From c5fcf7179a83ef65c86c6a4a390029149e518649 Mon Sep 17 00:00:00 2001
From: Franciszek Malinka <franciszek.malinka@gmail.com>
Date: Tue, 5 Oct 2021 21:49:54 +0200
Subject: Duzy commit ze smieciami

---
 semestr-3/pf/lista4/logic/_build/logic.cma         | Bin 0 -> 3109 bytes
 semestr-3/pf/lista4/logic/_build/logic.cmi         | Bin 0 -> 1513 bytes
 semestr-3/pf/lista4/logic/_build/logic.cmo         | Bin 0 -> 3102 bytes
 semestr-3/pf/lista4/logic/_build/logic.ml          |  78 +++++++++++++++++++++
 semestr-3/pf/lista4/logic/_build/logic.ml.depends  |   1 +
 semestr-3/pf/lista4/logic/_build/logic.mli         |  44 ++++++++++++
 semestr-3/pf/lista4/logic/_build/logic.mli.depends |   1 +
 semestr-3/pf/lista4/logic/_build/logic.mllib       |   2 +
 semestr-3/pf/lista4/logic/_build/ocamlc.where      |   1 +
 semestr-3/pf/lista4/logic/logic.cma                | Bin 0 -> 3109 bytes
 semestr-3/pf/lista4/logic/logic.cmi                | Bin 0 -> 1513 bytes
 semestr-3/pf/lista4/logic/logic.mllib              |   2 +
 12 files changed, 129 insertions(+)
 create mode 100644 semestr-3/pf/lista4/logic/_build/logic.cma
 create mode 100644 semestr-3/pf/lista4/logic/_build/logic.cmi
 create mode 100644 semestr-3/pf/lista4/logic/_build/logic.cmo
 create mode 100644 semestr-3/pf/lista4/logic/_build/logic.ml
 create mode 100644 semestr-3/pf/lista4/logic/_build/logic.ml.depends
 create mode 100644 semestr-3/pf/lista4/logic/_build/logic.mli
 create mode 100644 semestr-3/pf/lista4/logic/_build/logic.mli.depends
 create mode 100644 semestr-3/pf/lista4/logic/_build/logic.mllib
 create mode 100644 semestr-3/pf/lista4/logic/_build/ocamlc.where
 create mode 100644 semestr-3/pf/lista4/logic/logic.cma
 create mode 100644 semestr-3/pf/lista4/logic/logic.cmi
 create mode 100644 semestr-3/pf/lista4/logic/logic.mllib

(limited to 'semestr-3/pf/lista4/logic')

diff --git a/semestr-3/pf/lista4/logic/_build/logic.cma b/semestr-3/pf/lista4/logic/_build/logic.cma
new file mode 100644
index 0000000..5fca9f1
Binary files /dev/null and b/semestr-3/pf/lista4/logic/_build/logic.cma differ
diff --git a/semestr-3/pf/lista4/logic/_build/logic.cmi b/semestr-3/pf/lista4/logic/_build/logic.cmi
new file mode 100644
index 0000000..d9d951f
Binary files /dev/null and b/semestr-3/pf/lista4/logic/_build/logic.cmi differ
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
Binary files /dev/null and b/semestr-3/pf/lista4/logic/_build/logic.cmo differ
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
Binary files /dev/null and b/semestr-3/pf/lista4/logic/logic.cma differ
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
Binary files /dev/null and b/semestr-3/pf/lista4/logic/logic.cmi differ
diff --git a/semestr-3/pf/lista4/logic/logic.mllib b/semestr-3/pf/lista4/logic/logic.mllib
new file mode 100644
index 0000000..3732649
--- /dev/null
+++ b/semestr-3/pf/lista4/logic/logic.mllib
@@ -0,0 +1,2 @@
+Logic
+
-- 
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