Make progress on the standard library for HOL4

1 files changed, 202 insertions, 0 deletions

diff --git a/backends/hol4/testHashmapTheory.sig b/backends/hol4/testHashmapTheory.sig
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+signature testHashmapTheory =
+sig
+  type thm = Thm.thm
+  
+  (*  Axioms  *)
+    val insert_def : thm
+  
+  (*  Definitions  *)
+    val distinct_keys_def : thm
+    val list_t_TY_DEF : thm
+    val list_t_case_def : thm
+    val list_t_size_def : thm
+    val list_t_v_def : thm
+    val lookup_def : thm
+  
+  (*  Theorems  *)
+    val datatype_list_t : thm
+    val index_eq : thm
+    val insert_lem : 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 lookup_raw_def : thm
+    val lookup_raw_ind : thm
+    val nth_mut_fwd_def : thm
+    val nth_mut_fwd_ind : thm
+    val nth_mut_fwd_lem : thm
+  
+  val testHashmap_grammars : type_grammar.grammar * term_grammar.grammar
+(*
+   [primitives] Parent theory of "testHashmap"
+   
+   [insert_def]  Axiom
+      
+      [oracles: ] [axioms: insert_def] []
+      ⊢ insert key value ls =
+        case ls of
+          ListCons (ckey,cvalue) tl =>
+            if ckey = key then Return (ListCons (ckey,value) tl)
+            else
+              do
+                tl0 <- insert key value tl;
+                Return (ListCons (ckey,cvalue) tl0)
+              od
+        | ListNil => Return (ListCons (key,value) ListNil)
+   
+   [distinct_keys_def]  Definition
+      
+      ⊢ ∀ls.
+          distinct_keys ls ⇔
+          ∀i j.
+            0 < i ⇒
+            i < len ls ⇒
+            0 < j ⇒
+            j < len ls ⇒
+            FST (index i ls) = FST (index j ls) ⇒
+            i = j
+   
+   [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
+   
+   [list_t_v_def]  Definition
+      
+      ⊢ list_t_v ListNil = [] ∧
+        ∀x tl. list_t_v (ListCons x tl) = x::list_t_v tl
+   
+   [lookup_def]  Definition
+      
+      ⊢ ∀key ls. lookup key ls = lookup_raw key (list_t_v ls)
+   
+   [datatype_list_t]  Theorem
+      
+      ⊢ DATATYPE (list_t ListCons ListNil)
+   
+   [index_eq]  Theorem
+      
+      ⊢ (∀x ls. index 0 (x::ls) = x) ∧
+        ∀i x ls.
+          index i (x::ls) =
+          if 0 < i ∨ 0 ≤ i ∧ i ≠ 0 then index (i − 1) ls
+          else if i = 0 then x
+          else ARB
+   
+   [insert_lem]  Theorem
+      
+      [oracles: DISK_THM] [axioms: insert_def] []
+      ⊢ ∀ls key value.
+          distinct_keys (list_t_v ls) ⇒
+          case insert key value ls of
+            Return ls1 =>
+              lookup key ls1 = SOME value ∧
+              ∀k. k ≠ key ⇒ lookup k ls = lookup k ls1
+          | Fail v1 => F
+          | Loop => F
+   
+   [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
+   
+   [lookup_raw_def]  Theorem
+      
+      ⊢ (∀key. lookup_raw key [] = NONE) ∧
+        ∀v ls key k.
+          lookup_raw key ((k,v)::ls) =
+          if k = key then SOME v else lookup_raw key ls
+   
+   [lookup_raw_ind]  Theorem
+      
+      ⊢ ∀P. (∀key. P key []) ∧
+            (∀key k v ls. (k ≠ key ⇒ P key ls) ⇒ P key ((k,v)::ls)) ⇒
+            ∀v v1. P v v1
+   
+   [nth_mut_fwd_def]  Theorem
+      
+      ⊢ ∀ls i.
+          nth_mut_fwd ls i =
+          case ls of
+            ListCons x tl =>
+              if u32_to_int i = 0 then Return x
+              else do i0 <- u32_sub i (int_to_u32 1); nth_mut_fwd tl i0 od
+          | ListNil => Fail Failure
+   
+   [nth_mut_fwd_ind]  Theorem
+      
+      ⊢ ∀P. (∀ls i.
+               (∀x tl i0. ls = ListCons x tl ∧ u32_to_int i ≠ 0 ⇒ P tl i0) ⇒
+               P ls i) ⇒
+            ∀v v1. P v v1
+   
+   [nth_mut_fwd_lem]  Theorem
+      
+      ⊢ ∀ls i.
+          u32_to_int i < len (list_t_v ls) ⇒
+          case nth_mut_fwd ls i of
+            Return x => x = index (u32_to_int i) (list_t_v ls)
+          | Fail v1 => F
+          | Loop => F
+   
+   
+*)
+end