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--All rights reserved.
-- Copyright (C) 2007-2010, Gabriel Dos Reis.
-- All rights reserved.
--
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-- names of its contributors may be used to endorse or promote products
-- derived from this software without specific prior written permission.
--
--THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS
--IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED
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import Type
import ListAggregate
)abbrev domain LIST List
++ Author: Michael Monagan
++ Date Created: Sep 1987
++ Date Last Changed: September 9, 2011.
++ Basic Operations:
++ \#, append, concat, concat!, cons, construct, copy, elt, elt,
++ empty, empty?, eq?, first, member?, merge!, mergeSort, minIndex,
++ nil, null, parts, removeDuplicates!, rest, rest, reverse,
++ reverse!, setDifference, setIntersection, setUnion, setelt,
++ setfirst!, setrest!, sort!, split!
++ Related Constructors: ListFunctions2, ListFunctions3, ListToMap
++ Also See: IndexList, ListAggregate
++ AMS Classification:
++ Keywords: list, index, aggregate, lisp
++ Description:
++ \spadtype{List} implements singly-linked lists that are
++ addressable by indices; the index of the first element
++ is 1. this constructor provides some LISP-like functions
++ such as \spadfun{null} and \spadfun{cons}.
List(S:Type): Exports == Implementation where
Exports == ListAggregate S with
nil : %
++ \spad{nil} is the empty list.
null : % -> Boolean
++ null(u) tests if list \spad{u} is the
++ empty list.
cons : (S, %) -> %
++ cons(element,u) appends \spad{element} onto the front
++ of list \spad{u} and returns the new list. This new list
++ and the old one will share some structure.
append : (%, %) -> %
++ append(u1,u2) appends the elements of list \spad{u1}
++ onto the front of list \spad{u2}. This new list
++ and \spad{u2} will share some structure.
if S has SetCategory then
setUnion : (%, %) -> %
++ setUnion(u1,u2) appends the two lists u1 and u2, then
++ removes all duplicates. The order of elements in the
++ resulting list is unspecified.
setIntersection : (%, %) -> %
++ setIntersection(u1,u2) returns a list of the elements
++ that lists \spad{u1} and \spad{u2} have in common.
++ The order of elements in the resulting list is unspecified.
setDifference : (%, %) -> %
++ setDifference(u1,u2) returns a list of the elements
++ of \spad{u1} that are not also in \spad{u2}.
++ The order of elements in the resulting list is unspecified.
Implementation == add
import %nil: % from Foreign Builtin
import %peq: (%,%) -> Boolean from Foreign Builtin
import %pair: (S,%) -> % from Foreign Builtin
import %lconcat: (%,%) -> % from Foreign Builtin
import %lempty?: % -> Boolean from Foreign Builtin
import %head: % -> S from Foreign Builtin
import %tail: % -> % from Foreign Builtin
import %lreverse: % -> % from Foreign Builtin
import %lreverse!: % -> % from Foreign Builtin
import %llength: % -> NonNegativeInteger from Foreign Builtin
import %icst0: NonNegativeInteger from Foreign Builtin
import %icst1: NonNegativeInteger from Foreign Builtin
import %idec: Integer -> Integer from Foreign Builtin
Qpush ==> PUSH$Lisp
cycleMax ==> 1000 -- value used in checking for cycles
nil == %nil
null l == %peq(l,%nil)
cons(s, l) == %pair(s,l)
append(l:%, t:%) == %lconcat(l,t)
#x == %llength x
concat(s:S,x:%) == %pair(s,x)
eq?(x,y) == %peq(x,y)
first x == SPADfirst(x)$Lisp
elt(x,"first") == SPADfirst(x)$Lisp
empty() == %nil
empty? x == %lempty? x
rest x == %tail x
elt(x,"rest") == %tail x
setfirst!(x,s) ==
empty? x => error "Cannot update an empty list"
%store(%head x,s)$Foreign(Builtin)
s
setelt(x,"first",s) ==
empty? x => error "Cannot update an empty list"
%store(%head x,s)$Foreign(Builtin)
s
setrest!(x,y) ==
empty? x => error "Cannot update an empty list"
%store(%tail x,y)$Foreign(Builtin)
%tail x
setelt(x,"rest",y) ==
empty? x => error "Cannot update an empty list"
%store(%tail x,y)$Foreign(Builtin)
%tail x
construct l == l pretend %
parts s == s pretend List S
reverse! x == %lreverse! x
reverse x == %lreverse x
minIndex x == 1
rest(x, n) ==
for i in %icst1..n repeat
if empty? x then error "index out of range"
x := %tail x
x
copy x ==
y := empty()
for i in %icst0.. while not empty? x repeat
if i = cycleMax and cyclic? x then error "cyclic list"
y := %pair(%head x,y)
x := %tail x
%lreverse! y
if S has CoercibleTo(OutputForm) then
coerce(x):OutputForm ==
-- displays cycle with overbar over the cycle
y := empty()$List(OutputForm)
s := cycleEntry x
while not %peq(x, s) repeat
y := concat((first x)::OutputForm, y)
x := rest x
y := reverse! y
empty? s => bracket y
-- cyclic case: z is cylic part
z := list((first x)::OutputForm)
while not %peq(s, rest x) repeat
x := rest x
z := concat((first x)::OutputForm, z)
bracket concat!(y, overbar commaSeparate reverse! z)
if S has SetCategory then
x = y ==
%peq(x,y) => true
while not empty? x and not empty? y repeat
%head x ~=$S %head y => return false
x := %tail x
y := %tail y
empty? x and empty? y
latex(x : %): String ==
s : String := "\left["
while not empty? x repeat
s := concat(s, latex(%head x)$S)$String
x := %tail x
if not empty? x then s := concat(s, ", ")$String
concat(s, " \right]")$String
member?(s,x) ==
while not empty? x repeat
if s = %head x then return true else x := %tail x
false
-- Lots of code from parts of AGGCAT, repeated here to
-- get faster compilation
concat!(x:%,y:%) ==
empty? x =>
empty? y => x
Qpush(first y,x)
%store(%tail x,rest y)$Foreign(Builtin)
x
z:=x
while not empty? %tail z repeat
z:=%tail z
%store(%tail z,y)$Foreign(Builtin)
x
-- Then a quicky:
if S has SetCategory then
removeDuplicates! l ==
p := l
while not empty? p repeat
-- p := setrest!(p, remove!(#1 = %head p, %tail p))
-- far too expensive - builds closures etc.
pp:=p
f:S:=%head p
p:=%tail p
while not empty? (pr:=%tail pp) repeat
if (%head pr)@S = f then
%store(%tail pp,%tail pr)$Foreign(Builtin)
else pp:=pr
l
-- then sorting
mergeSort: ((S, S) -> Boolean, %, Integer) -> %
sort!(f, l) == mergeSort(f, l, #l)
merge!(f, p, q) ==
empty? p => q
empty? q => p
r,t: %
%peq(p, q) => error "cannot merge a list into itself"
if f(%head p, %head q)
then (r := t := p; p := %tail p)
else (r := t := q; q := %tail q)
while not empty? p and not empty? q repeat
if f(%head p, %head q)
then (%store(%tail t, p)$Foreign(Builtin); t := p; p := %tail p)
else (%store(%tail t, q)$Foreign(Builtin); t := q; q := %tail q)
%store(%tail t, if empty? p then q else p)$Foreign(Builtin)
r
split!(p, n) ==
n < %icst1 => error "index out of range"
p := rest(p, %idec(n)::NonNegativeInteger)
q := %tail p
%store(%tail p,%nil)$Foreign(Builtin)
q
mergeSort(f, p, n) ==
if n = 2 and f(first rest p, first p) then p := reverse! p
n < 3 => p
l := (n quo 2)::NonNegativeInteger
q := split!(p, l)
p := mergeSort(f, p, l)
q := mergeSort(f, q, n - l)
merge!(f, p, q)
if S has SetCategory then
setUnion(l1:%,l2:%) == removeDuplicates concat(l1,l2)
setIntersection(l1:%,l2:%) ==
u :% := empty()
l1 := removeDuplicates l1
while not empty? l1 repeat
if member?(first l1,l2) then u := cons(first l1,u)
l1 := rest l1
u
setDifference(l1:%,l2:%) ==
l1 := removeDuplicates l1
lu:% := empty()
while not empty? l1 repeat
l11:=l1.1
if not member?(l11,l2) then lu := concat(l11,lu)
l1 := rest l1
lu
if S has ConvertibleTo InputForm then
convert(x:%):InputForm ==
convert concat(convert('construct)@InputForm,
[convert a for a in (x pretend List S)]$List(InputForm))
import Type
import FiniteLinearAggregateFunctions2
)abbrev package LIST2 ListFunctions2
++ Author:
++ Date Created:
++ Change History:
++ Basic Operations: map, reduce, scan
++ Related Constructors: List
++ Also See: ListFunctions3
++ AMS Classification:
++ Keywords: list, aggregate, map, reduce
++ Description:
++ \spadtype{ListFunctions2} implements utility functions that
++ operate on two kinds of lists, each with a possibly different
++ type of element.
ListFunctions2(A:Type, B:Type): public == private where
LA ==> List A
LB ==> List B
O2 ==> FiniteLinearAggregateFunctions2(A, LA, B, LB)
public ==> with
scan: ((A, B) -> B, LA, B) -> LB
++ scan(fn,u,ident) successively uses the binary function
++ \spad{fn} to reduce more and more of list \spad{u}.
++ \spad{ident} is returned if the \spad{u} is empty.
++ The result is a list of the reductions at each step. See
++ \spadfun{reduce} for more information. Examples:
++ \spad{scan(fn,[1,2],0) = [fn(2,fn(1,0)),fn(1,0)]} and
++ \spad{scan(*,[2,3],1) = [2 * 1, 3 * (2 * 1)]}.
reduce: ((A, B) -> B, LA, B) -> B
++ reduce(fn,u,ident) successively uses the binary function
++ \spad{fn} on the elements of list \spad{u} and the result
++ of previous applications. \spad{ident} is returned if the
++ \spad{u} is empty. Note the order of application in
++ the following examples:
++ \spad{reduce(fn,[1,2,3],0) = fn(3,fn(2,fn(1,0)))} and
++ \spad{reduce(*,[2,3],1) = 3 * (2 * 1)}.
map: (A -> B, LA) -> LB
++ map(fn,u) applies \spad{fn} to each element of
++ list \spad{u} and returns a new list with the results.
++ For example \spad{map(square,[1,2,3]) = [1,4,9]}.
private ==> add
map(f, l) == map(f, l)$O2
scan(f, l, b) == scan(f, l, b)$O2
reduce(f, l, b) == reduce(f, l, b)$O2
import Type
import Type
)abbrev package LIST3 ListFunctions3
++ Author:
++ Date Created:
++ Change History:
++ Basic Operations: map
++ Related Constructors: List
++ Also See: ListFunctions2
++ AMS Classification:
++ Keywords: list, aggregate, map
++ Description:
++ \spadtype{ListFunctions3} implements utility functions that
++ operate on three kinds of lists, each with a possibly different
++ type of element.
ListFunctions3(A:Type, B:Type, C:Type): public == private where
LA ==> List A
LB ==> List B
LC ==> List C
public ==> with
map: ( (A,B)->C, LA, LB) -> LC
++ map(fn,list1, u2) applies the binary function \spad{fn}
++ to corresponding elements of lists \spad{u1} and \spad{u2}
++ and returns a list of the results (in the same order). Thus
++ \spad{map(/,[1,2,3],[4,5,6]) = [1/4,2/4,1/2]}. The computation
++ terminates when the end of either list is reached. That is,
++ the length of the result list is equal to the minimum of the
++ lengths of \spad{u1} and \spad{u2}.
private ==> add
map(fn : (A,B) -> C, la : LA, lb : LB): LC ==
empty?(la) or empty?(lb) => empty()$LC
concat(fn(first la, first lb), map(fn, rest la, rest lb))
import Type
import SetCategory
import List
)abbrev package LIST2MAP ListToMap
++ Author: Manuel Bronstein
++ Date Created: 22 Mar 1988
++ Change History:
++ 11 Oct 1989 MB ?
++ Basic Operations: match
++ Related Constructors: List
++ Also See:
++ AMS Classification:
++ Keywords: mapping, list
++ Description:
++ \spadtype{ListToMap} allows mappings to be described by a pair of
++ lists of equal lengths. The image of an element \spad{x},
++ which appears in position \spad{n} in the first list, is then
++ the \spad{n}th element of the second list. A default value or
++ default function can be specified to be used when \spad{x}
++ does not appear in the first list. In the absence of defaults,
++ an error will occur in that case.
ListToMap(A:SetCategory, B:Type): Exports == Implementation where
LA ==> List A
LB ==> List B
AB ==> (A -> B)
Exports ==> with
match: (LA, LB ) -> AB
++ match(la, lb) creates a map with no default source or target values
++ defined by lists la and lb of equal length.
++ The target of a source value \spad{x} in la is the
++ value y with the same index lb.
++ Error: if la and lb are not of equal length.
++ Note: when this map is applied, an error occurs when
++ applied to a value missing from la.
match: (LA, LB, A) -> B
++ match(la, lb, a) creates a map
++ defined by lists la and lb of equal length, where \spad{a} is used
++ as the default source value if the given one is not in \spad{la}.
++ The target of a source value \spad{x} in la is the
++ value y with the same index lb.
++ Error: if la and lb are not of equal length.
match: (LA, LB, B) -> AB
++ match(la, lb, b) creates a map
++ defined by lists la and lb of equal length, where \spad{b} is used
++ as the default target value if the given function argument is
++ not in \spad{la}.
++ The target of a source value \spad{x} in la is the
++ value y with the same index lb.
++ Error: if la and lb are not of equal length.
match: (LA, LB, A, B) -> B
++ match(la, lb, a, b) creates a map
++ defined by lists la and lb of equal length.
++ and applies this map to a.
++ The target of a source value \spad{x} in la is the
++ value y with the same index lb.
++ Argument b is the default target value if a is not in la.
++ Error: if la and lb are not of equal length.
match: (LA, LB, AB) -> AB
++ match(la, lb, f) creates a map
++ defined by lists la and lb of equal length.
++ The target of a source value \spad{x} in la is the
++ value y with the same index lb.
++ Argument \spad{f} is used as the
++ function to call when the given function argument is not in
++ \spad{la}.
++ The value returned is f applied to that argument.
match: (LA, LB, A, AB) -> B
++ match(la, lb, a, f) creates a map
++ defined by lists la and lb of equal length.
++ and applies this map to a.
++ The target of a source value \spad{x} in la is the
++ value y with the same index lb.
++ Argument \spad{f} is a default function to call if a is not in la.
++ The value returned is then obtained by applying f to argument a.
Implementation ==> add
match(la, lb) == match(la, lb, #1)
match(la:LA, lb:LB, a:A) == lb.position(a, la)
match(la:LA, lb:LB, b:B) == match(la, lb, #1, b)
match(la:LA, lb:LB, f:AB) == match(la, lb, #1, f)
match(la:LA, lb:LB, a:A, b:B) ==
(p := position(a, la)) < minIndex(la) => b
lb.p
match(la:LA, lb:LB, a:A, f:AB) ==
(p := position(a, la)) < minIndex(la) => f a
lb.p
import SetCategory
import List
import Reference
)abbrev domain ALIST AssociationList
++ Author:
++ Date Created:
++ Change History:
++ Basic Operations: empty, empty?, keys, \#, concat, first, rest,
++ setrest!, search, setelt, remove!
++ Related Constructors:
++ Also See: List
++ AMS Classification:
++ Keywords: list, association list
++ Description:
++ \spadtype{AssociationList} implements association lists. These
++ may be viewed as lists of pairs where the first part is a key
++ and the second is the stored value. For example, the key might
++ be a string with a persons employee identification number and
++ the value might be a record with personnel data.
AssociationList(Key:SetCategory, Entry:SetCategory):
AssociationListAggregate(Key, Entry) == add
Pair ==> Record(key:Key, entry:Entry)
Rep := Reference List Pair
dictionary() == ref empty()
empty() == dictionary()
empty? t == empty? deref t
entries(t:%):List(Pair) == deref t
parts(t:%):List(Pair) == deref t
keys t == [k.key for k in deref t]
# t == # deref t
first(t:%):Pair == first deref t
rest t == ref rest deref t
concat(p:Pair, t:%) == ref concat(p, deref t)
setrest!(a:%, b:%) == ref setrest!(deref a, deref b)
setfirst!(a:%, p:Pair) == setfirst!(deref a,p)
minIndex(a:%):Integer == minIndex(deref a)
maxIndex(a:%):Integer == maxIndex(deref a)
search(k, t) ==
for r in deref t repeat
k = r.key => return(r.entry)
"failed"
latex(a : %) : String ==
l : List Pair := entries a
s : String := "\left["
while not empty?(l) repeat
r : Pair := first l
l := rest l
s := concat(s, concat(latex r.key, concat(" = ", latex r.entry)$String)$String)$String
if not empty?(l) then s := concat(s, ", ")$String
concat(s, " \right]")$String
-- assoc(k, l) ==
-- (r := find(#1.key=k, l)) case "failed" => "failed"
-- r
assoc(k, t) ==
for r in deref t repeat
k = r.key => return r
"failed"
setelt(t:%, k:Key, e:Entry) ==
(r := assoc(k, t)) case Pair => (r::Pair).entry := e
setref(t, concat([k, e], deref t))
e
remove!(k:Key, t:%) ==
empty?(l := deref t) => "failed"
k = first(l).key =>
setref(t, rest l)
first(l).entry
prev := l
curr := rest l
while not empty? curr and first(curr).key ~= k repeat
prev := curr
curr := rest curr
empty? curr => "failed"
setrest!(prev, rest curr)
first(curr).entry
|