diff options
Diffstat (limited to 'tests/lean/betree/BetreeMain/Funs.lean')
| -rw-r--r-- | tests/lean/betree/BetreeMain/Funs.lean | 1167 |
1 files changed, 0 insertions, 1167 deletions
diff --git a/tests/lean/betree/BetreeMain/Funs.lean b/tests/lean/betree/BetreeMain/Funs.lean deleted file mode 100644 index 7177e2ec..00000000 --- a/tests/lean/betree/BetreeMain/Funs.lean +++ /dev/null @@ -1,1167 +0,0 @@ --- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS --- [betree_main]: function definitions -import Base.Primitives -import BetreeMain.Types -import BetreeMain.Opaque -import BetreeMain.Clauses.Clauses - -section variable (opaque_defs: OpaqueDefs) - -/- [betree_main::betree::load_internal_node] -/ -def betree_load_internal_node_fwd - (id : UInt64) (st : State) : - Result (State × (betree_list_t (UInt64 × betree_message_t))) - := - opaque_defs.betree_utils_load_internal_node_fwd id st - -/- [betree_main::betree::store_internal_node] -/ -def betree_store_internal_node_fwd - (id : UInt64) (content : betree_list_t (UInt64 × betree_message_t)) - (st : State) : - Result (State × Unit) - := - do - let (st0, _) ← - opaque_defs.betree_utils_store_internal_node_fwd id content st - Result.ret (st0, ()) - -/- [betree_main::betree::load_leaf_node] -/ -def betree_load_leaf_node_fwd - (id : UInt64) (st : State) : - Result (State × (betree_list_t (UInt64 × UInt64))) - := - opaque_defs.betree_utils_load_leaf_node_fwd id st - -/- [betree_main::betree::store_leaf_node] -/ -def betree_store_leaf_node_fwd - (id : UInt64) (content : betree_list_t (UInt64 × UInt64)) (st : State) : - Result (State × Unit) - := - do - let (st0, _) ← opaque_defs.betree_utils_store_leaf_node_fwd id content st - Result.ret (st0, ()) - -/- [betree_main::betree::fresh_node_id] -/ -def betree_fresh_node_id_fwd (counter : UInt64) : Result UInt64 := - do - let _ ← UInt64.checked_add counter (UInt64.ofNatCore 1 (by intlit)) - Result.ret counter - -/- [betree_main::betree::fresh_node_id] -/ -def betree_fresh_node_id_back (counter : UInt64) : Result UInt64 := - UInt64.checked_add counter (UInt64.ofNatCore 1 (by intlit)) - -/- [betree_main::betree::NodeIdCounter::{0}::new] -/ -def betree_node_id_counter_new_fwd : Result betree_node_id_counter_t := - Result.ret - { betree_node_id_counter_next_node_id := (UInt64.ofNatCore 0 (by intlit)) } - -/- [betree_main::betree::NodeIdCounter::{0}::fresh_id] -/ -def betree_node_id_counter_fresh_id_fwd - (self : betree_node_id_counter_t) : Result UInt64 := - do - let _ ← UInt64.checked_add self.betree_node_id_counter_next_node_id - (UInt64.ofNatCore 1 (by intlit)) - Result.ret self.betree_node_id_counter_next_node_id - -/- [betree_main::betree::NodeIdCounter::{0}::fresh_id] -/ -def betree_node_id_counter_fresh_id_back - (self : betree_node_id_counter_t) : Result betree_node_id_counter_t := - do - let i ← UInt64.checked_add self.betree_node_id_counter_next_node_id - (UInt64.ofNatCore 1 (by intlit)) - Result.ret { betree_node_id_counter_next_node_id := i } - -/- [core::num::u64::{10}::MAX] -/ -def core_num_u64_max_body : Result UInt64 := - Result.ret (UInt64.ofNatCore 18446744073709551615 (by intlit)) -def core_num_u64_max_c : UInt64 := eval_global core_num_u64_max_body (by simp) - -/- [betree_main::betree::upsert_update] -/ -def betree_upsert_update_fwd - (prev : Option UInt64) (st : betree_upsert_fun_state_t) : Result UInt64 := - match h: prev with - | Option.none => - match h: st with - | betree_upsert_fun_state_t.Add v => Result.ret v - | betree_upsert_fun_state_t.Sub i => - Result.ret (UInt64.ofNatCore 0 (by intlit)) - | Option.some prev0 => - match h: st with - | betree_upsert_fun_state_t.Add v => - do - let margin ← UInt64.checked_sub core_num_u64_max_c prev0 - if h: margin >= v - then UInt64.checked_add prev0 v - else Result.ret core_num_u64_max_c - | betree_upsert_fun_state_t.Sub v => - if h: prev0 >= v - then UInt64.checked_sub prev0 v - else Result.ret (UInt64.ofNatCore 0 (by intlit)) - -/- [betree_main::betree::List::{1}::len] -/ -def betree_list_len_fwd - (T : Type) (self : betree_list_t T) : (Result UInt64) := - match h: self with - | betree_list_t.Cons t tl => - do - let i ← betree_list_len_fwd T tl - UInt64.checked_add (UInt64.ofNatCore 1 (by intlit)) i - | betree_list_t.Nil => Result.ret (UInt64.ofNatCore 0 (by intlit)) -termination_by betree_list_len_fwd self => betree_list_len_terminates T self -decreasing_by betree_list_len_decreases self - -/- [betree_main::betree::List::{1}::split_at] -/ -def betree_list_split_at_fwd - (T : Type) (self : betree_list_t T) (n : UInt64) : - (Result ((betree_list_t T) × (betree_list_t T))) - := - if h: n = (UInt64.ofNatCore 0 (by intlit)) - then Result.ret (betree_list_t.Nil, self) - else - match h: self with - | betree_list_t.Cons hd tl => - do - let i ← UInt64.checked_sub n (UInt64.ofNatCore 1 (by intlit)) - let p ← betree_list_split_at_fwd T tl i - let (ls0, ls1) := p - let l := ls0 - Result.ret (betree_list_t.Cons hd l, ls1) - | betree_list_t.Nil => Result.fail Error.panic -termination_by betree_list_split_at_fwd self n => - betree_list_split_at_terminates T self n -decreasing_by betree_list_split_at_decreases self n - -/- [betree_main::betree::List::{1}::push_front] -/ -def betree_list_push_front_fwd_back - (T : Type) (self : betree_list_t T) (x : T) : Result (betree_list_t T) := - let tl := mem_replace_fwd (betree_list_t T) self betree_list_t.Nil - let l := tl - Result.ret (betree_list_t.Cons x l) - -/- [betree_main::betree::List::{1}::pop_front] -/ -def betree_list_pop_front_fwd (T : Type) (self : betree_list_t T) : Result T := - let ls := mem_replace_fwd (betree_list_t T) self betree_list_t.Nil - match h: ls with - | betree_list_t.Cons x tl => Result.ret x - | betree_list_t.Nil => Result.fail Error.panic - -/- [betree_main::betree::List::{1}::pop_front] -/ -def betree_list_pop_front_back - (T : Type) (self : betree_list_t T) : Result (betree_list_t T) := - let ls := mem_replace_fwd (betree_list_t T) self betree_list_t.Nil - match h: ls with - | betree_list_t.Cons x tl => Result.ret tl - | betree_list_t.Nil => Result.fail Error.panic - -/- [betree_main::betree::List::{1}::hd] -/ -def betree_list_hd_fwd (T : Type) (self : betree_list_t T) : Result T := - match h: self with - | betree_list_t.Cons hd l => Result.ret hd - | betree_list_t.Nil => Result.fail Error.panic - -/- [betree_main::betree::List::{2}::head_has_key] -/ -def betree_list_head_has_key_fwd - (T : Type) (self : betree_list_t (UInt64 × T)) (key : UInt64) : - Result Bool - := - match h: self with - | betree_list_t.Cons hd l => let (i, _) := hd - Result.ret (i = key) - | betree_list_t.Nil => Result.ret false - -/- [betree_main::betree::List::{2}::partition_at_pivot] -/ -def betree_list_partition_at_pivot_fwd - (T : Type) (self : betree_list_t (UInt64 × T)) (pivot : UInt64) : - (Result ((betree_list_t (UInt64 × T)) × (betree_list_t (UInt64 × T)))) - := - match h: self with - | betree_list_t.Cons hd tl => - let (i, t) := hd - if h: i >= pivot - then Result.ret (betree_list_t.Nil, betree_list_t.Cons (i, t) tl) - else - do - let p ← betree_list_partition_at_pivot_fwd T tl pivot - let (ls0, ls1) := p - let l := ls0 - Result.ret (betree_list_t.Cons (i, t) l, ls1) - | betree_list_t.Nil => Result.ret (betree_list_t.Nil, betree_list_t.Nil) -termination_by betree_list_partition_at_pivot_fwd self pivot => - betree_list_partition_at_pivot_terminates T self pivot -decreasing_by betree_list_partition_at_pivot_decreases self pivot - -/- [betree_main::betree::Leaf::{3}::split] -/ -def betree_leaf_split_fwd - (self : betree_leaf_t) (content : betree_list_t (UInt64 × UInt64)) - (params : betree_params_t) (node_id_cnt : betree_node_id_counter_t) - (st : State) : - Result (State × betree_internal_t) - := - do - let p ← - betree_list_split_at_fwd (UInt64 × UInt64) content - params.betree_params_split_size - let (content0, content1) := p - let p0 ← betree_list_hd_fwd (UInt64 × UInt64) content1 - let (pivot, _) := p0 - let id0 ← betree_node_id_counter_fresh_id_fwd node_id_cnt - let node_id_cnt0 ← betree_node_id_counter_fresh_id_back node_id_cnt - let id1 ← betree_node_id_counter_fresh_id_fwd node_id_cnt0 - let (st0, _) ← betree_store_leaf_node_fwd id0 content0 st - let (st1, _) ← betree_store_leaf_node_fwd id1 content1 st0 - let n := betree_node_t.Leaf - { - betree_leaf_id := id0, - betree_leaf_size := params.betree_params_split_size - } - let n0 := betree_node_t.Leaf - { - betree_leaf_id := id1, - betree_leaf_size := params.betree_params_split_size - } - Result.ret (st1, mkbetree_internal_t self.betree_leaf_id pivot n n0) - -/- [betree_main::betree::Leaf::{3}::split] -/ -def betree_leaf_split_back - (self : betree_leaf_t) (content : betree_list_t (UInt64 × UInt64)) - (params : betree_params_t) (node_id_cnt : betree_node_id_counter_t) - (st : State) : - Result betree_node_id_counter_t - := - do - let p ← - betree_list_split_at_fwd (UInt64 × UInt64) content - params.betree_params_split_size - let (content0, content1) := p - let _ ← betree_list_hd_fwd (UInt64 × UInt64) content1 - let id0 ← betree_node_id_counter_fresh_id_fwd node_id_cnt - let node_id_cnt0 ← betree_node_id_counter_fresh_id_back node_id_cnt - let id1 ← betree_node_id_counter_fresh_id_fwd node_id_cnt0 - let (st0, _) ← betree_store_leaf_node_fwd id0 content0 st - let _ ← betree_store_leaf_node_fwd id1 content1 st0 - betree_node_id_counter_fresh_id_back node_id_cnt0 - -/- [betree_main::betree::Node::{5}::lookup_in_bindings] -/ -def betree_node_lookup_in_bindings_fwd - (key : UInt64) (bindings : betree_list_t (UInt64 × UInt64)) : - (Result (Option UInt64)) - := - match h: bindings with - | betree_list_t.Cons hd tl => - let (i, i0) := hd - if h: i = key - then Result.ret (Option.some i0) - else - if h: i > key - then Result.ret Option.none - else betree_node_lookup_in_bindings_fwd key tl - | betree_list_t.Nil => Result.ret Option.none -termination_by betree_node_lookup_in_bindings_fwd key bindings => - betree_node_lookup_in_bindings_terminates key bindings -decreasing_by betree_node_lookup_in_bindings_decreases key bindings - -/- [betree_main::betree::Node::{5}::lookup_first_message_for_key] -/ -def betree_node_lookup_first_message_for_key_fwd - (key : UInt64) (msgs : betree_list_t (UInt64 × betree_message_t)) : - (Result (betree_list_t (UInt64 × betree_message_t))) - := - match h: msgs with - | betree_list_t.Cons x next_msgs => - let (i, m) := x - if h: i >= key - then Result.ret (betree_list_t.Cons (i, m) next_msgs) - else betree_node_lookup_first_message_for_key_fwd key next_msgs - | betree_list_t.Nil => Result.ret betree_list_t.Nil -termination_by betree_node_lookup_first_message_for_key_fwd key msgs => - betree_node_lookup_first_message_for_key_terminates key msgs -decreasing_by betree_node_lookup_first_message_for_key_decreases key msgs - -/- [betree_main::betree::Node::{5}::lookup_first_message_for_key] -/ -def betree_node_lookup_first_message_for_key_back - (key : UInt64) (msgs : betree_list_t (UInt64 × betree_message_t)) - (ret0 : betree_list_t (UInt64 × betree_message_t)) : - (Result (betree_list_t (UInt64 × betree_message_t))) - := - match h: msgs with - | betree_list_t.Cons x next_msgs => - let (i, m) := x - if h: i >= key - then Result.ret ret0 - else - do - let next_msgs0 ← - betree_node_lookup_first_message_for_key_back key next_msgs ret0 - Result.ret (betree_list_t.Cons (i, m) next_msgs0) - | betree_list_t.Nil => Result.ret ret0 -termination_by betree_node_lookup_first_message_for_key_back key msgs ret0 => - betree_node_lookup_first_message_for_key_terminates key msgs -decreasing_by betree_node_lookup_first_message_for_key_decreases key msgs - -/- [betree_main::betree::Node::{5}::apply_upserts] -/ -def betree_node_apply_upserts_fwd - (msgs : betree_list_t (UInt64 × betree_message_t)) (prev : Option UInt64) - (key : UInt64) (st : State) : - (Result (State × UInt64)) - := - do - let b ← betree_list_head_has_key_fwd betree_message_t msgs key - if h: b - then - do - let msg ← betree_list_pop_front_fwd (UInt64 × betree_message_t) msgs - let (_, m) := msg - match h: m with - | betree_message_t.Insert i => Result.fail Error.panic - | betree_message_t.Delete => Result.fail Error.panic - | betree_message_t.Upsert s => - do - let v ← betree_upsert_update_fwd prev s - let msgs0 ← - betree_list_pop_front_back (UInt64 × betree_message_t) msgs - betree_node_apply_upserts_fwd msgs0 (Option.some v) key st - else - do - let (st0, v) ← - opaque_defs.core_option_option_unwrap_fwd UInt64 prev st - let _ ← - betree_list_push_front_fwd_back (UInt64 × betree_message_t) msgs - (key, betree_message_t.Insert v) - Result.ret (st0, v) -termination_by betree_node_apply_upserts_fwd msgs prev key st => - betree_node_apply_upserts_terminates msgs prev key st -decreasing_by betree_node_apply_upserts_decreases msgs prev key st - -/- [betree_main::betree::Node::{5}::apply_upserts] -/ -def betree_node_apply_upserts_back - (msgs : betree_list_t (UInt64 × betree_message_t)) (prev : Option UInt64) - (key : UInt64) (st : State) : - (Result (betree_list_t (UInt64 × betree_message_t))) - := - do - let b ← betree_list_head_has_key_fwd betree_message_t msgs key - if h: b - then - do - let msg ← betree_list_pop_front_fwd (UInt64 × betree_message_t) msgs - let (_, m) := msg - match h: m with - | betree_message_t.Insert i => Result.fail Error.panic - | betree_message_t.Delete => Result.fail Error.panic - | betree_message_t.Upsert s => - do - let v ← betree_upsert_update_fwd prev s - let msgs0 ← - betree_list_pop_front_back (UInt64 × betree_message_t) msgs - betree_node_apply_upserts_back msgs0 (Option.some v) key st - else - do - let (_, v) ← opaque_defs.core_option_option_unwrap_fwd UInt64 prev st - betree_list_push_front_fwd_back (UInt64 × betree_message_t) msgs (key, - betree_message_t.Insert v) -termination_by betree_node_apply_upserts_back msgs prev key st => - betree_node_apply_upserts_terminates msgs prev key st -decreasing_by betree_node_apply_upserts_decreases msgs prev key st - -/- [betree_main::betree::Node::{5}::lookup] -/ -mutual def betree_node_lookup_fwd - (self : betree_node_t) (key : UInt64) (st : State) : - (Result (State × (Option UInt64))) - := - match h: self with - | betree_node_t.Internal node => - do - let (mkbetree_internal_t i i0 n n0) := node - let (st0, msgs) ← betree_load_internal_node_fwd i st - let pending ← betree_node_lookup_first_message_for_key_fwd key msgs - match h: pending with - | betree_list_t.Cons p l => - let (k, msg) := p - if h: k != key - then - do - let (st1, opt) ← - betree_internal_lookup_in_children_fwd (mkbetree_internal_t i i0 - n n0) key st0 - let _ ← - betree_node_lookup_first_message_for_key_back key msgs - (betree_list_t.Cons (k, msg) l) - Result.ret (st1, opt) - else - match h: msg with - | betree_message_t.Insert v => - do - let _ ← - betree_node_lookup_first_message_for_key_back key msgs - (betree_list_t.Cons (k, betree_message_t.Insert v) l) - Result.ret (st0, Option.some v) - | betree_message_t.Delete => - do - let _ ← - betree_node_lookup_first_message_for_key_back key msgs - (betree_list_t.Cons (k, betree_message_t.Delete) l) - Result.ret (st0, Option.none) - | betree_message_t.Upsert ufs => - do - let (st1, v) ← - betree_internal_lookup_in_children_fwd (mkbetree_internal_t i - i0 n n0) key st0 - let (st2, v0) ← - betree_node_apply_upserts_fwd (betree_list_t.Cons (k, - betree_message_t.Upsert ufs) l) v key st1 - let node0 ← - betree_internal_lookup_in_children_back (mkbetree_internal_t i - i0 n n0) key st0 - let (mkbetree_internal_t i1 _ _ _) := node0 - let pending0 ← - betree_node_apply_upserts_back (betree_list_t.Cons (k, - betree_message_t.Upsert ufs) l) v key st1 - let msgs0 ← - betree_node_lookup_first_message_for_key_back key msgs pending0 - let (st3, _) ← betree_store_internal_node_fwd i1 msgs0 st2 - Result.ret (st3, Option.some v0) - | betree_list_t.Nil => - do - let (st1, opt) ← - betree_internal_lookup_in_children_fwd (mkbetree_internal_t i i0 n - n0) key st0 - let _ ← - betree_node_lookup_first_message_for_key_back key msgs - betree_list_t.Nil - Result.ret (st1, opt) - | betree_node_t.Leaf node => - do - let (st0, bindings) ← betree_load_leaf_node_fwd node.betree_leaf_id st - let opt ← betree_node_lookup_in_bindings_fwd key bindings - Result.ret (st0, opt) -termination_by betree_node_lookup_fwd self key st => - betree_node_lookup_terminates self key st -decreasing_by betree_node_lookup_decreases self key st - -/- [betree_main::betree::Node::{5}::lookup] -/ -def betree_node_lookup_back - (self : betree_node_t) (key : UInt64) (st : State) : - (Result betree_node_t) - := - match h: self with - | betree_node_t.Internal node => - do - let (mkbetree_internal_t i i0 n n0) := node - let (st0, msgs) ← betree_load_internal_node_fwd i st - let pending ← betree_node_lookup_first_message_for_key_fwd key msgs - match h: pending with - | betree_list_t.Cons p l => - let (k, msg) := p - if h: k != key - then - do - let _ ← - betree_node_lookup_first_message_for_key_back key msgs - (betree_list_t.Cons (k, msg) l) - let node0 ← - betree_internal_lookup_in_children_back (mkbetree_internal_t i i0 - n n0) key st0 - Result.ret (betree_node_t.Internal node0) - else - match h: msg with - | betree_message_t.Insert v => - do - let _ ← - betree_node_lookup_first_message_for_key_back key msgs - (betree_list_t.Cons (k, betree_message_t.Insert v) l) - Result.ret (betree_node_t.Internal (mkbetree_internal_t i i0 n - n0)) - | betree_message_t.Delete => - do - let _ ← - betree_node_lookup_first_message_for_key_back key msgs - (betree_list_t.Cons (k, betree_message_t.Delete) l) - Result.ret (betree_node_t.Internal (mkbetree_internal_t i i0 n - n0)) - | betree_message_t.Upsert ufs => - do - let (st1, v) ← - betree_internal_lookup_in_children_fwd (mkbetree_internal_t i - i0 n n0) key st0 - let (st2, _) ← - betree_node_apply_upserts_fwd (betree_list_t.Cons (k, - betree_message_t.Upsert ufs) l) v key st1 - let node0 ← - betree_internal_lookup_in_children_back (mkbetree_internal_t i - i0 n n0) key st0 - let (mkbetree_internal_t i1 i2 n1 n2) := node0 - let pending0 ← - betree_node_apply_upserts_back (betree_list_t.Cons (k, - betree_message_t.Upsert ufs) l) v key st1 - let msgs0 ← - betree_node_lookup_first_message_for_key_back key msgs pending0 - let _ ← betree_store_internal_node_fwd i1 msgs0 st2 - Result.ret (betree_node_t.Internal (mkbetree_internal_t i1 i2 n1 - n2)) - | betree_list_t.Nil => - do - let _ ← - betree_node_lookup_first_message_for_key_back key msgs - betree_list_t.Nil - let node0 ← - betree_internal_lookup_in_children_back (mkbetree_internal_t i i0 n - n0) key st0 - Result.ret (betree_node_t.Internal node0) - | betree_node_t.Leaf node => - do - let (_, bindings) ← betree_load_leaf_node_fwd node.betree_leaf_id st - let _ ← betree_node_lookup_in_bindings_fwd key bindings - Result.ret (betree_node_t.Leaf node) -termination_by betree_node_lookup_back self key st => - betree_node_lookup_terminates self key st -decreasing_by betree_node_lookup_decreases self key st - -/- [betree_main::betree::Internal::{4}::lookup_in_children] -/ -def betree_internal_lookup_in_children_fwd - (self : betree_internal_t) (key : UInt64) (st : State) : - (Result (State × (Option UInt64))) - := - let (mkbetree_internal_t _ i n n0) := self - if h: key < i - then betree_node_lookup_fwd n key st - else betree_node_lookup_fwd n0 key st -termination_by betree_internal_lookup_in_children_fwd self key st => - betree_internal_lookup_in_children_terminates self key st -decreasing_by betree_internal_lookup_in_children_decreases self key st - -/- [betree_main::betree::Internal::{4}::lookup_in_children] -/ -def betree_internal_lookup_in_children_back - (self : betree_internal_t) (key : UInt64) (st : State) : - (Result betree_internal_t) - := - let (mkbetree_internal_t i i0 n n0) := self - if h: key < i0 - then - do - let n1 ← betree_node_lookup_back n key st - Result.ret (mkbetree_internal_t i i0 n1 n0) - else - do - let n1 ← betree_node_lookup_back n0 key st - Result.ret (mkbetree_internal_t i i0 n n1) -termination_by betree_internal_lookup_in_children_back self key st => - betree_internal_lookup_in_children_terminates self key st -decreasing_by betree_internal_lookup_in_children_decreases self key st - -/- [betree_main::betree::Node::{5}::lookup_mut_in_bindings] -/ -def betree_node_lookup_mut_in_bindings_fwd - (key : UInt64) (bindings : betree_list_t (UInt64 × UInt64)) : - (Result (betree_list_t (UInt64 × UInt64))) - := - match h: bindings with - | betree_list_t.Cons hd tl => - let (i, i0) := hd - if h: i >= key - then Result.ret (betree_list_t.Cons (i, i0) tl) - else betree_node_lookup_mut_in_bindings_fwd key tl - | betree_list_t.Nil => Result.ret betree_list_t.Nil -termination_by betree_node_lookup_mut_in_bindings_fwd key bindings => - betree_node_lookup_mut_in_bindings_terminates key bindings -decreasing_by betree_node_lookup_mut_in_bindings_decreases key bindings - -/- [betree_main::betree::Node::{5}::lookup_mut_in_bindings] -/ -def betree_node_lookup_mut_in_bindings_back - (key : UInt64) (bindings : betree_list_t (UInt64 × UInt64)) - (ret0 : betree_list_t (UInt64 × UInt64)) : - (Result (betree_list_t (UInt64 × UInt64))) - := - match h: bindings with - | betree_list_t.Cons hd tl => - let (i, i0) := hd - if h: i >= key - then Result.ret ret0 - else - do - let tl0 ← betree_node_lookup_mut_in_bindings_back key tl ret0 - Result.ret (betree_list_t.Cons (i, i0) tl0) - | betree_list_t.Nil => Result.ret ret0 -termination_by betree_node_lookup_mut_in_bindings_back key bindings ret0 => - betree_node_lookup_mut_in_bindings_terminates key bindings -decreasing_by betree_node_lookup_mut_in_bindings_decreases key bindings - -/- [betree_main::betree::Node::{5}::apply_to_leaf] -/ -def betree_node_apply_to_leaf_fwd_back - (bindings : betree_list_t (UInt64 × UInt64)) (key : UInt64) - (new_msg : betree_message_t) : - Result (betree_list_t (UInt64 × UInt64)) - := - do - let bindings0 ← betree_node_lookup_mut_in_bindings_fwd key bindings - let b ← betree_list_head_has_key_fwd UInt64 bindings0 key - if h: b - then - do - let hd ← betree_list_pop_front_fwd (UInt64 × UInt64) bindings0 - match h: new_msg with - | betree_message_t.Insert v => - do - let bindings1 ← - betree_list_pop_front_back (UInt64 × UInt64) bindings0 - let bindings2 ← - betree_list_push_front_fwd_back (UInt64 × UInt64) bindings1 - (key, v) - betree_node_lookup_mut_in_bindings_back key bindings bindings2 - | betree_message_t.Delete => - do - let bindings1 ← - betree_list_pop_front_back (UInt64 × UInt64) bindings0 - betree_node_lookup_mut_in_bindings_back key bindings bindings1 - | betree_message_t.Upsert s => - do - let (_, i) := hd - let v ← betree_upsert_update_fwd (Option.some i) s - let bindings1 ← - betree_list_pop_front_back (UInt64 × UInt64) bindings0 - let bindings2 ← - betree_list_push_front_fwd_back (UInt64 × UInt64) bindings1 - (key, v) - betree_node_lookup_mut_in_bindings_back key bindings bindings2 - else - match h: new_msg with - | betree_message_t.Insert v => - do - let bindings1 ← - betree_list_push_front_fwd_back (UInt64 × UInt64) bindings0 (key, - v) - betree_node_lookup_mut_in_bindings_back key bindings bindings1 - | betree_message_t.Delete => - betree_node_lookup_mut_in_bindings_back key bindings bindings0 - | betree_message_t.Upsert s => - do - let v ← betree_upsert_update_fwd Option.none s - let bindings1 ← - betree_list_push_front_fwd_back (UInt64 × UInt64) bindings0 (key, - v) - betree_node_lookup_mut_in_bindings_back key bindings bindings1 - -/- [betree_main::betree::Node::{5}::apply_messages_to_leaf] -/ -def betree_node_apply_messages_to_leaf_fwd_back - (bindings : betree_list_t (UInt64 × UInt64)) - (new_msgs : betree_list_t (UInt64 × betree_message_t)) : - (Result (betree_list_t (UInt64 × UInt64))) - := - match h: new_msgs with - | betree_list_t.Cons new_msg new_msgs_tl => - do - let (i, m) := new_msg - let bindings0 ← betree_node_apply_to_leaf_fwd_back bindings i m - betree_node_apply_messages_to_leaf_fwd_back bindings0 new_msgs_tl - | betree_list_t.Nil => Result.ret bindings -termination_by betree_node_apply_messages_to_leaf_fwd_back bindings new_msgs => - betree_node_apply_messages_to_leaf_terminates bindings new_msgs -decreasing_by betree_node_apply_messages_to_leaf_decreases bindings new_msgs - -/- [betree_main::betree::Node::{5}::filter_messages_for_key] -/ -def betree_node_filter_messages_for_key_fwd_back - (key : UInt64) (msgs : betree_list_t (UInt64 × betree_message_t)) : - (Result (betree_list_t (UInt64 × betree_message_t))) - := - match h: msgs with - | betree_list_t.Cons p l => - let (k, m) := p - if h: k = key - then - do - let msgs0 ← - betree_list_pop_front_back (UInt64 × betree_message_t) - (betree_list_t.Cons (k, m) l) - betree_node_filter_messages_for_key_fwd_back key msgs0 - else Result.ret (betree_list_t.Cons (k, m) l) - | betree_list_t.Nil => Result.ret betree_list_t.Nil -termination_by betree_node_filter_messages_for_key_fwd_back key msgs => - betree_node_filter_messages_for_key_terminates key msgs -decreasing_by betree_node_filter_messages_for_key_decreases key msgs - -/- [betree_main::betree::Node::{5}::lookup_first_message_after_key] -/ -def betree_node_lookup_first_message_after_key_fwd - (key : UInt64) (msgs : betree_list_t (UInt64 × betree_message_t)) : - (Result (betree_list_t (UInt64 × betree_message_t))) - := - match h: msgs with - | betree_list_t.Cons p next_msgs => - let (k, m) := p - if h: k = key - then betree_node_lookup_first_message_after_key_fwd key next_msgs - else Result.ret (betree_list_t.Cons (k, m) next_msgs) - | betree_list_t.Nil => Result.ret betree_list_t.Nil -termination_by betree_node_lookup_first_message_after_key_fwd key msgs => - betree_node_lookup_first_message_after_key_terminates key msgs -decreasing_by betree_node_lookup_first_message_after_key_decreases key msgs - -/- [betree_main::betree::Node::{5}::lookup_first_message_after_key] -/ -def betree_node_lookup_first_message_after_key_back - (key : UInt64) (msgs : betree_list_t (UInt64 × betree_message_t)) - (ret0 : betree_list_t (UInt64 × betree_message_t)) : - (Result (betree_list_t (UInt64 × betree_message_t))) - := - match h: msgs with - | betree_list_t.Cons p next_msgs => - let (k, m) := p - if h: k = key - then - do - let next_msgs0 ← - betree_node_lookup_first_message_after_key_back key next_msgs ret0 - Result.ret (betree_list_t.Cons (k, m) next_msgs0) - else Result.ret ret0 - | betree_list_t.Nil => Result.ret ret0 -termination_by betree_node_lookup_first_message_after_key_back key msgs ret0 => - betree_node_lookup_first_message_after_key_terminates key msgs -decreasing_by betree_node_lookup_first_message_after_key_decreases key msgs - -/- [betree_main::betree::Node::{5}::apply_to_internal] -/ -def betree_node_apply_to_internal_fwd_back - (msgs : betree_list_t (UInt64 × betree_message_t)) (key : UInt64) - (new_msg : betree_message_t) : - Result (betree_list_t (UInt64 × betree_message_t)) - := - do - let msgs0 ← betree_node_lookup_first_message_for_key_fwd key msgs - let b ← betree_list_head_has_key_fwd betree_message_t msgs0 key - if h: b - then - match h: new_msg with - | betree_message_t.Insert i => - do - let msgs1 ← betree_node_filter_messages_for_key_fwd_back key msgs0 - let msgs2 ← - betree_list_push_front_fwd_back (UInt64 × betree_message_t) msgs1 - (key, betree_message_t.Insert i) - betree_node_lookup_first_message_for_key_back key msgs msgs2 - | betree_message_t.Delete => - do - let msgs1 ← betree_node_filter_messages_for_key_fwd_back key msgs0 - let msgs2 ← - betree_list_push_front_fwd_back (UInt64 × betree_message_t) msgs1 - (key, betree_message_t.Delete) - betree_node_lookup_first_message_for_key_back key msgs msgs2 - | betree_message_t.Upsert s => - do - let p ← betree_list_hd_fwd (UInt64 × betree_message_t) msgs0 - let (_, m) := p - match h: m with - | betree_message_t.Insert prev => - do - let v ← betree_upsert_update_fwd (Option.some prev) s - let msgs1 ← - betree_list_pop_front_back (UInt64 × betree_message_t) msgs0 - let msgs2 ← - betree_list_push_front_fwd_back (UInt64 × betree_message_t) - msgs1 (key, betree_message_t.Insert v) - betree_node_lookup_first_message_for_key_back key msgs msgs2 - | betree_message_t.Delete => - do - let v ← betree_upsert_update_fwd Option.none s - let msgs1 ← - betree_list_pop_front_back (UInt64 × betree_message_t) msgs0 - let msgs2 ← - betree_list_push_front_fwd_back (UInt64 × betree_message_t) - msgs1 (key, betree_message_t.Insert v) - betree_node_lookup_first_message_for_key_back key msgs msgs2 - | betree_message_t.Upsert ufs => - do - let msgs1 ← - betree_node_lookup_first_message_after_key_fwd key msgs0 - let msgs2 ← - betree_list_push_front_fwd_back (UInt64 × betree_message_t) - msgs1 (key, betree_message_t.Upsert s) - let msgs3 ← - betree_node_lookup_first_message_after_key_back key msgs0 msgs2 - betree_node_lookup_first_message_for_key_back key msgs msgs3 - else - do - let msgs1 ← - betree_list_push_front_fwd_back (UInt64 × betree_message_t) msgs0 - (key, new_msg) - betree_node_lookup_first_message_for_key_back key msgs msgs1 - -/- [betree_main::betree::Node::{5}::apply_messages_to_internal] -/ -def betree_node_apply_messages_to_internal_fwd_back - (msgs : betree_list_t (UInt64 × betree_message_t)) - (new_msgs : betree_list_t (UInt64 × betree_message_t)) : - (Result (betree_list_t (UInt64 × betree_message_t))) - := - match h: new_msgs with - | betree_list_t.Cons new_msg new_msgs_tl => - do - let (i, m) := new_msg - let msgs0 ← betree_node_apply_to_internal_fwd_back msgs i m - betree_node_apply_messages_to_internal_fwd_back msgs0 new_msgs_tl - | betree_list_t.Nil => Result.ret msgs -termination_by betree_node_apply_messages_to_internal_fwd_back msgs new_msgs => - betree_node_apply_messages_to_internal_terminates msgs new_msgs -decreasing_by betree_node_apply_messages_to_internal_decreases msgs new_msgs - -/- [betree_main::betree::Node::{5}::apply_messages] -/ -mutual def betree_node_apply_messages_fwd - (self : betree_node_t) (params : betree_params_t) - (node_id_cnt : betree_node_id_counter_t) - (msgs : betree_list_t (UInt64 × betree_message_t)) (st : State) : - (Result (State × Unit)) - := - match h: self with - | betree_node_t.Internal node => - do - let (mkbetree_internal_t i i0 n n0) := node - let (st0, content) ← betree_load_internal_node_fwd i st - let content0 ← - betree_node_apply_messages_to_internal_fwd_back content msgs - let num_msgs ← - betree_list_len_fwd (UInt64 × betree_message_t) content0 - if h: num_msgs >= params.betree_params_min_flush_size - then - do - let (st1, content1) ← - betree_internal_flush_fwd (mkbetree_internal_t i i0 n n0) params - node_id_cnt content0 st0 - let (node0, _) ← - betree_internal_flush_back (mkbetree_internal_t i i0 n n0) params - node_id_cnt content0 st0 - let (mkbetree_internal_t i1 _ _ _) := node0 - let (st2, _) ← betree_store_internal_node_fwd i1 content1 st1 - Result.ret (st2, ()) - else - do - let (st1, _) ← betree_store_internal_node_fwd i content0 st0 - Result.ret (st1, ()) - | betree_node_t.Leaf node => - do - let (st0, content) ← betree_load_leaf_node_fwd node.betree_leaf_id st - let content0 ← betree_node_apply_messages_to_leaf_fwd_back content msgs - let len ← betree_list_len_fwd (UInt64 × UInt64) content0 - let i ← UInt64.checked_mul (UInt64.ofNatCore 2 (by intlit)) - params.betree_params_split_size - if h: len >= i - then - do - let (st1, _) ← - betree_leaf_split_fwd node content0 params node_id_cnt st0 - let (st2, _) ← - betree_store_leaf_node_fwd node.betree_leaf_id betree_list_t.Nil - st1 - Result.ret (st2, ()) - else - do - let (st1, _) ← - betree_store_leaf_node_fwd node.betree_leaf_id content0 st0 - Result.ret (st1, ()) -termination_by betree_node_apply_messages_fwd self params node_id_cnt msgs st - => - betree_node_apply_messages_terminates self params node_id_cnt msgs st -decreasing_by - betree_node_apply_messages_decreases self params node_id_cnt msgs st - -/- [betree_main::betree::Node::{5}::apply_messages] -/ -def betree_node_apply_messages_back - (self : betree_node_t) (params : betree_params_t) - (node_id_cnt : betree_node_id_counter_t) - (msgs : betree_list_t (UInt64 × betree_message_t)) (st : State) : - (Result (betree_node_t × betree_node_id_counter_t)) - := - match h: self with - | betree_node_t.Internal node => - do - let (mkbetree_internal_t i i0 n n0) := node - let (st0, content) ← betree_load_internal_node_fwd i st - let content0 ← - betree_node_apply_messages_to_internal_fwd_back content msgs - let num_msgs ← - betree_list_len_fwd (UInt64 × betree_message_t) content0 - if h: num_msgs >= params.betree_params_min_flush_size - then - do - let (st1, content1) ← - betree_internal_flush_fwd (mkbetree_internal_t i i0 n n0) params - node_id_cnt content0 st0 - let (node0, node_id_cnt0) ← - betree_internal_flush_back (mkbetree_internal_t i i0 n n0) params - node_id_cnt content0 st0 - let (mkbetree_internal_t i1 i2 n1 n2) := node0 - let _ ← betree_store_internal_node_fwd i1 content1 st1 - Result.ret (betree_node_t.Internal (mkbetree_internal_t i1 i2 n1 n2), - node_id_cnt0) - else - do - let _ ← betree_store_internal_node_fwd i content0 st0 - Result.ret (betree_node_t.Internal (mkbetree_internal_t i i0 n n0), - node_id_cnt) - | betree_node_t.Leaf node => - do - let (st0, content) ← betree_load_leaf_node_fwd node.betree_leaf_id st - let content0 ← betree_node_apply_messages_to_leaf_fwd_back content msgs - let len ← betree_list_len_fwd (UInt64 × UInt64) content0 - let i ← UInt64.checked_mul (UInt64.ofNatCore 2 (by intlit)) - params.betree_params_split_size - if h: len >= i - then - do - let (st1, new_node) ← - betree_leaf_split_fwd node content0 params node_id_cnt st0 - let _ ← - betree_store_leaf_node_fwd node.betree_leaf_id betree_list_t.Nil - st1 - let node_id_cnt0 ← - betree_leaf_split_back node content0 params node_id_cnt st0 - Result.ret (betree_node_t.Internal new_node, node_id_cnt0) - else - do - let _ ← betree_store_leaf_node_fwd node.betree_leaf_id content0 st0 - Result.ret (betree_node_t.Leaf { node with betree_leaf_size := len }, - node_id_cnt) -termination_by betree_node_apply_messages_back self params node_id_cnt msgs st - => - betree_node_apply_messages_terminates self params node_id_cnt msgs st -decreasing_by - betree_node_apply_messages_decreases self params node_id_cnt msgs st - -/- [betree_main::betree::Internal::{4}::flush] -/ -def betree_internal_flush_fwd - (self : betree_internal_t) (params : betree_params_t) - (node_id_cnt : betree_node_id_counter_t) - (content : betree_list_t (UInt64 × betree_message_t)) (st : State) : - (Result (State × (betree_list_t (UInt64 × betree_message_t)))) - := - do - let (mkbetree_internal_t _ i n n0) := self - let p ← betree_list_partition_at_pivot_fwd betree_message_t content i - let (msgs_left, msgs_right) := p - let len_left ← betree_list_len_fwd (UInt64 × betree_message_t) msgs_left - if h: len_left >= params.betree_params_min_flush_size - then - do - let (st0, _) ← - betree_node_apply_messages_fwd n params node_id_cnt msgs_left st - let (_, node_id_cnt0) ← - betree_node_apply_messages_back n params node_id_cnt msgs_left st - let len_right ← - betree_list_len_fwd (UInt64 × betree_message_t) msgs_right - if h: len_right >= params.betree_params_min_flush_size - then - do - let (st1, _) ← - betree_node_apply_messages_fwd n0 params node_id_cnt0 msgs_right - st0 - let _ ← - betree_node_apply_messages_back n0 params node_id_cnt0 msgs_right - st0 - Result.ret (st1, betree_list_t.Nil) - else Result.ret (st0, msgs_right) - else - do - let (st0, _) ← - betree_node_apply_messages_fwd n0 params node_id_cnt msgs_right st - let _ ← - betree_node_apply_messages_back n0 params node_id_cnt msgs_right st - Result.ret (st0, msgs_left) -termination_by betree_internal_flush_fwd self params node_id_cnt content st => - betree_internal_flush_terminates self params node_id_cnt content st -decreasing_by - betree_internal_flush_decreases self params node_id_cnt content st - -/- [betree_main::betree::Internal::{4}::flush] -/ -def betree_internal_flush_back - (self : betree_internal_t) (params : betree_params_t) - (node_id_cnt : betree_node_id_counter_t) - (content : betree_list_t (UInt64 × betree_message_t)) (st : State) : - (Result (betree_internal_t × betree_node_id_counter_t)) - := - do - let (mkbetree_internal_t i i0 n n0) := self - let p ← betree_list_partition_at_pivot_fwd betree_message_t content i0 - let (msgs_left, msgs_right) := p - let len_left ← betree_list_len_fwd (UInt64 × betree_message_t) msgs_left - if h: len_left >= params.betree_params_min_flush_size - then - do - let (st0, _) ← - betree_node_apply_messages_fwd n params node_id_cnt msgs_left st - let (n1, node_id_cnt0) ← - betree_node_apply_messages_back n params node_id_cnt msgs_left st - let len_right ← - betree_list_len_fwd (UInt64 × betree_message_t) msgs_right - if h: len_right >= params.betree_params_min_flush_size - then - do - let (n2, node_id_cnt1) ← - betree_node_apply_messages_back n0 params node_id_cnt0 msgs_right - st0 - Result.ret (mkbetree_internal_t i i0 n1 n2, node_id_cnt1) - else Result.ret (mkbetree_internal_t i i0 n1 n0, node_id_cnt0) - else - do - let (n1, node_id_cnt0) ← - betree_node_apply_messages_back n0 params node_id_cnt msgs_right st - Result.ret (mkbetree_internal_t i i0 n n1, node_id_cnt0) -termination_by betree_internal_flush_back self params node_id_cnt content st => - betree_internal_flush_terminates self params node_id_cnt content st -decreasing_by - betree_internal_flush_decreases self params node_id_cnt content st - -/- [betree_main::betree::Node::{5}::apply] -/ -def betree_node_apply_fwd - (self : betree_node_t) (params : betree_params_t) - (node_id_cnt : betree_node_id_counter_t) (key : UInt64) - (new_msg : betree_message_t) (st : State) : - Result (State × Unit) - := - do - let l := betree_list_t.Nil - let (st0, _) ← - betree_node_apply_messages_fwd self params node_id_cnt - (betree_list_t.Cons (key, new_msg) l) st - let _ ← - betree_node_apply_messages_back self params node_id_cnt - (betree_list_t.Cons (key, new_msg) l) st - Result.ret (st0, ()) - -/- [betree_main::betree::Node::{5}::apply] -/ -def betree_node_apply_back - (self : betree_node_t) (params : betree_params_t) - (node_id_cnt : betree_node_id_counter_t) (key : UInt64) - (new_msg : betree_message_t) (st : State) : - Result (betree_node_t × betree_node_id_counter_t) - := - let l := betree_list_t.Nil - betree_node_apply_messages_back self params node_id_cnt (betree_list_t.Cons - (key, new_msg) l) st - -/- [betree_main::betree::BeTree::{6}::new] -/ -def betree_be_tree_new_fwd - (min_flush_size : UInt64) (split_size : UInt64) (st : State) : - Result (State × betree_be_tree_t) - := - do - let node_id_cnt ← betree_node_id_counter_new_fwd - let id ← betree_node_id_counter_fresh_id_fwd node_id_cnt - let (st0, _) ← betree_store_leaf_node_fwd id betree_list_t.Nil st - let node_id_cnt0 ← betree_node_id_counter_fresh_id_back node_id_cnt - Result.ret (st0, - { - betree_be_tree_params := - { - betree_params_min_flush_size := min_flush_size, - betree_params_split_size := split_size - }, - betree_be_tree_node_id_cnt := node_id_cnt0, - betree_be_tree_root := - (betree_node_t.Leaf - { - betree_leaf_id := id, - betree_leaf_size := (UInt64.ofNatCore 0 (by intlit)) - }) - }) - -/- [betree_main::betree::BeTree::{6}::apply] -/ -def betree_be_tree_apply_fwd - (self : betree_be_tree_t) (key : UInt64) (msg : betree_message_t) - (st : State) : - Result (State × Unit) - := - do - let (st0, _) ← - betree_node_apply_fwd self.betree_be_tree_root self.betree_be_tree_params - self.betree_be_tree_node_id_cnt key msg st - let _ ← - betree_node_apply_back self.betree_be_tree_root - self.betree_be_tree_params self.betree_be_tree_node_id_cnt key msg st - Result.ret (st0, ()) - -/- [betree_main::betree::BeTree::{6}::apply] -/ -def betree_be_tree_apply_back - (self : betree_be_tree_t) (key : UInt64) (msg : betree_message_t) - (st : State) : - Result betree_be_tree_t - := - do - let (n, nic) ← - betree_node_apply_back self.betree_be_tree_root - self.betree_be_tree_params self.betree_be_tree_node_id_cnt key msg st - Result.ret - { self with betree_be_tree_node_id_cnt := nic, betree_be_tree_root := n } - -/- [betree_main::betree::BeTree::{6}::insert] -/ -def betree_be_tree_insert_fwd - (self : betree_be_tree_t) (key : UInt64) (value : UInt64) (st : State) : - Result (State × Unit) - := - do - let (st0, _) ← - betree_be_tree_apply_fwd self key (betree_message_t.Insert value) st - let _ ← - betree_be_tree_apply_back self key (betree_message_t.Insert value) st - Result.ret (st0, ()) - -/- [betree_main::betree::BeTree::{6}::insert] -/ -def betree_be_tree_insert_back - (self : betree_be_tree_t) (key : UInt64) (value : UInt64) (st : State) : - Result betree_be_tree_t - := - betree_be_tree_apply_back self key (betree_message_t.Insert value) st - -/- [betree_main::betree::BeTree::{6}::delete] -/ -def betree_be_tree_delete_fwd - (self : betree_be_tree_t) (key : UInt64) (st : State) : - Result (State × Unit) - := - do - let (st0, _) ← - betree_be_tree_apply_fwd self key betree_message_t.Delete st - let _ ← betree_be_tree_apply_back self key betree_message_t.Delete st - Result.ret (st0, ()) - -/- [betree_main::betree::BeTree::{6}::delete] -/ -def betree_be_tree_delete_back - (self : betree_be_tree_t) (key : UInt64) (st : State) : - Result betree_be_tree_t - := - betree_be_tree_apply_back self key betree_message_t.Delete st - -/- [betree_main::betree::BeTree::{6}::upsert] -/ -def betree_be_tree_upsert_fwd - (self : betree_be_tree_t) (key : UInt64) (upd : betree_upsert_fun_state_t) - (st : State) : - Result (State × Unit) - := - do - let (st0, _) ← - betree_be_tree_apply_fwd self key (betree_message_t.Upsert upd) st - let _ ← - betree_be_tree_apply_back self key (betree_message_t.Upsert upd) st - Result.ret (st0, ()) - -/- [betree_main::betree::BeTree::{6}::upsert] -/ -def betree_be_tree_upsert_back - (self : betree_be_tree_t) (key : UInt64) (upd : betree_upsert_fun_state_t) - (st : State) : - Result betree_be_tree_t - := - betree_be_tree_apply_back self key (betree_message_t.Upsert upd) st - -/- [betree_main::betree::BeTree::{6}::lookup] -/ -def betree_be_tree_lookup_fwd - (self : betree_be_tree_t) (key : UInt64) (st : State) : - Result (State × (Option UInt64)) - := - betree_node_lookup_fwd self.betree_be_tree_root key st - -/- [betree_main::betree::BeTree::{6}::lookup] -/ -def betree_be_tree_lookup_back - (self : betree_be_tree_t) (key : UInt64) (st : State) : - Result betree_be_tree_t - := - do - let n ← betree_node_lookup_back self.betree_be_tree_root key st - Result.ret { self with betree_be_tree_root := n } - -/- [betree_main::main] -/ -def main_fwd : Result Unit := - Result.ret () - -/- Unit test for [betree_main::main] -/ -#assert (main_fwd == .ret ()) - |