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## 2 array2d

```%--------------------------------------------------%
% vim: ft=mercury ts=4 sw=4 et
%--------------------------------------------------%
% Copyright (C) 2003, 2005-2007, 2011-2012 The University of Melbourne.
% Copyright (C) 2013-2018 The Mercury team.
%--------------------------------------------------%
%
% File: array2d.m.
% Author: Ralph Becket <rafe@cs.mu.oz.au>.
% Stability: medium-low.
%
% Two-dimensional rectangular (i.e. not ragged) array ADT.
%
% XXX The same caveats re: uniqueness of arrays apply to array2ds.
%
%--------------------------------------------------%
%--------------------------------------------------%

:- module array2d.
:- interface.

:- import_module array.
:- import_module list.

%--------------------------------------------------%

% An array2d is a two-dimensional array stored in row-major order
% (that is, the elements of the first row in left-to-right
% order, followed by the elements of the second row and so forth.)
%
:- type array2d(T).

:- inst array2d for array2d/1
--->    array2d(ground, ground, array).

% XXX These are work-arounds until we get nested uniqueness working.
%
:- mode array2d_di == di(array2d).
:- mode array2d_ui == in(array2d).
:- mode array2d_uo == out(array2d).

% init(NumRows, NumColumns, Elem):
% Creates a 2d array with the given numbers of rows and columns
% whose every element is set to Elem.
%
% Throws an exception if either NumRows or NumColumns is negative.
%
:- func init(int, int, T) = array2d(T).
:- mode init(in, in, in) = array2d_uo is det.

% array2d([[X11, ..., X1N], ..., [XM1, ..., XMN]]) constructs an array2d
% of size M * N, with the special case that bounds(array2d([]), 0, 0).
%
% In other words, the elements of the top level list each represent
% one row, and each row is itself a list of the values in the columns
% of that row.
%
% Throws an exception unless all rows have the same number of columns.
%
:- func array2d(list(list(T))) = array2d(T).
:- mode array2d(in) = array2d_uo is det.

% A synonym for the array2d function above.
%
:- func from_lists(list(list(T))) = array2d(T).
:- mode from_lists(in) = array2d_uo is det.

% from_array(NumRows, NumColumns, Array) constructs an array2d
% of size NumRows * NumColumns where the elements are taken from Array
% in row-major order, i.e. the element at row R column C is taken from
% Array at index (R * NumColumns + C). Indices start from zero.
%
% Throws an exception if NumRows < 0 or NumColumns < 0, or if
% the number of elements in Array does not equal NumRows * NumColumns.
%
:- func from_array(int, int, array(T)) = array2d(T).
:- mode from_array(in, in, array_di) = array2d_uo is det.

% is_empty(Array):
% True iff Array contains zero elements.
%
:- pred is_empty(array2d(T)).
% :- mode is_empty(array2d_ui) is semidet.
:- mode is_empty(in) is semidet.

% bounds(Array, NumRows, NumColumns):
%
% Returns the number of rows and columns in the given 2d array.
%
:- pred bounds(array2d(T), int, int).
% :- mode bounds(array2d_ui, out, out) is det.
:- mode bounds(in, out, out) is det.

% in_bounds(Array, R, C):
%
% Succeeds if and only if 0 =< C < NumRows, 0 =< C < NumColumns.
%
:- pred in_bounds(array2d(T), int, int).
% :- mode in_bounds(array2d_ui, in, in) is semidet.
:- mode in_bounds(in, in, in) is semidet.

% lookup(Array, R, C):
%
% Given a 2d array Array with NumRows rows and NumColumns columns,
% return the element at row R and column C. Indices start at zero.
%
% This function requires 0 =< R < NumRows and 0 =< C < NumColumns.
% If this requirement is not satisfied, this function will throw
% an exception.
%
:- func lookup(array2d(T), int, int) = T.
% :- mode lookup(array2d_ui, in, in) = out is det.
:- mode lookup(in, in, in) = out is det.
:- pred lookup(array2d(T), int, int, T).
% :- mode lookup(array2d_ui, in, in, out) is det.
:- mode lookup(in, in, in, out) is det.
:- func array2d(T) ^ elem(int, int) = T.
% :- mode array2d_ui ^ elem(in, in) = out is det.
:- mode in ^ elem(in, in) = out is det.

% unsafe_lookup(Array, R, C):
%
% Given a 2d array Array with NumRows rows and NumColumns columns,
% return the element at row R and column C. Indices start at zero.
%
% This function requires 0 =< R < NumRows and 0 =< C < NumColumns.
% If this requirement is not satisfied, the behavior of this function
% is undefined.
%
:- func unsafe_lookup(array2d(T), int, int) = T.
% :- mode unsafe_lookup(array2d_ui, in, in) = out is det.
:- mode unsafe_lookup(in, in, in) = out is det.
:- pred unsafe_lookup(array2d(T), int, int, T).
% :- mode unsafe_lookup(array2d_ui, in, in, out) is det.
:- mode unsafe_lookup(in, in, in, out) is det.
:- func array2d(T) ^ unsafe_elem(int, int) = T.
% :- mode array2d_ui ^ unsafe_elem(in, in) = out is det.
:- mode in ^ unsafe_elem(in, in) = out is det.

% set(R, C, NewElem, Array0, Array):
%
% Return Array, which differs from Array0 only in that
% the value at row R and column C is NewElem.
%
% Throws an exception unless 0 =< R < NumRows, 0 =< C < NumColumns.
%
:- pred set(int, int, T, array2d(T), array2d(T)).
:- mode set(in, in, in, array2d_di, array2d_uo) is det.
:- func (array2d(T) ^ elem(int, int) := T) = array2d(T).
:- mode (array2d_di ^ elem(in, in) := in) = array2d_uo is det.

% unsafe_set(R, C, NewElem, Array0, Array):
%
% Return Array, which differs from Array0 only in that
% the value at row R and column C is NewElem.
%
% The behavior is defined only if 0 =< R < NumRows, 0 =< C < NumColumns.
%
:- pred unsafe_set(int, int, T, array2d(T), array2d(T)).
:- mode unsafe_set(in, in, in, array2d_di, array2d_uo) is det.
:- func (array2d(T) ^ unsafe_elem(int, int) := T ) = array2d(T).
:- mode (array2d_di ^ unsafe_elem(in, in) := in) = array2d_uo is det.

% lists(Array):
%
% Return the contents of the given 2d array as a list of rows,
% with each row containing the values in its columns.
%
% This function is the converse of from_lists.
% For every Array, from_lists(lists(Array) = Array,
% and for every Lists for from_lists(Lists) does not throw
% an exception, lists(from_lists(Lists) = Lists.
%
:- func lists(array2d(T)) = list(list(T)).
% :- mode lists(array2d_ui) = out is det.
:- mode lists(in) = out is det.

% fill(Item, !Array):
% Sets every element of the array to Item.
%
:- pred fill(T::in, array2d(T)::array2d_di, array2d(T)::array2d_uo) is det.

%--------------------------------------------------%
%--------------------------------------------------%

```

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