commiting latest

Author: kmurphypolygon

docs/miden/vm/intro/overview.md

@@ -14,7 +14,7 @@ These components are:
 Miden VM comes with a default implementation of the host interface (with an in-memory advice provider). However, the users are able to provide their own implementations which can connect the VM to arbitrary data sources (e.g., a database or RPC calls) and define custom logic for handling events emitted by the VM.
 
 ## Writing programs
-Our goal is to make Miden VM an easy compilation target for high-level languages such as Rust, Move, Sway, and others. We believe it is important to let people write programs in the languages of their choice. However, compilers to help with this have not been developed yet. Thus, for now, the primary way to write programs for Miden VM is to use [Miden assembly](../user_docs/assembly/main.md).
+Our goal is to make Miden VM an easy compilation target for high-level languages such as Rust, Move, Sway, and others. We believe it is important to let people write programs in the languages of their choice. However, compilers to help with this have not been developed yet. Thus, for now, the primary way to write programs for Miden VM is to use [Miden assembly](../user-docs/assembly/index.md).
 
 While writing programs in assembly is far from ideal, Miden assembly does make this task a little bit easier by supporting high-level flow control structures and named procedures.
 
@@ -24,11 +24,11 @@ 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. Any number of stack items can be initialized in this way, but providing a large number of public inputs will increase the cost for the verifier.
 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. Since these outputs will be public inputs for the verifier, having a large stack at the end of execution will increase cost to the verifier. Therefore, it's best to drop unneeded output values. We've provided the [`truncate_stack`](../user_docs/stdlib/sys.md) utility function in the standard library for this purpose.
+After a program finishes executing, the elements remaining on the stack become the outputs of the program. Since these outputs will be public inputs for the verifier, having a large stack at the end of execution will increase cost to the verifier. Therefore, it's best to drop unneeded output values. We've provided the [`truncate_stack`](../user-docs/stdlib/sys.md) utility function 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.
 
-For example, if we wanted to provide a thousand public input values to the VM, we could put these values into a Merkle tree, initialize the stack with the root of this tree, initialize the advice provider with the tree itself, and then retrieve values from the tree during program execution using `mtree_get` instruction (described [here](../user_docs/assembly/cryptographic_operations.md#hashing-and-merkle-trees)).
+For example, if we wanted to provide a thousand public input values to the VM, we could put these values into a Merkle tree, initialize the stack with the root of this tree, initialize the advice provider with the tree itself, and then retrieve values from the tree during program execution using `mtree_get` instruction (described [here](../user-docs/assembly/cryptographic_operations.md#hashing-and-merkle-trees)).
 
 ### Stack depth restrictions
 For reasons explained [here](../design/stack/main.md), the VM imposes the restriction that the stack depth cannot be smaller than $16$. This has the following effects: