docs: improve overview, fix mistakes

docs/src/intro/overview.md

@@ -28,7 +28,7 @@ External inputs can be provided to Miden VM in two ways:
 1. Public inputs can be supplied to the VM by initializing the stack with desired values before a program starts executing. At most 16 values can be initialized in this way, so providing more than 16 values will cause an error.
 2. Secret (or nondeterministic) inputs can be supplied to the VM via the [*advice provider*](#nondeterministic-inputs). There is no limit on how much data the advice provider can hold.
 
-After a program finishes executing, the elements remaining on the stack become the outputs of the program. Notice that having more than 16 values on the stack at the end of execution will cause an error, so the values outside the stack top should be dropped. We've provided the [`truncate_stack`](../user_docs/stdlib/sys.md) utility procedure in the standard library for this purpose.
+After a program finishes executing, the elements remaining on the stack become the outputs of the program. Notice that having more than 16 values on the stack at the end of execution will cause an error, so the values beyond the top 16 elements of the stack should be dropped. We've provided the [`truncate_stack`](../user_docs/stdlib/sys.md) utility procedure in the standard library for this purpose.
 
 The number of public inputs and outputs of a program can be reduced by making use of the advice stack and Merkle trees. Just 4 elements are sufficient to represent a root of a Merkle tree, which can be expanded into an arbitrary number of values.
 

miden/README.md

@@ -21,12 +21,12 @@ All Miden programs can be reduced to a single 32-byte value, called program hash
 Currently, there are 3 ways to get values onto the stack:
 
 1. You can use `push` instruction to push values onto the stack. These values become a part of the program itself, and, therefore, cannot be changed between program executions. You can think of them as constants.
-2. The stack can be initialized to some set of values at the beginning of the program. These inputs are public and must be shared with the verifier for them to verify a proof of the correct execution of a Miden program. At most 16 values could be provided for the stack initialization, attempt to provide more than 16 values will cause an error.
+2. The stack can be initialized to some set of values at the beginning of the program. These inputs are public and must be shared with the verifier for them to verify a proof of the correct execution of a Miden program. At most 16 values could be provided for the stack initialization, attempts to provide more than 16 values will cause an error.
 3. The program may request nondeterministic advice inputs from the prover. These inputs are secret inputs. This means that the prover does not need to share them with the verifier. There are three types of advice inputs: (1) a single advice stack which can contain any number of elements; (2) a key-mapped element lists which can be pushed onto the advice stack; (3) a Merkle store, which is used to provide nondeterministic inputs for instructions which work with Merkle trees. There are no restrictions on the number of advice inputs a program can request.
 
 The stack is provided to Miden VM via `StackInputs` struct. These are public inputs of the execution, and should also be provided to the verifier. The secret inputs for the program are provided via the `Host` interface. The default implementation of the host relies on in-memory advice provider (`MemAdviceProvider`) that can be commonly used for operations that won't require persistence.
 
-Values remaining on the stack after a program is executed can be returned as stack outputs. You can specify exactly how many values (from the top of the stack) should be returned. Notice, that, similar to stack inputs, at most 16 values can be returned via the stack. Attempt to return more than 16 values will cause an error.
+Values remaining on the stack after a program is executed can be returned as stack outputs. You can specify exactly how many values (from the top of the stack) should be returned. Notice, that, similar to stack inputs, at most 16 values can be returned via the stack. Attempts to return more than 16 values will cause an error.
 
 Having a small number elements to describe public inputs and outputs of a program may seem limiting, however, just 4 elements are sufficient to represent a root of a Merkle tree or a sequential hash of elements. Both of these can be expanded into an arbitrary number of values by supplying the actual values non-deterministically via the host interface.