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Co-authored-by: Ingo Müller <[email protected]>

site/docs/relations/basics.md

@@ -1,15 +1,12 @@
 # Basics
 
-Substrait is designed to allow a user to describe arbitrarily complex data transformations.  These transformations are composed of one
-or more relational operations.  Relational operations are well-defined transformation operations that work by taking zero or more input datasets and transforming them into zero or more output transformations.  Substrait defines a core set of transformations, but users are also able to extend the operations with their own specialized operations.
+Substrait is designed to allow a user to describe arbitrarily complex data transformations.  These transformations are composed of one or more relational operations.  Relational operations are well-defined transformation operations that work by taking zero or more input datasets and transforming them into zero or more output transformations.  Substrait defines a core set of transformations, but users are also able to extend the operations with their own specialized operations.
 
 ## Plans
 
 A plan is a tree of relations.  The root of the tree is the final output of the plan.  Each node in the tree is a relational operation.  The children of a node are the inputs to the operation.  The leaves of the tree are the input datasets to the plan.
 
-Plans can be composed together using reference relations.  This allows for the construction of common plans that can be reused in multiple
-places.  If a plan has no cycles (there is only one plan or each reference relation only references later plans) then the plan will form a
- DAG (Directed Acyclic Graph).
+Plans can be composed together using reference relations.  This allows for the construction of common plans that can be reused in multiple places.  If a plan has no cycles (there is only one plan or each reference relation only references later plans) then the plan will form a  DAG (Directed Acyclic Graph).
 
 ## Relational Operators
 

site/docs/serialization/basics.md

@@ -1,8 +1,7 @@
 # Basics
 
 Substrait is designed to be serialized into various different formats. Currently we support a binary serialization for
-transmission of plans between programs (e.g. IPC or network communication) and a text serialization for debugging and
-human readability. Other formats may be added in the future.
+transmission of plans between programs (e.g. IPC or network communication) and a text serialization for debugging and human readability. Other formats may be added in the future.
 
 These formats serialize a collection of plans. Substrait does not define how a collection of plans is to be interpreted.
 For example, the following scenarios are all valid uses of a collection of plans:
@@ -11,7 +10,7 @@ For example, the following scenarios are all valid uses of a collection of plans
   top-level node of the root plan defines the output of the query. Non-root plans may be included as common subplans
   which are referenced from the root plan.
 - A transpiler may convert plans from one dialect to another. It could take, as input, a single root plan. Then
-  it could output a serialized binary containing mulitple root plans. Each root plan is a representation of the
+  it could output a serialized binary containing multiple root plans. Each root plan is a representation of the
   input plan in a different dialect.
 - A distributed scheduler might expect 1+ root plans. Each root plan describes a different stage of computation.
 
@@ -21,6 +20,6 @@ Libraries should make sure to thoroughly describe the way plan collections will
 
 We often refer to query plans as a graph of nodes (typically a DAG unless the query is recursive). However, we
 encode this graph as a collection of trees with a single root tree that references other trees (which may also
-transtively reference other trees). Plan serializations all have some way to indicate which plan(s) are "root"
+transitively reference other trees). Plan serializations all have some way to indicate which plan(s) are "root"
 plans. Any plan that is not a root plan and is not referenced (directly or transitively) by some root plan
 can safely be ignored.