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Remco Bloemen

2014-02-27, last updated 2014-03-04

This is a short abstract to demonstrate what the abstract thingy can do. sus urna, eget pretium mauris dictum ut. Donec gravida arcu et lorem auctor pharetra. Aenean at tellus tortor, sit amet euismod enim. Etiam massa urna, ornare ac ornare nec, molestie vel tortor. Vivamus pulv

Langragian

Given a space-time manifols MM and a Langragian density :M\mathcal L : M \mapsto ℝ one can define an action SS:

S=M S = \int _M \mathcal L

Noether’s theorem.

For every continuous symmetry of the Langrangian there is a conserverd current jμ(x)j^\mu (x) such that the equations of motion imply μjμ=0∂_\mu j^\mu = 0 Consequently, one can introduce a conserved charge Q=Mj0Q = \int _M j^0

such that $\int _a^b \frac{\d Q}{\d t} = 0$.

PROOF: By definition $\frac{\d Q}{\d t} = \frac{\d}{\d t} \int _M j^0 $ therefore.

Maxwell’s equation

=½(μAν)(μAν)+½(μAμ)2 \mathcal L = - ½ (∂_\mu A_\nu ) (∂^\mu A^\nu ) + ½(∂_\mu A^\mu )^2

Vacuum Einstein equation

𝓛=R2Λ𝓛 = R - 2 \Lambda where R is the Rici tensor and Λ\Lambda is the cosmological constant. The relevant manifold is 4ℝ^4 with metric gg.

Σn=112n \mathrm{\Sigma }^{n=1}_{}{\infty } \frac{1} {2^n }

Lorem Ipsum

Miss Brooke had that kind of beauty which seems to be thrown into relief by poor dress. Her hand and wrist were so finely formed that she could wear sleeves not less bare of style than those in which the Blessed Virgin appeared to Italian painters; and her profile as well as her stature and bearing seemed to gain the more dignity from her plain garments, which by the side of provincial fashion gave her the impressiveness of a fine quotation from the Bible,—or from one of our elder poets,—in a paragraph of to-day’s newspaper. She was usually spoken of as being remarkably clever, but with the addition that her sister Celia had more common-sense. Nevertheless, Celia wore scarcely more trimmings; and it was only to close observers that her dress differed from her sister’s, and had a shade of coquetry in its arrangements; for Miss Brooke’s plain dressing was due to mixed conditions, in most of which her sister shared. The pride of being ladies had something to do with it: the Brooke connections, though not exactly aristocratic, were Σn=112n\mathrm{\Sigma }^{n=1}_{}{\infty } \frac{1} {2^n } unquestionably “good:” if you inquired backward for a generation or two, you would not find any yard-measuring or parcel-tying forefathers—anything lower than an admiral or a clergyman; and there was even an ancestor discernible as a Puritan gentleman who served under Cromwell, but afterwards conformed, and managed to come out of all political troubles as the proprietor of a respectable family estate. Young women of such birth, living in a quiet country-house, and attending a village church hardly larger than a parlor, naturally regarded frippery as the ambition of a huckster’s daughter. Then there was well-bred economy, which in those days made show in dress the first item to be deducted from, when any margin was required for expenses more distinctive of rank. Such reasons would have been enough to account for plain dress, quite apart from religious feeling; but in Miss Brooke’s case, religion alone would have determined it; and Celia

Lorem ipsum dolor sit amet, consectetur adipiscing elit. Mauris nibh est, posuere sit amet pulvinar a, porttitor sed urna. Cras sed enim a lorem lobortis aliquet id at tortor. Aliquam tincidunt adipiscing orci, ut dapibus odio eleifend in. Integer felis libero, tincidunt eget facilisis ut, dapibus sit amet libero. Pellentesque aliquam cursus urna, eget pretium mauris dictum ut. Donec gravida arcu et lorem auctor pharetra. Aenean at tellus tortor, sit amet euismod enim. Etiam massa urna, ornare ac ornare nec, molestie vel tortor. Vivamus pulvinar elit pellentesque metus porta ut venenatis ante congue. Proin est lorem, condimentum non sodales a, viverra vehicula purus. Pellentesque habitant morbi tristique senectus et netus et malesuada fames ac turpis egestas. Pellentesque dignissim, eros vel laoreet malesuada, erat neque ultrices ligula, quis viverra lectus mi a nulla. In elit mauris, eleifend egestas lobortis et, tristique sed turpis. Donec ullamcorper lacinia iaculis. Nulla facilisi. Ut ut sapien vitae tortor pellentesque adipiscing.

Note

A note.

Tip

A tip.

Important

Something important.

Warning

A warning.

Caution

Something to caution for.

Nam facilisis rutrum nunc sed consectetur. Donec scelerisque luctus scelerisque. Nunc id enim ut arcu fermentum tincidunt. Vestibulum ante ipsum primis in faucibus orci luctus et ultrices posuere cubilia Curae; Nullam in sollicitudin urna. Pellentesque habitant morbi tristique senectus et netus et malesuada fames ac turpis egestas. Pellentesque habitant morbi tristique senectus et netus et malesuada fames ac turpis egestas. In porttitor interdum nisi at dignissim. Cras semper purus sit amet elit interdum semper. Vestibulum vitae nibh quam, ac pharetra eros. Donec mauris augue, laoreet eu pellentesque sit amet, tincidunt vitae justo. Aliquam commodo, enim vitae ultrices feugiat, magna risus placerat diam, ac feugiat dolor nisl sed orci. Suspendisse justo elit, fermentum nec lacinia in, facilisis sed ante. Proin sed turpis eros. Aliquam sed urna nibh, non ultricies orci. Mauris scelerisque consectetur luctus. Ut quam nulla, volutpat egestas tempor nec, consequat quis turpis. Mauris lorem nisl, feugiat id auctor non, feugiat quis mi. Vestibulum tristique gravida enim, ac gravida tortor lobortis et. Lorem ipsum dolor sit amet, consectetur adipiscing elit.

PROOF: Phasellus imperdiet, magna tincidunt cursus sodales, dolor felis pretium magna, in pharetra massa nisl vehicula nisi. Nullam vehicula tristique nulla, fringilla scelerisque nulla cursus et. Vestibulum consectetur tincidunt odio sed volutpat. Aenean id libero in risus iaculis feugiat. Praesent lacinia turpis id mauris rutrum ut iaculis dui tincidunt. Phasellus non quam risus. Suspendisse potenti. Phasellus elementum sem in urna volutpat tempus. Praesent eget lectus sed nisl interdum consequat vitae sed orci. Aliquam ultrices erat at tortor adipiscing dictum ultrices dui cursus. Nunc in dui neque, ut viverra nulla. Nulla mi eros, porta pharetra bibendum sit amet, laoreet non purus. Donec pretium libero ac est interdum a dignissim felis euismod. Donec luctus mi eu est pretium tincidunt. Praesent eget est dolor, quis volutpat eros. Vivamus tristique imperdiet erat non interdum. Duis in felis in massa malesuada interdum vel in metus.

Vestibulum vitae nibh quam, ac pharetra eros. Donec mauris augue, laoreet eu pellentesque sit amet, tincidunt vitae justo. Aliquam commodo, enim vitae ultrices feugiat, magna risus placerat diam, ac feugiat dolor nisl sed orci. Suspendisse justo elit, fermentum nec lacinia in, facilisis sed ante. Proin sed turpis eros. Aliquam sed urna nibh, non ultricies orci. Mauris scelerisque consectetur luctus. Ut quam nulla, volutpat egestas tempor nec, consequat quis turpis. Mauris lorem nisl, feugiat id auctor non, feugiat quis mi. Vestibulum tristique gravida enim, ac gravida tortor lobortis et. Lorem ipsum dolor sit amet, consectetur adipiscing elit.

Dit is een klein voorbeeld van programmacode. Het gaat hier om main.cpp uit mijn proglang prgrameer taaltje—waarover later meer. Voor nu, hier is de code:

main.cpp.

#include "fixups.h"
#include "Parser/Parser.h"
#include "IR/IntRep.h"
#include "IR/SymbolVertex.h"
#include "Interpreter/Interpreter.h"
#include "Interpreter/Value.h"
#include <fstream>
#include "Passes/Validator.h"

sint32 Main(const vector<string>& args)
{
    wcerr << L"Simple C++ interpreter for the "
        L"language using ≔ and ↦." << endl;
    wcerr << endl;
    if(args.size() < 3)
    {
        wcerr << "Usage: proglang source_file "
            L"function [arguments]*" << endl;
        throw std::runtime_error("Not enough arguments.");
    }

    // Open
    std::wifstream input;
    input.open(encodeLocal(args[1]), std::ios_base::in);
    if(!input.good())
        throw std::runtime_error("Could not open source file.");
    
    // Parse file
    wcerr << L"Parsing file…" << flush;
    IntRep* ir = new IntRep();
    Parser parser(ir);
    while(input.good())
    {
        string line;
        std::getline<wchar>(input, line);
        parser.parseLine(line);
    }
    wcerr << endl;
    
    // Validate IR
    wcerr << L"Validating…" << flush;
    wcerr << endl << endl;
    Validator validator(ir);
    validator.validate();
    wcerr << endl;
    
    // Find function to call
    SymbolVertex* functionSymbol = 0;
    foreach(SymbolVertex* symbol, ir->symbols())
        if(symbol->identifier() == args[2])
            functionSymbol = symbol;
    if(!functionSymbol)
        throw std::runtime_error(
            "Could not find specified function.");
    
    // Parse arguments
    vector<Value> arguments;
    for(unsigned int i = 3; i < args.size(); i++)
    {
        sint64 integer;
        double real;
        if(parse<sint64>(args[i], integer))
            arguments.push_back(integer);
        else if(parse<double>(args[i], real))
            arguments.push_back(real);
        else
            throw "Could not parse argument";
    }
    
    // Execute IR
    wcerr << L"Executing…" << flush;
    Interpreter interpreter(ir);
    vector<Value> returns;
    returns = interpreter.evaluateFunction(
        functionSymbol, arguments);
    wcerr << endl;

    wcout << returns << endl;
    return 0;
}

Donec mollis commodo porttitor. Cras volutpat placerat nulla in molestie. Etiam hendrerit enim auctor dolor consequat eu interdum orci posuere. Cum sociis natoque penatibus et magnis dis parturient montes, nascetur.

Gravida eget.

gravida eget.

Donec mollis commodo porttitor. Cras volutpat placerat nulla in molestie. Etiam hendrerit enim auctor dolor consequat eu interdum orci posuere. Cum sociis natoque penatibus et magnis dis parturient montes, nascetur ridiculus mus. Suspendisse et eros mauris, ut pharetra quam. Cras vulputate magna sed nulla lacinia nec porttitor leo luctus. Mauris ut est nec augue ornare sollicitudin id vel mauris. Proin est erat, tincidunt eu gravida eget, blandit sit amet tortor. Mauris auctor, lorem sed rhoncus congue, odio sem commodo dolor, ac sollicitudin orci nunc at ipsum. Nullam sit amet mauris in mauris iaculis consequat. Duis ante nibh, consequat vel placerat quis, egestas ut magna. Lorem ipsum dolor sit amet, consectetur adipiscing elit. Cras turpis magna, aliquet non pulvinar eget, mattis porttitor purus. Pellentesque pulvinar fringilla suscipit. Nullam malesuada ullamcorper justo at pellentesque. Integer rutrum vulputate vehicula. Sed tincidunt iaculis fermentum. Aenean fermentum aliquam semper.

Fusce viverra laoreet quam sit amet aliquam. In in ante purus, sit amet pretium magna. Nulla ut massa in nunc condimentum varius non eget dolor. Duis est nisl, posuere id ornare a, sagittis laoreet mi. Morbi pulvinar cursus semper. Donec convallis luctus quam, at pharetra augue luctus at. Aliquam eget pellentesque justo. Donec malesuada sagittis ligula, ac hendrerit quam vestibulum imperdiet. Donec a libero sed ligula vehicula commodo luctus vel nisl. Integer accumsan, odio sed bibendum lacinia, lectus nulla pharetra leo, id tincidunt dolor arcu porttitor magna. Vivamus id tellus euismod urna laoreet aliquet aliquam a nunc. Proin velit sapien, interdum a dapibus vitae, consequat ut felis. Etiam sodales tortor et lorem pharetra semper. Aenean quis metus eros. Donec tempus nisl vel eros aliquam faucibus. In feugiat sapien suscipit nibh venenatis lobortis. Donec gravida, lorem sit amet euismod tempor, sapien magna vehicula mauris, sit amet ornare felis dui eu tortor. Curabitur vel ligula diam.

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