Changes between Version 124 and Version 125 of IR2

Timestamp:

06/09/21 07:33:05 (5 years ago)

Author:

Alex Wilton

Comment:

Added $rel API

IR2

@@ -470 +470 @@
 <K,V> $set<$pair<K,V>> $map_entries( $map<K,V> m ); // key value pairs of m arranged in a sequence
 <K,V> $map<K,V> $map_put( $map<K,V> m, K k, V v ); // result of (re)defining k to map to v.
-<K,V> $map<K,V> $map_putAll( $map<K,V> m1, $map<K,V> m2); // result of (re)defining k to map to v for every pair (k,v) in m2
+<K,V> $map<K,V> $map_putAll( $map<K,V> m1, $map<K,V> m2 ); // result of (re)defining k to map to v for every pair (k,v) in m2
 <K,V> $map<K,V> $map_remove( $map<K,V> m, K k ); // result of declaring k undefined
 <K,V> $map<K,V> $map_removeAll( $map<K,V> m, $set<K> ks ); // result of declaring k undefined for every k in ks
@@ -483 +483 @@
 === `rel.cvh` ===
 
+The domain of `$rel<X,Y>` consists of all finite sets R of ordered pairs (x,y) such that x is in X and y is in Y.
+
+{{{
+<X,Y> $set<X> $rel_domain( $rel<X,Y> r ); // Returns the set of x in X such that (x,y) in r for at least one y in Y.
+<X,Y> $set<Y> $rel_range( $rel<X,Y> r ); // Returns the set of y in Y such that (x,y) in r for at least one x in X.
+<X,Y> $set<Y> $rel_getRelated( $rel<X,Y> r, X x); // Returns a $set<Y> B such that y in B iff (x,y) in r.
+<X,Y> $set<X> $rel_getRelated( $rel<X,Y> r, Y y); // Returns a $set<X> A such that x in A iff (x,y) in r.
+<X,Y> $rel<X,Y> $rel_complement( $rel<X,Y> r ); // Returns the relation c such that (x,y) in c iff (x,y) not in r.
+<X,Y> $rel<Y,X> $rel_converse( $rel<X,Y> r ); // Returns the relation r' such that (y,x) in r' iff (x,y) in r.
+<X> $rel<X,X> $rel_identity( $set<X> s ); // Returns the relation r such that (x,x) in r for every x in s.
+<X,Y,Z> $rel<X,Z> $rel_join( $rel<X,Y> r1, $rel<Y,Z> r2 ); // Returns the relation r3 such that (x,z) in r3 iff (x,y) in r1 and (y,z) in r2 for some element y of Y.
+<X> $rel<X,X> $rel_reflexiveClosure( $rel<X,X> r ); // Returns the reflexive closure of r.
+<X> $rel<X,X> $rel_transitiveClosure( $rel<X,X> r ); // Returns the transitive closure of r.
+// Operations "Inherited" from $set
+<X,Y> $bool $rel_contains( $rel<X,Y> r, X x, Y y ); // does r contain (x,y) as member?
+<X,Y> $bool $rel_containsAll( $rel<X,Y> r1, $rel<X,Y> r2 ); // is r2 a subset of r1?
+<X,Y> $rel<X,Y> $rel_add( $rel<X,Y> r, X x, Y y ); // result of adding (x,y) to r
+<X,Y> $rel<X,Y> $rel_union( $rel<X,Y> r1, $rel<X,Y> 2 ); // union of r1 and r2
+<X,Y> $rel<X,Y> $rel_intersection( $rel<X,Y> r1, $rel<X,Y> r2 ); // intersection of r1 and r2
+<X,Y> $rel<X,Y> $rel_difference( $rel<X,Y> r1, $rel<X,Y> r2 ); // elements of r1 not in r2
+}}}
 === `concurrency.cvh` ===