On this page:
make-proj-contract
raise-contract-error
contract-proc

7.8 Legacy Contracts

(make-proj-contract name proj first-order)  contract?
  name : any/c
  proj : 
(or/c (-> any/c
          any/c
          (list/c any/c any/c)
          contact?
          (-> any/c any/c))
      (-> any/c
          any/c
          (list/c any/c any/c)
          contact?
          boolean?
          (-> any/c any/c)))
  first-order : (-> any/c boolean?)
Builds a contract using an old interface.

Modulo errors, it is equivalent to:
(make-contract
 #:name name
 #:first-order first-order
 #:projection
 (cond
   [(procedure-arity-includes? proj 5)
    (lambda (blame)
      (proj (blame-positive blame)
            (blame-negative blame)
            (list (blame-source blame) (blame-value blame))
            (blame-contract blame)
            (not (blame-swapped? blame))))]
   [(procedure-arity-includes? proj 4)
    (lambda (blame)
      (proj (blame-positive blame)
            (blame-negative blame)
            (list (blame-source blame) (blame-value blame))
            (blame-contract blame)))]))

(raise-contract-error val    
  src    
  pos    
  name    
  fmt    
  arg ...)  any/c
  val : any/c
  src : any/c
  pos : any/c
  name : any/c
  fmt : string?
  arg : any/c
Calls raise-blame-error after building a blame struct from the val, src, pos, and name arguments. The fmt string and following arguments are passed to format and used as the string in the error message.

(contract-proc c)
  
(->* (symbol? symbol? (or/c syntax? (list/c any/c any/c)))
     (boolean?)
     (-> any/c any))
  c : contract?
Constructs an old-style projection from a contract.

The resulting function accepts the information that is in a blame struct and returns a projection function that checks the contract.