diff options
Diffstat (limited to 'src/algebra/aggcat.spad.pamphlet')
| -rw-r--r-- | src/algebra/aggcat.spad.pamphlet | 24 |
1 files changed, 23 insertions, 1 deletions
diff --git a/src/algebra/aggcat.spad.pamphlet b/src/algebra/aggcat.spad.pamphlet index de3c92a9..118ac45a 100644 --- a/src/algebra/aggcat.spad.pamphlet +++ b/src/algebra/aggcat.spad.pamphlet @@ -178,6 +178,20 @@ FiniteAggregate(S: Type): Category == Exports where members: % -> List S ++ \spad{members(u)} returns a list of the consecutive elements of u. ++ For collections, \axiom{members([x,y,...,z]) = (x,y,...,z)}. + reduce: ((S,S)->S,%) -> S + ++ \spad{reduce(f,u)} reduces the binary operation \spad{f} + ++ across \spad{u}. For example, if \spad{u} is \spad{[x,y,...,z]} + ++ then \spad{reduce(f,u)} returns \spad{f(..f(f(x,y),...),z)}. + ++ Note: if \spad{u} has one element \spad{x}, + ++ \spad{reduce(f,u)} returns \spad{x}. Error: if \spad{u} is empty. + reduce: ((S,S)->S,%,S) -> S + ++ \spad{reduce(f,u,x)} reduces the binary operation \spad{f} + ++ across \spad{u}, where \spad{x} is the starting value, usually + ++ the identity operation of \spad{f}. Same as + ++ \spad{reduce(f,u)} if \spad{u} has 2 or more elements. + ++ Returns \spad{f(x,y)} if \spad{u} has one element \spad{y}, + ++ \spad{x} if \spad{u} is empty. For example, + ++ \spad{reduce(+,u,0)} returns the sum of the elements of \spad{u}. if S has BasicType then count: (S,%) -> NonNegativeInteger ++ \spad{count(x,u)} returns the number of occurrences @@ -187,6 +201,14 @@ FiniteAggregate(S: Type): Category == Exports where ++ \spad{member?(x,u)} tests if \spad{x} is a member of \spad{u}. ++ For collections, ++ \axiom{member?(x,u) = reduce(or,[x=y for y in u],false)}. + reduce: ((S,S)->S,%,S,S) -> S + ++ \spad{reduce(f,u,x,z)} reduces the binary operation \spad{f} + ++ across \spad{u}, stopping when an "absorbing element" + ++ \spad{z} is encountered. As for \spad{reduce(f,u,x)}, + ++ \spad{x} is the identity operation of \spad{f}. + ++ Same as \spad{reduce(f,u,x)} when \spad{u} contains no + ++ element \spad{z}. Thus the third argument \spad{x} is + ++ returned when u is empty. add empty? x == #x = 0 #x == # members x @@ -196,7 +218,7 @@ FiniteAggregate(S: Type): Category == Exports where if S has BasicType then count(s:S, x:%) == count(s = #1, x) member?(e, x) == any?(e = #1,x) - + reduce(f,x,e,z) == reduce(f,members x,e,z) @ |