diff options
Diffstat (limited to 'sem7/pp/prolog')
| -rw-r--r-- | sem7/pp/prolog/lec1.dl | 33 | ||||
| -rw-r--r-- | sem7/pp/prolog/lec3.pl | 110 | ||||
| -rw-r--r-- | sem7/pp/prolog/lec4.pl | 50 | ||||
| -rw-r--r-- | sem7/pp/prolog/notes_lec2.md | 22 | ||||
| -rw-r--r-- | sem7/pp/prolog/shell.nix | 13 |
5 files changed, 228 insertions, 0 deletions
diff --git a/sem7/pp/prolog/lec1.dl b/sem7/pp/prolog/lec1.dl new file mode 100644 index 0000000..84154c2 --- /dev/null +++ b/sem7/pp/prolog/lec1.dl @@ -0,0 +1,33 @@ +#lang datalog + +% It finds whether a parent is a father or a mother depending on the gender of the parent. + + + +% Opgave 2 + +% In the first program, a person is only happy if he/she is both rich and famous. +% In the second program, a person is happy if he/she is either rich or famous. + + +% Opgave 3 + +% There is one program containing 3 clauses. +% The first two clauses are called facts each only containing a single atom. +% The first two facts each contain a atom with the single term beyonce which is a constant + +% Last line is a clause with a head and a body containing two atoms. +% The body uses the predicates created in the last two lines, while the clause introduces the new predicate happy. +% The clause uses the variable Person, which is used once in all 3 atoms. + + +% Opgave 4 + +destinct(red, green). +destinct(green, blue). +destinct(red, blue). + +% It is symmetric +destinct(X, Y) :- destinct(Y, X). + +colouring(X, Y, XC, YC) :- neighbour(X, Y), destinct(XC, YC). diff --git a/sem7/pp/prolog/lec3.pl b/sem7/pp/prolog/lec3.pl new file mode 100644 index 0000000..d434134 --- /dev/null +++ b/sem7/pp/prolog/lec3.pl @@ -0,0 +1,110 @@ + +/* Opgave 1 + +{ + loves(rose, jack). + loves(jack, rose). + loves(caledon, rose). + happy(rose). + happy(jack). +} +{ + loves(rose, jack). + loves(caledon, rose). +} +{ + loves(jack, rose). + loves(caledon, rose). +} +{ + loves(rose, jack). + loves(jack, rose). +} +{ + loves(rose, jack). + loves(jack, rose). + loves(caledon, rose). + happy(jack). +} +{ + loves(rose, jack). + loves(jack, rose). + loves(caledon, rose). + happy(rose). +} +{ + loves(rose, jack). + loves(jack, rose). + loves(caledon, rose). +} +{ + loves(rose, jack). + loves(jack, rose). + happy(jack). +} +{ + loves(rose, jack). + loves(jack, rose). + happy(rose). +} +{ + loves(rose, jack). + loves(jack, rose). + happy(rose). + happy(jack) +} + +Well okay i feel stupid + +We say that the universe U_p = {rose, jack, caledon}. +We will then way that the base is: + +U_b = { loves(x, y) | x, y \in U_p } \cup { happy(x) | x \in U_p } + +Then all the interpretations are. + +I = { S | S \subseteq U_b } + +*/ + + +/* Opgave 2 + +loves(rose, jack). +happy(rose) + +happy(rose) <= loves(rose, jack),loves(jack,rose) +We know rose is happy, we do not need to check the predicates. +For some reason, kind of TODO. + +*/ + +/* Opgave 3 + +I_4 og I_5 er modeller for P, hvor I_4 lige har en extra happy(caledon). + +Her er I_4 minimal fordi ingen anden model for P er mindre. + +*/ + +/* Opgave 4 + +M_1 = T_P(Ø) = {god(odin),son(odin,thor),son(odin,baldr),son(thor,mothi),son(thor,magni)} +M_2 = T_P(M_1) = M_1 \cup {demigod(thor),demigod(baldr)} +M_3 = T_P(M_2) = M_2 \cup {mortal(mothi),mortal(magni)} + +*/ + +/* Opgave 5 + +B -+-> A +D -+-> C +B -+-> A +C ---> A +C -+-> B +D ---> B + +D, C -> A, B +D -> C -> B -> A + +Det er stratifyable. diff --git a/sem7/pp/prolog/lec4.pl b/sem7/pp/prolog/lec4.pl new file mode 100644 index 0000000..36d3880 --- /dev/null +++ b/sem7/pp/prolog/lec4.pl @@ -0,0 +1,50 @@ + +last([X], X). +last([_|XS], X) :- last(XS, X). + +/* +last([1,2,3], X) # Bruger regel 2 +last([2,3], Y) # Bruger regel 2 +last([3], Z) # Bruger regel 1, så Z = 3 +# Så Y = Z = 3 +# Så X = Y = Z = 3 + + +Okay det er også bare fint at skrive +last([1,2,3],X) + | +last([2,3],X) + | +last([3], X) +*/ + +attach([], E, [E]). +attach([X|XS], E, [X|R]) :- attach(XS, E, R). + + +/* +Proof search of attach + +attach([1,2], a, L) + | X = 1, XS = [2], E = a, L = [1|L1] +attach([2], a, L1) + | X1 = 2, XS1 = [], E1 = a, L1 = [2|L2] +attach([], a, L2) + | E2 = a, L2 = [a] +*/ + +nat(zero). +nat(succ(X)) :- nat(X). + +after(succ(X), X). + +leq(zero, Y) :- nat(Y). +leq(succ(X), succ(Y)) :- leq(X, Y), nat(X), nat(Y). + +add(X, zero, X) :- nat(X). +add(X, succ(Y), succ(R)) :- add(X, Y, R), nat(X), nat(Y), nat(R). + +sub(X, Y, R) :- add(R, Y, X). + +min(X, Y, X) :- leq(X, Y). +min(succ(X), Y, Y) :- leq(Y, X). diff --git a/sem7/pp/prolog/notes_lec2.md b/sem7/pp/prolog/notes_lec2.md new file mode 100644 index 0000000..49511e8 --- /dev/null +++ b/sem7/pp/prolog/notes_lec2.md @@ -0,0 +1,22 @@ +# Logic Programming + +## Herbrand + +The *herbrand universe* denotes all the constants in the program. +Thus all the things we can talk about. + +While the *herbrand base* is the set of possible facts. +So all the things that one can build using predicates and constants. +So any model is the subset of the *herbrand base*. +Just because something is in the *herbrand base* does not mean that it holds. + +The *herbrand universe* is what we can talk about, while the *herbrand base* is what we can say about it. + +## Minimal Model + +A minimal model for some program P, does not contain a smaller Herbrand model for P. + +Compute finite model with *least fixed point*, which calculates all things that are true. +Has something to do with *minimal model*, probably the saaaaaame??. TODO + + diff --git a/sem7/pp/prolog/shell.nix b/sem7/pp/prolog/shell.nix new file mode 100644 index 0000000..45b9e32 --- /dev/null +++ b/sem7/pp/prolog/shell.nix @@ -0,0 +1,13 @@ +{ pkgs ? import <nixpkgs> {} }: +let + pkgs_old = import (builtins.fetchTarball { + name = "nixpkgs-racket"; + url = "https://github.com/nixos/nixpkgs/archive/1bf0327ef6d7e0959f3250758b4d33b4066a732b.tar.gz"; + sha256 = "1pz4xaimpb1y8xmqz9c8a2g1nsr77jc7nxi6m8v4ph8q1r3c7pz9"; + }) {}; +in +pkgs.mkShell { + buildInputs = with pkgs; [ + pkgs_old.racket swiProlog + ]; +} |