
+
+               pa = isl_multi_pw_aff_get_pw_aff(tuple, i);
+               space = isl_pw_aff_get_domain_space(pa);
+               aff = isl_aff_zero_on_domain(isl_local_space_from_space(space));
+               aff = isl_aff_add_coefficient_si(aff,
+                                               isl_dim_in, v->n - n + i, -1);
+               pa = isl_pw_aff_add(pa, isl_pw_aff_from_aff(aff));
+               if (rational)
+                       pa = isl_pw_aff_set_rational(pa);
+               set = isl_pw_aff_zero_set(pa);
+               map_i = isl_map_from_range(set);
+               map_i = isl_map_reset_space(map_i, isl_map_get_space(map));
+               map = isl_map_intersect(map, map_i);
+       }
+
+       isl_space_free(space);
+       isl_multi_pw_aff_free(tuple);
+       return map;
 error:
-       isl_basic_map_free(bmap);
+       isl_space_free(space);
+       isl_multi_pw_aff_free(tuple);
+       isl_map_free(map);
        return NULL;
 }
 
-static int is_comparator(struct isl_token *tok)
+static __isl_give isl_set *construct_constraints(
+       __isl_take isl_set *set, int type,
+       __isl_keep isl_pw_aff_list *left, __isl_keep isl_pw_aff_list *right,
+       int rational)
 {
-       if (!tok)
-               return 0;
+       isl_set *cond;
 
-       switch (tok->type) {
-       case ISL_TOKEN_LT:
-       case ISL_TOKEN_GT:
-       case ISL_TOKEN_LE:
-       case ISL_TOKEN_GE:
-       case '=':
-               return 1;
-       default:
-               return 0;
+       left = isl_pw_aff_list_copy(left);
+       right = isl_pw_aff_list_copy(right);
+       if (rational) {
+               left = isl_pw_aff_list_set_rational(left);
+               right = isl_pw_aff_list_set_rational(right);
        }
+       if (type == ISL_TOKEN_LE)
+               cond = isl_pw_aff_list_le_set(left, right);
+       else if (type == ISL_TOKEN_GE)
+               cond = isl_pw_aff_list_ge_set(left, right);
+       else if (type == ISL_TOKEN_LT)
+               cond = isl_pw_aff_list_lt_set(left, right);
+       else if (type == ISL_TOKEN_GT)
+               cond = isl_pw_aff_list_gt_set(left, right);
+       else if (type == ISL_TOKEN_NE)
+               cond = isl_pw_aff_list_ne_set(left, right);
+       else
+               cond = isl_pw_aff_list_eq_set(left, right);
+
+       return isl_set_intersect(set, cond);
 }
 
-static struct isl_basic_map *add_constraint(struct isl_stream *s,
-       struct vars *v, struct isl_basic_map *bmap)
+static __isl_give isl_map *add_constraint(struct isl_stream *s,
+       struct vars *v, __isl_take isl_map *map, int rational)
 {
-       int i, j;
-       unsigned total = isl_basic_map_total_dim(bmap);
        struct isl_token *tok = NULL;
-       struct isl_mat *aff1 = NULL, *aff2 = NULL;
-
-       tok = isl_stream_next_token(s);
-       if (!tok)
-               goto error;
-       if (tok->type == ISL_TOKEN_EXISTS) {
-               isl_token_free(tok);
-               return add_exists(s, v, bmap);
-       }
-       isl_stream_push_token(s, tok);
-       tok = NULL;
+       isl_pw_aff_list *list1 = NULL, *list2 = NULL;
+       isl_set *set;
 
-       bmap = isl_basic_map_cow(bmap);
-
-       aff1 = accept_affine_list(s, v);
-       if (!aff1)
+       set = isl_map_wrap(map);
+       list1 = accept_affine_list(s, isl_set_get_space(set), v);
+       if (!list1)
                goto error;
        tok = isl_stream_next_token(s);
        if (!is_comparator(tok)) {
@@ -691,22 +1245,16 @@ static struct isl_basic_map *add_constraint(struct isl_stream *s,
                tok = NULL;
                goto error;
        }
-       isl_assert(aff1->ctx, aff1->n_col == 1 + total, goto error);
        for (;;) {
-               aff2 = accept_affine_list(s, v);
-               if (!aff2)
+               list2 = accept_affine_list(s, isl_set_get_space(set), v);
+               if (!list2)
                        goto error;
-               isl_assert(aff2->ctx, aff2->n_col == 1 + total, goto error);
-
-               bmap = isl_basic_map_extend_constraints(bmap, 0,
-                                               aff1->n_row * aff2->n_row);
-               for (i = 0; i < aff1->n_row; ++i)
-                       for (j = 0; j < aff2->n_row; ++j)
-                               bmap = construct_constraint(bmap, tok->type,
-                                                   aff1->row[i], aff2->row[j]);
+
+               set = construct_constraints(set, tok->type, list1, list2,
+                                               rational);
                isl_token_free(tok);
-               isl_mat_free(aff1);
-               aff1 = aff2;
+               isl_pw_aff_list_free(list1);
+               list1 = list2;
 
                tok = isl_stream_next_token(s);
                if (!is_comparator(tok)) {
@@ -715,121 +1263,215 @@ static struct isl_basic_map *add_constraint(struct isl_stream *s,
                        break;
                }
        }
-       isl_mat_free(aff1);
+       isl_pw_aff_list_free(list1);
 
-       return bmap;
+       return isl_set_unwrap(set);
 error:
        if (tok)
                isl_token_free(tok);
-       isl_mat_free(aff1);
-       isl_mat_free(aff2);
-       isl_basic_map_free(bmap);
+       isl_pw_aff_list_free(list1);
+       isl_pw_aff_list_free(list2);
+       isl_set_free(set);
        return NULL;
 }
 
-static struct isl_basic_map *add_constraints(struct isl_stream *s,
-       struct vars *v, struct isl_basic_map *bmap)
+static __isl_give isl_map *read_exists(struct isl_stream *s,
+       struct vars *v, __isl_take isl_map *map, int rational)
 {
-       struct isl_token *tok;
+       int n = v->n;
+       int seen_paren = isl_stream_eat_if_available(s, '(');
 
-       for (;;) {
-               bmap = add_constraint(s, v, bmap);
-               if (!bmap)
-                       return NULL;
-               tok = isl_stream_next_token(s);
-               if (!tok) {
-                       isl_stream_error(s, NULL, "unexpected EOF");
-                       goto error;
-               }
-               if (tok->type != ISL_TOKEN_AND)
-                       break;
-               isl_token_free(tok);
-       }
-       isl_stream_push_token(s, tok);
+       map = isl_map_from_domain(isl_map_wrap(map));
+       map = read_defined_var_list(s, v, map, rational);
 
-       return bmap;
-error:
-       if (tok)
-               isl_token_free(tok);
-       isl_basic_map_free(bmap);
-       return NULL;
-}
-
-static struct isl_basic_map *read_disjunct(struct isl_stream *s,
-       struct vars *v, __isl_take isl_dim *dim)
-{
-       int seen_paren = 0;
-       struct isl_token *tok;
-       struct isl_basic_map *bmap;
-
-       bmap = isl_basic_map_alloc_dim(dim, 0, 0, 0);
-       if (!bmap)
-               return NULL;
-
-       tok = isl_stream_next_token(s);
-       if (!tok)
+       if (isl_stream_eat(s, ':'))
                goto error;
-       if (tok->type == '(') {
-               seen_paren = 1;
-               isl_token_free(tok);
-       } else
-               isl_stream_push_token(s, tok);
 
-       bmap = add_constraints(s, v, bmap);
-       bmap = isl_basic_map_simplify(bmap);
-       bmap = isl_basic_map_finalize(bmap);
+       map = read_disjuncts(s, v, map, rational);
+       map = isl_set_unwrap(isl_map_domain(map));
 
+       vars_drop(v, v->n - n);
        if (seen_paren && isl_stream_eat(s, ')'))
                goto error;
 
-       return bmap;
+       return map;
 error:
-       isl_basic_map_free(bmap);
+       isl_map_free(map);
        return NULL;
 }
 
-static struct isl_map *read_disjuncts(struct isl_stream *s,
-       struct vars *v, __isl_take isl_dim *dim)
+/* Parse an expression between parentheses and push the result
+ * back on the stream.
+ *
+ * The parsed expression may be either an affine expression
+ * or a condition.  The first type is pushed onto the stream
+ * as an isl_pw_aff, while the second is pushed as an isl_map.
+ *
+ * If the initial token indicates the start of a condition,
+ * we parse it as such.
+ * Otherwise, we first parse an affine expression and push
+ * that onto the stream.  If the affine expression covers the
+ * entire expression between parentheses, we return.
+ * Otherwise, we assume that the affine expression is the
+ * start of a condition and continue parsing.
+ */
+static int resolve_paren_expr(struct isl_stream *s,
+       struct vars *v, __isl_take isl_map *map, int rational)
 {
-       struct isl_token *tok;
-       struct isl_map *map;
+       struct isl_token *tok, *tok2;
+       int line, col;
+       isl_pw_aff *pwaff;
 
        tok = isl_stream_next_token(s);
-       if (!tok) {
-               isl_stream_error(s, NULL, "unexpected EOF");
+       if (!tok || tok->type != '(')
                goto error;
-       }
-       if (tok->type == '}') {
+
+       if (isl_stream_next_token_is(s, '('))
+               if (resolve_paren_expr(s, v, isl_map_copy(map), rational))
+                       goto error;
+
+       if (isl_stream_next_token_is(s, ISL_TOKEN_EXISTS) ||
+           isl_stream_next_token_is(s, ISL_TOKEN_NOT) ||
+           isl_stream_next_token_is(s, ISL_TOKEN_TRUE) ||
+           isl_stream_next_token_is(s, ISL_TOKEN_FALSE) ||
+           isl_stream_next_token_is(s, ISL_TOKEN_MAP)) {
+               map = read_disjuncts(s, v, map, rational);
+               if (isl_stream_eat(s, ')'))
+                       goto error;
+               tok->type = ISL_TOKEN_MAP;
+               tok->u.map = map;
                isl_stream_push_token(s, tok);
-               return isl_map_universe(dim);
+               return 0;
        }
-       isl_stream_push_token(s, tok);
 
-       map = isl_map_empty(isl_dim_copy(dim));
-       for (;;) {
-               struct isl_basic_map *bmap;
-               int n = v->n;
+       tok2 = isl_stream_next_token(s);
+       if (!tok2)
+               goto error;
+       line = tok2->line;
+       col = tok2->col;
+       isl_stream_push_token(s, tok2);
+
+       pwaff = accept_affine(s, isl_space_wrap(isl_map_get_space(map)), v);
+       if (!pwaff)
+               goto error;
 
-               bmap = read_disjunct(s, v, isl_dim_copy(dim));
-               map = isl_map_union(map, isl_map_from_basic_map(bmap));
+       tok2 = isl_token_new(s->ctx, line, col, 0);
+       if (!tok2)
+               goto error2;
+       tok2->type = ISL_TOKEN_AFF;
+       tok2->u.pwaff = pwaff;
 
-               vars_drop(v, v->n - n);
+       if (isl_stream_eat_if_available(s, ')')) {
+               isl_stream_push_token(s, tok2);
+               isl_token_free(tok);
+               isl_map_free(map);
+               return 0;
+       }
+
+       isl_stream_push_token(s, tok2);
+
+       map = read_disjuncts(s, v, map, rational);
+       if (isl_stream_eat(s, ')'))
+               goto error;
+
+       tok->type = ISL_TOKEN_MAP;
+       tok->u.map = map;
+       isl_stream_push_token(s, tok);
+
+       return 0;
+error2:
+       isl_pw_aff_free(pwaff);
+error:
+       isl_token_free(tok);
+       isl_map_free(map);
+       return -1;
+}
 
+static __isl_give isl_map *read_conjunct(struct isl_stream *s,
+       struct vars *v, __isl_take isl_map *map, int rational)
+{
+       if (isl_stream_next_token_is(s, '('))
+               if (resolve_paren_expr(s, v, isl_map_copy(map), rational))
+                       goto error;
+
+       if (isl_stream_next_token_is(s, ISL_TOKEN_MAP)) {
+               struct isl_token *tok;
                tok = isl_stream_next_token(s);
-               if (!tok || tok->type != ISL_TOKEN_OR)
-                       break;
+               if (!tok)
+                       goto error;
+               isl_map_free(map);
+               map = isl_map_copy(tok->u.map);
                isl_token_free(tok);
+               return map;
        }
-       if (tok)
-               isl_stream_push_token(s, tok);
 
-       isl_dim_free(dim);
-       return map;
+       if (isl_stream_eat_if_available(s, ISL_TOKEN_EXISTS))
+               return read_exists(s, v, map, rational);
+
+       if (isl_stream_eat_if_available(s, ISL_TOKEN_TRUE))
+               return map;
+
+       if (isl_stream_eat_if_available(s, ISL_TOKEN_FALSE)) {
+               isl_space *dim = isl_map_get_space(map);
+               isl_map_free(map);
+               return isl_map_empty(dim);
+       }
+               
+       return add_constraint(s, v, map, rational);
 error:
-       isl_dim_free(dim);
+       isl_map_free(map);
        return NULL;
 }
 
+static __isl_give isl_map *read_conjuncts(struct isl_stream *s,
+       struct vars *v, __isl_take isl_map *map, int rational)
+{
+       isl_map *res;
+       int negate;
+
+       negate = isl_stream_eat_if_available(s, ISL_TOKEN_NOT);
+       res = read_conjunct(s, v, isl_map_copy(map), rational);
+       if (negate)
+               res = isl_map_subtract(isl_map_copy(map), res);
+
+       while (res && isl_stream_eat_if_available(s, ISL_TOKEN_AND)) {
+               isl_map *res_i;
+
+               negate = isl_stream_eat_if_available(s, ISL_TOKEN_NOT);
+               res_i = read_conjunct(s, v, isl_map_copy(map), rational);
+               if (negate)
+                       res = isl_map_subtract(res, res_i);
+               else
+                       res = isl_map_intersect(res, res_i);
+       }
+
+       isl_map_free(map);
+       return res;
+}
+
+static struct isl_map *read_disjuncts(struct isl_stream *s,
+       struct vars *v, __isl_take isl_map *map, int rational)
+{
+       isl_map *res;
+
+       if (isl_stream_next_token_is(s, '}')) {
+               isl_space *dim = isl_map_get_space(map);
+               isl_map_free(map);
+               return isl_map_universe(dim);
+       }
+
+       res = read_conjuncts(s, v, isl_map_copy(map), rational);
+       while (isl_stream_eat_if_available(s, ISL_TOKEN_OR)) {
+               isl_map *res_i;
+
+               res_i = read_conjuncts(s, v, isl_map_copy(map), rational);
+               res = isl_map_union(res, res_i);
+       }
+
+       isl_map_free(map);
+       return res;
+}
+
 static int polylib_pos_to_isl_pos(__isl_keep isl_basic_map *bmap, int pos)
 {
        if (pos < isl_basic_map_dim(bmap, isl_dim_out))
@@ -923,8 +1565,7 @@ error:
        return NULL;
 }
 
-static __isl_give isl_basic_map *basic_map_read_polylib(struct isl_stream *s,
-       int nparam)
+static __isl_give isl_basic_map *basic_map_read_polylib(struct isl_stream *s)
 {
        int i;
        struct isl_token *tok;
@@ -933,9 +1574,7 @@ static __isl_give isl_basic_map *basic_map_read_polylib(struct isl_stream *s,
        int on_new_line;
        unsigned in = 0, out, local = 0;
        struct isl_basic_map *bmap = NULL;
-
-       if (nparam < 0)
-               nparam = 0;
+       int nparam = 0;
 
        tok = isl_stream_next_token(s);
        if (!tok) {
@@ -948,6 +1587,13 @@ static __isl_give isl_basic_map *basic_map_read_polylib(struct isl_stream *s,
                isl_stream_error(s, NULL, "unexpected EOF");
                return NULL;
        }
+       if (tok->type != ISL_TOKEN_VALUE || tok2->type != ISL_TOKEN_VALUE) {
+               isl_stream_push_token(s, tok2);
+               isl_stream_push_token(s, tok);
+               isl_stream_error(s, NULL,
+                                "expecting constraint matrix dimensions");
+               return NULL;
+       }
        n_row = isl_int_get_si(tok->u.v);
        n_col = isl_int_get_si(tok2->u.v);
        on_new_line = tok2->on_new_line;
@@ -1014,6 +1660,7 @@ static __isl_give isl_basic_map *basic_map_read_polylib(struct isl_stream *s,
                int k = isl_basic_map_alloc_div(bmap);
                if (k < 0)
                        goto error;
+               isl_seq_clr(bmap->div[k], 1 + 1 + nparam + in + out + local);
        }
 
        for (i = 0; i < n_row; ++i)
@@ -1034,7 +1681,7 @@ error:
        return NULL;
 }
 
-static struct isl_map *map_read_polylib(struct isl_stream *s, int nparam)
+static struct isl_map *map_read_polylib(struct isl_stream *s)
 {
        struct isl_token *tok;
        struct isl_token *tok2;
@@ -1047,21 +1694,27 @@ static struct isl_map *map_read_polylib(struct isl_stream *s, int nparam)
                return NULL;
        }
        tok2 = isl_stream_next_token_on_same_line(s);
+       if (tok2 && tok2->type == ISL_TOKEN_VALUE) {
+               isl_stream_push_token(s, tok2);
+               isl_stream_push_token(s, tok);
+               return isl_map_from_basic_map(basic_map_read_polylib(s));
+       }
        if (tok2) {
+               isl_stream_error(s, tok2, "unexpected token");
                isl_stream_push_token(s, tok2);
                isl_stream_push_token(s, tok);
-               return isl_map_from_basic_map(basic_map_read_polylib(s, nparam));
+               return NULL;
        }
        n = isl_int_get_si(tok->u.v);
        isl_token_free(tok);
 
        isl_assert(s->ctx, n >= 1, return NULL);
 
-       map = isl_map_from_basic_map(basic_map_read_polylib(s, nparam));
+       map = isl_map_from_basic_map(basic_map_read_polylib(s));
 
-       for (i = 1; i < n; ++i)
+       for (i = 1; map && i < n; ++i)
                map = isl_map_union(map,
-                       isl_map_from_basic_map(basic_map_read_polylib(s, nparam)));
+                       isl_map_from_basic_map(basic_map_read_polylib(s)));
 
        return map;
 }
@@ -1091,105 +1744,97 @@ static int optional_power(struct isl_stream *s)
        return pow;
 }
 
-static __isl_give isl_div *read_div(struct isl_stream *s,
-       __isl_keep isl_basic_map *bmap, struct vars *v)
-{
-       unsigned total = isl_basic_map_total_dim(bmap);
-       int k;
-
-       bmap = isl_basic_map_copy(bmap);
-       bmap = isl_basic_map_cow(bmap);
-       bmap = isl_basic_map_extend_dim(bmap, isl_dim_copy(bmap->dim),
-                                       1, 0, 2);
-
-       if ((k = isl_basic_map_alloc_div(bmap)) < 0)
-               goto error;
-       isl_seq_clr(bmap->div[k], 1 + 1 + total);
-       bmap = add_div_definition(s, v, bmap, k);
-
-       return isl_basic_map_div(bmap, k);
-error:
-       isl_basic_map_free(bmap);
-       return NULL;
-}
-
-static __isl_give isl_qpolynomial *read_term(struct isl_stream *s,
-       __isl_keep isl_basic_map *bmap, struct vars *v);
+static __isl_give isl_pw_qpolynomial *read_term(struct isl_stream *s,
+       __isl_keep isl_map *map, struct vars *v);
 
-static __isl_give isl_qpolynomial *read_factor(struct isl_stream *s,
-       __isl_keep isl_basic_map *bmap, struct vars *v)
+static __isl_give isl_pw_qpolynomial *read_factor(struct isl_stream *s,
+       __isl_keep isl_map *map, struct vars *v)
 {
-       struct isl_qpolynomial *qp;
+       isl_pw_qpolynomial *pwqp;
        struct isl_token *tok;
 
-       tok = isl_stream_next_token(s);
+       tok = next_token(s);
        if (!tok) {
                isl_stream_error(s, NULL, "unexpected EOF");
                return NULL;
        }
        if (tok->type == '(') {
+               int pow;
+
                isl_token_free(tok);
-               qp = read_term(s, bmap, v);
-               if (!qp)
+               pwqp = read_term(s, map, v);
+               if (!pwqp)
                        return NULL;
                if (isl_stream_eat(s, ')'))
                        goto error;
+               pow = optional_power(s);
+               pwqp = isl_pw_qpolynomial_pow(pwqp, pow);
        } else if (tok->type == ISL_TOKEN_VALUE) {
                struct isl_token *tok2;
+               isl_qpolynomial *qp;
+
                tok2 = isl_stream_next_token(s);
                if (tok2 && tok2->type == '/') {
                        isl_token_free(tok2);
-                       tok2 = isl_stream_next_token(s);
+                       tok2 = next_token(s);
                        if (!tok2 || tok2->type != ISL_TOKEN_VALUE) {
                                isl_stream_error(s, tok2, "expected denominator");
                                isl_token_free(tok);
                                isl_token_free(tok2);
                                return NULL;
                        }
-                       qp = isl_qpolynomial_rat_cst(isl_basic_map_get_dim(bmap),
+                       qp = isl_qpolynomial_rat_cst_on_domain(isl_map_get_space(map),
                                                    tok->u.v, tok2->u.v);
                        isl_token_free(tok2);
                } else {
                        isl_stream_push_token(s, tok2);
-                       qp = isl_qpolynomial_cst(isl_basic_map_get_dim(bmap),
+                       qp = isl_qpolynomial_cst_on_domain(isl_map_get_space(map),
                                                tok->u.v);
                }
                isl_token_free(tok);
+               pwqp = isl_pw_qpolynomial_from_qpolynomial(qp);
        } else if (tok->type == ISL_TOKEN_INFTY) {
+               isl_qpolynomial *qp;
                isl_token_free(tok);
-               qp = isl_qpolynomial_infty(isl_basic_map_get_dim(bmap));
+               qp = isl_qpolynomial_infty_on_domain(isl_map_get_space(map));
+               pwqp = isl_pw_qpolynomial_from_qpolynomial(qp);
        } else if (tok->type == ISL_TOKEN_NAN) {
+               isl_qpolynomial *qp;
                isl_token_free(tok);
-               qp = isl_qpolynomial_nan(isl_basic_map_get_dim(bmap));
+               qp = isl_qpolynomial_nan_on_domain(isl_map_get_space(map));
+               pwqp = isl_pw_qpolynomial_from_qpolynomial(qp);
        } else if (tok->type == ISL_TOKEN_IDENT) {
                int n = v->n;
                int pos = vars_pos(v, tok->u.s, -1);
                int pow;
-               isl_token_free(tok);
-               if (pos < 0)
-                       goto error;
+               isl_qpolynomial *qp;
+               if (pos < 0) {
+                       isl_token_free(tok);
+                       return NULL;
+               }
                if (pos >= n) {
+                       vars_drop(v, v->n - n);
                        isl_stream_error(s, tok, "unknown identifier");
+                       isl_token_free(tok);
                        return NULL;
                }
+               isl_token_free(tok);
                pow = optional_power(s);
-               qp = isl_qpolynomial_pow(isl_basic_map_get_dim(bmap), pos, pow);
+               qp = isl_qpolynomial_var_pow_on_domain(isl_map_get_space(map), pos, pow);
+               pwqp = isl_pw_qpolynomial_from_qpolynomial(qp);
        } else if (tok->type == '[') {
-               isl_div *div;
+               isl_pw_aff *pwaff;
                int pow;
 
                isl_stream_push_token(s, tok);
-               div = read_div(s, bmap, v);
+               pwaff = accept_div(s, isl_map_get_space(map), v);
                pow = optional_power(s);
-               qp = isl_qpolynomial_div_pow(div, pow);
+               pwqp = isl_pw_qpolynomial_from_pw_aff(pwaff);
+               pwqp = isl_pw_qpolynomial_pow(pwqp, pow);
        } else if (tok->type == '-') {
-               struct isl_qpolynomial *qp2;
-
                isl_token_free(tok);
-               qp = isl_qpolynomial_cst(isl_basic_map_get_dim(bmap),
-                                           s->ctx->negone);
-               qp2 = read_factor(s, bmap, v);
-               qp = isl_qpolynomial_mul(qp, qp2);
+               pwqp = read_factor(s, map, v);
+               pwqp = isl_pw_qpolynomial_neg(pwqp);
        } else {
                isl_stream_error(s, tok, "unexpected isl_token");
                isl_stream_push_token(s, tok);
@@ -1198,103 +1843,94 @@ static __isl_give isl_qpolynomial *read_factor(struct isl_stream *s,
 
        if (isl_stream_eat_if_available(s, '*') ||
            isl_stream_next_token_is(s, ISL_TOKEN_IDENT)) {
-               struct isl_qpolynomial *qp2;
+               isl_pw_qpolynomial *pwqp2;
 
-               qp2 = read_factor(s, bmap, v);
-               qp = isl_qpolynomial_mul(qp, qp2);
+               pwqp2 = read_factor(s, map, v);
+               pwqp = isl_pw_qpolynomial_mul(pwqp, pwqp2);
        }
 
-       return qp;
+       return pwqp;
 error:
-       isl_qpolynomial_free(qp);
+       isl_pw_qpolynomial_free(pwqp);
        return NULL;
 }
 
-static __isl_give isl_qpolynomial *read_term(struct isl_stream *s,
-       __isl_keep isl_basic_map *bmap, struct vars *v)
+static __isl_give isl_pw_qpolynomial *read_term(struct isl_stream *s,
+       __isl_keep isl_map *map, struct vars *v)
 {
        struct isl_token *tok;
-       struct isl_qpolynomial *qp;
+       isl_pw_qpolynomial *pwqp;
 
-       qp = read_factor(s, bmap, v);
+       pwqp = read_factor(s, map, v);
 
        for (;;) {
-               tok = isl_stream_next_token(s);
+               tok = next_token(s);
                if (!tok)
-                       return qp;
+                       return pwqp;
 
                if (tok->type == '+') {
-                       struct isl_qpolynomial *qp2;
+                       isl_pw_qpolynomial *pwqp2;
 
                        isl_token_free(tok);
-                       qp2 = read_factor(s, bmap, v);
-                       qp = isl_qpolynomial_add(qp, qp2);
+                       pwqp2 = read_factor(s, map, v);
+                       pwqp = isl_pw_qpolynomial_add(pwqp, pwqp2);
                } else if (tok->type == '-') {
-                       struct isl_qpolynomial *qp2;
+                       isl_pw_qpolynomial *pwqp2;
 
                        isl_token_free(tok);
-                       qp2 = read_factor(s, bmap, v);
-                       qp = isl_qpolynomial_sub(qp, qp2);
+                       pwqp2 = read_factor(s, map, v);
+                       pwqp = isl_pw_qpolynomial_sub(pwqp, pwqp2);
                } else if (tok->type == ISL_TOKEN_VALUE &&
                            isl_int_is_neg(tok->u.v)) {
-                       struct isl_qpolynomial *qp2;
+                       isl_pw_qpolynomial *pwqp2;
 
-                       qp2 = isl_qpolynomial_cst(isl_basic_map_get_dim(bmap),
-                                                       tok->u.v);
-                       isl_token_free(tok);
-                       qp = isl_qpolynomial_add(qp, qp2);
+                       isl_stream_push_token(s, tok);
+                       pwqp2 = read_factor(s, map, v);
+                       pwqp = isl_pw_qpolynomial_add(pwqp, pwqp2);
                } else {
                        isl_stream_push_token(s, tok);
                        break;
                }
        }
 
-       return qp;
+       return pwqp;
 }
 
 static __isl_give isl_map *read_optional_disjuncts(struct isl_stream *s,
-       __isl_take isl_basic_map *bmap, struct vars *v)
+       __isl_take isl_map *map, struct vars *v, int rational)
 {
        struct isl_token *tok;
-       struct isl_map *map;
 
        tok = isl_stream_next_token(s);
        if (!tok) {
                isl_stream_error(s, NULL, "unexpected EOF");
                goto error;
        }
-       map = isl_map_from_basic_map(isl_basic_map_copy(bmap));
-       if (tok->type == ':') {
+       if (tok->type == ':' ||
+           (tok->type == ISL_TOKEN_OR && !strcmp(tok->u.s, "|"))) {
                isl_token_free(tok);
-               map = isl_map_intersect(map,
-                           read_disjuncts(s, v, isl_basic_map_get_dim(bmap)));
+               map = read_disjuncts(s, v, map, rational);
        } else
                isl_stream_push_token(s, tok);
 
-       isl_basic_map_free(bmap);
-
        return map;
 error:
-       isl_basic_map_free(bmap);
+       isl_map_free(map);
        return NULL;
 }
 
 static struct isl_obj obj_read_poly(struct isl_stream *s,
-       __isl_take isl_basic_map *bmap, struct vars *v, int n)
+       __isl_take isl_map *map, struct vars *v, int n)
 {
        struct isl_obj obj = { isl_obj_pw_qpolynomial, NULL };
-       struct isl_pw_qpolynomial *pwqp;
-       struct isl_qpolynomial *qp;
-       struct isl_map *map;
+       isl_pw_qpolynomial *pwqp;
        struct isl_set *set;
 
-       bmap = isl_basic_map_reverse(bmap);
+       pwqp = read_term(s, map, v);
+       map = read_optional_disjuncts(s, map, v, 0);
+       set = isl_map_range(map);
 
-       qp = read_term(s, bmap, v);
-       map = read_optional_disjuncts(s, bmap, v);
-       set = isl_set_from_map(map);
-
-       pwqp = isl_pw_qpolynomial_alloc(set, qp);
+       pwqp = isl_pw_qpolynomial_intersect_domain(pwqp, set);
 
        vars_drop(v, v->n - n);
 
@@ -1302,47 +1938,138 @@ static struct isl_obj obj_read_poly(struct isl_stream *s,
        return obj;
 }
 
+static struct isl_obj obj_read_poly_or_fold(struct isl_stream *s,
+       __isl_take isl_set *set, struct vars *v, int n)
+{
+       struct isl_obj obj = { isl_obj_pw_qpolynomial_fold, NULL };
+       isl_pw_qpolynomial *pwqp;
+       isl_pw_qpolynomial_fold *pwf = NULL;
+
+       if (!isl_stream_eat_if_available(s, ISL_TOKEN_MAX))
+               return obj_read_poly(s, set, v, n);
+
+       if (isl_stream_eat(s, '('))
+               goto error;
+
+       pwqp = read_term(s, set, v);
+       pwf = isl_pw_qpolynomial_fold_from_pw_qpolynomial(isl_fold_max, pwqp);
+
+       while (isl_stream_eat_if_available(s, ',')) {
+               isl_pw_qpolynomial_fold *pwf_i;
+               pwqp = read_term(s, set, v);
+               pwf_i = isl_pw_qpolynomial_fold_from_pw_qpolynomial(isl_fold_max,
+                                                                       pwqp);
+               pwf = isl_pw_qpolynomial_fold_fold(pwf, pwf_i);
+       }
+
+       if (isl_stream_eat(s, ')'))
+               goto error;
+
+       set = read_optional_disjuncts(s, set, v, 0);
+       pwf = isl_pw_qpolynomial_fold_intersect_domain(pwf, set);
+
+       vars_drop(v, v->n - n);
+
+       obj.v = pwf;
+       return obj;
+error:
+       isl_set_free(set);
+       isl_pw_qpolynomial_fold_free(pwf);
+       obj.type = isl_obj_none;
+       return obj;
+}
+
+static int is_rational(struct isl_stream *s)
+{
+       struct isl_token *tok;
+
+       tok = isl_stream_next_token(s);
+       if (!tok)
+               return 0;
+       if (tok->type == ISL_TOKEN_RAT && isl_stream_next_token_is(s, ':')) {
+               isl_token_free(tok);
+               isl_stream_eat(s, ':');
+               return 1;
+       }
+
+       isl_stream_push_token(s, tok);
+
+       return 0;
+}
+
 static struct isl_obj obj_read_body(struct isl_stream *s,
-       __isl_take isl_basic_map *bmap, struct vars *v, isl_obj_type type)
+       __isl_take isl_map *map, struct vars *v)
 {
-       struct isl_map *map = NULL;
        struct isl_token *tok;
-       struct isl_obj obj = { type, NULL };
+       struct isl_obj obj = { isl_obj_set, NULL };
        int n = v->n;
+       int rational;
 
-       if (!isl_stream_next_token_is(s, '['))
-               return obj_read_poly(s, bmap, v, n);
+       rational = is_rational(s);
+       if (rational)
+               map = isl_map_set_rational(map);
 
-       bmap = read_tuple(s, bmap, isl_dim_in, v);
-       if (!bmap)
+       if (isl_stream_next_token_is(s, ':')) {
+               obj.type = isl_obj_set;
+               obj.v = read_optional_disjuncts(s, map, v, rational);
+               return obj;
+       }
+
+       if (!next_is_tuple(s))
+               return obj_read_poly_or_fold(s, map, v, n);
+
+       map = read_map_tuple(s, map, isl_dim_in, v, rational, 0);
+       if (!map)
                goto error;
        tok = isl_stream_next_token(s);
-       if (tok && tok->type == ISL_TOKEN_TO) {
+       if (!tok)
+               goto error;
+       if (tok->type == ISL_TOKEN_TO) {
                obj.type = isl_obj_map;
                isl_token_free(tok);
-               tok = isl_stream_next_token(s);
-               if (tok && tok->type != '[') {
-                       isl_stream_push_token(s, tok);
-                       return obj_read_poly(s, bmap, v, n);
+               if (!next_is_tuple(s)) {
+                       isl_set *set = isl_map_domain(map);
+                       return obj_read_poly_or_fold(s, set, v, n);
                }
-               isl_stream_push_token(s, tok);
-               bmap = read_tuple(s, bmap, isl_dim_out, v);
-               if (!bmap)
+               map = read_map_tuple(s, map, isl_dim_out, v, rational, 0);
+               if (!map)
                        goto error;
        } else {
-               bmap = isl_basic_map_reverse(bmap);
-               if (tok)
-                       isl_stream_push_token(s, tok);
+               map = isl_map_domain(map);
+               isl_stream_push_token(s, tok);
        }
 
-       map = read_optional_disjuncts(s, bmap, v);
+       map = read_optional_disjuncts(s, map, v, rational);
 
        vars_drop(v, v->n - n);
 
        obj.v = map;
        return obj;
 error:
-       isl_basic_map_free(bmap);
+       isl_map_free(map);
+       obj.type = isl_obj_none;
+       return obj;
+}
+
+static struct isl_obj to_union(isl_ctx *ctx, struct isl_obj obj)
+{
+       if (obj.type == isl_obj_map) {
+               obj.v = isl_union_map_from_map(obj.v);
+               obj.type = isl_obj_union_map;
+       } else if (obj.type == isl_obj_set) {
+               obj.v = isl_union_set_from_set(obj.v);
+               obj.type = isl_obj_union_set;
+       } else if (obj.type == isl_obj_pw_qpolynomial) {
+               obj.v = isl_union_pw_qpolynomial_from_pw_qpolynomial(obj.v);
+               obj.type = isl_obj_union_pw_qpolynomial;
+       } else if (obj.type == isl_obj_pw_qpolynomial_fold) {
+               obj.v = isl_union_pw_qpolynomial_fold_from_pw_qpolynomial_fold(obj.v);
+               obj.type = isl_obj_union_pw_qpolynomial_fold;
+       } else
+               isl_assert(ctx, 0, goto error);
+       return obj;
+error:
+       obj.type->free(obj.v);
        obj.type = isl_obj_none;
        return obj;
 }
@@ -1350,7 +2077,45 @@ error:
 static struct isl_obj obj_add(struct isl_ctx *ctx,
        struct isl_obj obj1, struct isl_obj obj2)
 {
+       if (obj1.type == isl_obj_set && obj2.type == isl_obj_union_set)
+               obj1 = to_union(ctx, obj1);
+       if (obj1.type == isl_obj_union_set && obj2.type == isl_obj_set)
+               obj2 = to_union(ctx, obj2);
+       if (obj1.type == isl_obj_map && obj2.type == isl_obj_union_map)
+               obj1 = to_union(ctx, obj1);
+       if (obj1.type == isl_obj_union_map && obj2.type == isl_obj_map)
+               obj2 = to_union(ctx, obj2);
+       if (obj1.type == isl_obj_pw_qpolynomial &&
+           obj2.type == isl_obj_union_pw_qpolynomial)
+               obj1 = to_union(ctx, obj1);
+       if (obj1.type == isl_obj_union_pw_qpolynomial &&
+           obj2.type == isl_obj_pw_qpolynomial)
+               obj2 = to_union(ctx, obj2);
+       if (obj1.type == isl_obj_pw_qpolynomial_fold &&
+           obj2.type == isl_obj_union_pw_qpolynomial_fold)
+               obj1 = to_union(ctx, obj1);
+       if (obj1.type == isl_obj_union_pw_qpolynomial_fold &&
+           obj2.type == isl_obj_pw_qpolynomial_fold)
+               obj2 = to_union(ctx, obj2);
        isl_assert(ctx, obj1.type == obj2.type, goto error);
+       if (obj1.type == isl_obj_map && !isl_map_has_equal_space(obj1.v, obj2.v)) {
+               obj1 = to_union(ctx, obj1);
+               obj2 = to_union(ctx, obj2);
+       }
+       if (obj1.type == isl_obj_set && !isl_set_has_equal_space(obj1.v, obj2.v)) {
+               obj1 = to_union(ctx, obj1);
+               obj2 = to_union(ctx, obj2);
+       }
+       if (obj1.type == isl_obj_pw_qpolynomial &&
+           !isl_pw_qpolynomial_has_equal_space(obj1.v, obj2.v)) {
+               obj1 = to_union(ctx, obj1);
+               obj2 = to_union(ctx, obj2);
+       }
+       if (obj1.type == isl_obj_pw_qpolynomial_fold &&
+           !isl_pw_qpolynomial_fold_has_equal_space(obj1.v, obj2.v)) {
+               obj1 = to_union(ctx, obj1);
+               obj2 = to_union(ctx, obj2);
+       }
        obj1.v = obj1.type->add(obj1.v, obj2.v);
        return obj1;
 error:
@@ -1361,38 +2126,56 @@ error:
        return obj1;
 }
 
-static struct isl_obj obj_read(struct isl_stream *s, int nparam)
+static struct isl_obj obj_read(struct isl_stream *s)
 {
-       struct isl_basic_map *bmap = NULL;
+       isl_map *map = NULL;
        struct isl_token *tok;
        struct vars *v = NULL;
        struct isl_obj obj = { isl_obj_set, NULL };
 
-       tok = isl_stream_next_token(s);
+       tok = next_token(s);
        if (!tok) {
                isl_stream_error(s, NULL, "unexpected EOF");
                goto error;
        }
        if (tok->type == ISL_TOKEN_VALUE) {
+               struct isl_token *tok2;
                struct isl_map *map;
+
+               tok2 = isl_stream_next_token(s);
+               if (!tok2 || tok2->type != ISL_TOKEN_VALUE ||
+                   isl_int_is_neg(tok2->u.v)) {
+                       if (tok2)
+                               isl_stream_push_token(s, tok2);
+                       obj.type = isl_obj_int;
+                       obj.v = isl_int_obj_alloc(s->ctx, tok->u.v);
+                       isl_token_free(tok);
+                       return obj;
+               }
+               isl_stream_push_token(s, tok2);
                isl_stream_push_token(s, tok);
-               map = map_read_polylib(s, nparam);
+               map = map_read_polylib(s);
                if (!map)
                        goto error;
-               if (isl_map_dim(map, isl_dim_in) > 0)
+               if (isl_map_may_be_set(map))
+                       obj.v = isl_map_range(map);
+               else {
                        obj.type = isl_obj_map;
-               obj.v = map;
+                       obj.v = map;
+               }
                return obj;
        }
        v = vars_new(s->ctx);
-       bmap = isl_basic_map_alloc(s->ctx, 0, 0, 0, 0, 0, 0);
+       if (!v) {
+               isl_stream_push_token(s, tok);
+               goto error;
+       }
+       map = isl_map_universe(isl_space_params_alloc(s->ctx, 0));
        if (tok->type == '[') {
                isl_stream_push_token(s, tok);
-               bmap = read_tuple(s, bmap, isl_dim_param, v);
-               if (!bmap)
+               map = read_map_tuple(s, map, isl_dim_param, v, 0, 0);
+               if (!map)
                        goto error;
-               if (nparam >= 0)
-                       isl_assert(s->ctx, nparam == v->n, goto error);
                tok = isl_stream_next_token(s);
                if (!tok || tok->type != ISL_TOKEN_TO) {
                        isl_stream_error(s, tok, "expecting '->'");
@@ -1402,8 +2185,7 @@ static struct isl_obj obj_read(struct isl_stream *s, int nparam)
                }
                isl_token_free(tok);
                tok = isl_stream_next_token(s);
-       } else if (nparam > 0)
-               bmap = isl_basic_map_add(bmap, isl_dim_param, nparam);
+       }
        if (!tok || tok->type != '{') {
                isl_stream_error(s, tok, "expecting '{'");
                if (tok)
@@ -1419,31 +2201,38 @@ static struct isl_obj obj_read(struct isl_stream *s, int nparam)
                isl_token_free(tok);
                if (isl_stream_eat(s, '='))
                        goto error;
-               bmap = read_tuple(s, bmap, isl_dim_param, v);
-               if (!bmap)
+               map = read_map_tuple(s, map, isl_dim_param, v, 0, 1);
+               if (!map)
                        goto error;
-               if (nparam >= 0)
-                       isl_assert(s->ctx, nparam == v->n, goto error);
+       } else if (tok->type == '}') {
+               obj.type = isl_obj_union_set;
+               obj.v = isl_union_set_empty(isl_map_get_space(map));
+               isl_token_free(tok);
+               goto done;
        } else
                isl_stream_push_token(s, tok);
 
        for (;;) {
                struct isl_obj o;
                tok = NULL;
-               o = obj_read_body(s, isl_basic_map_copy(bmap), v, obj.type);
-               if (o.type == isl_obj_none)
-                       break;
+               o = obj_read_body(s, isl_map_copy(map), v);
+               if (o.type == isl_obj_none || !o.v)
+                       goto error;
                if (!obj.v)
                        obj = o;
                else {
                        obj = obj_add(s->ctx, obj, o);
-                       if (obj.type == isl_obj_none)
-                               break;
+                       if (obj.type == isl_obj_none || !obj.v)
+                               goto error;
                }
                tok = isl_stream_next_token(s);
                if (!tok || tok->type != ';')
                        break;
                isl_token_free(tok);
+               if (isl_stream_next_token_is(s, '}')) {
+                       tok = isl_stream_next_token(s);
+                       break;
+               }
        }
 
        if (tok && tok->type == '}') {
@@ -1454,12 +2243,13 @@ static struct isl_obj obj_read(struct isl_stream *s, int nparam)
                        isl_token_free(tok);
                goto error;
        }
+done:
        vars_free(v);
-       isl_basic_map_free(bmap);
+       isl_map_free(map);
 
        return obj;
 error:
-       isl_basic_map_free(bmap);
+       isl_map_free(map);
        obj.type->free(obj.v);
        if (v)
                vars_free(v);
@@ -1469,18 +2259,20 @@ error:
 
 struct isl_obj isl_stream_read_obj(struct isl_stream *s)
 {
-       return obj_read(s, -1);
+       return obj_read(s);
 }
 
-__isl_give isl_map *isl_stream_read_map(struct isl_stream *s, int nparam)
+__isl_give isl_map *isl_stream_read_map(struct isl_stream *s)
 {
        struct isl_obj obj;
-       struct isl_map *map;
 
-       obj = obj_read(s, nparam);
+       obj = obj_read(s);
        if (obj.v)
                isl_assert(s->ctx, obj.type == isl_obj_map ||
                                   obj.type == isl_obj_set, goto error);
+       
+       if (obj.type == isl_obj_set)
+               obj.v = isl_map_from_range(obj.v);
 
        return obj.v;
 error:
@@ -1488,14 +2280,18 @@ error:
        return NULL;
 }
 
-__isl_give isl_set *isl_stream_read_set(struct isl_stream *s, int nparam)
+__isl_give isl_set *isl_stream_read_set(struct isl_stream *s)
 {
        struct isl_obj obj;
-       struct isl_set *set;
 
-       obj = obj_read(s, nparam);
-       if (obj.v)
+       obj = obj_read(s);
+       if (obj.v) {
+               if (obj.type == isl_obj_map && isl_map_may_be_set(obj.v)) {
+                       obj.v = isl_map_range(obj.v);
+                       obj.type = isl_obj_set;
+               }
                isl_assert(s->ctx, obj.type == isl_obj_set, goto error);
+       }
 
        return obj.v;
 error:
@@ -1503,199 +2299,291 @@ error:
        return NULL;
 }
 
-static struct isl_basic_map *basic_map_read(struct isl_stream *s, int nparam)
+__isl_give isl_union_map *isl_stream_read_union_map(struct isl_stream *s)
 {
        struct isl_obj obj;
-       struct isl_map *map;
-       struct isl_basic_map *bmap;
-
-       obj = obj_read(s, nparam);
-       map = obj.v;
-       if (!map)
-               return NULL;
-
-       isl_assert(map->ctx, map->n <= 1, goto error);
-
-       if (map->n == 0)
-               bmap = isl_basic_map_empty_like_map(map);
-       else
-               bmap = isl_basic_map_copy(map->p[0]);
 
-       isl_map_free(map);
+       obj = obj_read(s);
+       if (obj.type == isl_obj_map) {
+               obj.type = isl_obj_union_map;
+               obj.v = isl_union_map_from_map(obj.v);
+       }
+       if (obj.type == isl_obj_set) {
+               obj.type = isl_obj_union_set;
+               obj.v = isl_union_set_from_set(obj.v);
+       }
+       if (obj.v && obj.type == isl_obj_union_set &&
+           isl_union_set_is_empty(obj.v))
+               obj.type = isl_obj_union_map;
+       if (obj.v && obj.type != isl_obj_union_map)
+               isl_die(s->ctx, isl_error_invalid, "invalid input", goto error);
 
-       return bmap;
+       return obj.v;
 error:
-       isl_map_free(map);
+       obj.type->free(obj.v);
+       return NULL;
+}
+
+__isl_give isl_union_set *isl_stream_read_union_set(struct isl_stream *s)
+{
+       struct isl_obj obj;
+
+       obj = obj_read(s);
+       if (obj.type == isl_obj_set) {
+               obj.type = isl_obj_union_set;
+               obj.v = isl_union_set_from_set(obj.v);
+       }
+       if (obj.v)
+               isl_assert(s->ctx, obj.type == isl_obj_union_set, goto error);
+
+       return obj.v;
+error:
+       obj.type->free(obj.v);
+       return NULL;
+}
+
+static __isl_give isl_basic_map *basic_map_read(struct isl_stream *s)
+{
+       struct isl_obj obj;
+       struct isl_map *map;
+       struct isl_basic_map *bmap;
+
+       obj = obj_read(s);
+       map = obj.v;
+       if (!map)
+               return NULL;
+
+       isl_assert(map->ctx, map->n <= 1, goto error);
+
+       if (map->n == 0)
+               bmap = isl_basic_map_empty_like_map(map);
+       else
+               bmap = isl_basic_map_copy(map->p[0]);
+
+       isl_map_free(map);
+
+       return bmap;
+error:
+       isl_map_free(map);
+       return NULL;
+}
+
+static __isl_give isl_basic_set *basic_set_read(struct isl_stream *s)
+{
+       isl_basic_map *bmap;
+       bmap = basic_map_read(s);
+       if (!bmap)
+               return NULL;
+       if (!isl_basic_map_may_be_set(bmap))
+               isl_die(s->ctx, isl_error_invalid,
+                       "input is not a set", goto error);
+       return isl_basic_map_range(bmap);
+error:
+       isl_basic_map_free(bmap);
        return NULL;
 }
 
 __isl_give isl_basic_map *isl_basic_map_read_from_file(isl_ctx *ctx,
-               FILE *input, int nparam)
+       FILE *input)
 {
        struct isl_basic_map *bmap;
        struct isl_stream *s = isl_stream_new_file(ctx, input);
        if (!s)
                return NULL;
-       bmap = basic_map_read(s, nparam);
+       bmap = basic_map_read(s);
        isl_stream_free(s);
        return bmap;
 }
 
 __isl_give isl_basic_set *isl_basic_set_read_from_file(isl_ctx *ctx,
-               FILE *input, int nparam)
+       FILE *input)
 {
-       struct isl_basic_map *bmap;
-       bmap = isl_basic_map_read_from_file(ctx, input, nparam);
-       if (!bmap)
+       isl_basic_set *bset;
+       struct isl_stream *s = isl_stream_new_file(ctx, input);
+       if (!s)
                return NULL;
-       isl_assert(ctx, isl_basic_map_n_in(bmap) == 0, goto error);
-       return (struct isl_basic_set *)bmap;
-error:
-       isl_basic_map_free(bmap);
-       return NULL;
+       bset = basic_set_read(s);
+       isl_stream_free(s);
+       return bset;
 }
 
 struct isl_basic_map *isl_basic_map_read_from_str(struct isl_ctx *ctx,
-               const char *str, int nparam)
+       const char *str)
 {
        struct isl_basic_map *bmap;
        struct isl_stream *s = isl_stream_new_str(ctx, str);
        if (!s)
                return NULL;
-       bmap = basic_map_read(s, nparam);
+       bmap = basic_map_read(s);
        isl_stream_free(s);
        return bmap;
 }
 
 struct isl_basic_set *isl_basic_set_read_from_str(struct isl_ctx *ctx,
-               const char *str, int nparam)
+       const char *str)
 {
-       struct isl_basic_map *bmap;
-       bmap = isl_basic_map_read_from_str(ctx, str, nparam);
-       if (!bmap)
+       isl_basic_set *bset;
+       struct isl_stream *s = isl_stream_new_str(ctx, str);
+       if (!s)
                return NULL;
-       isl_assert(ctx, isl_basic_map_n_in(bmap) == 0, goto error);
-       return (struct isl_basic_set *)bmap;
-error:
-       isl_basic_map_free(bmap);
-       return NULL;
+       bset = basic_set_read(s);
+       isl_stream_free(s);
+       return bset;
 }
 
 __isl_give isl_map *isl_map_read_from_file(struct isl_ctx *ctx,
-               FILE *input, int nparam)
+       FILE *input)
 {
        struct isl_map *map;
        struct isl_stream *s = isl_stream_new_file(ctx, input);
        if (!s)
                return NULL;
-       map = isl_stream_read_map(s, nparam);
+       map = isl_stream_read_map(s);
        isl_stream_free(s);
        return map;
 }
 
 __isl_give isl_map *isl_map_read_from_str(struct isl_ctx *ctx,
-               const char *str, int nparam)
+       const char *str)
 {
        struct isl_map *map;
        struct isl_stream *s = isl_stream_new_str(ctx, str);
        if (!s)
                return NULL;
-       map = isl_stream_read_map(s, nparam);
+       map = isl_stream_read_map(s);
        isl_stream_free(s);
        return map;
 }
 
 __isl_give isl_set *isl_set_read_from_file(struct isl_ctx *ctx,
-               FILE *input, int nparam)
+       FILE *input)
 {
-       struct isl_map *map;
-       map = isl_map_read_from_file(ctx, input, nparam);
-       if (!map)
+       isl_set *set;
+       struct isl_stream *s = isl_stream_new_file(ctx, input);
+       if (!s)
                return NULL;
-       isl_assert(ctx, isl_map_n_in(map) == 0, goto error);
-       return (struct isl_set *)map;
-error:
-       isl_map_free(map);
-       return NULL;
+       set = isl_stream_read_set(s);
+       isl_stream_free(s);
+       return set;
 }
 
 struct isl_set *isl_set_read_from_str(struct isl_ctx *ctx,
-               const char *str, int nparam)
+       const char *str)
 {
-       struct isl_map *map;
-       map = isl_map_read_from_str(ctx, str, nparam);
-       if (!map)
+       isl_set *set;
+       struct isl_stream *s = isl_stream_new_str(ctx, str);
+       if (!s)
                return NULL;
-       isl_assert(ctx, isl_map_n_in(map) == 0, goto error);
-       return (struct isl_set *)map;
-error:
-       isl_map_free(map);
-       return NULL;
+       set = isl_stream_read_set(s);
+       isl_stream_free(s);
+       return set;
 }
 
-static char *next_line(FILE *input, char *line, unsigned len)
+__isl_give isl_union_map *isl_union_map_read_from_file(isl_ctx *ctx,
+       FILE *input)
 {
-       char *p;
+       isl_union_map *umap;
+       struct isl_stream *s = isl_stream_new_file(ctx, input);
+       if (!s)
+               return NULL;
+       umap = isl_stream_read_union_map(s);
+       isl_stream_free(s);
+       return umap;
+}
 
-       do {
-               if (!(p = fgets(line, len, input)))
-                       return NULL;
-               while (isspace(*p) && *p != '\n')
-                       ++p;
-       } while (*p == '#' || *p == '\n');
+__isl_give isl_union_map *isl_union_map_read_from_str(struct isl_ctx *ctx,
+               const char *str)
+{
+       isl_union_map *umap;
+       struct isl_stream *s = isl_stream_new_str(ctx, str);
+       if (!s)
+               return NULL;
+       umap = isl_stream_read_union_map(s);
+       isl_stream_free(s);
+       return umap;
+}
 
-       return p;
+__isl_give isl_union_set *isl_union_set_read_from_file(isl_ctx *ctx,
+       FILE *input)
+{
+       isl_union_set *uset;
+       struct isl_stream *s = isl_stream_new_file(ctx, input);
+       if (!s)
+               return NULL;
+       uset = isl_stream_read_union_set(s);
+       isl_stream_free(s);
+       return uset;
 }
 
-static struct isl_vec *isl_vec_read_from_file_polylib(struct isl_ctx *ctx,
-               FILE *input)
+__isl_give isl_union_set *isl_union_set_read_from_str(struct isl_ctx *ctx,
+               const char *str)
+{
+       isl_union_set *uset;
+       struct isl_stream *s = isl_stream_new_str(ctx, str);
+       if (!s)
+               return NULL;
+       uset = isl_stream_read_union_set(s);
+       isl_stream_free(s);
+       return uset;
+}
+
+static __isl_give isl_vec *isl_vec_read_polylib(struct isl_stream *s)
 {
        struct isl_vec *vec = NULL;
-       char line[1024];
-       char val[1024];
-       char *p;
+       struct isl_token *tok;
        unsigned size;
        int j;
-       int n;
-       int offset;
 
-       isl_assert(ctx, next_line(input, line, sizeof(line)), return NULL);
-       isl_assert(ctx, sscanf(line, "%u", &size) == 1, return NULL);
+       tok = isl_stream_next_token(s);
+       if (!tok || tok->type != ISL_TOKEN_VALUE) {
+               isl_stream_error(s, tok, "expecting vector length");
+               goto error;
+       }
 
-       vec = isl_vec_alloc(ctx, size);
+       size = isl_int_get_si(tok->u.v);
+       isl_token_free(tok);
 
-       p = next_line(input, line, sizeof(line));
-       isl_assert(ctx, p, goto error);
+       vec = isl_vec_alloc(s->ctx, size);
 
        for (j = 0; j < size; ++j) {
-               n = sscanf(p, "%s%n", val, &offset);
-               isl_assert(ctx, n != 0, goto error);
-               isl_int_read(vec->el[j], val);
-               p += offset;
+               tok = isl_stream_next_token(s);
+               if (!tok || tok->type != ISL_TOKEN_VALUE) {
+                       isl_stream_error(s, tok, "expecting constant value");
+                       goto error;
+               }
+               isl_int_set(vec->el[j], tok->u.v);
+               isl_token_free(tok);
        }
 
        return vec;
 error:
+       isl_token_free(tok);
        isl_vec_free(vec);
        return NULL;
 }
 
-struct isl_vec *isl_vec_read_from_file(struct isl_ctx *ctx,
-               FILE *input, unsigned input_format)
+static __isl_give isl_vec *vec_read(struct isl_stream *s)
 {
-       if (input_format == ISL_FORMAT_POLYLIB)
-               return isl_vec_read_from_file_polylib(ctx, input);
-       else
-               isl_assert(ctx, 0, return NULL);
+       return isl_vec_read_polylib(s);
+}
+
+__isl_give isl_vec *isl_vec_read_from_file(isl_ctx *ctx, FILE *input)
+{
+       isl_vec *v;
+       struct isl_stream *s = isl_stream_new_file(ctx, input);
+       if (!s)
+               return NULL;
+       v = vec_read(s);
+       isl_stream_free(s);
+       return v;
 }
 
 __isl_give isl_pw_qpolynomial *isl_stream_read_pw_qpolynomial(
        struct isl_stream *s)
 {
        struct isl_obj obj;
-       struct isl_pw_qpolynomial *pwqp;
 
-       obj = obj_read(s, -1);
+       obj = obj_read(s);
        if (obj.v)
                isl_assert(s->ctx, obj.type == isl_obj_pw_qpolynomial,
                           goto error);
@@ -1705,3 +2593,454 @@ error:
        obj.type->free(obj.v);
        return NULL;
 }
+
+__isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_read_from_str(isl_ctx *ctx,
+               const char *str)
+{
+       isl_pw_qpolynomial *pwqp;
+       struct isl_stream *s = isl_stream_new_str(ctx, str);
+       if (!s)
+               return NULL;
+       pwqp = isl_stream_read_pw_qpolynomial(s);
+       isl_stream_free(s);
+       return pwqp;
+}
+
+__isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_read_from_file(isl_ctx *ctx,
+               FILE *input)
+{
+       isl_pw_qpolynomial *pwqp;
+       struct isl_stream *s = isl_stream_new_file(ctx, input);
+       if (!s)
+               return NULL;
+       pwqp = isl_stream_read_pw_qpolynomial(s);
+       isl_stream_free(s);
+       return pwqp;
+}
+
+/* Is the next token an identifer not in "v"?
+ */
+static int next_is_fresh_ident(struct isl_stream *s, struct vars *v)
+{
+       int n = v->n;
+       int fresh;
+       struct isl_token *tok;
+
+       tok = isl_stream_next_token(s);
+       if (!tok)
+               return 0;
+       fresh = tok->type == ISL_TOKEN_IDENT && vars_pos(v, tok->u.s, -1) >= n;
+       isl_stream_push_token(s, tok);
+
+       vars_drop(v, v->n - n);
+
+       return fresh;
+}
+
+/* First read the domain of the affine expression, which may be
+ * a parameter space or a set.
+ * The tricky part is that we don't know if the domain is a set or not,
+ * so when we are trying to read the domain, we may actually be reading
+ * the affine expression itself (defined on a parameter domains)
+ * If the tuple we are reading is named, we assume it's the domain.
+ * Also, if inside the tuple, the first thing we find is a nested tuple
+ * or a new identifier, we again assume it's the domain.
+ * Otherwise, we assume we are reading an affine expression.
+ */
+static __isl_give isl_set *read_aff_domain(struct isl_stream *s,
+       __isl_take isl_set *dom, struct vars *v)
+{
+       struct isl_token *tok;
+
+       tok = isl_stream_next_token(s);
+       if (tok && (tok->type == ISL_TOKEN_IDENT || tok->is_keyword)) {
+               isl_stream_push_token(s, tok);
+               return read_map_tuple(s, dom, isl_dim_set, v, 1, 0);
+       }
+       if (!tok || tok->type != '[') {
+               isl_stream_error(s, tok, "expecting '['");
+               goto error;
+       }
+       if (next_is_tuple(s) || next_is_fresh_ident(s, v)) {
+               isl_stream_push_token(s, tok);
+               dom = read_map_tuple(s, dom, isl_dim_set, v, 1, 0);
+       } else
+               isl_stream_push_token(s, tok);
+
+       return dom;
+error:
+       if (tok)
+               isl_stream_push_token(s, tok);
+       isl_set_free(dom);
+       return NULL;
+}
+
+/* Read an affine expression from "s".
+ */
+__isl_give isl_aff *isl_stream_read_aff(struct isl_stream *s)
+{
+       isl_aff *aff;
+       isl_multi_aff *ma;
+
+       ma = isl_stream_read_multi_aff(s);
+       if (!ma)
+               return NULL;
+       if (isl_multi_aff_dim(ma, isl_dim_out) != 1)
+               isl_die(s->ctx, isl_error_invalid,
+                       "expecting single affine expression",
+                       goto error);
+
+       aff = isl_multi_aff_get_aff(ma, 0);
+       isl_multi_aff_free(ma);
+       return aff;
+error:
+       isl_multi_aff_free(ma);
+       return NULL;
+}
+
+/* Read a piecewise affine expression from "s" with domain (space) "dom".
+ */
+static __isl_give isl_pw_aff *read_pw_aff_with_dom(struct isl_stream *s,
+       __isl_take isl_set *dom, struct vars *v)
+{
+       isl_pw_aff *pwaff = NULL;
+
+       if (!isl_set_is_params(dom) && isl_stream_eat(s, ISL_TOKEN_TO))
+               goto error;
+
+       if (isl_stream_eat(s, '['))
+               goto error;
+
+       pwaff = accept_affine(s, isl_set_get_space(dom), v);
+
+       if (isl_stream_eat(s, ']'))
+               goto error;
+
+       dom = read_optional_disjuncts(s, dom, v, 0);
+       pwaff = isl_pw_aff_intersect_domain(pwaff, dom);
+
+       return pwaff;
+error:
+       isl_set_free(dom);
+       isl_pw_aff_free(pwaff);
+       return NULL;
+}
+
+__isl_give isl_pw_aff *isl_stream_read_pw_aff(struct isl_stream *s)
+{
+       struct vars *v;
+       isl_set *dom = NULL;
+       isl_set *aff_dom;
+       isl_pw_aff *pa = NULL;
+       int n;
+
+       v = vars_new(s->ctx);
+       if (!v)
+               return NULL;
+
+       dom = isl_set_universe(isl_space_params_alloc(s->ctx, 0));
+       if (next_is_tuple(s)) {
+               dom = read_map_tuple(s, dom, isl_dim_param, v, 1, 0);
+               if (isl_stream_eat(s, ISL_TOKEN_TO))
+                       goto error;
+       }
+       if (isl_stream_eat(s, '{'))
+               goto error;
+
+       n = v->n;
+       aff_dom = read_aff_domain(s, isl_set_copy(dom), v);
+       pa = read_pw_aff_with_dom(s, aff_dom, v);
+       vars_drop(v, v->n - n);
+
+       while (isl_stream_eat_if_available(s, ';')) {
+               isl_pw_aff *pa_i;
+
+               n = v->n;
+               aff_dom = read_aff_domain(s, isl_set_copy(dom), v);
+               pa_i = read_pw_aff_with_dom(s, aff_dom, v);
+               vars_drop(v, v->n - n);
+
+               pa = isl_pw_aff_union_add(pa, pa_i);
+       }
+
+       if (isl_stream_eat(s, '}'))
+               goto error;
+
+       vars_free(v);
+       isl_set_free(dom);
+       return pa;
+error:
+       vars_free(v);
+       isl_set_free(dom);
+       isl_pw_aff_free(pa);
+       return NULL;
+}
+
+__isl_give isl_aff *isl_aff_read_from_str(isl_ctx *ctx, const char *str)
+{
+       isl_aff *aff;
+       struct isl_stream *s = isl_stream_new_str(ctx, str);
+       if (!s)
+               return NULL;
+       aff = isl_stream_read_aff(s);
+       isl_stream_free(s);
+       return aff;
+}
+
+__isl_give isl_pw_aff *isl_pw_aff_read_from_str(isl_ctx *ctx, const char *str)
+{
+       isl_pw_aff *pa;
+       struct isl_stream *s = isl_stream_new_str(ctx, str);
+       if (!s)
+               return NULL;
+       pa = isl_stream_read_pw_aff(s);
+       isl_stream_free(s);
+       return pa;
+}
+
+/* Read an isl_pw_multi_aff from "s".
+ * We currently read a generic object and if it turns out to be a set or
+ * a map, we convert that to an isl_pw_multi_aff.
+ * It would be more efficient if we were to construct the isl_pw_multi_aff
+ * directly.
+ */
+__isl_give isl_pw_multi_aff *isl_stream_read_pw_multi_aff(struct isl_stream *s)
+{
+       struct isl_obj obj;
+
+       obj = obj_read(s);
+       if (!obj.v)
+               return NULL;
+
+       if (obj.type == isl_obj_map)
+               return isl_pw_multi_aff_from_map(obj.v);
+       if (obj.type == isl_obj_set)
+               return isl_pw_multi_aff_from_set(obj.v);
+
+       obj.type->free(obj.v);
+       isl_die(s->ctx, isl_error_invalid, "unexpected object type",
+               return NULL);
+}
+
+__isl_give isl_pw_multi_aff *isl_pw_multi_aff_read_from_str(isl_ctx *ctx,
+       const char *str)
+{
+       isl_pw_multi_aff *pma;
+       struct isl_stream *s = isl_stream_new_str(ctx, str);
+       if (!s)
+               return NULL;
+       pma = isl_stream_read_pw_multi_aff(s);
+       isl_stream_free(s);
+       return pma;
+}
+
+/* Read an isl_union_pw_multi_aff from "s".
+ * We currently read a generic object and if it turns out to be a set or
+ * a map, we convert that to an isl_union_pw_multi_aff.
+ * It would be more efficient if we were to construct
+ * the isl_union_pw_multi_aff directly.
+ */
+__isl_give isl_union_pw_multi_aff *isl_stream_read_union_pw_multi_aff(
+       struct isl_stream *s)
+{
+       struct isl_obj obj;
+
+       obj = obj_read(s);
+       if (!obj.v)
+               return NULL;
+
+       if (obj.type == isl_obj_map || obj.type == isl_obj_set)
+               obj = to_union(s->ctx, obj);
+       if (obj.type == isl_obj_union_map)
+               return isl_union_pw_multi_aff_from_union_map(obj.v);
+       if (obj.type == isl_obj_union_set)
+               return isl_union_pw_multi_aff_from_union_set(obj.v);
+
+       obj.type->free(obj.v);
+       isl_die(s->ctx, isl_error_invalid, "unexpected object type",
+               return NULL);
+}
+
+/* Read an isl_union_pw_multi_aff from "str".
+ */
+__isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_read_from_str(
+       isl_ctx *ctx, const char *str)
+{
+       isl_union_pw_multi_aff *upma;
+       struct isl_stream *s = isl_stream_new_str(ctx, str);
+       if (!s)
+               return NULL;
+       upma = isl_stream_read_union_pw_multi_aff(s);
+       isl_stream_free(s);
+       return upma;
+}
+
+/* Assuming "pa" represents a single affine expression defined on a universe
+ * domain, extract this affine expression.
+ */
+static __isl_give isl_aff *aff_from_pw_aff(__isl_take isl_pw_aff *pa)
+{
+       isl_aff *aff;
+
+       if (!pa)
+               return NULL;
+       if (pa->n != 1)
+               isl_die(isl_pw_aff_get_ctx(pa), isl_error_invalid,
+                       "expecting single affine expression",
+                       goto error);
+       if (!isl_set_plain_is_universe(pa->p[0].set))
+               isl_die(isl_pw_aff_get_ctx(pa), isl_error_invalid,
+                       "expecting universe domain",
+                       goto error);
+
+       aff = isl_aff_copy(pa->p[0].aff);
+       isl_pw_aff_free(pa);
+       return aff;
+error:
+       isl_pw_aff_free(pa);
+       return NULL;
+}
+
+/* Read a multi-affine expression from "s".
+ * If the multi-affine expression has a domain, then then tuple
+ * representing this domain cannot involve any affine expressions.
+ * The tuple representing the actual expressions needs to consist
+ * of only affine expressions.  Moreover, these expressions can
+ * only depend on parameters and input dimensions and not on other
+ * output dimensions.
+ */
+__isl_give isl_multi_aff *isl_stream_read_multi_aff(struct isl_stream *s)
+{
+       struct vars *v;
+       isl_set *dom = NULL;
+       isl_multi_pw_aff *tuple = NULL;
+       int dim, i, n;
+       isl_space *space, *dom_space;
+       isl_multi_aff *ma = NULL;
+
+       v = vars_new(s->ctx);
+       if (!v)
+               return NULL;
+
+       dom = isl_set_universe(isl_space_params_alloc(s->ctx, 0));
+       if (next_is_tuple(s)) {
+               dom = read_map_tuple(s, dom, isl_dim_param, v, 1, 0);
+               if (isl_stream_eat(s, ISL_TOKEN_TO))
+                       goto error;
+       }
+       if (!isl_set_plain_is_universe(dom))
+               isl_die(s->ctx, isl_error_invalid,
+                       "expecting universe parameter domain", goto error);
+       if (isl_stream_eat(s, '{'))
+               goto error;
+
+       tuple = read_tuple(s, v, 0, 0);
+       if (!tuple)
+               goto error;
+       if (isl_stream_eat_if_available(s, ISL_TOKEN_TO)) {
+               isl_set *set;
+               isl_space *space;
+               int has_expr;
+
+               has_expr = tuple_has_expr(tuple);
+               if (has_expr < 0)
+                       goto error;
+               if (has_expr)
+                       isl_die(s->ctx, isl_error_invalid,
+                               "expecting universe domain", goto error);
+               space = isl_space_range(isl_multi_pw_aff_get_space(tuple));
+               set = isl_set_universe(space);
+               dom = isl_set_intersect_params(set, dom);
+               isl_multi_pw_aff_free(tuple);
+               tuple = read_tuple(s, v, 0, 0);
+               if (!tuple)
+                       goto error;
+       }
+
+       if (isl_stream_eat(s, '}'))
+               goto error;
+
+       n = isl_multi_pw_aff_dim(tuple, isl_dim_out);
+       dim = isl_set_dim(dom, isl_dim_all);
+       dom_space = isl_set_get_space(dom);
+       space = isl_space_range(isl_multi_pw_aff_get_space(tuple));
+       space = isl_space_align_params(space, isl_space_copy(dom_space));
+       if (!isl_space_is_params(dom_space))
+               space = isl_space_map_from_domain_and_range(
+                               isl_space_copy(dom_space), space);
+       isl_space_free(dom_space);
+       ma = isl_multi_aff_alloc(space);
+
+       for (i = 0; i < n; ++i) {
+               isl_pw_aff *pa;
+               isl_aff *aff;
+               pa = isl_multi_pw_aff_get_pw_aff(tuple, i);
+               aff = aff_from_pw_aff(pa);
+               if (!aff)
+                       goto error;
+               if (isl_aff_involves_dims(aff, isl_dim_in, dim, i + 1)) {
+                       isl_aff_free(aff);
+                       isl_die(s->ctx, isl_error_invalid,
+                               "not an affine expression", goto error);
+               }
+               aff = isl_aff_drop_dims(aff, isl_dim_in, dim, n);
+               space = isl_multi_aff_get_domain_space(ma);
+               aff = isl_aff_reset_domain_space(aff, space);
+               ma = isl_multi_aff_set_aff(ma, i, aff);
+       }
+
+       isl_multi_pw_aff_free(tuple);
+       vars_free(v);
+       isl_set_free(dom);
+       return ma;
+error:
+       isl_multi_pw_aff_free(tuple);
+       vars_free(v);
+       isl_set_free(dom);
+       isl_multi_aff_free(ma);
+       return NULL;
+}
+
+__isl_give isl_multi_aff *isl_multi_aff_read_from_str(isl_ctx *ctx,
+       const char *str)
+{
+       isl_multi_aff *maff;
+       struct isl_stream *s = isl_stream_new_str(ctx, str);
+       if (!s)
+               return NULL;
+       maff = isl_stream_read_multi_aff(s);
+       isl_stream_free(s);
+       return maff;
+}
+
+__isl_give isl_union_pw_qpolynomial *isl_stream_read_union_pw_qpolynomial(
+       struct isl_stream *s)
+{
+       struct isl_obj obj;
+
+       obj = obj_read(s);
+       if (obj.type == isl_obj_pw_qpolynomial) {
+               obj.type = isl_obj_union_pw_qpolynomial;
+               obj.v = isl_union_pw_qpolynomial_from_pw_qpolynomial(obj.v);
+       }
+       if (obj.v)
+               isl_assert(s->ctx, obj.type == isl_obj_union_pw_qpolynomial,
+                          goto error);
+
+       return obj.v;
+error:
+       obj.type->free(obj.v);
+       return NULL;
+}
+
+__isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_read_from_str(
+       isl_ctx *ctx, const char *str)
+{
+       isl_union_pw_qpolynomial *upwqp;
+       struct isl_stream *s = isl_stream_new_str(ctx, str);
+       if (!s)
+               return NULL;
+       upwqp = isl_stream_read_union_pw_qpolynomial(s);
+       isl_stream_free(s);
+       return upwqp;
+}