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-rw-r--r--tests/hol4/loops/Holmakefile5
-rw-r--r--tests/hol4/loops/loops_FunsScript.sml755
-rw-r--r--tests/hol4/loops/loops_FunsTheory.sig731
-rw-r--r--tests/hol4/loops/loops_TypesScript.sml13
-rw-r--r--tests/hol4/loops/loops_TypesTheory.sig94
5 files changed, 1598 insertions, 0 deletions
diff --git a/tests/hol4/loops/Holmakefile b/tests/hol4/loops/Holmakefile
new file mode 100644
index 00000000..3c4b8973
--- /dev/null
+++ b/tests/hol4/loops/Holmakefile
@@ -0,0 +1,5 @@
+# This file was automatically generated - modify ../Holmakefile.template instead
+INCLUDES = ../../../backends/hol4
+
+all: $(DEFAULT_TARGETS)
+.PHONY: all
diff --git a/tests/hol4/loops/loops_FunsScript.sml b/tests/hol4/loops/loops_FunsScript.sml
new file mode 100644
index 00000000..65cf77d4
--- /dev/null
+++ b/tests/hol4/loops/loops_FunsScript.sml
@@ -0,0 +1,755 @@
+(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *)
+(** [loops]: function definitions *)
+open primitivesLib divDefLib
+open loops_TypesTheory
+
+val _ = new_theory "loops_Funs"
+
+
+val [sum_loop_fwd_def] = DefineDiv ‘
+ (** [loops::sum]: loop 0: forward function *)
+ sum_loop_fwd (max : u32) (i : u32) (s : u32) : u32 result =
+ if u32_lt i max
+ then (
+ do
+ s0 <- u32_add s i;
+ i0 <- u32_add i (int_to_u32 1);
+ sum_loop_fwd max i0 s0
+ od)
+ else u32_mul s (int_to_u32 2)
+’
+
+val sum_fwd_def = Define ‘
+ (** [loops::sum]: forward function *)
+ sum_fwd (max : u32) : u32 result =
+ sum_loop_fwd max (int_to_u32 0) (int_to_u32 0)
+’
+
+val [sum_with_mut_borrows_loop_fwd_def] = DefineDiv ‘
+ (** [loops::sum_with_mut_borrows]: loop 0: forward function *)
+ sum_with_mut_borrows_loop_fwd
+ (max : u32) (mi : u32) (ms : u32) : u32 result =
+ if u32_lt mi max
+ then (
+ do
+ ms0 <- u32_add ms mi;
+ mi0 <- u32_add mi (int_to_u32 1);
+ sum_with_mut_borrows_loop_fwd max mi0 ms0
+ od)
+ else u32_mul ms (int_to_u32 2)
+’
+
+val sum_with_mut_borrows_fwd_def = Define ‘
+ (** [loops::sum_with_mut_borrows]: forward function *)
+ sum_with_mut_borrows_fwd (max : u32) : u32 result =
+ sum_with_mut_borrows_loop_fwd max (int_to_u32 0) (int_to_u32 0)
+’
+
+val [sum_with_shared_borrows_loop_fwd_def] = DefineDiv ‘
+ (** [loops::sum_with_shared_borrows]: loop 0: forward function *)
+ sum_with_shared_borrows_loop_fwd
+ (max : u32) (i : u32) (s : u32) : u32 result =
+ if u32_lt i max
+ then (
+ do
+ i0 <- u32_add i (int_to_u32 1);
+ s0 <- u32_add s i0;
+ sum_with_shared_borrows_loop_fwd max i0 s0
+ od)
+ else u32_mul s (int_to_u32 2)
+’
+
+val sum_with_shared_borrows_fwd_def = Define ‘
+ (** [loops::sum_with_shared_borrows]: forward function *)
+ sum_with_shared_borrows_fwd (max : u32) : u32 result =
+ sum_with_shared_borrows_loop_fwd max (int_to_u32 0) (int_to_u32 0)
+’
+
+val [clear_loop_fwd_back_def] = DefineDiv ‘
+ (** [loops::clear]: loop 0: merged forward/backward function
+ (there is a single backward function, and the forward function returns ()) *)
+ clear_loop_fwd_back (v : u32 vec) (i : usize) : u32 vec result =
+ let i0 = vec_len v in
+ if usize_lt i i0
+ then (
+ do
+ i1 <- usize_add i (int_to_usize 1);
+ v0 <- vec_index_mut_back v i (int_to_u32 0);
+ clear_loop_fwd_back v0 i1
+ od)
+ else Return v
+’
+
+val clear_fwd_back_def = Define ‘
+ (** [loops::clear]: merged forward/backward function
+ (there is a single backward function, and the forward function returns ()) *)
+ clear_fwd_back (v : u32 vec) : u32 vec result =
+ clear_loop_fwd_back v (int_to_usize 0)
+’
+
+val [list_mem_loop_fwd_def] = DefineDiv ‘
+ (** [loops::list_mem]: loop 0: forward function *)
+ list_mem_loop_fwd (x : u32) (ls : u32 list_t) : bool result =
+ (case ls of
+ | ListCons y tl => if y = x then Return T else list_mem_loop_fwd x tl
+ | ListNil => Return F)
+’
+
+val list_mem_fwd_def = Define ‘
+ (** [loops::list_mem]: forward function *)
+ list_mem_fwd (x : u32) (ls : u32 list_t) : bool result =
+ list_mem_loop_fwd x ls
+’
+
+val [list_nth_mut_loop_loop_fwd_def] = DefineDiv ‘
+ (** [loops::list_nth_mut_loop]: loop 0: forward function *)
+ list_nth_mut_loop_loop_fwd (ls : 't list_t) (i : u32) : 't result =
+ (case ls 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_loop_loop_fwd tl i0
+ od)
+ | ListNil => Fail Failure)
+’
+
+val list_nth_mut_loop_fwd_def = Define ‘
+ (** [loops::list_nth_mut_loop]: forward function *)
+ list_nth_mut_loop_fwd (ls : 't list_t) (i : u32) : 't result =
+ list_nth_mut_loop_loop_fwd ls i
+’
+
+val [list_nth_mut_loop_loop_back_def] = DefineDiv ‘
+ (** [loops::list_nth_mut_loop]: loop 0: backward function 0 *)
+ list_nth_mut_loop_loop_back
+ (ls : 't list_t) (i : u32) (ret : 't) : 't list_t result =
+ (case ls 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_loop_loop_back tl i0 ret;
+ Return (ListCons x tl0)
+ od)
+ | ListNil => Fail Failure)
+’
+
+val list_nth_mut_loop_back_def = Define ‘
+ (** [loops::list_nth_mut_loop]: backward function 0 *)
+ list_nth_mut_loop_back
+ (ls : 't list_t) (i : u32) (ret : 't) : 't list_t result =
+ list_nth_mut_loop_loop_back ls i ret
+’
+
+val [list_nth_shared_loop_loop_fwd_def] = DefineDiv ‘
+ (** [loops::list_nth_shared_loop]: loop 0: forward function *)
+ list_nth_shared_loop_loop_fwd (ls : 't list_t) (i : u32) : 't result =
+ (case ls 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_shared_loop_loop_fwd tl i0
+ od)
+ | ListNil => Fail Failure)
+’
+
+val list_nth_shared_loop_fwd_def = Define ‘
+ (** [loops::list_nth_shared_loop]: forward function *)
+ list_nth_shared_loop_fwd (ls : 't list_t) (i : u32) : 't result =
+ list_nth_shared_loop_loop_fwd ls i
+’
+
+val [get_elem_mut_loop_fwd_def] = DefineDiv ‘
+ (** [loops::get_elem_mut]: loop 0: forward function *)
+ get_elem_mut_loop_fwd (x : usize) (ls : usize list_t) : usize result =
+ (case ls of
+ | ListCons y tl => if y = x then Return y else get_elem_mut_loop_fwd x tl
+ | ListNil => Fail Failure)
+’
+
+val get_elem_mut_fwd_def = Define ‘
+ (** [loops::get_elem_mut]: forward function *)
+ get_elem_mut_fwd (slots : usize list_t vec) (x : usize) : usize result =
+ do
+ l <- vec_index_mut_fwd slots (int_to_usize 0);
+ get_elem_mut_loop_fwd x l
+ od
+’
+
+val [get_elem_mut_loop_back_def] = DefineDiv ‘
+ (** [loops::get_elem_mut]: loop 0: backward function 0 *)
+ get_elem_mut_loop_back
+ (x : usize) (ls : usize list_t) (ret : usize) : usize list_t result =
+ (case ls of
+ | ListCons y tl =>
+ if y = x
+ then Return (ListCons ret tl)
+ else (
+ do
+ tl0 <- get_elem_mut_loop_back x tl ret;
+ Return (ListCons y tl0)
+ od)
+ | ListNil => Fail Failure)
+’
+
+val get_elem_mut_back_def = Define ‘
+ (** [loops::get_elem_mut]: backward function 0 *)
+ get_elem_mut_back
+ (slots : usize list_t vec) (x : usize) (ret : usize) :
+ usize list_t vec result
+ =
+ do
+ l <- vec_index_mut_fwd slots (int_to_usize 0);
+ l0 <- get_elem_mut_loop_back x l ret;
+ vec_index_mut_back slots (int_to_usize 0) l0
+ od
+’
+
+val [get_elem_shared_loop_fwd_def] = DefineDiv ‘
+ (** [loops::get_elem_shared]: loop 0: forward function *)
+ get_elem_shared_loop_fwd (x : usize) (ls : usize list_t) : usize result =
+ (case ls of
+ | ListCons y tl =>
+ if y = x then Return y else get_elem_shared_loop_fwd x tl
+ | ListNil => Fail Failure)
+’
+
+val get_elem_shared_fwd_def = Define ‘
+ (** [loops::get_elem_shared]: forward function *)
+ get_elem_shared_fwd (slots : usize list_t vec) (x : usize) : usize result =
+ do
+ l <- vec_index_fwd slots (int_to_usize 0);
+ get_elem_shared_loop_fwd x l
+ od
+’
+
+val id_mut_fwd_def = Define ‘
+ (** [loops::id_mut]: forward function *)
+ id_mut_fwd (ls : 't list_t) : 't list_t result =
+ Return ls
+’
+
+val id_mut_back_def = Define ‘
+ (** [loops::id_mut]: backward function 0 *)
+ id_mut_back (ls : 't list_t) (ret : 't list_t) : 't list_t result =
+ Return ret
+’
+
+val id_shared_fwd_def = Define ‘
+ (** [loops::id_shared]: forward function *)
+ id_shared_fwd (ls : 't list_t) : 't list_t result =
+ Return ls
+’
+
+val [list_nth_mut_loop_with_id_loop_fwd_def] = DefineDiv ‘
+ (** [loops::list_nth_mut_loop_with_id]: loop 0: forward function *)
+ list_nth_mut_loop_with_id_loop_fwd (i : u32) (ls : 't list_t) : 't result =
+ (case ls 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_loop_with_id_loop_fwd i0 tl
+ od)
+ | ListNil => Fail Failure)
+’
+
+val list_nth_mut_loop_with_id_fwd_def = Define ‘
+ (** [loops::list_nth_mut_loop_with_id]: forward function *)
+ list_nth_mut_loop_with_id_fwd (ls : 't list_t) (i : u32) : 't result =
+ do
+ ls0 <- id_mut_fwd ls;
+ list_nth_mut_loop_with_id_loop_fwd i ls0
+ od
+’
+
+val [list_nth_mut_loop_with_id_loop_back_def] = DefineDiv ‘
+ (** [loops::list_nth_mut_loop_with_id]: loop 0: backward function 0 *)
+ list_nth_mut_loop_with_id_loop_back
+ (i : u32) (ls : 't list_t) (ret : 't) : 't list_t result =
+ (case ls 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_loop_with_id_loop_back i0 tl ret;
+ Return (ListCons x tl0)
+ od)
+ | ListNil => Fail Failure)
+’
+
+val list_nth_mut_loop_with_id_back_def = Define ‘
+ (** [loops::list_nth_mut_loop_with_id]: backward function 0 *)
+ list_nth_mut_loop_with_id_back
+ (ls : 't list_t) (i : u32) (ret : 't) : 't list_t result =
+ do
+ ls0 <- id_mut_fwd ls;
+ l <- list_nth_mut_loop_with_id_loop_back i ls0 ret;
+ id_mut_back ls l
+ od
+’
+
+val [list_nth_shared_loop_with_id_loop_fwd_def] = DefineDiv ‘
+ (** [loops::list_nth_shared_loop_with_id]: loop 0: forward function *)
+ list_nth_shared_loop_with_id_loop_fwd
+ (i : u32) (ls : 't list_t) : 't result =
+ (case ls 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_shared_loop_with_id_loop_fwd i0 tl
+ od)
+ | ListNil => Fail Failure)
+’
+
+val list_nth_shared_loop_with_id_fwd_def = Define ‘
+ (** [loops::list_nth_shared_loop_with_id]: forward function *)
+ list_nth_shared_loop_with_id_fwd (ls : 't list_t) (i : u32) : 't result =
+ do
+ ls0 <- id_shared_fwd ls;
+ list_nth_shared_loop_with_id_loop_fwd i ls0
+ od
+’
+
+val [list_nth_mut_loop_pair_loop_fwd_def] = DefineDiv ‘
+ (** [loops::list_nth_mut_loop_pair]: loop 0: forward function *)
+ list_nth_mut_loop_pair_loop_fwd
+ (ls0 : 't list_t) (ls1 : 't list_t) (i : u32) : ('t # 't) result =
+ (case ls0 of
+ | ListCons x0 tl0 =>
+ (case ls1 of
+ | ListCons x1 tl1 =>
+ if i = int_to_u32 0
+ then Return (x0, x1)
+ else (
+ do
+ i0 <- u32_sub i (int_to_u32 1);
+ list_nth_mut_loop_pair_loop_fwd tl0 tl1 i0
+ od)
+ | ListNil => Fail Failure)
+ | ListNil => Fail Failure)
+’
+
+val list_nth_mut_loop_pair_fwd_def = Define ‘
+ (** [loops::list_nth_mut_loop_pair]: forward function *)
+ list_nth_mut_loop_pair_fwd
+ (ls0 : 't list_t) (ls1 : 't list_t) (i : u32) : ('t # 't) result =
+ list_nth_mut_loop_pair_loop_fwd ls0 ls1 i
+’
+
+val [list_nth_mut_loop_pair_loop_back'a_def] = DefineDiv ‘
+ (** [loops::list_nth_mut_loop_pair]: loop 0: backward function 0 *)
+ list_nth_mut_loop_pair_loop_back'a
+ (ls0 : 't list_t) (ls1 : 't list_t) (i : u32) (ret : 't) :
+ 't list_t result
+ =
+ (case ls0 of
+ | ListCons x0 tl0 =>
+ (case ls1 of
+ | ListCons x1 tl1 =>
+ if i = int_to_u32 0
+ then Return (ListCons ret tl0)
+ else (
+ do
+ i0 <- u32_sub i (int_to_u32 1);
+ tl00 <- list_nth_mut_loop_pair_loop_back'a tl0 tl1 i0 ret;
+ Return (ListCons x0 tl00)
+ od)
+ | ListNil => Fail Failure)
+ | ListNil => Fail Failure)
+’
+
+val list_nth_mut_loop_pair_back'a_def = Define ‘
+ (** [loops::list_nth_mut_loop_pair]: backward function 0 *)
+ list_nth_mut_loop_pair_back'a
+ (ls0 : 't list_t) (ls1 : 't list_t) (i : u32) (ret : 't) :
+ 't list_t result
+ =
+ list_nth_mut_loop_pair_loop_back'a ls0 ls1 i ret
+’
+
+val [list_nth_mut_loop_pair_loop_back'b_def] = DefineDiv ‘
+ (** [loops::list_nth_mut_loop_pair]: loop 0: backward function 1 *)
+ list_nth_mut_loop_pair_loop_back'b
+ (ls0 : 't list_t) (ls1 : 't list_t) (i : u32) (ret : 't) :
+ 't list_t result
+ =
+ (case ls0 of
+ | ListCons x0 tl0 =>
+ (case ls1 of
+ | ListCons x1 tl1 =>
+ if i = int_to_u32 0
+ then Return (ListCons ret tl1)
+ else (
+ do
+ i0 <- u32_sub i (int_to_u32 1);
+ tl10 <- list_nth_mut_loop_pair_loop_back'b tl0 tl1 i0 ret;
+ Return (ListCons x1 tl10)
+ od)
+ | ListNil => Fail Failure)
+ | ListNil => Fail Failure)
+’
+
+val list_nth_mut_loop_pair_back'b_def = Define ‘
+ (** [loops::list_nth_mut_loop_pair]: backward function 1 *)
+ list_nth_mut_loop_pair_back'b
+ (ls0 : 't list_t) (ls1 : 't list_t) (i : u32) (ret : 't) :
+ 't list_t result
+ =
+ list_nth_mut_loop_pair_loop_back'b ls0 ls1 i ret
+’
+
+val [list_nth_shared_loop_pair_loop_fwd_def] = DefineDiv ‘
+ (** [loops::list_nth_shared_loop_pair]: loop 0: forward function *)
+ list_nth_shared_loop_pair_loop_fwd
+ (ls0 : 't list_t) (ls1 : 't list_t) (i : u32) : ('t # 't) result =
+ (case ls0 of
+ | ListCons x0 tl0 =>
+ (case ls1 of
+ | ListCons x1 tl1 =>
+ if i = int_to_u32 0
+ then Return (x0, x1)
+ else (
+ do
+ i0 <- u32_sub i (int_to_u32 1);
+ list_nth_shared_loop_pair_loop_fwd tl0 tl1 i0
+ od)
+ | ListNil => Fail Failure)
+ | ListNil => Fail Failure)
+’
+
+val list_nth_shared_loop_pair_fwd_def = Define ‘
+ (** [loops::list_nth_shared_loop_pair]: forward function *)
+ list_nth_shared_loop_pair_fwd
+ (ls0 : 't list_t) (ls1 : 't list_t) (i : u32) : ('t # 't) result =
+ list_nth_shared_loop_pair_loop_fwd ls0 ls1 i
+’
+
+val [list_nth_mut_loop_pair_merge_loop_fwd_def] = DefineDiv ‘
+ (** [loops::list_nth_mut_loop_pair_merge]: loop 0: forward function *)
+ list_nth_mut_loop_pair_merge_loop_fwd
+ (ls0 : 't list_t) (ls1 : 't list_t) (i : u32) : ('t # 't) result =
+ (case ls0 of
+ | ListCons x0 tl0 =>
+ (case ls1 of
+ | ListCons x1 tl1 =>
+ if i = int_to_u32 0
+ then Return (x0, x1)
+ else (
+ do
+ i0 <- u32_sub i (int_to_u32 1);
+ list_nth_mut_loop_pair_merge_loop_fwd tl0 tl1 i0
+ od)
+ | ListNil => Fail Failure)
+ | ListNil => Fail Failure)
+’
+
+val list_nth_mut_loop_pair_merge_fwd_def = Define ‘
+ (** [loops::list_nth_mut_loop_pair_merge]: forward function *)
+ list_nth_mut_loop_pair_merge_fwd
+ (ls0 : 't list_t) (ls1 : 't list_t) (i : u32) : ('t # 't) result =
+ list_nth_mut_loop_pair_merge_loop_fwd ls0 ls1 i
+’
+
+val [list_nth_mut_loop_pair_merge_loop_back_def] = DefineDiv ‘
+ (** [loops::list_nth_mut_loop_pair_merge]: loop 0: backward function 0 *)
+ list_nth_mut_loop_pair_merge_loop_back
+ (ls0 : 't list_t) (ls1 : 't list_t) (i : u32) (ret : ('t # 't)) :
+ ('t list_t # 't list_t) result
+ =
+ (case ls0 of
+ | ListCons x0 tl0 =>
+ (case ls1 of
+ | ListCons x1 tl1 =>
+ if i = int_to_u32 0
+ then let (t, t0) = ret in Return (ListCons t tl0, ListCons t0 tl1)
+ else (
+ do
+ i0 <- u32_sub i (int_to_u32 1);
+ (tl00, tl10) <-
+ list_nth_mut_loop_pair_merge_loop_back tl0 tl1 i0 ret;
+ Return (ListCons x0 tl00, ListCons x1 tl10)
+ od)
+ | ListNil => Fail Failure)
+ | ListNil => Fail Failure)
+’
+
+val list_nth_mut_loop_pair_merge_back_def = Define ‘
+ (** [loops::list_nth_mut_loop_pair_merge]: backward function 0 *)
+ list_nth_mut_loop_pair_merge_back
+ (ls0 : 't list_t) (ls1 : 't list_t) (i : u32) (ret : ('t # 't)) :
+ ('t list_t # 't list_t) result
+ =
+ list_nth_mut_loop_pair_merge_loop_back ls0 ls1 i ret
+’
+
+val [list_nth_shared_loop_pair_merge_loop_fwd_def] = DefineDiv ‘
+ (** [loops::list_nth_shared_loop_pair_merge]: loop 0: forward function *)
+ list_nth_shared_loop_pair_merge_loop_fwd
+ (ls0 : 't list_t) (ls1 : 't list_t) (i : u32) : ('t # 't) result =
+ (case ls0 of
+ | ListCons x0 tl0 =>
+ (case ls1 of
+ | ListCons x1 tl1 =>
+ if i = int_to_u32 0
+ then Return (x0, x1)
+ else (
+ do
+ i0 <- u32_sub i (int_to_u32 1);
+ list_nth_shared_loop_pair_merge_loop_fwd tl0 tl1 i0
+ od)
+ | ListNil => Fail Failure)
+ | ListNil => Fail Failure)
+’
+
+val list_nth_shared_loop_pair_merge_fwd_def = Define ‘
+ (** [loops::list_nth_shared_loop_pair_merge]: forward function *)
+ list_nth_shared_loop_pair_merge_fwd
+ (ls0 : 't list_t) (ls1 : 't list_t) (i : u32) : ('t # 't) result =
+ list_nth_shared_loop_pair_merge_loop_fwd ls0 ls1 i
+’
+
+val [list_nth_mut_shared_loop_pair_loop_fwd_def] = DefineDiv ‘
+ (** [loops::list_nth_mut_shared_loop_pair]: loop 0: forward function *)
+ list_nth_mut_shared_loop_pair_loop_fwd
+ (ls0 : 't list_t) (ls1 : 't list_t) (i : u32) : ('t # 't) result =
+ (case ls0 of
+ | ListCons x0 tl0 =>
+ (case ls1 of
+ | ListCons x1 tl1 =>
+ if i = int_to_u32 0
+ then Return (x0, x1)
+ else (
+ do
+ i0 <- u32_sub i (int_to_u32 1);
+ list_nth_mut_shared_loop_pair_loop_fwd tl0 tl1 i0
+ od)
+ | ListNil => Fail Failure)
+ | ListNil => Fail Failure)
+’
+
+val list_nth_mut_shared_loop_pair_fwd_def = Define ‘
+ (** [loops::list_nth_mut_shared_loop_pair]: forward function *)
+ list_nth_mut_shared_loop_pair_fwd
+ (ls0 : 't list_t) (ls1 : 't list_t) (i : u32) : ('t # 't) result =
+ list_nth_mut_shared_loop_pair_loop_fwd ls0 ls1 i
+’
+
+val [list_nth_mut_shared_loop_pair_loop_back_def] = DefineDiv ‘
+ (** [loops::list_nth_mut_shared_loop_pair]: loop 0: backward function 0 *)
+ list_nth_mut_shared_loop_pair_loop_back
+ (ls0 : 't list_t) (ls1 : 't list_t) (i : u32) (ret : 't) :
+ 't list_t result
+ =
+ (case ls0 of
+ | ListCons x0 tl0 =>
+ (case ls1 of
+ | ListCons x1 tl1 =>
+ if i = int_to_u32 0
+ then Return (ListCons ret tl0)
+ else (
+ do
+ i0 <- u32_sub i (int_to_u32 1);
+ tl00 <- list_nth_mut_shared_loop_pair_loop_back tl0 tl1 i0 ret;
+ Return (ListCons x0 tl00)
+ od)
+ | ListNil => Fail Failure)
+ | ListNil => Fail Failure)
+’
+
+val list_nth_mut_shared_loop_pair_back_def = Define ‘
+ (** [loops::list_nth_mut_shared_loop_pair]: backward function 0 *)
+ list_nth_mut_shared_loop_pair_back
+ (ls0 : 't list_t) (ls1 : 't list_t) (i : u32) (ret : 't) :
+ 't list_t result
+ =
+ list_nth_mut_shared_loop_pair_loop_back ls0 ls1 i ret
+’
+
+val [list_nth_mut_shared_loop_pair_merge_loop_fwd_def] = DefineDiv ‘
+ (** [loops::list_nth_mut_shared_loop_pair_merge]: loop 0: forward function *)
+ list_nth_mut_shared_loop_pair_merge_loop_fwd
+ (ls0 : 't list_t) (ls1 : 't list_t) (i : u32) : ('t # 't) result =
+ (case ls0 of
+ | ListCons x0 tl0 =>
+ (case ls1 of
+ | ListCons x1 tl1 =>
+ if i = int_to_u32 0
+ then Return (x0, x1)
+ else (
+ do
+ i0 <- u32_sub i (int_to_u32 1);
+ list_nth_mut_shared_loop_pair_merge_loop_fwd tl0 tl1 i0
+ od)
+ | ListNil => Fail Failure)
+ | ListNil => Fail Failure)
+’
+
+val list_nth_mut_shared_loop_pair_merge_fwd_def = Define ‘
+ (** [loops::list_nth_mut_shared_loop_pair_merge]: forward function *)
+ list_nth_mut_shared_loop_pair_merge_fwd
+ (ls0 : 't list_t) (ls1 : 't list_t) (i : u32) : ('t # 't) result =
+ list_nth_mut_shared_loop_pair_merge_loop_fwd ls0 ls1 i
+’
+
+val [list_nth_mut_shared_loop_pair_merge_loop_back_def] = DefineDiv ‘
+ (** [loops::list_nth_mut_shared_loop_pair_merge]: loop 0: backward function 0 *)
+ list_nth_mut_shared_loop_pair_merge_loop_back
+ (ls0 : 't list_t) (ls1 : 't list_t) (i : u32) (ret : 't) :
+ 't list_t result
+ =
+ (case ls0 of
+ | ListCons x0 tl0 =>
+ (case ls1 of
+ | ListCons x1 tl1 =>
+ if i = int_to_u32 0
+ then Return (ListCons ret tl0)
+ else (
+ do
+ i0 <- u32_sub i (int_to_u32 1);
+ tl00 <- list_nth_mut_shared_loop_pair_merge_loop_back tl0 tl1 i0 ret;
+ Return (ListCons x0 tl00)
+ od)
+ | ListNil => Fail Failure)
+ | ListNil => Fail Failure)
+’
+
+val list_nth_mut_shared_loop_pair_merge_back_def = Define ‘
+ (** [loops::list_nth_mut_shared_loop_pair_merge]: backward function 0 *)
+ list_nth_mut_shared_loop_pair_merge_back
+ (ls0 : 't list_t) (ls1 : 't list_t) (i : u32) (ret : 't) :
+ 't list_t result
+ =
+ list_nth_mut_shared_loop_pair_merge_loop_back ls0 ls1 i ret
+’
+
+val [list_nth_shared_mut_loop_pair_loop_fwd_def] = DefineDiv ‘
+ (** [loops::list_nth_shared_mut_loop_pair]: loop 0: forward function *)
+ list_nth_shared_mut_loop_pair_loop_fwd
+ (ls0 : 't list_t) (ls1 : 't list_t) (i : u32) : ('t # 't) result =
+ (case ls0 of
+ | ListCons x0 tl0 =>
+ (case ls1 of
+ | ListCons x1 tl1 =>
+ if i = int_to_u32 0
+ then Return (x0, x1)
+ else (
+ do
+ i0 <- u32_sub i (int_to_u32 1);
+ list_nth_shared_mut_loop_pair_loop_fwd tl0 tl1 i0
+ od)
+ | ListNil => Fail Failure)
+ | ListNil => Fail Failure)
+’
+
+val list_nth_shared_mut_loop_pair_fwd_def = Define ‘
+ (** [loops::list_nth_shared_mut_loop_pair]: forward function *)
+ list_nth_shared_mut_loop_pair_fwd
+ (ls0 : 't list_t) (ls1 : 't list_t) (i : u32) : ('t # 't) result =
+ list_nth_shared_mut_loop_pair_loop_fwd ls0 ls1 i
+’
+
+val [list_nth_shared_mut_loop_pair_loop_back_def] = DefineDiv ‘
+ (** [loops::list_nth_shared_mut_loop_pair]: loop 0: backward function 1 *)
+ list_nth_shared_mut_loop_pair_loop_back
+ (ls0 : 't list_t) (ls1 : 't list_t) (i : u32) (ret : 't) :
+ 't list_t result
+ =
+ (case ls0 of
+ | ListCons x0 tl0 =>
+ (case ls1 of
+ | ListCons x1 tl1 =>
+ if i = int_to_u32 0
+ then Return (ListCons ret tl1)
+ else (
+ do
+ i0 <- u32_sub i (int_to_u32 1);
+ tl10 <- list_nth_shared_mut_loop_pair_loop_back tl0 tl1 i0 ret;
+ Return (ListCons x1 tl10)
+ od)
+ | ListNil => Fail Failure)
+ | ListNil => Fail Failure)
+’
+
+val list_nth_shared_mut_loop_pair_back_def = Define ‘
+ (** [loops::list_nth_shared_mut_loop_pair]: backward function 1 *)
+ list_nth_shared_mut_loop_pair_back
+ (ls0 : 't list_t) (ls1 : 't list_t) (i : u32) (ret : 't) :
+ 't list_t result
+ =
+ list_nth_shared_mut_loop_pair_loop_back ls0 ls1 i ret
+’
+
+val [list_nth_shared_mut_loop_pair_merge_loop_fwd_def] = DefineDiv ‘
+ (** [loops::list_nth_shared_mut_loop_pair_merge]: loop 0: forward function *)
+ list_nth_shared_mut_loop_pair_merge_loop_fwd
+ (ls0 : 't list_t) (ls1 : 't list_t) (i : u32) : ('t # 't) result =
+ (case ls0 of
+ | ListCons x0 tl0 =>
+ (case ls1 of
+ | ListCons x1 tl1 =>
+ if i = int_to_u32 0
+ then Return (x0, x1)
+ else (
+ do
+ i0 <- u32_sub i (int_to_u32 1);
+ list_nth_shared_mut_loop_pair_merge_loop_fwd tl0 tl1 i0
+ od)
+ | ListNil => Fail Failure)
+ | ListNil => Fail Failure)
+’
+
+val list_nth_shared_mut_loop_pair_merge_fwd_def = Define ‘
+ (** [loops::list_nth_shared_mut_loop_pair_merge]: forward function *)
+ list_nth_shared_mut_loop_pair_merge_fwd
+ (ls0 : 't list_t) (ls1 : 't list_t) (i : u32) : ('t # 't) result =
+ list_nth_shared_mut_loop_pair_merge_loop_fwd ls0 ls1 i
+’
+
+val [list_nth_shared_mut_loop_pair_merge_loop_back_def] = DefineDiv ‘
+ (** [loops::list_nth_shared_mut_loop_pair_merge]: loop 0: backward function 0 *)
+ list_nth_shared_mut_loop_pair_merge_loop_back
+ (ls0 : 't list_t) (ls1 : 't list_t) (i : u32) (ret : 't) :
+ 't list_t result
+ =
+ (case ls0 of
+ | ListCons x0 tl0 =>
+ (case ls1 of
+ | ListCons x1 tl1 =>
+ if i = int_to_u32 0
+ then Return (ListCons ret tl1)
+ else (
+ do
+ i0 <- u32_sub i (int_to_u32 1);
+ tl10 <- list_nth_shared_mut_loop_pair_merge_loop_back tl0 tl1 i0 ret;
+ Return (ListCons x1 tl10)
+ od)
+ | ListNil => Fail Failure)
+ | ListNil => Fail Failure)
+’
+
+val list_nth_shared_mut_loop_pair_merge_back_def = Define ‘
+ (** [loops::list_nth_shared_mut_loop_pair_merge]: backward function 0 *)
+ list_nth_shared_mut_loop_pair_merge_back
+ (ls0 : 't list_t) (ls1 : 't list_t) (i : u32) (ret : 't) :
+ 't list_t result
+ =
+ list_nth_shared_mut_loop_pair_merge_loop_back ls0 ls1 i ret
+’
+
+val _ = export_theory ()
diff --git a/tests/hol4/loops/loops_FunsTheory.sig b/tests/hol4/loops/loops_FunsTheory.sig
new file mode 100644
index 00000000..63fe56c9
--- /dev/null
+++ b/tests/hol4/loops/loops_FunsTheory.sig
@@ -0,0 +1,731 @@
+signature loops_FunsTheory =
+sig
+ type thm = Thm.thm
+
+ (* Definitions *)
+ val clear_fwd_back_def : thm
+ val clear_loop_fwd_back_def : thm
+ val get_elem_mut_back_def : thm
+ val get_elem_mut_fwd_def : thm
+ val get_elem_mut_loop_back_def : thm
+ val get_elem_mut_loop_fwd_def : thm
+ val get_elem_shared_fwd_def : thm
+ val get_elem_shared_loop_fwd_def : thm
+ val id_mut_back_def : thm
+ val id_mut_fwd_def : thm
+ val id_shared_fwd_def : thm
+ val list_mem_fwd_def : thm
+ val list_mem_loop_fwd_def : thm
+ val list_nth_mut_loop_back_def : thm
+ val list_nth_mut_loop_fwd_def : thm
+ val list_nth_mut_loop_loop_back_def : thm
+ val list_nth_mut_loop_loop_fwd_def : thm
+ val list_nth_mut_loop_pair_back'a_def : thm
+ val list_nth_mut_loop_pair_back'b_def : thm
+ val list_nth_mut_loop_pair_fwd_def : thm
+ val list_nth_mut_loop_pair_loop_back'a_def : thm
+ val list_nth_mut_loop_pair_loop_back'b_def : thm
+ val list_nth_mut_loop_pair_loop_fwd_def : thm
+ val list_nth_mut_loop_pair_merge_back_def : thm
+ val list_nth_mut_loop_pair_merge_fwd_def : thm
+ val list_nth_mut_loop_pair_merge_loop_back_def : thm
+ val list_nth_mut_loop_pair_merge_loop_fwd_def : thm
+ val list_nth_mut_loop_with_id_back_def : thm
+ val list_nth_mut_loop_with_id_fwd_def : thm
+ val list_nth_mut_loop_with_id_loop_back_def : thm
+ val list_nth_mut_loop_with_id_loop_fwd_def : thm
+ val list_nth_mut_shared_loop_pair_back_def : thm
+ val list_nth_mut_shared_loop_pair_fwd_def : thm
+ val list_nth_mut_shared_loop_pair_loop_back_def : thm
+ val list_nth_mut_shared_loop_pair_loop_fwd_def : thm
+ val list_nth_mut_shared_loop_pair_merge_back_def : thm
+ val list_nth_mut_shared_loop_pair_merge_fwd_def : thm
+ val list_nth_mut_shared_loop_pair_merge_loop_back_def : thm
+ val list_nth_mut_shared_loop_pair_merge_loop_fwd_def : thm
+ val list_nth_shared_loop_fwd_def : thm
+ val list_nth_shared_loop_loop_fwd_def : thm
+ val list_nth_shared_loop_pair_fwd_def : thm
+ val list_nth_shared_loop_pair_loop_fwd_def : thm
+ val list_nth_shared_loop_pair_merge_fwd_def : thm
+ val list_nth_shared_loop_pair_merge_loop_fwd_def : thm
+ val list_nth_shared_loop_with_id_fwd_def : thm
+ val list_nth_shared_loop_with_id_loop_fwd_def : thm
+ val list_nth_shared_mut_loop_pair_back_def : thm
+ val list_nth_shared_mut_loop_pair_fwd_def : thm
+ val list_nth_shared_mut_loop_pair_loop_back_def : thm
+ val list_nth_shared_mut_loop_pair_loop_fwd_def : thm
+ val list_nth_shared_mut_loop_pair_merge_back_def : thm
+ val list_nth_shared_mut_loop_pair_merge_fwd_def : thm
+ val list_nth_shared_mut_loop_pair_merge_loop_back_def : thm
+ val list_nth_shared_mut_loop_pair_merge_loop_fwd_def : thm
+ val sum_fwd_def : thm
+ val sum_loop_fwd_def : thm
+ val sum_with_mut_borrows_fwd_def : thm
+ val sum_with_mut_borrows_loop_fwd_def : thm
+ val sum_with_shared_borrows_fwd_def : thm
+ val sum_with_shared_borrows_loop_fwd_def : thm
+
+ val loops_Funs_grammars : type_grammar.grammar * term_grammar.grammar
+(*
+ [loops_Types] Parent theory of "loops_Funs"
+
+ [clear_fwd_back_def] Definition
+
+ ⊢ ∀v. clear_fwd_back v = clear_loop_fwd_back v (int_to_usize 0)
+
+ [clear_loop_fwd_back_def] Definition
+
+ ⊢ ∀v i.
+ clear_loop_fwd_back v i =
+ (let
+ i0 = vec_len v
+ in
+ if usize_lt i i0 then
+ do
+ i1 <- usize_add i (int_to_usize 1);
+ v0 <- vec_index_mut_back v i (int_to_u32 0);
+ clear_loop_fwd_back v0 i1
+ od
+ else Return v)
+
+ [get_elem_mut_back_def] Definition
+
+ ⊢ ∀slots x ret.
+ get_elem_mut_back slots x ret =
+ do
+ l <- vec_index_mut_fwd slots (int_to_usize 0);
+ l0 <- get_elem_mut_loop_back x l ret;
+ vec_index_mut_back slots (int_to_usize 0) l0
+ od
+
+ [get_elem_mut_fwd_def] Definition
+
+ ⊢ ∀slots x.
+ get_elem_mut_fwd slots x =
+ do
+ l <- vec_index_mut_fwd slots (int_to_usize 0);
+ get_elem_mut_loop_fwd x l
+ od
+
+ [get_elem_mut_loop_back_def] Definition
+
+ ⊢ ∀x ls ret.
+ get_elem_mut_loop_back x ls ret =
+ case ls of
+ ListCons y tl =>
+ if y = x then Return (ListCons ret tl)
+ else
+ do
+ tl0 <- get_elem_mut_loop_back x tl ret;
+ Return (ListCons y tl0)
+ od
+ | ListNil => Fail Failure
+
+ [get_elem_mut_loop_fwd_def] Definition
+
+ ⊢ ∀x ls.
+ get_elem_mut_loop_fwd x ls =
+ case ls of
+ ListCons y tl =>
+ if y = x then Return y else get_elem_mut_loop_fwd x tl
+ | ListNil => Fail Failure
+
+ [get_elem_shared_fwd_def] Definition
+
+ ⊢ ∀slots x.
+ get_elem_shared_fwd slots x =
+ do
+ l <- vec_index_fwd slots (int_to_usize 0);
+ get_elem_shared_loop_fwd x l
+ od
+
+ [get_elem_shared_loop_fwd_def] Definition
+
+ ⊢ ∀x ls.
+ get_elem_shared_loop_fwd x ls =
+ case ls of
+ ListCons y tl =>
+ if y = x then Return y else get_elem_shared_loop_fwd x tl
+ | ListNil => Fail Failure
+
+ [id_mut_back_def] Definition
+
+ ⊢ ∀ls ret. id_mut_back ls ret = Return ret
+
+ [id_mut_fwd_def] Definition
+
+ ⊢ ∀ls. id_mut_fwd ls = Return ls
+
+ [id_shared_fwd_def] Definition
+
+ ⊢ ∀ls. id_shared_fwd ls = Return ls
+
+ [list_mem_fwd_def] Definition
+
+ ⊢ ∀x ls. list_mem_fwd x ls = list_mem_loop_fwd x ls
+
+ [list_mem_loop_fwd_def] Definition
+
+ ⊢ ∀x ls.
+ list_mem_loop_fwd x ls =
+ case ls of
+ ListCons y tl =>
+ if y = x then Return T else list_mem_loop_fwd x tl
+ | ListNil => Return F
+
+ [list_nth_mut_loop_back_def] Definition
+
+ ⊢ ∀ls i ret.
+ list_nth_mut_loop_back ls i ret =
+ list_nth_mut_loop_loop_back ls i ret
+
+ [list_nth_mut_loop_fwd_def] Definition
+
+ ⊢ ∀ls i. list_nth_mut_loop_fwd ls i = list_nth_mut_loop_loop_fwd ls i
+
+ [list_nth_mut_loop_loop_back_def] Definition
+
+ ⊢ ∀ls i ret.
+ list_nth_mut_loop_loop_back ls i ret =
+ case ls 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_loop_loop_back tl i0 ret;
+ Return (ListCons x tl0)
+ od
+ | ListNil => Fail Failure
+
+ [list_nth_mut_loop_loop_fwd_def] Definition
+
+ ⊢ ∀ls i.
+ list_nth_mut_loop_loop_fwd ls i =
+ case ls 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_loop_loop_fwd tl i0
+ od
+ | ListNil => Fail Failure
+
+ [list_nth_mut_loop_pair_back'a_def] Definition
+
+ ⊢ ∀ls0 ls1 i ret.
+ list_nth_mut_loop_pair_back'a ls0 ls1 i ret =
+ list_nth_mut_loop_pair_loop_back'a ls0 ls1 i ret
+
+ [list_nth_mut_loop_pair_back'b_def] Definition
+
+ ⊢ ∀ls0 ls1 i ret.
+ list_nth_mut_loop_pair_back'b ls0 ls1 i ret =
+ list_nth_mut_loop_pair_loop_back'b ls0 ls1 i ret
+
+ [list_nth_mut_loop_pair_fwd_def] Definition
+
+ ⊢ ∀ls0 ls1 i.
+ list_nth_mut_loop_pair_fwd ls0 ls1 i =
+ list_nth_mut_loop_pair_loop_fwd ls0 ls1 i
+
+ [list_nth_mut_loop_pair_loop_back'a_def] Definition
+
+ ⊢ ∀ls0 ls1 i ret.
+ list_nth_mut_loop_pair_loop_back'a ls0 ls1 i ret =
+ case ls0 of
+ ListCons x0 tl0 =>
+ (case ls1 of
+ ListCons x1 tl1 =>
+ if i = int_to_u32 0 then Return (ListCons ret tl0)
+ else
+ do
+ i0 <- u32_sub i (int_to_u32 1);
+ tl00 <-
+ list_nth_mut_loop_pair_loop_back'a tl0 tl1 i0 ret;
+ Return (ListCons x0 tl00)
+ od
+ | ListNil => Fail Failure)
+ | ListNil => Fail Failure
+
+ [list_nth_mut_loop_pair_loop_back'b_def] Definition
+
+ ⊢ ∀ls0 ls1 i ret.
+ list_nth_mut_loop_pair_loop_back'b ls0 ls1 i ret =
+ case ls0 of
+ ListCons x0 tl0 =>
+ (case ls1 of
+ ListCons x1 tl1 =>
+ if i = int_to_u32 0 then Return (ListCons ret tl1)
+ else
+ do
+ i0 <- u32_sub i (int_to_u32 1);
+ tl10 <-
+ list_nth_mut_loop_pair_loop_back'b tl0 tl1 i0 ret;
+ Return (ListCons x1 tl10)
+ od
+ | ListNil => Fail Failure)
+ | ListNil => Fail Failure
+
+ [list_nth_mut_loop_pair_loop_fwd_def] Definition
+
+ ⊢ ∀ls0 ls1 i.
+ list_nth_mut_loop_pair_loop_fwd ls0 ls1 i =
+ case ls0 of
+ ListCons x0 tl0 =>
+ (case ls1 of
+ ListCons x1 tl1 =>
+ if i = int_to_u32 0 then Return (x0,x1)
+ else
+ do
+ i0 <- u32_sub i (int_to_u32 1);
+ list_nth_mut_loop_pair_loop_fwd tl0 tl1 i0
+ od
+ | ListNil => Fail Failure)
+ | ListNil => Fail Failure
+
+ [list_nth_mut_loop_pair_merge_back_def] Definition
+
+ ⊢ ∀ls0 ls1 i ret.
+ list_nth_mut_loop_pair_merge_back ls0 ls1 i ret =
+ list_nth_mut_loop_pair_merge_loop_back ls0 ls1 i ret
+
+ [list_nth_mut_loop_pair_merge_fwd_def] Definition
+
+ ⊢ ∀ls0 ls1 i.
+ list_nth_mut_loop_pair_merge_fwd ls0 ls1 i =
+ list_nth_mut_loop_pair_merge_loop_fwd ls0 ls1 i
+
+ [list_nth_mut_loop_pair_merge_loop_back_def] Definition
+
+ ⊢ ∀ls0 ls1 i ret.
+ list_nth_mut_loop_pair_merge_loop_back ls0 ls1 i ret =
+ case ls0 of
+ ListCons x0 tl0 =>
+ (case ls1 of
+ ListCons x1 tl1 =>
+ if i = int_to_u32 0 then
+ (let
+ (t,t0) = ret
+ in
+ Return (ListCons t tl0,ListCons t0 tl1))
+ else
+ do
+ i0 <- u32_sub i (int_to_u32 1);
+ (tl00,tl10) <-
+ list_nth_mut_loop_pair_merge_loop_back tl0 tl1 i0
+ ret;
+ Return (ListCons x0 tl00,ListCons x1 tl10)
+ od
+ | ListNil => Fail Failure)
+ | ListNil => Fail Failure
+
+ [list_nth_mut_loop_pair_merge_loop_fwd_def] Definition
+
+ ⊢ ∀ls0 ls1 i.
+ list_nth_mut_loop_pair_merge_loop_fwd ls0 ls1 i =
+ case ls0 of
+ ListCons x0 tl0 =>
+ (case ls1 of
+ ListCons x1 tl1 =>
+ if i = int_to_u32 0 then Return (x0,x1)
+ else
+ do
+ i0 <- u32_sub i (int_to_u32 1);
+ list_nth_mut_loop_pair_merge_loop_fwd tl0 tl1 i0
+ od
+ | ListNil => Fail Failure)
+ | ListNil => Fail Failure
+
+ [list_nth_mut_loop_with_id_back_def] Definition
+
+ ⊢ ∀ls i ret.
+ list_nth_mut_loop_with_id_back ls i ret =
+ do
+ ls0 <- id_mut_fwd ls;
+ l <- list_nth_mut_loop_with_id_loop_back i ls0 ret;
+ id_mut_back ls l
+ od
+
+ [list_nth_mut_loop_with_id_fwd_def] Definition
+
+ ⊢ ∀ls i.
+ list_nth_mut_loop_with_id_fwd ls i =
+ do
+ ls0 <- id_mut_fwd ls;
+ list_nth_mut_loop_with_id_loop_fwd i ls0
+ od
+
+ [list_nth_mut_loop_with_id_loop_back_def] Definition
+
+ ⊢ ∀i ls ret.
+ list_nth_mut_loop_with_id_loop_back i ls ret =
+ case ls 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_loop_with_id_loop_back i0 tl ret;
+ Return (ListCons x tl0)
+ od
+ | ListNil => Fail Failure
+
+ [list_nth_mut_loop_with_id_loop_fwd_def] Definition
+
+ ⊢ ∀i ls.
+ list_nth_mut_loop_with_id_loop_fwd i ls =
+ case ls 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_loop_with_id_loop_fwd i0 tl
+ od
+ | ListNil => Fail Failure
+
+ [list_nth_mut_shared_loop_pair_back_def] Definition
+
+ ⊢ ∀ls0 ls1 i ret.
+ list_nth_mut_shared_loop_pair_back ls0 ls1 i ret =
+ list_nth_mut_shared_loop_pair_loop_back ls0 ls1 i ret
+
+ [list_nth_mut_shared_loop_pair_fwd_def] Definition
+
+ ⊢ ∀ls0 ls1 i.
+ list_nth_mut_shared_loop_pair_fwd ls0 ls1 i =
+ list_nth_mut_shared_loop_pair_loop_fwd ls0 ls1 i
+
+ [list_nth_mut_shared_loop_pair_loop_back_def] Definition
+
+ ⊢ ∀ls0 ls1 i ret.
+ list_nth_mut_shared_loop_pair_loop_back ls0 ls1 i ret =
+ case ls0 of
+ ListCons x0 tl0 =>
+ (case ls1 of
+ ListCons x1 tl1 =>
+ if i = int_to_u32 0 then Return (ListCons ret tl0)
+ else
+ do
+ i0 <- u32_sub i (int_to_u32 1);
+ tl00 <-
+ list_nth_mut_shared_loop_pair_loop_back tl0 tl1 i0
+ ret;
+ Return (ListCons x0 tl00)
+ od
+ | ListNil => Fail Failure)
+ | ListNil => Fail Failure
+
+ [list_nth_mut_shared_loop_pair_loop_fwd_def] Definition
+
+ ⊢ ∀ls0 ls1 i.
+ list_nth_mut_shared_loop_pair_loop_fwd ls0 ls1 i =
+ case ls0 of
+ ListCons x0 tl0 =>
+ (case ls1 of
+ ListCons x1 tl1 =>
+ if i = int_to_u32 0 then Return (x0,x1)
+ else
+ do
+ i0 <- u32_sub i (int_to_u32 1);
+ list_nth_mut_shared_loop_pair_loop_fwd tl0 tl1 i0
+ od
+ | ListNil => Fail Failure)
+ | ListNil => Fail Failure
+
+ [list_nth_mut_shared_loop_pair_merge_back_def] Definition
+
+ ⊢ ∀ls0 ls1 i ret.
+ list_nth_mut_shared_loop_pair_merge_back ls0 ls1 i ret =
+ list_nth_mut_shared_loop_pair_merge_loop_back ls0 ls1 i ret
+
+ [list_nth_mut_shared_loop_pair_merge_fwd_def] Definition
+
+ ⊢ ∀ls0 ls1 i.
+ list_nth_mut_shared_loop_pair_merge_fwd ls0 ls1 i =
+ list_nth_mut_shared_loop_pair_merge_loop_fwd ls0 ls1 i
+
+ [list_nth_mut_shared_loop_pair_merge_loop_back_def] Definition
+
+ ⊢ ∀ls0 ls1 i ret.
+ list_nth_mut_shared_loop_pair_merge_loop_back ls0 ls1 i ret =
+ case ls0 of
+ ListCons x0 tl0 =>
+ (case ls1 of
+ ListCons x1 tl1 =>
+ if i = int_to_u32 0 then Return (ListCons ret tl0)
+ else
+ do
+ i0 <- u32_sub i (int_to_u32 1);
+ tl00 <-
+ list_nth_mut_shared_loop_pair_merge_loop_back tl0
+ tl1 i0 ret;
+ Return (ListCons x0 tl00)
+ od
+ | ListNil => Fail Failure)
+ | ListNil => Fail Failure
+
+ [list_nth_mut_shared_loop_pair_merge_loop_fwd_def] Definition
+
+ ⊢ ∀ls0 ls1 i.
+ list_nth_mut_shared_loop_pair_merge_loop_fwd ls0 ls1 i =
+ case ls0 of
+ ListCons x0 tl0 =>
+ (case ls1 of
+ ListCons x1 tl1 =>
+ if i = int_to_u32 0 then Return (x0,x1)
+ else
+ do
+ i0 <- u32_sub i (int_to_u32 1);
+ list_nth_mut_shared_loop_pair_merge_loop_fwd tl0 tl1
+ i0
+ od
+ | ListNil => Fail Failure)
+ | ListNil => Fail Failure
+
+ [list_nth_shared_loop_fwd_def] Definition
+
+ ⊢ ∀ls i.
+ list_nth_shared_loop_fwd ls i =
+ list_nth_shared_loop_loop_fwd ls i
+
+ [list_nth_shared_loop_loop_fwd_def] Definition
+
+ ⊢ ∀ls i.
+ list_nth_shared_loop_loop_fwd ls i =
+ case ls 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_shared_loop_loop_fwd tl i0
+ od
+ | ListNil => Fail Failure
+
+ [list_nth_shared_loop_pair_fwd_def] Definition
+
+ ⊢ ∀ls0 ls1 i.
+ list_nth_shared_loop_pair_fwd ls0 ls1 i =
+ list_nth_shared_loop_pair_loop_fwd ls0 ls1 i
+
+ [list_nth_shared_loop_pair_loop_fwd_def] Definition
+
+ ⊢ ∀ls0 ls1 i.
+ list_nth_shared_loop_pair_loop_fwd ls0 ls1 i =
+ case ls0 of
+ ListCons x0 tl0 =>
+ (case ls1 of
+ ListCons x1 tl1 =>
+ if i = int_to_u32 0 then Return (x0,x1)
+ else
+ do
+ i0 <- u32_sub i (int_to_u32 1);
+ list_nth_shared_loop_pair_loop_fwd tl0 tl1 i0
+ od
+ | ListNil => Fail Failure)
+ | ListNil => Fail Failure
+
+ [list_nth_shared_loop_pair_merge_fwd_def] Definition
+
+ ⊢ ∀ls0 ls1 i.
+ list_nth_shared_loop_pair_merge_fwd ls0 ls1 i =
+ list_nth_shared_loop_pair_merge_loop_fwd ls0 ls1 i
+
+ [list_nth_shared_loop_pair_merge_loop_fwd_def] Definition
+
+ ⊢ ∀ls0 ls1 i.
+ list_nth_shared_loop_pair_merge_loop_fwd ls0 ls1 i =
+ case ls0 of
+ ListCons x0 tl0 =>
+ (case ls1 of
+ ListCons x1 tl1 =>
+ if i = int_to_u32 0 then Return (x0,x1)
+ else
+ do
+ i0 <- u32_sub i (int_to_u32 1);
+ list_nth_shared_loop_pair_merge_loop_fwd tl0 tl1 i0
+ od
+ | ListNil => Fail Failure)
+ | ListNil => Fail Failure
+
+ [list_nth_shared_loop_with_id_fwd_def] Definition
+
+ ⊢ ∀ls i.
+ list_nth_shared_loop_with_id_fwd ls i =
+ do
+ ls0 <- id_shared_fwd ls;
+ list_nth_shared_loop_with_id_loop_fwd i ls0
+ od
+
+ [list_nth_shared_loop_with_id_loop_fwd_def] Definition
+
+ ⊢ ∀i ls.
+ list_nth_shared_loop_with_id_loop_fwd i ls =
+ case ls 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_shared_loop_with_id_loop_fwd i0 tl
+ od
+ | ListNil => Fail Failure
+
+ [list_nth_shared_mut_loop_pair_back_def] Definition
+
+ ⊢ ∀ls0 ls1 i ret.
+ list_nth_shared_mut_loop_pair_back ls0 ls1 i ret =
+ list_nth_shared_mut_loop_pair_loop_back ls0 ls1 i ret
+
+ [list_nth_shared_mut_loop_pair_fwd_def] Definition
+
+ ⊢ ∀ls0 ls1 i.
+ list_nth_shared_mut_loop_pair_fwd ls0 ls1 i =
+ list_nth_shared_mut_loop_pair_loop_fwd ls0 ls1 i
+
+ [list_nth_shared_mut_loop_pair_loop_back_def] Definition
+
+ ⊢ ∀ls0 ls1 i ret.
+ list_nth_shared_mut_loop_pair_loop_back ls0 ls1 i ret =
+ case ls0 of
+ ListCons x0 tl0 =>
+ (case ls1 of
+ ListCons x1 tl1 =>
+ if i = int_to_u32 0 then Return (ListCons ret tl1)
+ else
+ do
+ i0 <- u32_sub i (int_to_u32 1);
+ tl10 <-
+ list_nth_shared_mut_loop_pair_loop_back tl0 tl1 i0
+ ret;
+ Return (ListCons x1 tl10)
+ od
+ | ListNil => Fail Failure)
+ | ListNil => Fail Failure
+
+ [list_nth_shared_mut_loop_pair_loop_fwd_def] Definition
+
+ ⊢ ∀ls0 ls1 i.
+ list_nth_shared_mut_loop_pair_loop_fwd ls0 ls1 i =
+ case ls0 of
+ ListCons x0 tl0 =>
+ (case ls1 of
+ ListCons x1 tl1 =>
+ if i = int_to_u32 0 then Return (x0,x1)
+ else
+ do
+ i0 <- u32_sub i (int_to_u32 1);
+ list_nth_shared_mut_loop_pair_loop_fwd tl0 tl1 i0
+ od
+ | ListNil => Fail Failure)
+ | ListNil => Fail Failure
+
+ [list_nth_shared_mut_loop_pair_merge_back_def] Definition
+
+ ⊢ ∀ls0 ls1 i ret.
+ list_nth_shared_mut_loop_pair_merge_back ls0 ls1 i ret =
+ list_nth_shared_mut_loop_pair_merge_loop_back ls0 ls1 i ret
+
+ [list_nth_shared_mut_loop_pair_merge_fwd_def] Definition
+
+ ⊢ ∀ls0 ls1 i.
+ list_nth_shared_mut_loop_pair_merge_fwd ls0 ls1 i =
+ list_nth_shared_mut_loop_pair_merge_loop_fwd ls0 ls1 i
+
+ [list_nth_shared_mut_loop_pair_merge_loop_back_def] Definition
+
+ ⊢ ∀ls0 ls1 i ret.
+ list_nth_shared_mut_loop_pair_merge_loop_back ls0 ls1 i ret =
+ case ls0 of
+ ListCons x0 tl0 =>
+ (case ls1 of
+ ListCons x1 tl1 =>
+ if i = int_to_u32 0 then Return (ListCons ret tl1)
+ else
+ do
+ i0 <- u32_sub i (int_to_u32 1);
+ tl10 <-
+ list_nth_shared_mut_loop_pair_merge_loop_back tl0
+ tl1 i0 ret;
+ Return (ListCons x1 tl10)
+ od
+ | ListNil => Fail Failure)
+ | ListNil => Fail Failure
+
+ [list_nth_shared_mut_loop_pair_merge_loop_fwd_def] Definition
+
+ ⊢ ∀ls0 ls1 i.
+ list_nth_shared_mut_loop_pair_merge_loop_fwd ls0 ls1 i =
+ case ls0 of
+ ListCons x0 tl0 =>
+ (case ls1 of
+ ListCons x1 tl1 =>
+ if i = int_to_u32 0 then Return (x0,x1)
+ else
+ do
+ i0 <- u32_sub i (int_to_u32 1);
+ list_nth_shared_mut_loop_pair_merge_loop_fwd tl0 tl1
+ i0
+ od
+ | ListNil => Fail Failure)
+ | ListNil => Fail Failure
+
+ [sum_fwd_def] Definition
+
+ ⊢ ∀max. sum_fwd max = sum_loop_fwd max (int_to_u32 0) (int_to_u32 0)
+
+ [sum_loop_fwd_def] Definition
+
+ ⊢ ∀max i s.
+ sum_loop_fwd max i s =
+ if u32_lt i max then
+ do
+ s0 <- u32_add s i;
+ i0 <- u32_add i (int_to_u32 1);
+ sum_loop_fwd max i0 s0
+ od
+ else u32_mul s (int_to_u32 2)
+
+ [sum_with_mut_borrows_fwd_def] Definition
+
+ ⊢ ∀max.
+ sum_with_mut_borrows_fwd max =
+ sum_with_mut_borrows_loop_fwd max (int_to_u32 0) (int_to_u32 0)
+
+ [sum_with_mut_borrows_loop_fwd_def] Definition
+
+ ⊢ ∀max mi ms.
+ sum_with_mut_borrows_loop_fwd max mi ms =
+ if u32_lt mi max then
+ do
+ ms0 <- u32_add ms mi;
+ mi0 <- u32_add mi (int_to_u32 1);
+ sum_with_mut_borrows_loop_fwd max mi0 ms0
+ od
+ else u32_mul ms (int_to_u32 2)
+
+ [sum_with_shared_borrows_fwd_def] Definition
+
+ ⊢ ∀max.
+ sum_with_shared_borrows_fwd max =
+ sum_with_shared_borrows_loop_fwd max (int_to_u32 0)
+ (int_to_u32 0)
+
+ [sum_with_shared_borrows_loop_fwd_def] Definition
+
+ ⊢ ∀max i s.
+ sum_with_shared_borrows_loop_fwd max i s =
+ if u32_lt i max then
+ do
+ i0 <- u32_add i (int_to_u32 1);
+ s0 <- u32_add s i0;
+ sum_with_shared_borrows_loop_fwd max i0 s0
+ od
+ else u32_mul s (int_to_u32 2)
+
+
+*)
+end
diff --git a/tests/hol4/loops/loops_TypesScript.sml b/tests/hol4/loops/loops_TypesScript.sml
new file mode 100644
index 00000000..e3e5b8d1
--- /dev/null
+++ b/tests/hol4/loops/loops_TypesScript.sml
@@ -0,0 +1,13 @@
+(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *)
+(** [loops]: type definitions *)
+open primitivesLib divDefLib
+
+val _ = new_theory "loops_Types"
+
+
+Datatype:
+ (** [loops::List] *)
+ list_t = | ListCons 't list_t | ListNil
+End
+
+val _ = export_theory ()
diff --git a/tests/hol4/loops/loops_TypesTheory.sig b/tests/hol4/loops/loops_TypesTheory.sig
new file mode 100644
index 00000000..c3e638d8
--- /dev/null
+++ b/tests/hol4/loops/loops_TypesTheory.sig
@@ -0,0 +1,94 @@
+signature loops_TypesTheory =
+sig
+ type thm = Thm.thm
+
+ (* Definitions *)
+ val list_t_TY_DEF : thm
+ val list_t_case_def : thm
+ val list_t_size_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 loops_Types_grammars : type_grammar.grammar * term_grammar.grammar
+(*
+ [divDef] Parent theory of "loops_Types"
+
+ [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
+
+ [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
generated by cgit v1.2.3 (git 2.25.1) at 2024-12-22 21:37:30 +0000