fix: capitalization

closes #356

docs/dev/explanation/COMPILATION.md

@@ -100,7 +100,7 @@ The implementation is a bit more complex than that but the idea is the same.
 
 Tracing is also responsible for indicating whether the values in the node would be encrypted or not, and the rule for that is if a node has an encrypted predecessor, it is encrypted as well.
 
-## Topological Transforms
+## Topological transforms
 
 The goal of topological transforms is to make more functions compilable.
 
@@ -109,12 +109,12 @@ However, if the floating points operations are intermediate operations, they can
 
 Let's take a closer look at the transforms we perform today.
 
-### Fusing Floating Point Operations
+### Fusing floating point operations
 
 We decided to allocate a whole new chapter to explain float fusing.
 You can find it [here](./FLOAT-FUSING.md).
 
-## Bounds Measurement
+## Bounds measurement
 
 Given an operation graph, goal of the bound measurement step is to assign the minimal data type to each node in the graph.
 
@@ -127,7 +127,7 @@ Bounds measurement is necessary because FHE supports limited precision, and we d
 There are several ways to perform bounds measurement.
 Let's take a closer look at the options we provide today.
 
-### Dataset Evaluation
+### Inputset evaluation
 
 This is the simplest approach, but it requires an inputset to be provided by the user.
 
@@ -197,13 +197,13 @@ Assigned Data Types:
 - `3`: Clear\<**uint2**>
 - `+`: Encrypted\<**uint4**>
 
-## MLIR Conversion
+## MLIR conversion
 
 The actual compilation will be done by the concrete compiler, which is expecting an MLIR input. The MLIR conversion goes from an operation graph to its MLIR equivalent. You can read more about it [here](./MLIR.md)
 
-## Example Walkthrough #1
+## Example walkthrough #1
 
-### Function to Homomorphize
+### Function to homomorphize
 
 ```
 def f(x):
@@ -216,17 +216,17 @@ def f(x):
 x = EncryptedScalar(UnsignedInteger(2))
 ```
 
-#### Corresponding Operation Graph
+#### Corresponding operation graph
 
 ![](../../_static/compilation-pipeline/two_x_plus_three.png)
 
-### Topological Transforms
+### Topological transforms
 
-#### Fusing Floating Point Operations
+#### Fusing floating point operations
 
 This transform isn't applied since the computation doesn't involve any floating point operations.
 
-### Bounds Measurement Using [2, 3, 1] as Dataset (same settings as above)
+### Bounds measurement using [2, 3, 1] as inputset (same settings as above)
 
 Data Types:
 - `x`: Encrypted\<**uint2**>
@@ -235,7 +235,7 @@ Data Types:
 - `3`: Clear\<**uint2**>
 - `+`: Encrypted\<**uint4**>
 
-### MLIR Lowering
+### MLIR lowering
 
 ```
 module  {
@@ -250,9 +250,9 @@ module  {
 ```
 
 
-## Example Walkthrough #2
+## Example walkthrough #2
 
-### Function to Homomorphize
+### Function to homomorphize
 
 ```
 def f(x, y):
@@ -266,17 +266,17 @@ x = EncryptedScalar(UnsignedInteger(3))
 y = EncryptedScalar(UnsignedInteger(1))
 ```
 
-#### Corresponding Operation Graph
+#### Corresponding operation graph
 
 ![](../../_static/compilation-pipeline/forty_two_minus_x_plus_y_times_two.png)
 
-### Topological Transforms
+### Topological transforms
 
-#### Fusing Floating Point Operations
+#### Fusing floating point operations
 
 This transform isn't applied since the computation doesn't involve any floating point operations.
 
-### Bounds Measurement Using [(6, 0), (5, 1), (3, 0), (4, 1)] as Dataset
+### Bounds measurement using [(6, 0), (5, 1), (3, 0), (4, 1)] as inputset
 
 Evaluation Result of `(6, 0)`:
 - `42`: 42
@@ -332,7 +332,7 @@ Data Types:
 - `*`: Encrypted\<**uint2**>
 - `+`: Encrypted\<**uint6**>
 
-### MLIR Lowering
+### MLIR lowering
 
 ```
 module  {

docs/dev/explanation/TERMINOLOGY_AND_STRUCTURE.md

@@ -13,7 +13,7 @@ In this section we will go over some terms that we use throughout the project.
     - before intermediate representation is sent to the compiler, we need to know which node will output which type (e.g., uint3 vs uint5)
     - there are several ways to do this but the simplest one is to evaluate the intermediate representation with all combinations of inputs and remember the maximum and the minimum values for each node, which is what we call bounds, and bounds can be used to determine the appropriate type for each node
 
-## Module Structure
+## Module structure
 
 In this section, we will discuss the module structure of `concretefhe` briefly. You are encouraged to check individual `.py` files to learn more!
 

docs/user/explanation/FHE_AND_FRAMEWORK_LIMITS.md

@@ -1,6 +1,6 @@
 # FHE and Concrete Framework Limits
 
-## FHE Limits
+## FHE limits
 
 FHE used to be an impossible thing to imagine, twenty years ago. Then, with advances due to [Craig Gentry](https://crypto.stanford.edu/craig/), this became a dream come true. And, even more recently, with several generations of new scheme, FHE became practical. 
 
@@ -16,7 +16,7 @@ In the scheme used in the Concrete Framework, namely [TFHE](https://tfhe.github.
 
 For most FHE scheme but TFHE, the application of a non-linear function is complicated and slow, if not impossible. Typically, this is a blocker, since activation functions _are_ non-linear. However, in the Concrete Framework, we use an operation called _programmable bootstrapping_ (described in this [white paper](https://whitepaper.zama.ai)), which allows to apply any table lookup: by quantizing the non-linear function, any function can thus be replaced. 
 
-## Concrete Framework Limits
+## Concrete Framework limits
 
 Since this is an early version of the product, not everything is done, to say the least. What we wanted to tackle first was the cryptographic complexities. This is why we concentrated on the cryptographic part, and let some engineering problems for later.