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-rw-r--r--tests/hol4/betree/betreeMain_FunsScript.sml516
-rw-r--r--tests/hol4/betree/betreeMain_TypesScript.sml12
-rw-r--r--tests/hol4/betree/betreeMain_TypesTheory.sig140
3 files changed, 334 insertions, 334 deletions
diff --git a/tests/hol4/betree/betreeMain_FunsScript.sml b/tests/hol4/betree/betreeMain_FunsScript.sml
index 03ff2671..b53c7b8d 100644
--- a/tests/hol4/betree/betreeMain_FunsScript.sml
+++ b/tests/hol4/betree/betreeMain_FunsScript.sml
@@ -279,22 +279,6 @@ val betree_leaf_split_back_def = Define ‘
od
-val [betree_node_lookup_in_bindings_fwd_def] = DefineDiv ‘
- (** [betree_main::betree::Node::{5}::lookup_in_bindings]: forward function *)
- betree_node_lookup_in_bindings_fwd
- (key : u64) (bindings : (u64 # u64) betree_list_t) : u64 option result =
- (case bindings of
- | BetreeListCons hd tl =>
- let (i, i0) = hd in
- if i = key
- then Return (SOME i0)
- else
- if u64_gt i key
- then Return NONE
- else betree_node_lookup_in_bindings_fwd key tl
- | BetreeListNil => Return NONE)
-’
-
val [betree_node_lookup_first_message_for_key_fwd_def] = DefineDiv ‘
(** [betree_main::betree::Node::{5}::lookup_first_message_for_key]: forward function *)
betree_node_lookup_first_message_for_key_fwd
@@ -396,7 +380,51 @@ val [betree_node_apply_upserts_back_def] = DefineDiv ‘
od
-val [betree_node_lookup_fwd_def, betree_node_lookup_back_def, betree_internal_lookup_in_children_fwd_def, betree_internal_lookup_in_children_back_def] = DefineDiv ‘
+val [betree_node_lookup_in_bindings_fwd_def] = DefineDiv ‘
+ (** [betree_main::betree::Node::{5}::lookup_in_bindings]: forward function *)
+ betree_node_lookup_in_bindings_fwd
+ (key : u64) (bindings : (u64 # u64) betree_list_t) : u64 option result =
+ (case bindings of
+ | BetreeListCons hd tl =>
+ let (i, i0) = hd in
+ if i = key
+ then Return (SOME i0)
+ else
+ if u64_gt i key
+ then Return NONE
+ else betree_node_lookup_in_bindings_fwd key tl
+ | BetreeListNil => Return NONE)
+’
+
+val [betree_internal_lookup_in_children_fwd_def, betree_internal_lookup_in_children_back_def, betree_node_lookup_fwd_def, betree_node_lookup_back_def] = DefineDiv ‘
+ (** [betree_main::betree::Internal::{4}::lookup_in_children]: forward function *)
+ (betree_internal_lookup_in_children_fwd
+ (self : betree_internal_t) (key : u64) (st : state) :
+ (state # u64 option) result
+ =
+ if u64_lt key self.betree_internal_pivot
+ then betree_node_lookup_fwd self.betree_internal_left key st
+ else betree_node_lookup_fwd self.betree_internal_right key st)
+ /\
+
+ (** [betree_main::betree::Internal::{4}::lookup_in_children]: backward function 0 *)
+ (betree_internal_lookup_in_children_back
+ (self : betree_internal_t) (key : u64) (st : state) :
+ betree_internal_t result
+ =
+ if u64_lt key self.betree_internal_pivot
+ then (
+ do
+ n <- betree_node_lookup_back self.betree_internal_left key st;
+ Return (self with <| betree_internal_left := n |>)
+ od)
+ else (
+ do
+ n <- betree_node_lookup_back self.betree_internal_right key st;
+ Return (self with <| betree_internal_right := n |>)
+ od))
+ /\
+
(** [betree_main::betree::Node::{5}::lookup]: forward function *)
(betree_node_lookup_fwd
(self : betree_node_t) (key : u64) (st : state) :
@@ -468,8 +496,8 @@ val [betree_node_lookup_fwd_def, betree_node_lookup_back_def, betree_internal_lo
/\
(** [betree_main::betree::Node::{5}::lookup]: backward function 0 *)
- (betree_node_lookup_back
- (self : betree_node_t) (key : u64) (st : state) : betree_node_t result =
+ betree_node_lookup_back
+ (self : betree_node_t) (key : u64) (st : state) : betree_node_t result =
(case self of
| BetreeNodeInternal node =>
do
@@ -532,142 +560,7 @@ val [betree_node_lookup_fwd_def, betree_node_lookup_back_def, betree_internal_lo
(_, bindings) <- betree_load_leaf_node_fwd node.betree_leaf_id st;
_ <- betree_node_lookup_in_bindings_fwd key bindings;
Return (BetreeNodeLeaf node)
- od))
- /\
-
- (** [betree_main::betree::Internal::{4}::lookup_in_children]: forward function *)
- (betree_internal_lookup_in_children_fwd
- (self : betree_internal_t) (key : u64) (st : state) :
- (state # u64 option) result
- =
- if u64_lt key self.betree_internal_pivot
- then betree_node_lookup_fwd self.betree_internal_left key st
- else betree_node_lookup_fwd self.betree_internal_right key st)
- /\
-
- (** [betree_main::betree::Internal::{4}::lookup_in_children]: backward function 0 *)
- betree_internal_lookup_in_children_back
- (self : betree_internal_t) (key : u64) (st : state) :
- betree_internal_t result
- =
- if u64_lt key self.betree_internal_pivot
- then (
- do
- n <- betree_node_lookup_back self.betree_internal_left key st;
- Return (self with <| betree_internal_left := n |>)
od)
- else (
- do
- n <- betree_node_lookup_back self.betree_internal_right key st;
- Return (self with <| betree_internal_right := n |>)
- od)
-’
-
-val [betree_node_lookup_mut_in_bindings_fwd_def] = DefineDiv ‘
- (** [betree_main::betree::Node::{5}::lookup_mut_in_bindings]: forward function *)
- betree_node_lookup_mut_in_bindings_fwd
- (key : u64) (bindings : (u64 # u64) betree_list_t) :
- (u64 # u64) betree_list_t result
- =
- (case bindings of
- | BetreeListCons hd tl =>
- let (i, i0) = hd in
- if u64_ge i key
- then Return (BetreeListCons (i, i0) tl)
- else betree_node_lookup_mut_in_bindings_fwd key tl
- | BetreeListNil => Return BetreeListNil)
-’
-
-val [betree_node_lookup_mut_in_bindings_back_def] = DefineDiv ‘
- (** [betree_main::betree::Node::{5}::lookup_mut_in_bindings]: backward function 0 *)
- betree_node_lookup_mut_in_bindings_back
- (key : u64) (bindings : (u64 # u64) betree_list_t)
- (ret : (u64 # u64) betree_list_t) :
- (u64 # u64) betree_list_t result
- =
- (case bindings of
- | BetreeListCons hd tl =>
- let (i, i0) = hd in
- if u64_ge i key
- then Return ret
- else (
- do
- tl0 <- betree_node_lookup_mut_in_bindings_back key tl ret;
- Return (BetreeListCons (i, i0) tl0)
- od)
- | BetreeListNil => Return ret)
-’
-
-val betree_node_apply_to_leaf_fwd_back_def = Define ‘
- (** [betree_main::betree::Node::{5}::apply_to_leaf]: merged forward/backward function
- (there is a single backward function, and the forward function returns ()) *)
- betree_node_apply_to_leaf_fwd_back
- (bindings : (u64 # u64) betree_list_t) (key : u64)
- (new_msg : betree_message_t) :
- (u64 # u64) betree_list_t result
- =
- do
- bindings0 <- betree_node_lookup_mut_in_bindings_fwd key bindings;
- b <- betree_list_head_has_key_fwd bindings0 key;
- if b
- then (
- do
- hd <- betree_list_pop_front_fwd bindings0;
- (case new_msg of
- | BetreeMessageInsert v =>
- do
- bindings1 <- betree_list_pop_front_back bindings0;
- bindings2 <- betree_list_push_front_fwd_back bindings1 (key, v);
- betree_node_lookup_mut_in_bindings_back key bindings bindings2
- od
- | BetreeMessageDelete =>
- do
- bindings1 <- betree_list_pop_front_back bindings0;
- betree_node_lookup_mut_in_bindings_back key bindings bindings1
- od
- | BetreeMessageUpsert s =>
- let (_, i) = hd in
- do
- v <- betree_upsert_update_fwd (SOME i) s;
- bindings1 <- betree_list_pop_front_back bindings0;
- bindings2 <- betree_list_push_front_fwd_back bindings1 (key, v);
- betree_node_lookup_mut_in_bindings_back key bindings bindings2
- od)
- od)
- else
- (case new_msg of
- | BetreeMessageInsert v =>
- do
- bindings1 <- betree_list_push_front_fwd_back bindings0 (key, v);
- betree_node_lookup_mut_in_bindings_back key bindings bindings1
- od
- | BetreeMessageDelete =>
- betree_node_lookup_mut_in_bindings_back key bindings bindings0
- | BetreeMessageUpsert s =>
- do
- v <- betree_upsert_update_fwd NONE s;
- bindings1 <- betree_list_push_front_fwd_back bindings0 (key, v);
- betree_node_lookup_mut_in_bindings_back key bindings bindings1
- od)
- od
-’
-
-val [betree_node_apply_messages_to_leaf_fwd_back_def] = DefineDiv ‘
- (** [betree_main::betree::Node::{5}::apply_messages_to_leaf]: merged forward/backward function
- (there is a single backward function, and the forward function returns ()) *)
- betree_node_apply_messages_to_leaf_fwd_back
- (bindings : (u64 # u64) betree_list_t)
- (new_msgs : (u64 # betree_message_t) betree_list_t) :
- (u64 # u64) betree_list_t result
- =
- (case new_msgs of
- | BetreeListCons new_msg new_msgs_tl =>
- let (i, m) = new_msg in
- do
- bindings0 <- betree_node_apply_to_leaf_fwd_back bindings i m;
- betree_node_apply_messages_to_leaf_fwd_back bindings0 new_msgs_tl
- od
- | BetreeListNil => Return bindings)
val [betree_node_filter_messages_for_key_fwd_back_def] = DefineDiv ‘
@@ -811,7 +704,211 @@ val [betree_node_apply_messages_to_internal_fwd_back_def] = DefineDiv ‘
| BetreeListNil => Return msgs)
-val [betree_node_apply_messages_fwd_def, betree_node_apply_messages_back_def, betree_internal_flush_fwd_def, betree_internal_flush_back_def] = DefineDiv ‘
+val [betree_node_lookup_mut_in_bindings_fwd_def] = DefineDiv ‘
+ (** [betree_main::betree::Node::{5}::lookup_mut_in_bindings]: forward function *)
+ betree_node_lookup_mut_in_bindings_fwd
+ (key : u64) (bindings : (u64 # u64) betree_list_t) :
+ (u64 # u64) betree_list_t result
+ =
+ (case bindings of
+ | BetreeListCons hd tl =>
+ let (i, i0) = hd in
+ if u64_ge i key
+ then Return (BetreeListCons (i, i0) tl)
+ else betree_node_lookup_mut_in_bindings_fwd key tl
+ | BetreeListNil => Return BetreeListNil)
+’
+
+val [betree_node_lookup_mut_in_bindings_back_def] = DefineDiv ‘
+ (** [betree_main::betree::Node::{5}::lookup_mut_in_bindings]: backward function 0 *)
+ betree_node_lookup_mut_in_bindings_back
+ (key : u64) (bindings : (u64 # u64) betree_list_t)
+ (ret : (u64 # u64) betree_list_t) :
+ (u64 # u64) betree_list_t result
+ =
+ (case bindings of
+ | BetreeListCons hd tl =>
+ let (i, i0) = hd in
+ if u64_ge i key
+ then Return ret
+ else (
+ do
+ tl0 <- betree_node_lookup_mut_in_bindings_back key tl ret;
+ Return (BetreeListCons (i, i0) tl0)
+ od)
+ | BetreeListNil => Return ret)
+’
+
+val betree_node_apply_to_leaf_fwd_back_def = Define ‘
+ (** [betree_main::betree::Node::{5}::apply_to_leaf]: merged forward/backward function
+ (there is a single backward function, and the forward function returns ()) *)
+ betree_node_apply_to_leaf_fwd_back
+ (bindings : (u64 # u64) betree_list_t) (key : u64)
+ (new_msg : betree_message_t) :
+ (u64 # u64) betree_list_t result
+ =
+ do
+ bindings0 <- betree_node_lookup_mut_in_bindings_fwd key bindings;
+ b <- betree_list_head_has_key_fwd bindings0 key;
+ if b
+ then (
+ do
+ hd <- betree_list_pop_front_fwd bindings0;
+ (case new_msg of
+ | BetreeMessageInsert v =>
+ do
+ bindings1 <- betree_list_pop_front_back bindings0;
+ bindings2 <- betree_list_push_front_fwd_back bindings1 (key, v);
+ betree_node_lookup_mut_in_bindings_back key bindings bindings2
+ od
+ | BetreeMessageDelete =>
+ do
+ bindings1 <- betree_list_pop_front_back bindings0;
+ betree_node_lookup_mut_in_bindings_back key bindings bindings1
+ od
+ | BetreeMessageUpsert s =>
+ let (_, i) = hd in
+ do
+ v <- betree_upsert_update_fwd (SOME i) s;
+ bindings1 <- betree_list_pop_front_back bindings0;
+ bindings2 <- betree_list_push_front_fwd_back bindings1 (key, v);
+ betree_node_lookup_mut_in_bindings_back key bindings bindings2
+ od)
+ od)
+ else
+ (case new_msg of
+ | BetreeMessageInsert v =>
+ do
+ bindings1 <- betree_list_push_front_fwd_back bindings0 (key, v);
+ betree_node_lookup_mut_in_bindings_back key bindings bindings1
+ od
+ | BetreeMessageDelete =>
+ betree_node_lookup_mut_in_bindings_back key bindings bindings0
+ | BetreeMessageUpsert s =>
+ do
+ v <- betree_upsert_update_fwd NONE s;
+ bindings1 <- betree_list_push_front_fwd_back bindings0 (key, v);
+ betree_node_lookup_mut_in_bindings_back key bindings bindings1
+ od)
+ od
+’
+
+val [betree_node_apply_messages_to_leaf_fwd_back_def] = DefineDiv ‘
+ (** [betree_main::betree::Node::{5}::apply_messages_to_leaf]: merged forward/backward function
+ (there is a single backward function, and the forward function returns ()) *)
+ betree_node_apply_messages_to_leaf_fwd_back
+ (bindings : (u64 # u64) betree_list_t)
+ (new_msgs : (u64 # betree_message_t) betree_list_t) :
+ (u64 # u64) betree_list_t result
+ =
+ (case new_msgs of
+ | BetreeListCons new_msg new_msgs_tl =>
+ let (i, m) = new_msg in
+ do
+ bindings0 <- betree_node_apply_to_leaf_fwd_back bindings i m;
+ betree_node_apply_messages_to_leaf_fwd_back bindings0 new_msgs_tl
+ od
+ | BetreeListNil => Return bindings)
+’
+
+val [betree_internal_flush_fwd_def, betree_internal_flush_back_def, betree_node_apply_messages_fwd_def, betree_node_apply_messages_back_def] = DefineDiv ‘
+ (** [betree_main::betree::Internal::{4}::flush]: forward function *)
+ (betree_internal_flush_fwd
+ (self : betree_internal_t) (params : betree_params_t)
+ (node_id_cnt : betree_node_id_counter_t)
+ (content : (u64 # betree_message_t) betree_list_t) (st : state) :
+ (state # (u64 # betree_message_t) betree_list_t) result
+ =
+ do
+ p <- betree_list_partition_at_pivot_fwd content self.betree_internal_pivot;
+ let (msgs_left, msgs_right) = p in
+ do
+ len_left <- betree_list_len_fwd msgs_left;
+ if u64_ge len_left params.betree_params_min_flush_size
+ then (
+ do
+ (st0, _) <-
+ betree_node_apply_messages_fwd self.betree_internal_left params
+ node_id_cnt msgs_left st;
+ (_, node_id_cnt0) <-
+ betree_node_apply_messages_back self.betree_internal_left params
+ node_id_cnt msgs_left st;
+ len_right <- betree_list_len_fwd msgs_right;
+ if u64_ge len_right params.betree_params_min_flush_size
+ then (
+ do
+ (st1, _) <-
+ betree_node_apply_messages_fwd self.betree_internal_right params
+ node_id_cnt0 msgs_right st0;
+ _ <-
+ betree_node_apply_messages_back self.betree_internal_right params
+ node_id_cnt0 msgs_right st0;
+ Return (st1, BetreeListNil)
+ od)
+ else Return (st0, msgs_right)
+ od)
+ else (
+ do
+ (st0, _) <-
+ betree_node_apply_messages_fwd self.betree_internal_right params
+ node_id_cnt msgs_right st;
+ _ <-
+ betree_node_apply_messages_back self.betree_internal_right params
+ node_id_cnt msgs_right st;
+ Return (st0, msgs_left)
+ od)
+ od
+ od)
+ /\
+
+ (** [betree_main::betree::Internal::{4}::flush]: backward function 0 *)
+ (betree_internal_flush_back
+ (self : betree_internal_t) (params : betree_params_t)
+ (node_id_cnt : betree_node_id_counter_t)
+ (content : (u64 # betree_message_t) betree_list_t) (st : state) :
+ (betree_internal_t # betree_node_id_counter_t) result
+ =
+ do
+ p <- betree_list_partition_at_pivot_fwd content self.betree_internal_pivot;
+ let (msgs_left, msgs_right) = p in
+ do
+ len_left <- betree_list_len_fwd msgs_left;
+ if u64_ge len_left params.betree_params_min_flush_size
+ then (
+ do
+ (st0, _) <-
+ betree_node_apply_messages_fwd self.betree_internal_left params
+ node_id_cnt msgs_left st;
+ (n, node_id_cnt0) <-
+ betree_node_apply_messages_back self.betree_internal_left params
+ node_id_cnt msgs_left st;
+ len_right <- betree_list_len_fwd msgs_right;
+ if u64_ge len_right params.betree_params_min_flush_size
+ then (
+ do
+ (n0, node_id_cnt1) <-
+ betree_node_apply_messages_back self.betree_internal_right params
+ node_id_cnt0 msgs_right st0;
+ Return
+ (self
+ with
+ <|
+ betree_internal_left := n; betree_internal_right := n0
+ |>, node_id_cnt1)
+ od)
+ else Return (self with <| betree_internal_left := n |>, node_id_cnt0)
+ od)
+ else (
+ do
+ (n, node_id_cnt0) <-
+ betree_node_apply_messages_back self.betree_internal_right params
+ node_id_cnt msgs_right st;
+ Return (self with <| betree_internal_right := n |>, node_id_cnt0)
+ od)
+ od
+ od)
+ /\
+
(** [betree_main::betree::Node::{5}::apply_messages]: forward function *)
(betree_node_apply_messages_fwd
(self : betree_node_t) (params : betree_params_t)
@@ -868,12 +965,12 @@ val [betree_node_apply_messages_fwd_def, betree_node_apply_messages_back_def, be
/\
(** [betree_main::betree::Node::{5}::apply_messages]: backward function 0 *)
- (betree_node_apply_messages_back
- (self : betree_node_t) (params : betree_params_t)
- (node_id_cnt : betree_node_id_counter_t)
- (msgs : (u64 # betree_message_t) betree_list_t) (st : state) :
- (betree_node_t # betree_node_id_counter_t) result
- =
+ betree_node_apply_messages_back
+ (self : betree_node_t) (params : betree_params_t)
+ (node_id_cnt : betree_node_id_counter_t)
+ (msgs : (u64 # betree_message_t) betree_list_t) (st : state) :
+ (betree_node_t # betree_node_id_counter_t) result
+ =
(case self of
| BetreeNodeInternal node =>
do
@@ -921,104 +1018,7 @@ val [betree_node_apply_messages_fwd_def, betree_node_apply_messages_back_def, be
Return (BetreeNodeLeaf (node with <| betree_leaf_size := len |>),
node_id_cnt)
od)
- od))
- /\
-
- (** [betree_main::betree::Internal::{4}::flush]: forward function *)
- (betree_internal_flush_fwd
- (self : betree_internal_t) (params : betree_params_t)
- (node_id_cnt : betree_node_id_counter_t)
- (content : (u64 # betree_message_t) betree_list_t) (st : state) :
- (state # (u64 # betree_message_t) betree_list_t) result
- =
- do
- p <- betree_list_partition_at_pivot_fwd content self.betree_internal_pivot;
- let (msgs_left, msgs_right) = p in
- do
- len_left <- betree_list_len_fwd msgs_left;
- if u64_ge len_left params.betree_params_min_flush_size
- then (
- do
- (st0, _) <-
- betree_node_apply_messages_fwd self.betree_internal_left params
- node_id_cnt msgs_left st;
- (_, node_id_cnt0) <-
- betree_node_apply_messages_back self.betree_internal_left params
- node_id_cnt msgs_left st;
- len_right <- betree_list_len_fwd msgs_right;
- if u64_ge len_right params.betree_params_min_flush_size
- then (
- do
- (st1, _) <-
- betree_node_apply_messages_fwd self.betree_internal_right params
- node_id_cnt0 msgs_right st0;
- _ <-
- betree_node_apply_messages_back self.betree_internal_right params
- node_id_cnt0 msgs_right st0;
- Return (st1, BetreeListNil)
- od)
- else Return (st0, msgs_right)
- od)
- else (
- do
- (st0, _) <-
- betree_node_apply_messages_fwd self.betree_internal_right params
- node_id_cnt msgs_right st;
- _ <-
- betree_node_apply_messages_back self.betree_internal_right params
- node_id_cnt msgs_right st;
- Return (st0, msgs_left)
od)
- od
- od)
- /\
-
- (** [betree_main::betree::Internal::{4}::flush]: backward function 0 *)
- betree_internal_flush_back
- (self : betree_internal_t) (params : betree_params_t)
- (node_id_cnt : betree_node_id_counter_t)
- (content : (u64 # betree_message_t) betree_list_t) (st : state) :
- (betree_internal_t # betree_node_id_counter_t) result
- =
- do
- p <- betree_list_partition_at_pivot_fwd content self.betree_internal_pivot;
- let (msgs_left, msgs_right) = p in
- do
- len_left <- betree_list_len_fwd msgs_left;
- if u64_ge len_left params.betree_params_min_flush_size
- then (
- do
- (st0, _) <-
- betree_node_apply_messages_fwd self.betree_internal_left params
- node_id_cnt msgs_left st;
- (n, node_id_cnt0) <-
- betree_node_apply_messages_back self.betree_internal_left params
- node_id_cnt msgs_left st;
- len_right <- betree_list_len_fwd msgs_right;
- if u64_ge len_right params.betree_params_min_flush_size
- then (
- do
- (n0, node_id_cnt1) <-
- betree_node_apply_messages_back self.betree_internal_right params
- node_id_cnt0 msgs_right st0;
- Return
- (self
- with
- <|
- betree_internal_left := n; betree_internal_right := n0
- |>, node_id_cnt1)
- od)
- else Return (self with <| betree_internal_left := n |>, node_id_cnt0)
- od)
- else (
- do
- (n, node_id_cnt0) <-
- betree_node_apply_messages_back self.betree_internal_right params
- node_id_cnt msgs_right st;
- Return (self with <| betree_internal_right := n |>, node_id_cnt0)
- od)
- od
- od
val betree_node_apply_fwd_def = Define ‘
diff --git a/tests/hol4/betree/betreeMain_TypesScript.sml b/tests/hol4/betree/betreeMain_TypesScript.sml
index c43421c2..779f6abb 100644
--- a/tests/hol4/betree/betreeMain_TypesScript.sml
+++ b/tests/hol4/betree/betreeMain_TypesScript.sml
@@ -31,12 +31,6 @@ Datatype:
End
Datatype:
- (** [betree_main::betree::Node] *)
- betree_node_t =
- | BetreeNodeInternal betree_internal_t
- | BetreeNodeLeaf betree_leaf_t
- ;
-
(** [betree_main::betree::Internal] *)
betree_internal_t =
<|
@@ -45,6 +39,12 @@ Datatype:
betree_internal_left : betree_node_t;
betree_internal_right : betree_node_t;
|>
+ ;
+
+ (** [betree_main::betree::Node] *)
+ betree_node_t =
+ | BetreeNodeInternal betree_internal_t
+ | BetreeNodeLeaf betree_leaf_t
End
Datatype:
diff --git a/tests/hol4/betree/betreeMain_TypesTheory.sig b/tests/hol4/betree/betreeMain_TypesTheory.sig
index a451eae9..cffe6afb 100644
--- a/tests/hol4/betree/betreeMain_TypesTheory.sig
+++ b/tests/hol4/betree/betreeMain_TypesTheory.sig
@@ -22,6 +22,7 @@ sig
val betree_internal_t_betree_internal_right : thm
val betree_internal_t_betree_internal_right_fupd : thm
val betree_internal_t_case_def : thm
+ val betree_internal_t_size_def : thm
val betree_leaf_t_TY_DEF : thm
val betree_leaf_t_betree_leaf_id : thm
val betree_leaf_t_betree_leaf_id_fupd : thm
@@ -42,7 +43,6 @@ sig
val betree_node_id_counter_t_size_def : thm
val betree_node_t_TY_DEF : thm
val betree_node_t_case_def : thm
- val betree_node_t_size_def : thm
val betree_params_t_TY_DEF : thm
val betree_params_t_betree_params_min_flush_size : thm
val betree_params_t_betree_params_min_flush_size_fupd : thm
@@ -177,11 +177,11 @@ sig
val betree_upsert_fun_state_t_induction : thm
val betree_upsert_fun_state_t_nchotomy : thm
val datatype_betree_be_tree_t : thm
+ val datatype_betree_internal_t : thm
val datatype_betree_leaf_t : thm
val datatype_betree_list_t : thm
val datatype_betree_message_t : thm
val datatype_betree_node_id_counter_t : thm
- val datatype_betree_node_t : thm
val datatype_betree_params_t : thm
val datatype_betree_upsert_fun_state_t : thm
@@ -253,30 +253,30 @@ sig
⊢ ∃rep.
TYPE_DEFINITION
- (λa1'.
- ∀ $var$('betree_node_t') $var$('betree_internal_t').
+ (λa0'.
+ ∀ $var$('betree_internal_t') $var$('betree_node_t').
(∀a0'.
- (∃a. a0' =
- (λa.
- ind_type$CONSTR 0 (ARB,ARB,ARB)
- (ind_type$FCONS a (λn. ind_type$BOTTOM)))
- a ∧ $var$('betree_internal_t') a) ∨
- (∃a. a0' =
- (λa.
- ind_type$CONSTR (SUC 0) (a,ARB,ARB)
- (λn. ind_type$BOTTOM)) a) ⇒
- $var$('betree_node_t') a0') ∧
- (∀a1'.
(∃a0 a1 a2 a3.
- a1' =
+ a0' =
(λa0 a1 a2 a3.
- ind_type$CONSTR (SUC (SUC 0)) (ARB,a0,a1)
+ ind_type$CONSTR 0 (a0,a1,ARB)
(ind_type$FCONS a2
(ind_type$FCONS a3 (λn. ind_type$BOTTOM))))
a0 a1 a2 a3 ∧ $var$('betree_node_t') a2 ∧
$var$('betree_node_t') a3) ⇒
- $var$('betree_internal_t') a1') ⇒
- $var$('betree_internal_t') a1') rep
+ $var$('betree_internal_t') a0') ∧
+ (∀a1'.
+ (∃a. a1' =
+ (λa.
+ ind_type$CONSTR (SUC 0) (ARB,ARB,ARB)
+ (ind_type$FCONS a (λn. ind_type$BOTTOM)))
+ a ∧ $var$('betree_internal_t') a) ∨
+ (∃a. a1' =
+ (λa.
+ ind_type$CONSTR (SUC (SUC 0)) (ARB,ARB,a)
+ (λn. ind_type$BOTTOM)) a) ⇒
+ $var$('betree_node_t') a1') ⇒
+ $var$('betree_internal_t') a0') rep
[betree_internal_t_betree_internal_id] Definition
@@ -329,6 +329,16 @@ sig
betree_internal_t_CASE (betree_internal_t a0 a1 a2 a3) f =
f a0 a1 a2 a3
+ [betree_internal_t_size_def] Definition
+
+ ⊢ (∀a0 a1 a2 a3.
+ betree_internal_t_size (betree_internal_t a0 a1 a2 a3) =
+ 1 + (betree_node_t_size a2 + betree_node_t_size a3)) ∧
+ (∀a. betree_node_t_size (BetreeNodeInternal a) =
+ 1 + betree_internal_t_size a) ∧
+ ∀a. betree_node_t_size (BetreeNodeLeaf a) =
+ 1 + betree_leaf_t_size a
+
[betree_leaf_t_TY_DEF] Definition
⊢ ∃rep.
@@ -479,46 +489,36 @@ sig
⊢ ∃rep.
TYPE_DEFINITION
- (λa0'.
- ∀ $var$('betree_node_t') $var$('betree_internal_t').
+ (λa1'.
+ ∀ $var$('betree_internal_t') $var$('betree_node_t').
(∀a0'.
- (∃a. a0' =
- (λa.
- ind_type$CONSTR 0 (ARB,ARB,ARB)
- (ind_type$FCONS a (λn. ind_type$BOTTOM)))
- a ∧ $var$('betree_internal_t') a) ∨
- (∃a. a0' =
- (λa.
- ind_type$CONSTR (SUC 0) (a,ARB,ARB)
- (λn. ind_type$BOTTOM)) a) ⇒
- $var$('betree_node_t') a0') ∧
- (∀a1'.
(∃a0 a1 a2 a3.
- a1' =
+ a0' =
(λa0 a1 a2 a3.
- ind_type$CONSTR (SUC (SUC 0)) (ARB,a0,a1)
+ ind_type$CONSTR 0 (a0,a1,ARB)
(ind_type$FCONS a2
(ind_type$FCONS a3 (λn. ind_type$BOTTOM))))
a0 a1 a2 a3 ∧ $var$('betree_node_t') a2 ∧
$var$('betree_node_t') a3) ⇒
- $var$('betree_internal_t') a1') ⇒
- $var$('betree_node_t') a0') rep
+ $var$('betree_internal_t') a0') ∧
+ (∀a1'.
+ (∃a. a1' =
+ (λa.
+ ind_type$CONSTR (SUC 0) (ARB,ARB,ARB)
+ (ind_type$FCONS a (λn. ind_type$BOTTOM)))
+ a ∧ $var$('betree_internal_t') a) ∨
+ (∃a. a1' =
+ (λa.
+ ind_type$CONSTR (SUC (SUC 0)) (ARB,ARB,a)
+ (λn. ind_type$BOTTOM)) a) ⇒
+ $var$('betree_node_t') a1') ⇒
+ $var$('betree_node_t') a1') rep
[betree_node_t_case_def] Definition
⊢ (∀a f f1. betree_node_t_CASE (BetreeNodeInternal a) f f1 = f a) ∧
∀a f f1. betree_node_t_CASE (BetreeNodeLeaf a) f f1 = f1 a
- [betree_node_t_size_def] Definition
-
- ⊢ (∀a. betree_node_t_size (BetreeNodeInternal a) =
- 1 + betree_internal_t_size a) ∧
- (∀a. betree_node_t_size (BetreeNodeLeaf a) =
- 1 + betree_leaf_t_size a) ∧
- ∀a0 a1 a2 a3.
- betree_internal_t_size (betree_internal_t a0 a1 a2 a3) =
- 1 + (betree_node_t_size a2 + betree_node_t_size a3)
-
[betree_params_t_TY_DEF] Definition
⊢ ∃rep.
@@ -883,11 +883,11 @@ sig
[betree_internal_t_Axiom] Theorem
⊢ ∀f0 f1 f2. ∃fn0 fn1.
- (∀a. fn0 (BetreeNodeInternal a) = f0 a (fn1 a)) ∧
- (∀a. fn0 (BetreeNodeLeaf a) = f1 a) ∧
- ∀a0 a1 a2 a3.
- fn1 (betree_internal_t a0 a1 a2 a3) =
- f2 a0 a1 a2 a3 (fn0 a2) (fn0 a3)
+ (∀a0 a1 a2 a3.
+ fn0 (betree_internal_t a0 a1 a2 a3) =
+ f0 a0 a1 a2 a3 (fn1 a2) (fn1 a3)) ∧
+ (∀a. fn1 (BetreeNodeInternal a) = f1 a (fn0 a)) ∧
+ ∀a. fn1 (BetreeNodeLeaf a) = f2 a
[betree_internal_t_accessors] Theorem
@@ -1130,9 +1130,9 @@ sig
[betree_internal_t_induction] Theorem
⊢ ∀P0 P1.
- (∀b. P1 b ⇒ P0 (BetreeNodeInternal b)) ∧
- (∀b. P0 (BetreeNodeLeaf b)) ∧
- (∀b b0. P0 b ∧ P0 b0 ⇒ ∀u u0. P1 (betree_internal_t u0 u b b0)) ⇒
+ (∀b b0. P1 b ∧ P1 b0 ⇒ ∀u u0. P0 (betree_internal_t u0 u b b0)) ∧
+ (∀b. P0 b ⇒ P1 (BetreeNodeInternal b)) ∧
+ (∀b. P1 (BetreeNodeLeaf b)) ⇒
(∀b. P0 b) ∧ ∀b. P1 b
[betree_internal_t_literal_11] Theorem
@@ -1472,11 +1472,11 @@ sig
[betree_node_t_Axiom] Theorem
⊢ ∀f0 f1 f2. ∃fn0 fn1.
- (∀a. fn0 (BetreeNodeInternal a) = f0 a (fn1 a)) ∧
- (∀a. fn0 (BetreeNodeLeaf a) = f1 a) ∧
- ∀a0 a1 a2 a3.
- fn1 (betree_internal_t a0 a1 a2 a3) =
- f2 a0 a1 a2 a3 (fn0 a2) (fn0 a3)
+ (∀a0 a1 a2 a3.
+ fn0 (betree_internal_t a0 a1 a2 a3) =
+ f0 a0 a1 a2 a3 (fn1 a2) (fn1 a3)) ∧
+ (∀a. fn1 (BetreeNodeInternal a) = f1 a (fn0 a)) ∧
+ ∀a. fn1 (BetreeNodeLeaf a) = f2 a
[betree_node_t_case_cong] Theorem
@@ -1498,9 +1498,9 @@ sig
[betree_node_t_induction] Theorem
⊢ ∀P0 P1.
- (∀b. P1 b ⇒ P0 (BetreeNodeInternal b)) ∧
- (∀b. P0 (BetreeNodeLeaf b)) ∧
- (∀b b0. P0 b ∧ P0 b0 ⇒ ∀u u0. P1 (betree_internal_t u0 u b b0)) ⇒
+ (∀b b0. P1 b ∧ P1 b0 ⇒ ∀u u0. P0 (betree_internal_t u0 u b b0)) ∧
+ (∀b. P0 b ⇒ P1 (BetreeNodeInternal b)) ∧
+ (∀b. P1 (BetreeNodeLeaf b)) ⇒
(∀b. P0 b) ∧ ∀b. P1 b
[betree_node_t_nchotomy] Theorem
@@ -1706,6 +1706,14 @@ sig
(record betree_be_tree_t betree_be_tree_params
betree_be_tree_node_id_cnt betree_be_tree_root)
+ [datatype_betree_internal_t] Theorem
+
+ ⊢ DATATYPE
+ (record betree_internal_t betree_internal_id
+ betree_internal_pivot betree_internal_left
+ betree_internal_right ∧
+ betree_node_t BetreeNodeInternal BetreeNodeLeaf)
+
[datatype_betree_leaf_t] Theorem
⊢ DATATYPE (record betree_leaf_t betree_leaf_id betree_leaf_size)
@@ -1726,14 +1734,6 @@ sig
(record betree_node_id_counter_t
betree_node_id_counter_next_node_id)
- [datatype_betree_node_t] Theorem
-
- ⊢ DATATYPE
- (betree_node_t BetreeNodeInternal BetreeNodeLeaf ∧
- record betree_internal_t betree_internal_id
- betree_internal_pivot betree_internal_left
- betree_internal_right)
-
[datatype_betree_params_t] Theorem
⊢ DATATYPE