From 3adbe18d36df3767e98f30b760ccd9c6ace640ad Mon Sep 17 00:00:00 2001
From: Nadrieril
Date: Fri, 24 May 2024 17:01:16 +0200
Subject: Rename some subdirectories for consistency

---
 tests/hol4/paper/paperTheory.sig | 210 +++++++++++++++++++++++++++++++++++++++
 1 file changed, 210 insertions(+)
 create mode 100644 tests/hol4/paper/paperTheory.sig

(limited to 'tests/hol4/paper/paperTheory.sig')

diff --git a/tests/hol4/paper/paperTheory.sig b/tests/hol4/paper/paperTheory.sig
new file mode 100644
index 00000000..2da80da1
--- /dev/null
+++ b/tests/hol4/paper/paperTheory.sig
@@ -0,0 +1,210 @@
+signature paperTheory =
+sig
+  type thm = Thm.thm
+  
+  (*  Definitions  *)
+    val call_choose_fwd_def : thm
+    val choose_back_def : thm
+    val choose_fwd_def : thm
+    val list_nth_mut_back_def : thm
+    val list_nth_mut_fwd_def : thm
+    val list_t_TY_DEF : thm
+    val list_t_case_def : thm
+    val list_t_size_def : thm
+    val ref_incr_fwd_back_def : thm
+    val sum_fwd_def : thm
+    val test_choose_fwd_def : thm
+    val test_incr_fwd_def : thm
+    val test_nth_fwd_def : thm
+  
+  (*  Theorems  *)
+    val datatype_list_t : thm
+    val list_t_11 : thm
+    val list_t_Axiom : thm
+    val list_t_case_cong : thm
+    val list_t_case_eq : thm
+    val list_t_distinct : thm
+    val list_t_induction : thm
+    val list_t_nchotomy : thm
+  
+  val paper_grammars : type_grammar.grammar * term_grammar.grammar
+(*
+   [divDef] Parent theory of "paper"
+   
+   [call_choose_fwd_def]  Definition
+      
+      ⊢ ∀p. call_choose_fwd p =
+            (let
+               (px,py) = p
+             in
+               do
+                 pz <- choose_fwd T px py;
+                 pz0 <- u32_add pz (int_to_u32 1);
+                 (px0,_) <- choose_back T px py pz0;
+                 Return px0
+               od)
+   
+   [choose_back_def]  Definition
+      
+      ⊢ ∀b x y ret.
+          choose_back b x y ret =
+          if b then Return (ret,y) else Return (x,ret)
+   
+   [choose_fwd_def]  Definition
+      
+      ⊢ ∀b x y. choose_fwd b x y = if b then Return x else Return y
+   
+   [list_nth_mut_back_def]  Definition
+      
+      ⊢ ∀l i ret.
+          list_nth_mut_back l i ret =
+          case l of
+            ListCons x tl =>
+              if i = int_to_u32 0 then Return (ListCons ret tl)
+              else
+                do
+                  i0 <- u32_sub i (int_to_u32 1);
+                  tl0 <- list_nth_mut_back tl i0 ret;
+                  Return (ListCons x tl0)
+                od
+          | ListNil => Fail Failure
+   
+   [list_nth_mut_fwd_def]  Definition
+      
+      ⊢ ∀l i.
+          list_nth_mut_fwd l i =
+          case l of
+            ListCons x tl =>
+              if i = int_to_u32 0 then Return x
+              else
+                do
+                  i0 <- u32_sub i (int_to_u32 1);
+                  list_nth_mut_fwd tl i0
+                od
+          | ListNil => Fail Failure
+   
+   [list_t_TY_DEF]  Definition
+      
+      ⊢ ∃rep.
+          TYPE_DEFINITION
+            (λa0'.
+                 ∀ $var$('list_t').
+                   (∀a0'.
+                      (∃a0 a1.
+                         a0' =
+                         (λa0 a1.
+                              ind_type$CONSTR 0 a0
+                                (ind_type$FCONS a1 (λn. ind_type$BOTTOM)))
+                           a0 a1 ∧ $var$('list_t') a1) ∨
+                      a0' =
+                      ind_type$CONSTR (SUC 0) ARB (λn. ind_type$BOTTOM) ⇒
+                      $var$('list_t') a0') ⇒
+                   $var$('list_t') a0') rep
+   
+   [list_t_case_def]  Definition
+      
+      ⊢ (∀a0 a1 f v. list_t_CASE (ListCons a0 a1) f v = f a0 a1) ∧
+        ∀f v. list_t_CASE ListNil f v = v
+   
+   [list_t_size_def]  Definition
+      
+      ⊢ (∀f a0 a1.
+           list_t_size f (ListCons a0 a1) = 1 + (f a0 + list_t_size f a1)) ∧
+        ∀f. list_t_size f ListNil = 0
+   
+   [ref_incr_fwd_back_def]  Definition
+      
+      ⊢ ∀x. ref_incr_fwd_back x = i32_add x (int_to_i32 1)
+   
+   [sum_fwd_def]  Definition
+      
+      ⊢ ∀l. sum_fwd l =
+            case l of
+              ListCons x tl => do i <- sum_fwd tl; i32_add x i od
+            | ListNil => Return (int_to_i32 0)
+   
+   [test_choose_fwd_def]  Definition
+      
+      ⊢ test_choose_fwd =
+        do
+          z <- choose_fwd T (int_to_i32 0) (int_to_i32 0);
+          z0 <- i32_add z (int_to_i32 1);
+          if z0 ≠ int_to_i32 1 then Fail Failure
+          else
+            do
+              (x,y) <- choose_back T (int_to_i32 0) (int_to_i32 0) z0;
+              if x ≠ int_to_i32 1 then Fail Failure
+              else if y ≠ int_to_i32 0 then Fail Failure
+              else Return ()
+            od
+        od
+   
+   [test_incr_fwd_def]  Definition
+      
+      ⊢ test_incr_fwd =
+        do
+          x <- ref_incr_fwd_back (int_to_i32 0);
+          if x ≠ int_to_i32 1 then Fail Failure else Return ()
+        od
+   
+   [test_nth_fwd_def]  Definition
+      
+      ⊢ test_nth_fwd =
+        (let
+           l = ListNil;
+           l0 = ListCons (int_to_i32 3) l;
+           l1 = ListCons (int_to_i32 2) l0
+         in
+           do
+             x <-
+               list_nth_mut_fwd (ListCons (int_to_i32 1) l1) (int_to_u32 2);
+             x0 <- i32_add x (int_to_i32 1);
+             l2 <-
+               list_nth_mut_back (ListCons (int_to_i32 1) l1)
+                 (int_to_u32 2) x0;
+             i <- sum_fwd l2;
+             if i ≠ int_to_i32 7 then Fail Failure else Return ()
+           od)
+   
+   [datatype_list_t]  Theorem
+      
+      ⊢ DATATYPE (list_t ListCons ListNil)
+   
+   [list_t_11]  Theorem
+      
+      ⊢ ∀a0 a1 a0' a1'.
+          ListCons a0 a1 = ListCons a0' a1' ⇔ a0 = a0' ∧ a1 = a1'
+   
+   [list_t_Axiom]  Theorem
+      
+      ⊢ ∀f0 f1. ∃fn.
+          (∀a0 a1. fn (ListCons a0 a1) = f0 a0 a1 (fn a1)) ∧
+          fn ListNil = f1
+   
+   [list_t_case_cong]  Theorem
+      
+      ⊢ ∀M M' f v.
+          M = M' ∧ (∀a0 a1. M' = ListCons a0 a1 ⇒ f a0 a1 = f' a0 a1) ∧
+          (M' = ListNil ⇒ v = v') ⇒
+          list_t_CASE M f v = list_t_CASE M' f' v'
+   
+   [list_t_case_eq]  Theorem
+      
+      ⊢ list_t_CASE x f v = v' ⇔
+        (∃t l. x = ListCons t l ∧ f t l = v') ∨ x = ListNil ∧ v = v'
+   
+   [list_t_distinct]  Theorem
+      
+      ⊢ ∀a1 a0. ListCons a0 a1 ≠ ListNil
+   
+   [list_t_induction]  Theorem
+      
+      ⊢ ∀P. (∀l. P l ⇒ ∀t. P (ListCons t l)) ∧ P ListNil ⇒ ∀l. P l
+   
+   [list_t_nchotomy]  Theorem
+      
+      ⊢ ∀ll. (∃t l. ll = ListCons t l) ∨ ll = ListNil
+   
+   
+*)
+end
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