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authorFranciszek Malinka <franciszek.malinka@gmail.com>2021-10-05 21:49:54 +0200
committerFranciszek Malinka <franciszek.malinka@gmail.com>2021-10-05 21:49:54 +0200
commitc5fcf7179a83ef65c86c6a4a390029149e518649 (patch)
treed29ffc5b86a0d257453cedcf87d91a13d8bf3b0d /semestr-3/pf/lista4/logic
parentf8a88b6a4aba1f66d04711a9330eaba49a50c463 (diff)
Duzy commit ze smieciami
Diffstat (limited to 'semestr-3/pf/lista4/logic')
-rw-r--r--semestr-3/pf/lista4/logic/_build/logic.cmabin0 -> 3109 bytes
-rw-r--r--semestr-3/pf/lista4/logic/_build/logic.cmibin0 -> 1513 bytes
-rw-r--r--semestr-3/pf/lista4/logic/_build/logic.cmobin0 -> 3102 bytes
-rw-r--r--semestr-3/pf/lista4/logic/_build/logic.ml78
-rw-r--r--semestr-3/pf/lista4/logic/_build/logic.ml.depends1
-rw-r--r--semestr-3/pf/lista4/logic/_build/logic.mli44
-rw-r--r--semestr-3/pf/lista4/logic/_build/logic.mli.depends1
-rw-r--r--semestr-3/pf/lista4/logic/_build/logic.mllib2
-rw-r--r--semestr-3/pf/lista4/logic/_build/ocamlc.where1
-rw-r--r--semestr-3/pf/lista4/logic/logic.cmabin0 -> 3109 bytes
-rw-r--r--semestr-3/pf/lista4/logic/logic.cmibin0 -> 1513 bytes
-rw-r--r--semestr-3/pf/lista4/logic/logic.mllib2
12 files changed, 129 insertions, 0 deletions
diff --git a/semestr-3/pf/lista4/logic/_build/logic.cma b/semestr-3/pf/lista4/logic/_build/logic.cma
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--- /dev/null
+++ b/semestr-3/pf/lista4/logic/_build/logic.cma
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diff --git a/semestr-3/pf/lista4/logic/_build/logic.cmi b/semestr-3/pf/lista4/logic/_build/logic.cmi
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diff --git a/semestr-3/pf/lista4/logic/_build/logic.cmo b/semestr-3/pf/lista4/logic/_build/logic.cmo
new file mode 100644
index 0000000..4f60b90
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+++ b/semestr-3/pf/lista4/logic/_build/logic.cmo
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diff --git a/semestr-3/pf/lista4/logic/_build/logic.ml b/semestr-3/pf/lista4/logic/_build/logic.ml
new file mode 100644
index 0000000..bb72fc2
--- /dev/null
+++ b/semestr-3/pf/lista4/logic/_build/logic.ml
@@ -0,0 +1,78 @@
+type formula = False | Var of string | Imp of formula * formula
+
+let rec string_of_formula = function
+ | False -> "F"
+ | Var s -> s
+ | Imp (f1, f2) -> "(" ^ (string_of_formula f1) ^ " -> " ^ (string_of_formula f2) ^ ")"
+(* match (f1, f2) with
+ | (Var v1, Var v2) -> (string_of_formula f1) ^ " -> " ^ (string_of_formula f2)
+ | (Var v1, False) | (False, Var v1) -> (string_of_formula f1) ^ " -> " ^ (string_of_formula f2)
+ | (False, False) -> (string_of_formula f1) ^ " -> " ^ (string_of_formula f2)
+ | (f1, f2) -> "(" ^ (string_of_formula f1) ^ " -> " ^ (string_of_formula f2) ^ ")" *)
+
+let pp_print_formula fmtr f =
+ Format.pp_print_string fmtr (string_of_formula f)
+
+type verdict = { assump : formula list; concl : formula }
+
+type theorem =
+ | Assumption of verdict
+ | ImpInsert of verdict * theorem
+ | ImpErase of verdict * theorem * theorem
+ | Contradiction of verdict * theorem
+
+let get_verdict thm = match thm with
+ | Assumption f -> f
+ | ImpInsert (v, _) | ImpErase (v, _, _) | Contradiction (v, _) -> v
+
+let assumptions thm = (get_verdict thm).assump
+let consequence thm = (get_verdict thm).concl
+
+let pp_print_theorem fmtr thm =
+ let open Format in
+ pp_open_hvbox fmtr 2;
+ begin match assumptions thm with
+ | [] -> ()
+ | f :: fs ->
+ pp_print_formula fmtr f;
+ fs |> List.iter (fun f ->
+ pp_print_string fmtr ",";
+ pp_print_space fmtr ();
+ pp_print_formula fmtr f);
+ pp_print_space fmtr ()
+ end;
+ pp_open_hbox fmtr ();
+ pp_print_string fmtr "⊢";
+ pp_print_space fmtr ();
+ pp_print_formula fmtr (consequence thm);
+ pp_close_box fmtr ();
+ pp_close_box fmtr ()
+
+let by_assumption f =
+ Assumption { assump=[f]; concl=f }
+
+let imp_i f thm =
+ let premise = get_verdict thm
+ in ImpInsert ({assump=(List.filter ((<>) f) premise.assump); concl=(Imp (f, premise.concl))}, thm)
+
+let imp_e th1 th2 =
+ let premise1 = get_verdict th1 in
+ let premise2 = get_verdict th2 in
+ match premise1.concl with
+ | False | Var _ -> failwith "th1 conclusion is not implication"
+ | Imp (phi, psi) -> if phi <> premise2.concl then failwith "th1 conclusion's premise is not th2 premise conclusion" else
+ ImpErase ({assump=(premise1.assump @ premise2.assump); concl=(psi)}, th1, th2)
+
+let bot_e f thm =
+ match get_verdict thm with
+ | {assump=ass; concl=False}-> (Contradiction ({assump=ass; concl=f}, thm))
+ | _ -> failwith "thm conclusion is not False"
+
+
+let taut = (imp_i (Var "p") (by_assumption (Var "p")))
+let taut2 = (imp_i (Var "p") (imp_i (Var "q") (by_assumption (Var "p"))))
+
+let imppqr = Imp (Imp (Var "p", Var "q"), Var "r")
+let imppq = Imp (Var "p", Var "q")
+let imppr = Imp (Var "p", Var "r")
+let taut3 = (imp_i (imppqr) (imp_i imppq (by_assumption imppr))) \ No newline at end of file
diff --git a/semestr-3/pf/lista4/logic/_build/logic.ml.depends b/semestr-3/pf/lista4/logic/_build/logic.ml.depends
new file mode 100644
index 0000000..5169b43
--- /dev/null
+++ b/semestr-3/pf/lista4/logic/_build/logic.ml.depends
@@ -0,0 +1 @@
+logic.ml: Format List
diff --git a/semestr-3/pf/lista4/logic/_build/logic.mli b/semestr-3/pf/lista4/logic/_build/logic.mli
new file mode 100644
index 0000000..afbdc7d
--- /dev/null
+++ b/semestr-3/pf/lista4/logic/_build/logic.mli
@@ -0,0 +1,44 @@
+(** reprezentacja formuł *)
+type formula = False | Var of string | Imp of formula * formula
+
+val pp_print_formula : Format.formatter -> formula -> unit
+
+(** reprezentacja twierdzeń *)
+type theorem
+
+(** założenia twierdzenia *)
+val assumptions : theorem -> formula list
+(** teza twierdzeni *)
+val consequence : theorem -> formula
+
+val pp_print_theorem : Format.formatter -> theorem -> unit
+
+(** by_assumption f konstuuje następujący dowód
+
+ -------(Ax)
+ {f} ⊢ f *)
+val by_assumption : formula -> theorem
+
+(** imp_i f thm konstuuje następujący dowód
+
+ thm
+ Γ ⊢ φ
+ ---------------(→I)
+ Γ \ {f} ⊢ f → φ *)
+val imp_i : formula -> theorem -> theorem
+
+(** imp_e thm1 thm2 konstuuje następujący dowód
+
+ thm1 thm2
+ Γ ⊢ φ → ψ Δ ⊢ φ
+ ------------------(→E)
+ Γ ∪ Δ ⊢ ψ *)
+val imp_e : theorem -> theorem -> theorem
+
+(** bot_e f thm konstruuje następujący dowód
+
+ thm
+ Γ ⊢ ⊥
+ -----(⊥E)
+ Γ ⊢ f *)
+val bot_e : formula -> theorem -> theorem
diff --git a/semestr-3/pf/lista4/logic/_build/logic.mli.depends b/semestr-3/pf/lista4/logic/_build/logic.mli.depends
new file mode 100644
index 0000000..3c54482
--- /dev/null
+++ b/semestr-3/pf/lista4/logic/_build/logic.mli.depends
@@ -0,0 +1 @@
+logic.mli: Format
diff --git a/semestr-3/pf/lista4/logic/_build/logic.mllib b/semestr-3/pf/lista4/logic/_build/logic.mllib
new file mode 100644
index 0000000..3732649
--- /dev/null
+++ b/semestr-3/pf/lista4/logic/_build/logic.mllib
@@ -0,0 +1,2 @@
+Logic
+
diff --git a/semestr-3/pf/lista4/logic/_build/ocamlc.where b/semestr-3/pf/lista4/logic/_build/ocamlc.where
new file mode 100644
index 0000000..49511f0
--- /dev/null
+++ b/semestr-3/pf/lista4/logic/_build/ocamlc.where
@@ -0,0 +1 @@
+/home/fmalinka/.opam/4.11.1/lib/ocaml
diff --git a/semestr-3/pf/lista4/logic/logic.cma b/semestr-3/pf/lista4/logic/logic.cma
new file mode 100644
index 0000000..5fca9f1
--- /dev/null
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diff --git a/semestr-3/pf/lista4/logic/logic.cmi b/semestr-3/pf/lista4/logic/logic.cmi
new file mode 100644
index 0000000..d9d951f
--- /dev/null
+++ b/semestr-3/pf/lista4/logic/logic.cmi
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diff --git a/semestr-3/pf/lista4/logic/logic.mllib b/semestr-3/pf/lista4/logic/logic.mllib
new file mode 100644
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@@ -0,0 +1,2 @@
+Logic
+