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|
-- Programmed by Jedidiah Barber
-- Licensed under the Sunset License v1.0
-- See license.txt for further details
generic
Zero_Element, One_Element : in Element_Type;
package Kompsos.Math is
---------------
-- Numbers --
---------------
-- Valid number Terms are little endian binary lists
-- representing non-negative integers.
-- The last digit in a non-empty list must always be
-- the One_Element.
-- 0 -> ()
-- 1 -> (1)
-- 2 -> (0 1)
-- 3 -> (1 1)
-- 4 -> (0 0 1)
-- 5 -> (1 0 1)
-- 6 -> (0 1 1)
-- 7 -> (1 1 1)
-- 8 -> (0 0 0 1)
-- ...and so forth.
Zero_Term, One_Term : constant Term;
-- Will only return True for number literals, not for variables.
-- If you want to check a variable Term then you must reify it first.
function Is_Number
(Item : in Term)
return Boolean;
function Build
(Value : in Natural)
return Term;
function Value
(Item : in Term)
return Natural
with Pre => Is_Number (Item);
------------------
-- Comparison --
------------------
-- poso --
function GT_Zero
(This : in Goal;
Num_Term : in Term'Class)
return Goal;
procedure GT_Zero
(This : in out Goal;
Num_Term : in Term'Class);
-- >1o --
function GT_One
(This : in Goal;
Num_Term : in Term'Class)
return Goal;
procedure GT_One
(This : in out Goal;
Num_Term : in Term'Class);
-- <lo --
-- Inputs = N_Term & M_Term
function LT_Length
(This : in Goal;
Inputs : in Term_Array)
return Goal
with Pre => Inputs'Length = 2;
-- Inputs = N_Term & M_Term
procedure LT_Length
(This : in out Goal;
Inputs : in Term_Array)
with Pre => Inputs'Length = 2;
-- <=lo --
-- Inputs = N_Term & M_Term
function LTE_Length
(This : in Goal;
Inputs : in Term_Array)
return Goal
with Pre => Inputs'Length = 2;
-- Inputs = N_Term & M_Term
procedure LTE_Length
(This : in out Goal;
Inputs : in Term_Array)
with Pre => Inputs'Length = 2;
-- =lo --
-- Inputs = N_Term & M_Term
function EQ_Length
(This : in Goal;
Inputs : in Term_Array)
return Goal
with Pre => Inputs'Length = 2;
-- Inputs = N_Term & M_Term
procedure EQ_Length
(This : in out Goal;
Inputs : in Term_Array)
with Pre => Inputs'Length = 2;
-- (extra function) --
-- Inputs = N_Term & M_Term
function GTE_Length
(This : in Goal;
Inputs : in Term_Array)
return Goal
with Pre => Inputs'Length = 2;
-- Inputs = N_Term & M_Term
procedure GTE_Length
(This : in out Goal;
Inputs : in Term_Array)
with Pre => Inputs'Length = 2;
-- (extra function) --
-- Inputs = N_Term & M_Term
function GT_Length
(This : in Goal;
Inputs : in Term_Array)
return Goal
with Pre => Inputs'Length = 2;
-- Inputs = N_Term & M_Term
procedure GT_Length
(This : in out Goal;
Inputs : in Term_Array)
with Pre => Inputs'Length = 2;
-- <o --
-- Inputs = N_Term & M_Term
function LT
(This : in Goal;
Inputs : in Term_Array)
return Goal
with Pre => Inputs'Length = 2;
-- Inputs = N_Term & M_Term
procedure LT
(This : in out Goal;
Inputs : in Term_Array)
with Pre => Inputs'Length = 2;
-- <=o --
-- Inputs = N_Term & M_Term
function LTE
(This : in Goal;
Inputs : in Term_Array)
return Goal
with Pre => Inputs'Length = 2;
-- Inputs = N_Term & M_Term
procedure LTE
(This : in out Goal;
Inputs : in Term_Array)
with Pre => Inputs'Length = 2;
-- Use Unify to assert two Terms must represent the same value.
-- (extra function) --
-- Inputs = N_Term & M_Term
function GTE
(This : in Goal;
Inputs : in Term_Array)
return Goal
with Pre => Inputs'Length = 2;
-- Inputs = N_Term & M_Term
procedure GTE
(This : in out Goal;
Inputs : in Term_Array)
with Pre => Inputs'Length = 2;
-- (extra function) --
-- Inputs = N_Term & M_Term
function GT
(This : in Goal;
Inputs : in Term_Array)
return Goal
with Pre => Inputs'Length = 2;
-- Inputs = N_Term & M_Term
procedure GT
(This : in out Goal;
Inputs : in Term_Array)
with Pre => Inputs'Length = 2;
------------------
-- Arithmetic --
------------------
-- full-addero --
-- Note the inputs here are all just the raw Zero_Element and One_Element,
-- not the proper numbers constructed by Build.
-- Inputs = Cin_Term & A_Term & B_Term & Sum_Term & Cout_Term
function Full_Adder
(This : in Goal;
Inputs : in Term_Array)
return Goal
with Pre => Inputs'Length = 5;
-- Inputs = Cin_Term & A_Term & B_Term & Sum_Term & Cout_Term
procedure Full_Adder
(This : in out Goal;
Inputs : in Term_Array)
with Pre => Inputs'Length = 5;
-- +o --
-- Inputs = N_Term & M_Term & Sum_Term
function Add
(This : in Goal;
Inputs : in Term_Array)
return Goal
with Pre => Inputs'Length = 3;
-- Inputs = N_Term & M_Term & Sum_Term
procedure Add
(This : in out Goal;
Inputs : in Term_Array)
with Pre => Inputs'Length = 3;
-- -o --
-- Inputs = N_Term & M_Term & Difference_Term
function Subtract
(This : in Goal;
Inputs : in Term_Array)
return Goal
with Pre => Inputs'Length = 3;
-- Inputs = N_Term & M_Term & Difference_Term
procedure Subtract
(This : in out Goal;
Inputs : in Term_Array)
with Pre => Inputs'Length = 3;
-- *o --
-- Inputs = N_Term & M_Term & Product_Term
function Multiply
(This : in Goal;
Inputs : in Term_Array)
return Goal
with Pre => Inputs'Length = 3;
-- Inputs = N_Term & M_Term & Product_Term
procedure Multiply
(This : in out Goal;
Inputs : in Term_Array)
with Pre => Inputs'Length = 3;
-- /o --
-- Inputs = N_Term & M_Term & Quotient_Term & Remainder_Term
function Divide
(This : in Goal;
Inputs : in Term_Array)
return Goal
with Pre => Inputs'Length = 4;
-- Inputs = N_Term & M_Term & Quotient_Term & Remainder_Term
procedure Divide
(This : in out Goal;
Inputs : in Term_Array)
with Pre => Inputs'Length = 4;
-- logo --
-- Finds solutions to
-- Base^Exponent + Remainder = Power
-- or rather
-- log_Base (Power - Remainder) = Exponent
-- Inputs = Power_Term & Base_Term & Exponent_Term & Remainder_Term
function Logarithm
(This : in Goal;
Inputs : in Term_Array)
return Goal
with Pre => Inputs'Length = 4;
-- Inputs = Power_Term & Base_Term & Exponent_Term & Remainder_Term
procedure Logarithm
(This : in out Goal;
Inputs : in Term_Array)
with Pre => Inputs'Length = 4;
-- expo --
-- Inputs = Base_Term & Exponent_Term & Power_Term
function Exponential
(This : in Goal;
Inputs : in Term_Array)
return Goal
with Pre => Inputs'Length = 3;
-- Inputs = Base_Term & Exponent_Term & Power_Term
procedure Exponential
(This : in out Goal;
Inputs : in Term_Array)
with Pre => Inputs'Length = 3;
-- repeated-mul --
-- Inputs = Base_Term & Exponent_Term & Power_Term
function Repeated_Multiply
(This : in Goal;
Inputs : in Term_Array)
return Goal
with Pre => Inputs'Length = 3;
-- Inputs = Base_Term & Exponent_Term & Power_Term
procedure Repeated_Multiply
(This : in out Goal;
Inputs : in Term_Array)
with Pre => Inputs'Length = 3;
private
Zero_Term : constant Term := Empty_Term;
One_Term : constant Term := T (T (One_Element), Empty_Term);
-- addero --
-- The carry-in input is a raw Zero_Element or One_Element.
-- Inputs = Cin_Term & N_Term & M_Term & Sum_Term
function Adder
(This : in Goal;
Inputs : in Term_Array)
return Goal
with Pre => Inputs'Length = 4;
-- Inputs = Cin_Term & N_Term & M_Term & Sum_Term
procedure Adder
(This : in out Goal;
Inputs : in Term_Array)
with Pre => Inputs'Length = 4;
-- gen-addero --
-- The carry-in input is a raw Zero_Element or One_Element.
-- Inputs = Cin_Term & N_Term & M_Term & Sum_Term
function General_Adder
(This : in Goal;
Inputs : in Term_Array)
return Goal
with Pre => Inputs'Length = 4;
-- Inputs = Cin_Term & N_Term & M_Term & Sum_Term
procedure General_Adder
(This : in out Goal;
Inputs : in Term_Array)
with Pre => Inputs'Length = 4;
-- odd-*o --
-- (What is the X_Term...?)
-- Inputs = X_Term & N_Term & M_Term & Product_Term
function Odd_Multiply
(This : in Goal;
Inputs : in Term_Array)
return Goal
with Pre => Inputs'Length = 4;
-- Inputs = X_Term & N_Term & M_Term & Product_Term
procedure Odd_Multiply
(This : in out Goal;
Inputs : in Term_Array)
with Pre => Inputs'Length = 4;
-- bound-*o --
-- (What is the Q_Term...?)
-- Inputs = Q_Term & Product_Term & N_Term & M_Term
function Bounded_Multiply
(This : in Goal;
Inputs : in Term_Array)
return Goal
with Pre => Inputs'Length = 4;
-- Inputs = Q_Term & Product_Term & N_Term & M_Term
procedure Bounded_Multiply
(This : in out Goal;
Inputs : in Term_Array)
with Pre => Inputs'Length = 4;
-- splito --
-- Inputs = N_Term & Remainder_Term & Low_Term & High_Term
function Split
(This : in Goal;
Inputs : in Term_Array)
return Goal
with Pre => Inputs'Length = 4;
-- Inputs = N_Term & Remainder_Term & Low_Term & High_Term
procedure Split
(This : in out Goal;
Inputs : in Term_Array)
with Pre => Inputs'Length = 4;
-- exp2 --
-- Inputs = Power_Term & Base_Term & Exponent_Term
function Exp_Two
(This : in Goal;
Inputs : in Term_Array)
return Goal
with Pre => Inputs'Length = 3;
-- Inputs = Power_Term & Base_Term & Exponent_Term
procedure Exp_Two
(This : in out Goal;
Inputs : in Term_Array)
with Pre => Inputs'Length = 3;
end Kompsos.Math;
|
