diff options
Diffstat (limited to 'src/algebra/aggcat.spad.pamphlet')
| -rw-r--r-- | src/algebra/aggcat.spad.pamphlet | 34 |
1 files changed, 17 insertions, 17 deletions
diff --git a/src/algebra/aggcat.spad.pamphlet b/src/algebra/aggcat.spad.pamphlet index 8e941ff8..9f802495 100644 --- a/src/algebra/aggcat.spad.pamphlet +++ b/src/algebra/aggcat.spad.pamphlet @@ -58,7 +58,7 @@ Aggregate: Category == Type with ++ size?(u,n) tests if u has exactly n elements. sample: constant -> % ++ sample yields a value of type % if % has finiteAggregate then - "#": % -> NonNegativeInteger ++ # u returns the number of items in u. + #: % -> NonNegativeInteger ++ # u returns the number of items in u. add eq?(a,b) == EQ(a,b)$Lisp sample() == empty() @@ -141,15 +141,15 @@ HomogeneousAggregate(S:Type): Category == Aggregate with eval(u:%,l:List Equation S):% == map(eval(#1,l),u) if % has finiteAggregate then #c == # parts c - any?(f, c) == _or/[f x for x in parts c] - every?(f, c) == _and/[f x for x in parts c] - count(f:S -> Boolean, c:%) == _+/[1 for x in parts c | f x] + any?(f, c) == or/[f x for x in parts c] + every?(f, c) == and/[f x for x in parts c] + count(f:S -> Boolean, c:%) == +/[1 for x in parts c | f x] members x == parts x if S has SetCategory then count(s:S, x:%) == count(s = #1, x) member?(e, c) == any?(e = #1,c) x = y == - size?(x, #y) and _and/[a = b for a in parts x for b in parts y] + size?(x, #y) and (and/[a = b for a in parts x for b in parts y]) if S has CoercibleTo(OutputForm) then coerce(x:%):OutputForm == bracket @@ -227,9 +227,9 @@ Collection(S:Type): Category == HomogeneousAggregate(S) with add if % has finiteAggregate then #c == # parts c - count(f:S -> Boolean, c:%) == _+/[1 for x in parts c | f x] - any?(f, c) == _or/[f x for x in parts c] - every?(f, c) == _and/[f x for x in parts c] + count(f:S -> Boolean, c:%) == +/[1 for x in parts c | f x] + any?(f, c) == or/[f x for x in parts c] + every?(f, c) == and/[f x for x in parts c] find(f:S -> Boolean, c:%) == find(f, parts c) reduce(f:(S,S)->S, x:%) == reduce(f, parts x) reduce(f:(S,S)->S, x:%, s:S) == reduce(f, parts x, s) @@ -544,7 +544,7 @@ Dictionary(S:SetCategory): Category == s = t == eq?(s,t) => true #s ~= #t => false - _and/[member?(x, t) for x in parts s] + and/[member?(x, t) for x in parts s] remove_!(f:S->Boolean, t:%) == for m in parts t repeat if f m then remove_!(m, t) @@ -718,7 +718,7 @@ FiniteSetAggregate(S:SetCategory): Category == cardinality s == #s construct l == (s := set(); for x in l repeat insert_!(x,s); s) count(x:S, s:%) == (member?(x, s) => 1; 0) - subset?(s, t) == #s < #t and _and/[member?(x, t) for x in parts s] + subset?(s, t) == #s < #t and (and/[member?(x, t) for x in parts s]) coerce(s:%):OutputForm == brace [x::OutputForm for x in parts s]$List(OutputForm) @@ -2175,7 +2175,7 @@ OneDimensionalArrayAggregate(S:Type): Category == concat l == empty? l => empty() - n := _+/[#a for a in l] + n := +/[#a for a in l] i := minIndex(r := new(n, stupidget l)) for a in l repeat copyInto_!(r, a, i) @@ -2683,7 +2683,7 @@ import OneDimensionalArrayAggregate Boolean ++ quantities of Boolean data. BitAggregate(): Category == Join(OrderedSet, Logic, OneDimensionalArrayAggregate Boolean) with - "not": % -> % + not: % -> % ++ not(b) returns the logical {\em not} of bit aggregate ++ \axiom{b}. nand : (%, %) -> % @@ -2692,10 +2692,10 @@ BitAggregate(): Category == nor : (%, %) -> % ++ nor(a,b) returns the logical {\em nor} of bit aggregates \axiom{a} and ++ \axiom{b}. - _and : (%, %) -> % + and : (%, %) -> % ++ a and b returns the logical {\em and} of bit aggregates \axiom{a} and ++ \axiom{b}. - _or : (%, %) -> % + or : (%, %) -> % ++ a or b returns the logical {\em or} of bit aggregates \axiom{a} and ++ \axiom{b}. xor : (%, %) -> % @@ -2704,9 +2704,9 @@ BitAggregate(): Category == add not v == map(_not, v) - _~(v) == map(_~, v) - _/_\(v, u) == map(_/_\, v, u) - _\_/(v, u) == map(_\_/, v, u) + ~ v == map(_~, v) + v /\ u == map(_/_\, v, u) + v \/ u == map(_\_/, v, u) nand(v, u) == map(nand, v, u) nor(v, u) == map(nor, v, u) |